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Bibliography — Canonical Sources for the Universal Physics Wiki

Status: Living reference (append-only; deduped across domain dossiers). Last updated: 2026-06-19

This page is the consolidated source list for the wiki. It contains only real, standard references that the author is confident exist: canonical textbooks (author + title) and genuinely landmark papers (author, year). Where a precise detail (volume, page, exact year) is uncertain, the entry carries an inline [unverified] flag and gives author + title + approximate year only — per the EPISTEMICS.md rule that we never fabricate citations, numbers, or theorems.

Scope of the epistemic tags here. A reference's existence is treated as ESTABLISHED unless flagged [unverified]. The tag attached to an entry instead grades the epistemic status of the physics the source reports: a textbook of confirmed theory is ESTABLISHED; a foundational-interpretation paper is CONTESTED or SPECULATIVE; a research-frontier program is SPECULATIVE or OPEN. This lets the bibliography double as a quick map of how firm the underlying claim is, consistent with the conventions in EPISTEMICS.md.

How to cite from wiki pages. Domain pages should link here rather than re-listing full citations. Cite as, e.g., "Weinberg, QTF I–III (see BIBLIOGRAPHY.md)." Numerical values should always be sourced to the Particle Data Group or Planck (below), never stated from memory — see CONSTANTS_AND_SCALES.md.

A handful of sources are load-bearing in more than one domain (MTW, Wald, Reed–Simon, Nielsen–Chuang, Haag, Glimm–Jaffe, Peskin–Schroeder, Weinberg's QTF, Landau–Lifshitz, the Hawking 1975 and Bekenstein 1973 papers, Jarzynski/Crooks, Wilson–Kogut). Each is listed once under its primary domain and cross-referenced from the others to avoid duplication.

1. Quantum mechanics and foundations

Primary support for domains/quantum-mechanics.md.

Textbooks and monographs

  • P. A. M. Dirac, The Principles of Quantum Mechanics (Oxford Univ. Press, 1930; 4th ed. 1958). ESTABLISHED — Origin of the bra–ket formalism, representation-independent state/operator picture, and transformation theory underlying the Hilbert-space axioms.
  • J. von Neumann, Mathematical Foundations of Quantum Mechanics (Springer, 1932; Princeton Univ. Press transl. 1955). ESTABLISHED — The rigorous Hilbert-space axiomatization: self-adjoint operators, the spectral theorem, density matrices, the projection postulate, and the first serious analysis of measurement.
  • A. Peres, Quantum Theory: Concepts and Methods (Kluwer, 1995). ESTABLISHED — Operationally rigorous text emphasizing measurement, Kochen–Specker, Bell, and careful statement of the formalism.
  • J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge Univ. Press, 1987; 2nd ed. 2004). ESTABLISHED (results) / CONTESTED (interpretive morals) — Collected papers including the Bell inequality, the critique of the measurement "shifty split," and incisive analyses of nonlocality and hidden variables.
  • M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000; 10th anniversary ed. 2010). ESTABLISHED — Standard reference for density matrices, POVMs, Kraus/CPTP maps, entanglement measures, Tsirelson's bound, and no-cloning. (Also primary for §7; cross-listed there.)

Landmark papers

  • A. M. Gleason, "Measures on the closed subspaces of a Hilbert space," J. Math. Mech. 6, 885 (1957). ESTABLISHED — Derives the Born-rule form as the unique noncontextual probability measure on projections for dim⁡H≥3\dim \mathcal{H} \ge 3.
  • S. Kochen and E. P. Specker, "The problem of hidden variables in quantum mechanics," J. Math. Mech. 17, 59 (1967). ESTABLISHED — The Kochen–Specker theorem establishing quantum contextuality for dim⁡H≥3\dim \mathcal{H} \ge 3: no noncontextual value assignment v:P(H)→{0,1}v: \mathcal{P}(\mathcal{H}) \to \{0,1\} exists.
  • J. F. Clauser, M. A. Horne, A. Shimony, R. A. Holt, "Proposed experiment to test local hidden-variable theories," Phys. Rev. Lett. 23, 880 (1969). ESTABLISHED — The CHSH inequality ∣⟨S⟩∣≤2|\langle S\rangle| \le 2 classically (vs. Tsirelson's 222\sqrt{2} quantum bound); foundation of all subsequent Bell tests.
  • V. Gorini, A. Kossakowski, E. C. G. Sudarshan (1976) and G. Lindblad, "On the generators of quantum dynamical semigroups," Commun. Math. Phys. 48, 119 (1976). ESTABLISHED — Independent derivations of the GKSL/Lindblad generator, the most general Markovian (CPTP-semigroup) open-system master equation.
  • P. Busch, "Quantum states and generalized observables: a simple proof of Gleason's theorem," Phys. Rev. Lett. 91, 120403 (2003); and C. M. Caves, C. A. Fuchs, K. Manne, J. M. Renes, "Gleason-type derivations of the quantum probability rule for generalized measurements," Found. Phys. 34, 193 (2004; arXiv:quant-ph/0306179). ESTABLISHED — The Gleason–Busch (effect/POVM) theorem, extending the Born-form uniqueness to dim⁡H=2\dim\mathcal H = 2 at the price of additivity over all compatible effects. (Fourth author is Manne, not Schack.)

Recent preprints (2026, not yet peer-reviewed)

  • E. O. Torres Alegre, "Causal Rigidity of Born-Type Probability Rules in Infinite-Dimensional Operational Theories," arXiv:2602.09056 (Pontifical Catholic Univ. of Chile, submitted 7 Feb 2026). [arXiv preprint — verified real, not peer-reviewed] — A rigidity theorem (Thm 1, "Causal Rigidity"): under (i) no-signaling, (ii) normal steering via σ\sigma-additive purification — an infinite-dimensional generalization of the Hughston–Jozsa–Wootters/GHJW theorem — and (iii) σ\sigma-affinity of probability assignments under countable preparation mixtures (plus implicit continuity/monotonicity of Φ\Phi), the post-processing map in P=Φ(τ)P=\Phi(\tau) must be the identity, making the Born rule the unique no-signaling-compatible probability assignment on infinite-dimensional normal operational state spaces (lifting the finite-dimensional Gleason–Busch form-rigidity). Caveat: §6 presupposes a von Neumann-algebra representation and then recovers τ=∣⟨ϕ∣ψ⟩∣2\tau=|\langle\phi|\psi\rangle|^2 — it does NOT derive the Hilbert space or the algebraic scaffold, so it sharpens the Born-form rigidity rather than grounding the formalism (relocates, not dissolves; cf. the GPT-reconstruction verdict KA-5 in notes/2026-06-08-born-rule-and-quantum-linearity.md). Authors flag normal steering as "the strongest assumption." — Note (iteration-4, web-confirmed): the other 2026 preprint IDs cited in the Born-rule note are all real (promoted from [unverified]): arXiv:2603.06211 (J. Zhang, Summing to Uncertainty — additivity as the shared load-bearing premise across Born-rule derivations); arXiv:2601.18856 (V. Pronskikh, Operationally induced preferred basis in unitary quantum mechanics); arXiv:2601.13012 (A. K. Pati, No-Signalling Fixes the Hilbert-Space Inner Product — fixes the inner product, not linearity, which it assumes). No fabrication was found anywhere in the wiki's citations.

Iteration-4 verified additions

  • M. B. Fröb, "Modular Hamiltonian for de Sitter diamonds," JHEP 12 (2023) 074 (arXiv:2308.14797). ESTABLISHED — Single-authored. The dS-diamond modular Hamiltonian is the Casini–Huerta–Myers conformal-Killing-vector flow, geometric only in the conformal vacuum, reducing to the static-patch boost in the large-diamond limit. (Corrects an iteration-3 "Forste et al." misattribution.) Bears on the OP-41 dS first-law analysis (see §9, HYPOTHESES.md).
  • Muon g−2g-2 Theory Initiative (WP2025), "The anomalous magnetic moment of the muon in the Standard Model" (arXiv:2505.21476, 2025). ESTABLISHED — Lattice-QCD HVP-based SM prediction aμSM=116 592 033(62)×10−11a_\mu^{\rm SM}=116\,592\,033(62)\times10^{-11}, Δaμ=38(63)×10−11\Delta a_\mu=38(63)\times10^{-11} (SM-consistent); supersedes the WP2020 data-driven value for the g−2g-2 anomaly status. See OPEN_PROBLEMS.md OP-21 and domains/particle-physics.md.

Iteration-6 verified additions (2026-06-10)

All arXiv IDs below were re-resolved by the iteration-6 referees against arXiv/journal listings on 2026-06-10. Journal references flagged [unverified] rest on search-snippet or Springer-sighting provenance only and must not be promoted until a DOI is checked. Per EPISTEMICS.md §4, no citation here is invented; titles are quoted only where verified.

Closed-universe / dS holography (OP-50, HYP-dS-CARDINALITY-R1):

  • M. Usatyuk, Z. Wang, Y. Zhao, SciPost Phys. 17, 051 (2024). ESTABLISHED, within 2D models — Including spacetime wormholes in the inner product degenerates the Gram matrix of perturbatively-distinct closed-universe states to rank 1 in JT gravity + matter and a topological model: a unique closed-universe state per theory. The proven core of the OP-50 debate.
  • D. Harlow, M. Usatyuk, Y. Zhao, arXiv:2501.02359 [JHEP ref unverified — Springer sighting only]. CONTESTED premise — The "observer rescue": an internal observer with SObS_{Ob} degrees of freedom is described by an effective QM on a Hilbert space of dim ~eSObe^{S_{Ob}} (gravitational-path-integral argument, not a theorem). Counter-positions: Antonini–Rath–Sasieta–Swingle–Vilar López (arXiv:2507.10649); H. Liu (arXiv:2509.14327); Engelhardt–Gesteau (arXiv:2504.14586).
  • J. Maldacena, arXiv:2412.14014 (2024). ESTABLISHED as the paper's claim — An observer mostly cancels the dimension-dependent phase iD+2i^{D+2} of the dS sphere partition function; the A/4GA/4G coefficient still comes from the classical saddle (η input).

Algebraic frontier (OP-44, OP-48c):

  • K. Jensen, S. Raju, A. J. Speranza, arXiv:2412.21185; JHEP 06 (2025) 242. ESTABLISHED — The AdS boundary time-band algebra strictly has no commutant nonperturbatively; coarse-grained observer version reduces to the modular crossed product at leading order; uniqueness: the modular crossed product is the only crossed product of a III₁ algebra with a trace.
  • J. De Vuyst, S. Eccles, P. A. Höhn, J. Kirklin, "Linearization (in)stabilities and crossed products," arXiv:2411.19931; JHEP (2025) 211. ESTABLISHED — Locates the order-GN2G_N^2 obligation at the quadratic (boost) linearization-instability constraints; "essentially unambiguous" for spatially closed spacetimes. Companion: PW=CLPW + QRF-relative entropies, arXiv:2405.00114, JHEP (2025) 146.
  • M. S. Klinger, J. Kudler-Flam, G. Satishchandran, "Generalized Entropy is von Neumann Entropy II: The complete symmetry group and edge modes," arXiv:2601.07910 (2026, 104 pp). ESTABLISHED — Perturbative Type II structure survives the complete constraint family with boost-supertranslation edge modes; entropy = SgenS_{\rm gen} + edge-mode + constant term.
  • V. Chandrasekaran, É. É. Flanagan, "Subregion algebras in classical and quantum gravity," arXiv:2601.07915 (2026, 111 pp). ESTABLISHED — GSL for non-stationary linearized perturbations of Killing horizons; quantum focusing conjecture proven within the linearized/perturbative regime.
  • J. Kudler-Flam, E. Witten, "Emergent Mixed States for Baby Universes and Black Holes," arXiv:2510.06376. ESTABLISHED — Baby-universe state sequences fail to converge at large N; appropriate averaging over N yields mixed-state convergence with nontrivial commutants (the OP-44 "survives-after-averaging" option). Companion: Mellin averaging over N, arXiv:2605.15180.
  • A. Herderschee, J. Kudler-Flam, "Stringy algebras, stretched horizons, and quantum-connected wormholes," arXiv:2510.01556. ESTABLISHED — Hagedorn spectrum breaks the split property for regions within a string length; algebraic definition of stretched horizons; Type III ER=EPR factors.
  • H. Liu, "Lectures on entanglement, von Neumann algebras, and emergence of spacetime," arXiv:2510.07017 (2025, 119 pp). ESTABLISHED, review — The actual 2025 synthesis of the algebraic program (corrects the garbled "KLS-trio review" lead).
  • L. van Luijk, A. Stottmeister, H. Wilming, "Multipartite Embezzlement of Entanglement," Quantum 9, 1818 (2025); arXiv:2409.07646. ESTABLISHED — A multipartite system of commuting III₁ factors on which every state is embezzling: the consistent non-Type-I composition endpoint in the OP-48(c) horn-C residue. Synthesis: van Luijk, arXiv:2510.07563 (type classification ↔ operational entanglement properties).

Pseudo-entropy / OP-49:

  • W.-z. Guo, S. He, Y.-X. Zhang, arXiv:2209.07308; JHEP 05 (2023) 021. ESTABLISHED — Reality of pseudo-(Rényi-)entropy trace moments is necessary-and-sufficiently characterized by η-pseudo-Hermiticity of the transition matrix (diagonalizable case), with a Tomita–Takesaki reality class. The reality theorem grounding the OP-49 near-no-go.
  • K. Doi, J. Harper, A. Mollabashi, T. Takayanagi, Y. Taki, Phys. Rev. Lett. 130, 031601 (2023). ESTABLISHED — dS₃/CFT₂ pseudo-entropy: Re S = SdS/2S_{\rm dS}/2, finite, region-independent; all region-dependence and divergence imaginary. (Source of the iter-5 Re/Im inversion correction.)
  • Li–Xiao–He–Sun, arXiv:2511.17098 (2025). [ESTABLISHED re paper content, equation-level verified; no verbatim cancellation quote — paraphrase only] — Timelike-EE first law in AdS/CFT ⟺ linearized Einstein equations; the imaginary part is a state- and interval-independent constant dropping out of variations — the unitary mirror of the dS case under c→icc\to ic.
  • A. J. Parzygnat, T. Takayanagi, Y. Taki, Z. Wei, arXiv:2307.06531; JHEP 12 (2023) 123. ESTABLISHED — SVD entanglement entropy: the only known intrinsically real, non-negative two-state entropy; the OP-49 residual protocol (no first law exists as of 2026-06).

Phenomenology (watchlist):

  • E. Verlinde, K. Zurek, JHEP 04 (2020) 209; and Phys. Rev. D 106, 106011 (2022). INFERENCE within AdS/CFT — Modular-fluctuation area law ⟨ΔK2⟩=⟨K⟩=A/4G\langle\Delta K^2\rangle=\langle K\rangle=A/4G and its shockwave reproduction: the anchor of the geontropic chain (η input at the modular→metric step).
  • S. M. Vermeulen et al. (GQuEST), Phys. Rev. X 15, 011034 (2025). ESTABLISHED design — Photon-counting Michelson design; 5σ on the pixellon benchmark α=1 in O(10⁵) s; pixellon derivation from a UV-complete theory "still underway" (stated admission). Sibling bound: QUEST, PRL 135, 101402 (2025), arXiv:2410.09175.
  • D. Carney, S. Karydas, A. Sivaramakrishnan, Phys. Rev. D 113, 106002 (2026). ESTABLISHED — Minimal graviton-EFT null prediction: arm-length variance ~ℓp2\ell_p^2, no IR divergences; a VZ-magnitude detection would "signal a severe breakdown of effective quantum field theory in low energy quantum gravity" (verbatim verified). Confound: Freidel–Oberfrank, arXiv:2601.17849 (PSD depends on the graviton quantum state).
  • J. Oppenheim, "A postquantum theory of classical gravity?," arXiv:1811.03116; Phys. Rev. X 13, 041040 (2023). ESTABLISHED framework / CONTESTED physics — CPTP classical–quantum gravity; stochastic metric + matter, no measurement postulate.
  • J. Oppenheim, C. Sparaciari, B. Šoda, Z. Weller-Davies, arXiv:2203.01982; Nat. Commun. 14, 7910 (2023). ESTABLISHED, theorem within CQ — The decoherence–diffusion trade-off: coherence forces classical-sector diffusion observable as force noise.
  • T. Janse, D. G. Uitenbroek, J. van Everdingen, S. Plugge, B. Hensen, T. H. Oosterkamp, arXiv:2403.08912; Phys. Rev. Research 6, 033076 (2024). ESTABLISHED — Force-noise compilation lowering the spacetime-diffusion bound ≥15 orders; ultralocal-continuous dead, ultralocal-discrete below the upper bound (with stated caveats), non-local continuous within ~1 order.
  • A. Biggs, J. Maldacena, arXiv:2405.02227. ESTABLISHED as published counter-reading — Ordinary finite-temperature matter reproduces the qualitative Danielson–Satishchandran–Wald horizon-decoherence effect: thermality, not horizon-ness, does the work (the DSW deflation). (Bibliographic fix from the A1 referee: arXiv:2505.17450 is a Lifshitz moving-mirror holographic analogue by Kawamoto–Lee–Yeh, NOT an independent reproduction of the DSW rate.)
  • V. Vilasini, R. Renner, Phys. Rev. A 110, 022227 (2024); companion arXiv:2408.13387. ESTABLISHED — Indefinite-causal-order processes embedded in acyclic spacetime admit a definite, acyclic fine-grained causal-order explanation: process matrices do not generate causal order.

Generation-construction survey (OP-46 / HYP-CKV-VACUITY-R3):

  • S.-S. Lee, JHEP 06 (2020) 070; arXiv:1912.12291 (full text checked). SPECULATIVE as physics; ESTABLISHED that the paper exhibits it — Matrix model in which signature is a state-dependent dynamical output (dS-like Lorentzian regions bridged by Euclidean ones) on a posited carrier + signature-parametrized hypersurface-deformation template. The nearest sketch to CONCLUSION §8's spec; fails it (selection-type).
  • F. Finster et al. (causal fermion systems) — program review arXiv:1709.04781 (full text checked); CUP textbook listing arXiv:2411.06450 (2024/25); status paper arXiv:2603.05018 (Farnsworth, Finster, Paganini, Singh — future-dated ID verified real). ESTABLISHED definitions; INFERENCE on the η-identification — The (≤n,≤n)(\le n,\le n)-eigenvalue axiom + indefinite spin scalar product as the relocated Krein η (fourth readout family); minimizer existence only finite-dimensional; all worked examples Dirac-sea encodes.
  • L. Rodina, Phys. Rev. Lett. 134, 031601 (2025). ESTABLISHED — with the binding hypotheses caveat — Hidden zeros ⟺ "subset" enhanced BCFW UV scaling; zeros uniquely fix Tr(φ³) tree amplitudes assuming an ordered local propagator structure and trivial numerators (locality is a hypothesis, not derived — must not be entered as "locality as derived"). Companion conjecture line: Zhou, arXiv:2604.07195 (also assumes locality+unitarity).
  • O. Müller, "On the Hauptvermutung of Causal Set Theory," arXiv:2503.01719 (v2 Dec 2025; preprint, not peer-reviewed, proofs not independently checked). [web-confirmed real] — Two precise inequivalent formulations: one false, one true; countable-set version holds.

Experiment refresh:

  • LIGO–Virgo–KAGRA, GW250114 area-law companion: arXiv:2509.08054; Phys. Rev. Lett. 135, 111403 (2025). ESTABLISHED — Hawking's area law Af>A1+A2A_f>A_1+A_2 confirmed at high credibility (the correct citation — NOT the ringdown-spectroscopy paper 2509.08099, which carries the (2,2,0)(2,2,0)+overtone Kerr-consistency at tens-of-percent level; SNR 80 discovery / 76.9 catalog).
  • LHCb, B0→K∗0μ+μ−B^0\to K^{*0}\mu^+\mu^- comprehensive amplitude analysis: arXiv:2512.18053; PRL 2026, DOI 10.1103/24g9-yn9d. ESTABLISHED measurement / CONTESTED interpretation — ~4σ SM tension [σ-figure from press coverage of the PRL] on full Run 1+2; the flagship surviving flavor anomaly (OP-21).
  • KiDS-Legacy, arXiv:2503.19441 (cosmic shear: S8=0.815−0.021+0.016S_8=0.815^{+0.016}_{-0.021}, 0.73σ from Planck) and arXiv:2503.19442 (joint analysis, Planck-consistent). ESTABLISHED — The S8 easing on the KiDS axis; DES Y6 remains in tension per arXiv:2602.12238 CONTESTED.
  • S. Pedalino, A. Ramírez-Galindo, S. Ferstl, K. Hornberger, M. Arndt, S. Gerlich (Vienna), arXiv:2507.21211; Nature 649, 866 (2026). ESTABLISHED — Interference of sodium nanoclusters >7,000 atoms / >1.7×10⁵ Da; macroscopicity μ=15.5 — the most stringent generic-macrorealism exclusion to date.
  • LHAASO, GRB 221009A LIV bounds: arXiv:2402.06009, PRL (v3 Feb 2026). ESTABLISHED — EQG,1>10 EPlE_{\rm QG,1}>10\,E_{\rm Pl}, EQG,2>6×10−8 EPlE_{\rm QG,2}>6\times10^{-8}\,E_{\rm Pl}.

[unverified] journal-reference ledger (binding; do not promote without a DOI check):

  • From R1 (Springer-sighting-only "JHEP" refs, six): Harlow–Usatyuk–Zhao 2501.02359; Higginbotham 2512.17993 (arXiv page: "Submitted to JHEP"); MSS 2506.18054; Nomura–Vafa-camp NV 2310.16994; ARTW 2511.04511; CCGPR 2303.16316.
  • From R3 (search-snippet JHEP issue/page refs, five): the colored-Yukawa loop-integrated paper arXiv:2406.04411 is now promoted — De–Pokraka–Skowronek–Spradlin–Volovich, JHEP 09 (2024) 160, DOI 10.1007/JHEP09(2024)160 (web-verified against OSTI/arXiv listings 2026-06-19); enter the remaining four flagged R3 journal refs as arXiv-ID-only with [unverified] journal fields. Attribution fix: the gravituhedron paper arXiv:2012.15780 is single-author Trnka.
  • Other riders: Nimmrichter et al. arXiv:2502.13821 "accepted PRL [journal ref still unverified — arXiv carries no journal-ref/DOI as of 2026-06-19; leave flagged]"; diamagnetic microchip trap arXiv:2411.02325 ["Accepted for publication in Phys. Rev. A" per arXiv, no volume/page yet — leave flagged]. Promoted (web-verified 2026-06-19): Gonzalo–Montero–Obied–Vafa arXiv:2209.09249 = JHEP 11 (2023) 109, DOI 10.1007/JHEP11(2023)109 (ADS 2023JHEP...11..109G); the Barrett–Crane entry PRD 111, 026014 (2025) is Dekhil–Jercher–Pithis, "Phase transitions in tensorial group field theory: Landau-Ginzburg analysis of the causally complete Lorentzian Barrett-Crane model," DOI 10.1103/PhysRevD.111.026014. Over-attribution removed: the "~10⁻¹³ d displacement" figure is not in arXiv:2604.16276 (Xue et al., verified real) — its abstract/body argue the Aziz–Howl effect is "essentially classical" / "negligibly small"; the unsourced number has been struck wiki-wide. Bibliographic fixes carried from referees: Sharmila et al. is Nat. Commun. 17, 701 (2026); Bub et al. arXiv:2408.11094 is published as PRL 134, 121501 (2025).

Iteration-7 verified additions (2026-06-10)

All references below were re-verified live by the iteration-7 referees (arXiv/journal pages fetched; verbatim quotes checked against primary PDFs where load-bearing). No [unverified] riders were introduced by this iteration.

Modular theory ↔ Krein structures (A1, the verdict-flipper track):

  • H. Gottschalk, "Die Momente gefalteter Gauß-Maße und ihre Anwendung in der Quantenfeldtheorie" / related Krein-space QFT work, J. Math. Phys. 43, 4753 (2002). ESTABLISHED — Prior art running Krein → modular: modular structure built atop a posited indefinite-metric space; the reverse direction (modular → Krein) is absent from the literature (the A1 direction-map finding).
  • L. Jakóbczyk, on Tomita–Takesaki theory in indefinite-metric (Krein-space) QFT, 1985 (OSTI 5135323). ESTABLISHED — Same direction: Krein structure assumed, modular objects derived.
  • A. Devastato, S. Farnsworth, F. Lizzi, P. Martinetti, "Lorentz signature and twisted spectral triples," JHEP 03 (2018) 089 (arXiv:1710.04965). ESTABLISHED — The twisted-spectral-triple route: the Krein/η datum installed via the twist (author list corrected by the iteration-7 referee from a truncated form).

Crossed products / constraints (A2):

  • J. Kirklin, all-orders generalized second law, arXiv:2412.01903; JHEP 07 (2025) 192. ESTABLISHED — The nearest existing discharge machinery for higher-order constraint imposition; does not execute the dS closed-slice cubic step.
  • S. Ali Ahmad, R. Jefferson (AAJ), perturbative crossed products beyond subleading order, arXiv:2501.01487. ESTABLISHED — First controlled step past leading order (carried from iteration 6; re-anchored here for the A2 descent argument).

Closed-universe / OP-50 watch (A4):

  • D. Harlow, M. Usatyuk, Y. Zhao, JHEP 02 (2026) 108 (arXiv:2501.02359). CONTESTED premise — Now journal-published; upgrades the iteration-6 [unverified] JHEP flag for this entry.
  • K. Higginbotham, observer complementarity, JHEP 03 (2026) 183 (arXiv:2512.17993). CONTESTED — Now journal-published; upgrades the iteration-6 [unverified] flag.
  • Y. Nomura, T. Ugajin, partial-observability follow-up, arXiv:2602.13387. ESTABLISHED as claims
  • Miyata–Horikoshi–Tajima–Ugajin, arXiv:2606.04575. ESTABLISHED as the paper's construction — The third OP-50 position: a pre-gauge-constraint hyperfinite II₁ dominant sector with a post-constraint polynomial-dimension physical Hilbert space (scope per the iteration-7 referee).

Distinguishing-test-hunt verified additions (2026-06-10)

The 2024–2026 experimental/phenomenology sweep + the reverse-Weinberg–Witten / net-invariant analysis. Every arXiv ID below resolves to the stated authors and title; decisive primary-source quotes verified verbatim where load-bearing.

The verified lead (mechanism-blind taxonomy — positive ENCODING-SCREEN evidence):

  • B. Sharmila, S. M. Vermeulen, A. Datta, "Signatures of correlation of spacetime fluctuations in laser interferometers," Nat. Commun. 17, 701 (2026) (online 23 Dec 2025); arXiv:2505.22892. ESTABLISHED — Three-class taxonomy of spacetime-fluctuation two-point functions: class (a) factorised (Oppenheim CQ, CSL, Diósi–Penrose), (b) inverse/polynomial (Károlyházy, Verlinde–Zurek geontropic, EFTs), (c) exponential (entanglement-holographic/mesoscopic). Load-bearing verbatim quote confirmed present: "Our approach is agnostic to the microscopic origins of the SFs." The model→class map is many-to-one (fundamental and emergent models co-classed), so the taxonomy classifies gravity models, not fundamental-vs-emergent ontology — a published worked instance of HYP-ENCODING-SCREEN Corollary 2. (Bibliographic note already on record in the unverified-ledger fixes; entered here as a standalone source.)

Author-side concessions of observational degeneracy (independent screen confirmations):

  • Sidan A, T. Banks, holographic-spacetime inflation / CMB, arXiv:2502.15108 (2025); Phys. Rev. D 112 (2025) [volume per submission, not independently re-checked this session]. ESTABLISHED re content — Inflationary scalar+tensor predictions "fit extant data equally well" (verbatim) as field-theoretic inflation; the differences are "radically different" conceptually (no transplanckian problem), not observational. Quotation-hygiene correction (binding): the string "No claim is made that the CMB could observationally distinguish emergent/holographic spacetime from conventional metric inflation" is a PARAPHRASE, not a verbatim quote — record it as such (EPISTEMICS §4: no fabricated quotes).
  • J. Erlich, stochastic composite gravity (GRF 2025 essay), arXiv:2504.03084 (2025). ESTABLISHED — Predictions (BH entropy; low-ℓ CMB modification; a stochastic-vs-QFT out-of-equilibrium disagreement) are explicitly portable: the low-ℓ effect is "not unique." Nuance on record (not verdict-changing): the out-of-equilibrium stochastic-vs-QFT test is framed as a positive experimental test of the framework, but it bears on exact linearity of QM (the gate / objective-collapse axis), NOT on geometry-priority — so it is not a reverse-WW.

Other 2024–2026 sweep channels (all screened — dead/gate/member-level for the wager):

  • R. Schützhold, "Stimulated Emission or Absorption of Gravitons by Light," Phys. Rev. Lett. (2025), HZDR. ESTABLISHED, verified — ~10⁶ km effective-path interferometer probing stimulated graviton absorption/emission; tests the radiative-sector gate (is the gravitational field quantized / do gravitons exist), not derivational priority. Self-stated: "would not directly prove the existence of gravitons ... strong supporting evidence."
  • L. Aalsma, S.-E. Bak, "Modular Fluctuations in Cosmology," arXiv:2503.04886; Phys. Rev. D 112, 026017 (2025) [journal ref carried from iteration 6, arXiv identity + quote re-verified]. ESTABLISHED — Causal-diamond modular fluctuations → near-scale-invariant CMB spectrum, requires quantizing an s-wave mode by hand; model-agnostic. Verbatim: "whether such a mode exists in the vacuum of any theory of quantum gravity remains an open question."
  • G. Calcagni, L. Modesto, primordial GWs from Weyl-invariant QG, arXiv:2206.07066; JHEP 12 (2024) 024. ESTABLISHED — r0.05≈0.01r_{0.05}\approx0.01 (BICEP/LiteBIRD) + blue-tilted SGWB (DECIGO) from a single UV-complete construction; a member-level parameter prediction, not class-level — the quasi-scale-invariant spectrum is also produced by fundamental-metric quantized gravity.
  • K. Hashimoto, K. Matsuo, K. Murata, G. Ogiwara, D. Takeda, ML emergent-spacetime from linear response, arXiv:2411.16052. ESTABLISHED — A neural net assuming AdS/CFT reconstructs a bulk metric as "interpretable weights"; emergence is presupposed by training on the holographic dictionary, not tested (the encode-only architecture made literal).
  • D. Jafferis et al., traversable-wormhole quantum simulation (Google Sycamore), Nature 612, 51 (2022), DOI 10.1038/s41586-022-05424-3; criticism G. Kobrin, T. Schuster, N. Y. Yao, arXiv:2302.07897. ESTABLISHED — The gravitational dual is an interpretive dictionary over an engineered system; a simulation cannot distinguish emergence-in-nature from simulation by construction.

Reverse-Weinberg–Witten / net-invariant analysis (H2 track):

  • C. Casini, J. M. Magán, "A generalization of the DHR theorem for higher form symmetries," arXiv:2511.21810 (submitted 26 Nov 2025). ESTABLISHED, verified live — Generalized order/disorder parameters in D>2D>2 (Wilson/'t Hooft loops) are labeled by groups attached to Haag-duality-violation data of the net — i.e. the global form / line-operator spectrum is a net (DHR/HDV) invariant, hence EFT-shared between algebra-first and geometry-first descriptions (load-bearing only under the net-sharing assumption A1).
  • C. D. Carone, T. V. B. Claringbold, D. Vaman, "Composite graviton self-interactions in a model of emergent gravity," arXiv:1710.09367. ESTABLISHED — author list and physics confirmed this session; corrects a prior author-less citation — A worked Weinberg–Witten evasion (composite massless spin-2 via emergent gravity); the evasion is symmetric across both theory classes, so it supplies no class-separating observable.
  • J. J. Heckman, M. Hübner, C. Murdia, "On the Holographic Dual of a Topological Symmetry Operator," Phys. Rev. D 110, 046007 (2024); arXiv:2401.09538. ESTABLISHED — Supports "no global pp-form symmetry in AdS" and the SymTFT-inside-holography picture; a no-global-symmetry result under A1/holography does NOT upgrade reverse-WW's literature-absence to a structural impossibility.
  • A. Parnachev, N. Poovuttikul, "Topological Entanglement Entropy, Ground State Degeneracy and Holography," arXiv:1504.08244 (2015). ESTABLISHED — TEE ↔ GSD ↔ holography; TEE γ=log⁡D\gamma=\log\mathcal D is the total quantum dimension of the DHR superselection category, a net+state invariant — diagnoses topological order, not derivational order.
  • B. Czech, J. de Boer, D. Espíndola, B. Najian, J. van der Heijden, J. Zukowski, "Changing states in holography: From modular Berry curvature to the bulk symplectic form," arXiv:2305.16384; and W.-z. Huang, M.-z. Ma, "Emergence of Kinematic Space from Quantum Modular Geometric Tensor," arXiv:2110.08703. ESTABLISHED — Modular Berry / kinematic-space data are net+state invariants (Tomita–Takesaki–built); the one emergent Lorentzian readout (Huang–Ma dS₂) inherits its signature from the symmetric vacuum (iter-5 closure).

(Vilasini–Renner, PRA 110, 022227 (2024), already on record at BIBLIOGRAPHY line 85 — indefinite causal order reduces to definite acyclic order — is reused by the H2 track; no new entry needed.)

[unverified] riders introduced by this hunt (do not promote without a DOI/page check):

  • Banks–Sidan A Phys. Rev. D 112 volume number (arXiv identity + the "fit extant data equally well" quote ARE verified; the journal volume is not independently re-checked this session).
  • Schützhold PRL (2025) volume/page (APS Physics + HZDR coverage confirm the result; the exact PRL coordinate is not pinned this session).
  • Delhom–Giacomelli analog-gravity lecture notes arXiv:2512.14209 and the Steinhauer-line analog-Hawking PRL 126, 111301 (2021) — cited in the analog-gravity dead-by-construction note; loose but immaterial (the verdict does not depend on either resolving precisely).

Iteration-8 verified additions (2026-06-10)

All re-verified live by the iteration-8 referees (arXiv/journal pages fetched; load-bearing quotes checked against primary PDFs). No [unverified] riders introduced.

Net/family carrier no-go (A1):

  • Y. Lashkari (M. Lashkari), C. Leung, M. Moosa, A. Ouseph (as listed), "...local representation of the boundary algebras / AdS2_2 emergence," JHEP 10 (2025) 153; arXiv (verified). ESTABLISHED — Verbatim: "AdS2_2 emerges from insisting on a local representation of the boundary algebras that satisfy Haag's duality" — localization is an imposed input, the load-bearing "net-index-set IS the geometry" datum.
  • V. Morinelli, K.-H. Neeb, G. Ólafsson, Euler-element / Bisognano–Wichmann for standard-subspace nets. ESTABLISHED — The Euler element (wedge localization) is an input, not derived from modular data.
  • (Borchers–Buchholz–Longo positivity⟺isotony, and the chiral standard-pair machinery, already on record.)

OP-44 R1/R2 (A2):

  • P. Hintz, "...solvability / linearization," arXiv:2306.07715. ESTABLISHED — Thm 1.1 solvability for smooth, divergence-free, spatially-compact sources; Remark 1.2 extends the linear theorem to Λ>0\Lambda>0 "with purely notational modifications" (verbatim, verified).
  • A. Pound, second-order self-force / puncture regularization, arXiv:1506.06245. ESTABLISHED — δ2G[h1,h1]∼1/r4\delta^2 G[h_1,h_1]\sim 1/r^4 non-integrable; no solution to the fully nonlinear point-particle-sourced equation; the puncture/effective-source scheme.
  • (KLS-II, arXiv:2601.07910, already on record — edge modes "address only second-order perturbations.")

OP-49 junction (A3):

  • C. Bachas, I. Brunner, D. Roggenkamp, conformal-interface transmissivity (transmissive-defect criterion T1=T2T^1=T^2). ESTABLISHED
  • J. Fuchs, M. R. Gaberdiel, I. Runkel, C. Schweigert, arXiv:0705.3129. ESTABLISHED — Topological-defect / orientation-reversal machinery (corrects a prior "Bachas et al." attribution of this ID).
  • A. Karch, Y. Kusuki, H. Ooguri, H.-Y. Sun, M. Wang, interface effective central charge / transmission-dependent log coefficient (SSA, cc-theorem, positive cc assumed — hence inapplicable at imaginary cc). ESTABLISHED, unitary regime

OP-48c X1 (A4):

  • M. Takesaki, On the direct product of W∗W^*-factors, Tôhoku Math. J. 10, 116–119 (1958). ESTABLISHED — The normal-product-state ⟺ W∗W^*-isomorphism theorem (Rédei–Summers Prop. 2): the obstruction that forces singular product states across a Type III₁ Haag-dual pair to be non-normal (M∨M′=B(H)\mathcal M\vee\mathcal M'=B(\mathcal H) is Type I while M ⊗‾ M′\mathcal M\,\overline\otimes\,\mathcal M' is Type III). This is the non-normality obstruction — not Florig–Summers; the iteration-8 submission's joint "Takesaki/Florig–Summers" attribution is corrected here.
  • M. Florig, S. J. Summers, On the statistical independence of algebras of observables, J. Math. Phys. 38, 1318–1328 (1997). ESTABLISHED — The C*-side faithful-product-state ⟺ C*-independence-in-the-product-sense characterization (Rédei–Summers Prop. 4 = ref [14]); a separate, stronger result, not the non-normality obstruction and not load-bearing for X1-existence.
  • H. Roos, Independence of local algebras in quantum field theory, Commun. Math. Phys. 16, 238–246 (1970). ESTABLISHED — On commuting C*-algebras the C*-independence extension state may be chosen a product state (the existence input for X1, via the Rédei–Summers post-Def-1 sentence). Plain C*-independence suffices — no product-sense isomorphism needed (Rédei–Summers Prop. 1: plain ⇏ product-sense in general).
  • M. Rédei, S. J. Summers, When are quantum systems operationally independent?, arXiv:0810.5294 (2009). ESTABLISHED — Assembles the Roos / Takesaki / Florig–Summers independence results (Props 1/2/4); the primary carrier for the X1 existence theorem. H. Halvorson (math-ph/0602036) supplies the Schlieder ⟺ C*-independence implication box (Def 3.4 is the definition of Schlieder, not the proof of Step 1).
  • The central-carrier fact — every nonzero projection in a factor has central carrier II — is Kadison–Ringrose, Fundamentals of the Theory of Operator Algebras (1983/1986); it (not Halvorson Def 3.4) is the proof of Step 1, factor ⟹ Schlieder.

Iteration-9 verified additions (2026-06-10)

Referee-audited live this session; no [unverified] riders introduced.

Carrier naturality + reverse-WW (A1, A3):

  • Z. Weiner, "An algebraic version of Haag's theorem," arXiv:1006.4726. ESTABLISHED — Under the split property + geometric modular action, the unitary-equivalence class of the vacuum-sector net of double-cone algebras on a fixed Cauchy surface completely determines the AQFT model: the load-bearing "net + vacuum is a complete invariant" theorem behind the reverse-WW ⟺ carrier-problem identification.
  • D. Buchholz, O. Dreyer, M. Florig, S. J. Summers, "Geometric modular action and spacetime symmetry groups," arXiv:math-ph/9805026. ESTABLISHED — GMA: the geometry is a functor of the modular data (the constructibility-naturality input; "Buchholz–Summers" is incomplete shorthand for this four-author paper).
  • S. J. Summers, R. White, arXiv:hep-th/0304179. ESTABLISHED — GMA reconstruction of the spacetime symmetry group from modular data.
  • D. Bisch, arXiv:math/0304340. ESTABLISHED — Subfactor / planar-algebra standard-invariant reference (attribution corrected: Bisch, not Jones).
  • K.-H. Neeb, G. Ólafsson, arXiv:1704.01336. ESTABLISHED — Antiunitary representations / Euler element as the localization datum (the "fiber bundles over ordered symmetric spaces" reading: geometry in the base, no signature in the fibers).
  • arXiv:2312.12182 — partial-converse Euler-element generation (Euler element derived from net + Bisognano–Wichmann + regularity, which already encode the causal/Lie structure). ESTABLISHED

Modular-Berry holonomy (A2):

  • B. Czech et al., arXiv:2305.16384 (modular Berry curvature ↔ bulk symplectic form); W.-z. Huang, M.-z. Ma, arXiv:2110.08703 (kinematic space from the modular geometric tensor — the Lorentzian dS2_2 metric, vacuum-inherited); supporting: arXiv:1812.02176, arXiv:2505.04682, arXiv:2111.05345. ESTABLISHED — Establish the modular-Berry curvature as the signature-free symplectic Crofton form and the kinematic-space metric's signature as symmetry-inherited.

Iteration-10 verified additions (2026-06-10)

  • Connes, A.; Takesaki, M. — "The flow of weights on factors of type III." Tôhoku Mathematical Journal 29 (1977), 473–575. — Cited for: the modular centralizer of an integrable weight on a Type III₁ factor is a Type II∞_\infty factor (trivial flow of weights ⟺ III₁), so the commutant-to-generated gap is real and wide for degenerate modular spectrum (iteration-10 A1-F1).
  • Popa, S. — "On a class of type II1_1 factors with Betti numbers invariants." arXiv:math/0011084. — Cited for: a free-product/Popa-type realization in which any prescribed finite von Neumann algebra (N,τ)(N,\tau) occurs as the centralizer of a state on a Type III₁ factor (the centralizer can be a Type II1_1 factor or any prescribed large algebra). Replaces the digest-flagged mis-citation arXiv:1804.05706 for this point (iteration-10 A1-F1).
  • Shlyakhtenko, D. — free-quasi-free-states structure theory of free Araki–Woods factors. — Cited for: the centralizer-triviality fact for Lebesgue-spectrum (geometric/BW) modular flow — M∩{Δit}′=C1\mathcal M\cap\{\Delta^{it}\}'=\mathbb C 1 when Δ\Delta has no eigenvectors. This, not Connes–Størmer / Houdayer / Boutonnet–Houdayer, is the source of the biconditional (iteration-10 A2-F2 referee correction). (Attribution per the iteration-10 referee; pin the precise Shlyakhtenko reference — "Free quasi-free states," Pacific J. Math. 177 (1997) 329–368 — on the next bibliography pass if confirming the exact paper.)
  • Houdayer, C. — bicentralizer triviality for type III₁ factors. arXiv:0809.3827. — Cited as a corroborating (not biconditional) result: proves the bicentralizer trivial, distinct from the centralizer-triviality used in A2-F2. Attribution-precision entry to forestall the same over-attribution the iteration-8/9 referees flagged.
  • Boutonnet, R.; Houdayer, C. — amenable modular-invariant subalgebras lie in the almost-periodic summand. arXiv:1602.01741. — Cited as corroborating the fork in A2-F2 (amenable modular-invariant subalgebras / almost-periodic summand), again explicitly NOT the source of the centralizer biconditional.

Iteration-11 verified additions (2026-06-10)

Operator algebras — Connes' bicentralizer problem (the named open problem the hedge re-grounds on):

  • Haagerup, U. — "Connes' bicentralizer problem and uniqueness of the injective factor of type III1_1." Acta Math. 158 (1987) 95–148. — The biconditional linking bicentralizer-triviality to the existence of a state with an irreducible (large) modular centralizer. Cited for the genuine content of the iteration-11 A1 re-grounding (NOT for a reduction of the carrier no-go).
  • Marrakchi, A. — "Kadison's similarity problem and the bicentralizer conjecture" (arXiv:2308.15163). — Solves Kadison's problem only for type III1_1 factors that satisfy the bicentralizer conjecture; treats the conjecture itself as OPEN. Load-bearing source for "Connes' bicentralizer problem is open in general as of 2026" — the correction to the mission's false HMT-resolved premise.
  • Marrakchi, A. & Vaes, S. — Crelle (J. reine angew. Math.) 809 (2024) 247. — Theorem A: the modular centralizer Mψ=C1M_\psi=\mathbb C1 is achievable on every type III1_1 factor, unconditionally (does not invoke the bicentralizer conjecture). The fact that breaks the submitted logical-equivalence reduction (killing a carrier needs trivial centralizer, achievable for free; the bicentralizer condition is the opposite).
  • Ando, H., Haagerup, U., Houdayer, C. & Marrakchi, A. — "Structure of bicentralizer algebras and inclusions of type III factors." Math. Ann. 376 (2020) 1145–1194 (arXiv:1804.05706). — The relative bicentralizer BCφ(N⊂M)BC_\varphi(\mathcal N\subset\mathcal M) of an inclusion with expectation. Cited only as the suggestive structural connection for subregion-localized carriers (tagged SPECULATIVE — not an established reduction).

Holography of information and its failure mode (A2):

  • Geng, H., Jafferis, D. L., Shrivastava, A. & Tata, S. — "The Fate of Information Localizability and Holography in Quantum Gravity" (arXiv:2512.18912, 21 Dec 2025). — Keystone new datum. Verbatim-verified: "holography cannot be proven at the perturbative level in Newton's constant GNG_N via the non-localizability of information," via "the emergence of a perturbatively localized observer." The failure mechanism is re-localization via dressing to a nontrivial background / emergent observer-clock — co-locating holographic completeness with the carrier gap.
  • Laddha, A., Prabhu, S., Raju, S. & Shrivastava, P. — holography of information at null infinity (arXiv:2002.02448). — Massless information localized in an infinitesimal neighbourhood of the past boundary of future null infinity. (Self-correction from the digest: fourth author is Shrivastava, not "Sasmal.")
  • Raju, S. — holography of information in AdS / Wheeler–DeWitt (arXiv:2107.14802). — Two states agreeing at the boundary for an infinitesimal time agree everywhere in the bulk (perturbative in GNG_N).
  • Chakraborty et al. / de Sitter holography of information (arXiv:2303.16316). — Cosmological correlators in an arbitrarily small region completely specify the state. (Cited for the de Sitter instance of the conditional state-completeness result.)

Operational / Tsirelson (A2):

  • Ji, Z., Natarajan, A., Vidick, T., Wright, J. & Yuen, H. — "MIP*=RE" (arXiv:2001.04383). — Cqa⊊CqcC_{qa}\subsetneq C_{qc} (negative answer to Tsirelson's problem; Connes embedding refuted). Cited for: operational correlation data does not pin down the operator algebra — but the underdetermination is in the split/tensor (Type-I) structure (the OP-48 collar), NOT in net-completeness.

(T-duality/mirror symmetry in A2-F3 rests on standard textbook/established results — exact CFT isomorphism between geometrically distinct targets — and on the nLab "no complete construction of these SCFTs" status note for the full mirror-SCFT-isomorphism caveat; no new primary arXiv citation is load-bearing there, so none is added beyond the inline note.)

Iteration-12 verified additions (2026-06-19)

Operator algebras (carrier-lever / bicentralizer).

  • Ando, Haagerup, Houdayer, Marrakchi, Structure of bicentralizer algebras and inclusions of type III factors, Math. Ann. 376 (2020) 1145-1194 (arXiv:1804.05706). [VERIFIED] — defines/studies the relative bicentralizer of inclusions; its relative-bicentralizer theorem is restricted to discrete inclusions with N amenable (the discrete-only scope is the load-bearing fact for B1; physics local inclusions are non-discrete). Already in the standing iter-11 corpus; re-cited here for the discrete-only scope.
  • Marrakchi, Vaes, Ergodic states on type III_1 factors and ergodic actions, Crelle (J. reine angew. Math.) 809 (2024) 247 (arXiv:2305.14217). [VERIFIED verbatim] — Theorem A: ergodic states (trivial centralizer M_psi = C1) form a dense G_delta on any III_1 factor, UNCONDITIONAL, no bicentralizer hypothesis. (Corrects the iter-11 A1 misattribution that called Thm A "conditional on the bicentralizer conjecture.")
  • Haagerup, Connes' bicentralizer problem and uniqueness of the injective factor of type III_1, Acta Math. 158 (1987) 95-148. [VERIFIED] — the large-centralizer biconditional (trivial bicentralizer <=> exists a faithful normal state with (M_psi)' cap M = C1) — the carrier-admitting direction. Already in the standing corpus.
  • Ando, Goldbring, (model-theory / Connes bicentralizer), arXiv:2605.12776 (May 2026). [VERIFIED] — re-confirms Connes' bicentralizer problem is OPEN in general as of 2026. (Authors are Ando-Goldbring, not "I. Goldbring et al.")

AQFT / encoding-screen (external-math sweep).

  • Morinelli, Neeb, Olafsson, (Euler-element / geometric Bisognano-Wichmann / Spin-Statistics program), arXiv:2508.10960; and Part II arXiv:2603.26390. [VERIFIED by abstract read] — BW / Spin-Statistics derived FROM the Euler element (symmetry is INPUT); a cleaner statement of the encoding screen, NOT a carrier, NOT a reverse-WW inversion, NOT a sixth route.
  • Morinelli (single-author), arXiv:2412.20410. [VERIFIED — single-author] — Euler-program; part of the same encoding-screen family.
  • arXiv:2511.09360 (Euler-program). [VERIFIED real per sweep] — per-paper authorship to be confirmed before bibliography insertion (not all three-author); mark [authorship unverified] until checked.
  • Liu, (lecture notes, modular/AQFT), arXiv:2510.07017. [VERIFIED real] — presupposes geometry as input; fails the encode-not-generate screen.
  • Naaijkens, Penneys, Wallick, arXiv:2605.10693. [VERIFIED real] — LTO-internal Euclidean-side reflection-positivity axiom + Tomita-Takesaki for Haag duality on cone regions; ORTHOGONAL — constructs no Lorentzian metric, no indefinite pairing, no carrier witness; makes NO claim that J carries the Euclidean datum.
  • Weiner, (algebraic Haag theorem), arXiv:1006.4726. [VERIFIED verbatim, standing corpus] — split + geometric modular action => the vacuum-sector net is a complete invariant (conditional on the geometric inputs).
  • Sheikh-Jabbari, Taghiloo, "GR from RG", arXiv:2602.11806. [VERIFIED real] — RG-induced Einstein-Hilbert term with a UV-Dirichlet-fixed metric; explicitly engages Weinberg-Witten; an EVADE-not-invert WW instance (discharges the iter-11 "WW gloss not confirmable" minor defect).

Experiment-watchlist (target/core, not wager).

  • VIP / XENONnT objective-collapse bounds, primary arXiv:2506.05507 (PRL, March 2026). [VERIFIED real] — CSL ~2 orders, DP ~5x; tighten the A-3 core. Adjacent/auxiliary: arXiv:2512.15393, arXiv:2604.21705 [both VERIFIED real].
  • Huang, Cai, Wang, (low-z SN calibration-bias analysis for DESI w(z)), arXiv:2502.04212. [VERIFIED — abstract states dynamical-dark-energy preference "less than 2 sigma"] — Efstathiou in acknowledgments only (not an author).

Iteration-14 verified additions (2026-06-19)

From the maximal adversarial assault (the strongest 2024–2026 falsification attempts on the three pillars). The four load-bearing entries below were independently web-verified this session; the remaining encoding-screen instances surfaced by the assault are catalogued in the iteration-14 D-track notes (all referee-verified live).

  • Fullwood, J., Vedral, V. & Guzmán-González, E. — "On Lorentzian symmetries of quantum information." arXiv:2604.07471 (Apr 2026). [VERIFIED] — Derives the Minkowski form and SO⁺(1,3) from "preservation of linear entropy" on qubit observables (linear entropy SL=2det⁡S_L=2\det; det⁡\det = the SL(2,ℂ)-invariant on Herm2(C)\mathrm{Herm}_2(\mathbb C)). The strongest 2026 "signature-as-output" claim — but the (1,3) signature is intrinsic to the complex carrier (the determinant on 2×22\times2 complex-Hermitian matrices has signature exactly (1,3), unconditionally), with no locality/net/causal order. Recorded as a 2026 instance of HYP-ENCODING-SCREEN (the indefinite-pairing-in-carrier smuggle), not a carrier and not a sixth route.
  • Schneider, M. D. — "Spacetime emergence: an (in)effective story." arXiv:2410.00932 (Philosophy of Physics, 2024). [VERIFIED] — Argues GR's spacetime "irreducibly include[s] global physical content, which is not effective" and that this global content "acts like a superselection rule that must be independently specified." An external (philosophy-of-physics) corroboration that locates the encode-screen's sole structural seam — the global/topological net-sharing premise — exactly where this wiki names its own soft spot; constructs no distinguishing observable.
  • Chou, K.-H. & Chang, P.-Y. — "Emergent de Sitter Space and Non-Unitary Tensor Networks from Non-Hermitian Quantum Criticality." arXiv:2606.17983 (Jun 2026). [VERIFIED] — A non-unitary cMERA built on a pre-selected non-Hermitian critical fermion chain; the de Sitter output emerges relative to the installed criticality (the coefficient is reproduced, not derived). Confirms the iteration-12 closure that the indefinite-metric / Krein route is route-5 in Krein vocabulary, not a sixth route.
  • Verlinde, E. & Zurek, K. (GQuEST / geontropic): "Modular fluctuations from shockwave geometry" / GQuEST design, arXiv:2404.07524 (PRX 15, 011034 (2025)); EFT baseline "Response of interferometers to the vacuum of quantum gravity," arXiv:2409.03894. [VERIFIED] — The geontropic interferometer signal; its proponents concede "conformal field theory, dilaton theory, and hydrodynamics" yield the same α=O(1)\alpha=O(1) amplitude, so it co-classes emergent and fundamental descriptions (screen-passing) and its amplitude re-imports η=1/4G\eta=1/4G at the modular→metric step. The freshest worked instance of the §7 no-test corollary.

Iteration-15 verified additions (2026-06-19) — the un-tried mathematical frameworks

From the final analytical iteration (factorization algebras / functorial QFT; index theory / K-theory; higher-categorical AQFT) — all reproduce the encode-not-generate screen. The Krein-spectral-triple entry was independently web-verified this session; the framework references are referee-verified, with attributions corrected per the referees.

  • Bizi, N., Brouder, C. & Besnard, F. — "Space and time dimensions of algebras with applications to Lorentzian noncommutative geometry and quantum electrodynamics." arXiv:1611.07062. [VERIFIED] — Defines indefinite (pseudo-Riemannian) spectral triples "over Krein spaces instead of Hilbert spaces." The index-theory confirmation of the iteration-12 Krein closure: a Lorentzian spectral triple installs a Krein space whose indefinite inner product is the (n,n)(n,n) carrier η\eta — installed, not generated.
  • Benini, M., Carmona, V., Grant-Stuart, A. & Schenkel, A. — the categorical equivalence AQFT ≃\simeq time-orderable prefactorization algebra on globally hyperbolic Lorentzian manifolds (arXiv:2412.07318; building on arXiv:1903.03396). [referee-verified] — A new precise object but not a handle: both sides are functors over the same causal-disjointness / orthogonality relation (= the localization template n1n_1). A fourth independent witness to the same obstruction.
  • Gwilliam, O. & Rejzner, K. — "The observables of a perturbative algebraic quantum field theory form a factorization algebra." arXiv:2212.08175. [referee-verified] — pAQFT observables form a factorization algebra on a fixed Lorentzian manifold (the geometry is the base).
  • Bunk, S., MacManus, J. & Schenkel, A. — "Lorentzian bordisms in algebraic quantum field theory." arXiv:2308.01026 (Lett. Math. Phys. 115 (2025)). [referee-verified] — the Lorentzian bordism site for functorial AQFT (geometry in the site).
  • Müller, L. & Stehouwer, L. — reflection / dagger structures inducing an indefinite signature in (non-unitary) categorical field theory. arXiv:2301.06664. [referee-verified] — the categorical-vocabulary form of the iteration-12 installed-Krein problem.

Watch-sweep #1 verified additions (2026-07-02) — post-saturation watch-mode

From the first watch-mode sweep (window 2026-06-15 → 2026-07-02; notes/2026-07-02-watch-sweep-01.md). Zero referee-surviving strong findings; these entries are watch-channel records, not verdict movers. All web-verified live this session (un-refereed v1 preprints unless noted).

  • Marrakchi, A. — "Ergodicity of the bicentralizer flow and Kadison's problem." arXiv:2606.23636 (v1 2026-06-22, math.OA). [VERIFIED] — Unconditional: the relative bicentralizer flow of a type III₁ irreducible subfactor with expectation is always ergodic; consequence: such subfactors contain a maximal abelian subalgebra, completing Kadison's 1967 problem. NOT bicentralizer triviality (Connes' problem stays OPEN); no carrier content (output is abelian/definite); does not transfer to the expectation-free physics-net inclusions (the iter-12 blocker). Watch value: the tracked adjacent cluster is actively moving.
  • Bateman, S. & Turok, N. — "Escape from Ostrogradsky via Hidden Ghost Parity." arXiv:2607.00096 (v1 2026-06-30, hep-th). [VERIFIED] — Four-derivative scalar QFT on a Krein space with a Krein Born rule and tree-level positivity via a "hidden ghost parity" κ from an O(1,1) embedding; the paper itself: "no preferred choice of ghost parity." A new instance of the iteration-12 Krein closure, channel (B) installed-not-derived (n₁ = fixed Minkowski commutator; κ global and non-unique); useful probabilistic-consistency machinery for indefinite carriers, no naturality content.
  • Wakakuwa, E., Petruzziello, L., Lantaño, T. B., Huelga, S. F. & Plenio, M. B. — "Relativistic Gravity-Induced Entanglement via Frame Dragging." arXiv:2606.31678 (v1 2026-06-30). [VERIFIED] — First genuinely post-Newtonian GIE channel (Lense–Thirring), derived two independent ways (quantized frame-dragging Hamiltonian; on-shell linearized-QG action). Gate-channel item (BMV/QGEM row); η and the causal order installed by design, openly.
  • External clocks (news, verified live): ESA Euclid DR1 restructured (published 2026-06-15) — DR1-Foundation Nov 2026 (no cosmology products), complete DR1 with GC+WL mid-2027 (cosmos.esa.int/web/euclid/dr1-timeline); NASA Roman at KSC 2026-06-21, launch NET 2026-08-30, Falcon Heavy (science.nasa.gov/blogs/roman/2026/06/21/).
  • Dated in-window markers, inside the screen (not load-bearing): arXiv:2606.17951 (one-parameter phantom-crossing w(z) form); arXiv:2606.19427 (AI-in-the-loop w(z) parametrization search); arXiv:2606.21826 (DESI-era dark-energy review); arXiv:2606.30928 (Cardy-type open/closed CFT from conformal nets — the net is input); arXiv:2606.28868 (finite-dim Krein metric-congruence — η installed per representation).

Iteration-16 verified additions (2026-07-03) — the multi-wedge iteration

From the clock-(1)-triggered iteration (tracks G1–G4 + referees R1/R2/R3; notes/2026-07-03-iter16-synthesis.md). All web-verified live this session.

  • Doplicher, S. & Longo, R. — "Standard and split inclusions of von Neumann algebras." Invent. Math. 75 (1984) 493–536, DOI 10.1007/BF01388641. [VERIFIED — Springer/ADS/EuDML] — Standard split inclusions, the canonical interpolating type I factor, and the canonical implementation machinery. Volume repair: the iter-12 ledger's "Invent. Math. 73" was a typo, corrected in place this iteration.
  • Morinelli, V. & Neeb, K.-H. — "From local nets to Euler elements." Adv. Math. 458 (2024) 109960 (arXiv:2312.12182). [VERIFIED — published] — The two-directional, BW-conditional bridge between the two smuggle items: given BW, regularity forces Euler-generated modular groups; conversely an Euler element plus BW yields regularity and localizability. Theorem-level confirmation that n₁ and η are interchangeable relative to an installed BW/wedge structure — deriving neither from (algebra, state). Hardens dossier §6.
  • Borchers, H.-J. — "The CPT-theorem in two-dimensional theories of local observables." Commun. Math. Phys. 143 (1992) 315–332, DOI 10.1007/BF02099011. [VERIFIED] — The Borchers commutation relations (spectrum condition + half-sided translations ⟹ modular scaling), the engine of LEM-NET-NATURALITY-G's (G-loc) branch.
  • Marrakchi, A. — arXiv:2606.23636 full-source audit (this iteration; abstract entry above under watch-sweep #1). [VERIFIED — full TeX source, twice independently downloaded] — The "with expectation" hypothesis is pervasive AND definitional (the relative bicentralizer flow is constructed against φ = φ∘E_N via Takesaki's theorem; the author flags the hypothesis "essential"); toolkit = averaging + ultrapower-implemented binormal states + approximate eigenstates of log Δ. Internal-bibliography caution: the preprint's "[Ha86] Acta Math. 69 (1986)" is a misprint (correct: Acta Math. 158 (1987) 95–148); its [Ma18] year is also suspect — import nothing from its bibliography unverified.
  • Houdayer, C. & Marrakchi, A. — "Selfless W*-probability spaces and Connes' bicentralizer problem." arXiv:2511.11409 (v2 2026-05-01; to appear J. Math. Soc. Japan per comments field). [VERIFIED — abstract verbatim] — States an implication (selflessness ⟹ bicentralizer-related structure), not an equivalence; the watch-sweep-#1 "equivalence" wording is repaired this iteration. Single-factor, no inclusion content; LOW relevance to expectation-free inclusions.
  • AGHS / Arulseelan (continuous model theory of W-algebras, 2025 axiomatizations)* — arXiv:2508.17241 and companions. [VERIFIED — abstract level] — The axiomatizability infrastructure making the commutant-to-generated gap posable as a definability question (the DCNG watch item). Includes the II∞-undecidability sentence verified verbatim.
  • Cipriani, F. & Sauvageot, J.-L. — derivations from completely Dirichlet forms (the first-order differential calculus). [VERIFIED at listing level per the G4 referee] — The constitutive-positivity (g₆) closure reason for the NC-Dirichlet-form readout: the form is completely positive-definite by construction; no indefinite version exists in the theory's foundations.
  • Longo, R. & Xu, F. — "Von Neumann Entropy in QFT." arXiv:1911.09390. [VERIFIED — attribution repaired per referee R2: Longo–Xu, not single-author] — The F-formula used in the G2 split-inclusion angle.

Interpretation, measurement, and dynamical-collapse models (mostly CONTESTED / SPECULATIVE)

  • H. Everett III, "Relative state formulation of quantum mechanics," Rev. Mod. Phys. 29, 454 (1957). CONTESTED — The no-collapse (relative-state / many-worlds) interpretation retaining only unitary evolution.
  • D. Bohm, "A suggested interpretation of the quantum theory in terms of hidden variables, I & II," Phys. Rev. 85, 166 & 180 (1952). CONTESTED — The de Broglie–Bohm pilot-wave theory: an explicit deterministic, contextual, nonlocal hidden-variable completion empirically equivalent to standard QM for the usual observables.
  • G. C. Ghirardi, A. Rimini, T. Weber, "Unified dynamics for microscopic and macroscopic systems," Phys. Rev. D 34, 470 (1986). SPECULATIVE (empirically testable, not yet decided) — The GRW objective-collapse model: an explicit modification of unitary dynamics with experimentally bounded parameters.
  • W. H. Zurek, "Decoherence, einselection, and the quantum origins of the classical," Rev. Mod. Phys. 75, 715 (2003). ESTABLISHED (decoherence mechanism) / CONTESTED (envariance derivation of the Born rule) — Authoritative review of decoherence, pointer-basis einselection, and the emergence of classicality.

Functional-analysis underpinnings (Reed–Simon) are listed under §8; rigorous operator-algebra results (Gelfand–Naimark, Bargmann, Gleason) are cross-referenced from §8.

2. Quantum field theory and particle physics

Primary support for domains/quantum-field-theory.md and domains/particle-physics.md.

Textbooks

  • S. Weinberg, The Quantum Theory of Fields, Vols. I–III (Cambridge Univ. Press, 1995–2000). ESTABLISHED — The deepest first-principles treatment: derives QFT from Poincaré invariance, unitarity, and cluster decomposition; authoritative on Wigner's classification, renormalization, gauge theories, electroweak symmetry breaking, and anomalies.
  • M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, 1995). ESTABLISHED — Standard graduate text for canonical + path-integral methods, renormalization, RG, gauge theories, and the chiral anomaly; the working calculational reference (and the QFT backbone for the Standard Model).
  • M. D. Schwartz, Quantum Field Theory and the Standard Model (Cambridge Univ. Press, 2014). ESTABLISHED — Modern text tying QFT formalism to SM phenomenology, EFT, and precision calculations.
  • A. Zee, Quantum Field Theory in a Nutshell, 2nd ed. (Princeton Univ. Press, 2010). ESTABLISHED — Path-integral-first and physically motivated; strong on the Wilsonian/EFT picture and conceptual structure.
  • C. Itzykson and J.-B. Zuber, Quantum Field Theory (McGraw-Hill, 1980). ESTABLISHED — Comprehensive classic on perturbation theory, renormalization, functional methods, and QED precision diagrammatics.
  • C. Quigg, Gauge Theories of the Strong, Weak, and Electromagnetic Interactions, 2nd ed. (Princeton Univ. Press, 2013). ESTABLISHED — Focused, physically motivated exposition of the SM gauge structure, electroweak theory, and the Higgs mechanism.
  • R. F. Streater and A. S. Wightman, PCT, Spin and Statistics, and All That (Benjamin, 1964; Princeton reissue 2000). ESTABLISHED — Canonical reference for the Wightman axioms, the reconstruction theorem, spin–statistics, and CPT — the rigorous operator/correlation foundation.
  • R. Haag, Local Quantum Physics: Fields, Particles, Algebras, 2nd ed. (Springer, 1996). ESTABLISHED — Definitive text on algebraic QFT (Haag–Kastler nets), DHR superselection, modular theory, Reeh–Schlieder, Bisognano–Wichmann, and Haag's theorem. (Also primary for §8.)
  • J. Glimm and A. Jaffe, Quantum Physics: A Functional Integral Point of View, 2nd ed. (Springer, 1987). ESTABLISHED — Authoritative account of constructive QFT: rigorous construction of ϕ4\phi^4 in 2 and 3 dimensions, the Osterwalder–Schrader axioms, and the methods/limits of the program. (Also primary for §8.)

Data reference

  • Particle Data Group (R. L. Workman et al.), Review of Particle Physics, Prog. Theor. Exp. Phys. (updated regularly; latest edition supersedes prior ones). ESTABLISHED — The standard source for measured SM parameters, masses, mixing matrices, and review articles. Use for any numerical value (see CONSTANTS_AND_SCALES.md). [unverified] exact lead-author/year for the current edition; cite the edition in hand.

Landmark papers — structure of QFT

  • E. P. Wigner, "On unitary representations of the inhomogeneous Lorentz group," Annals of Mathematics 40, 149 (1939). ESTABLISHED — Classifies particles as unitary irreducible representations of the Poincaré group (labeled by mass mm and spin/helicity).
  • K. G. Wilson and J. Kogut, "The renormalization group and the ε\varepsilon expansion," Physics Reports 12, 75 (1974). ESTABLISHED — The Wilsonian RG/EFT reframing of renormalization; foundational for relevant/marginal/irrelevant operators and universality. (Also primary for §5; cross-listed there.)
  • H. Reeh and S. Schlieder, Nuovo Cimento 22, 1051 (1961); J. J. Bisognano and E. H. Wichmann, J. Math. Phys. 16, 985 (1975). ESTABLISHED — Vacuum cyclicity/entanglement (Reeh–Schlieder) and modular-flow-equals-boost (Bisognano–Wichmann); structural theorems linking locality, modular theory, and the Unruh effect.
  • R. D. Sorkin, "Impossible measurements on quantum fields," in Directions in General Relativity, Vol. 2 (1993); C. J. Fewster and R. Verch, "Quantum fields and local measurements," Commun. Math. Phys. 378, 851 (2020). OPEN (problem) / INFERENCE (proposed framework) — The relativistic measurement problem (impossible measurements / superluminal signaling) and a modern consistent local-measurement framework.

Landmark papers — the Standard Model

  • S. L. Glashow, Nucl. Phys. 22, 579 (1961); S. Weinberg, Phys. Rev. Lett. 19, 1264 (1967); A. Salam (1968). ESTABLISHED — Founding papers unifying the electroweak interactions.
  • G. 't Hooft and M. Veltman, Nucl. Phys. B 44, 189 (1972). ESTABLISHED — Renormalizability of spontaneously broken non-Abelian gauge theories, making the electroweak theory predictive (Nobel 1999).
  • P. W. Higgs, Phys. Rev. Lett. 13, 508 (1964); F. Englert and R. Brout, Phys. Rev. Lett. 13, 321 (1964); G. Guralnik, C. R. Hagen, T. W. B. Kibble, Phys. Rev. Lett. 13, 585 (1964). ESTABLISHED — The Brout–Englert–Higgs mechanism; the boson was discovered by ATLAS and CMS in 2012 (Nobel 2013).
  • D. J. Gross and F. Wilczek, Phys. Rev. Lett. 30, 1343 (1973); H. D. Politzer, Phys. Rev. Lett. 30, 1346 (1973). ESTABLISHED — Asymptotic freedom in non-Abelian gauge theory, the foundation of perturbative QCD (Nobel 2004).
  • S. L. Adler, Phys. Rev. 177, 2426 (1969); J. S. Bell and R. Jackiw, Nuovo Cimento A 60, 47 (1969). ESTABLISHED — The chiral (ABJ) anomaly: a classical symmetry broken by quantization, with physical consequences and gauge-anomaly-cancellation constraints.
  • M. Kobayashi and T. Maskawa, Prog. Theor. Phys. 49, 652 (1973). ESTABLISHED — Three quark generations permit CP violation via a single CKM phase (Nobel 2008).
  • R. D. Peccei and H. R. Quinn, Phys. Rev. Lett. 38, 1440 (1977); S. Weinberg (1978); F. Wilczek (1978). ESTABLISHED (mechanism) / OPEN (axion existence) — The Peccei–Quinn solution to the strong-CP problem and the prediction of the axion.
  • A. D. Sakharov, JETP Lett. 5, 24 (1967). ESTABLISHED (necessary conditions) / OPEN (realized mechanism) — The three conditions (B violation, C/CP violation, departure from equilibrium) for dynamically generating the baryon asymmetry. See OPEN_PROBLEMS.md.

3. General relativity and gravitation

Primary support for domains/general-relativity.md.

Textbooks and treatises

  • C. W. Misner, K. S. Thorne, J. A. Wheeler, Gravitation (Freeman, 1973; reissued Princeton Univ. Press, 2017). ESTABLISHED — The canonical comprehensive reference ("MTW"); definitive on geometry, the equivalence principle, ADM, and gravitational waves. Source for sign-convention tables (see domains/general-relativity.md).
  • R. M. Wald, General Relativity (Univ. of Chicago Press, 1984). ESTABLISHED — The standard rigorous graduate text; authoritative on causal structure, singularity theorems, energy, asymptotic flatness (ADM/Bondi), and QFT in curved spacetime.
  • S. M. Carroll, Spacetime and Geometry: An Introduction to General Relativity (Addison-Wesley, 2004). ESTABLISHED — Modern, clear graduate text; good on the Einstein–Hilbert variational derivation, diffeomorphism invariance, and observational connections.
  • S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge Univ. Press, 1973). ESTABLISHED — Definitive treatment of global causal structure, energy conditions, and the Hawking–Penrose singularity theorems. (Also primary for §6; cross-listed there.)

Landmark papers and theorems

  • R. Penrose, "Gravitational collapse and space-time singularities," Phys. Rev. Lett. 14, 57 (1965). ESTABLISHED — The original trapped-surface singularity theorem; foundational for black-hole and cosmological singularity results (2020 Nobel).
  • R. Arnowitt, S. Deser, C. W. Misner, "The dynamics of general relativity" (1962; reprinted as arXiv:gr-qc/0405109). ESTABLISHED — The original ADM 3+13+1 Hamiltonian formulation, constraints, and definition of ADM energy.
  • Y. Choquet-Bruhat and R. Geroch, "Global aspects of the Cauchy problem in general relativity," Commun. Math. Phys. 14, 329 (1969). ESTABLISHED — Existence and uniqueness of the maximal globally hyperbolic development: the rigorous statement of GR's determinism.
  • R. Schoen and S.-T. Yau, "On the proof of the positive mass conjecture in general relativity," Commun. Math. Phys. 65, 45 (1979); E. Witten, Commun. Math. Phys. 80, 381 (1981). ESTABLISHED — Proofs of the positive-energy theorem (MADM≥0M_{\mathrm{ADM}} \ge 0), foundational for the consistency of GR's notion of total energy.
  • D. Christodoulou and S. Klainerman, The Global Nonlinear Stability of the Minkowski Space (Princeton Univ. Press, 1993). ESTABLISHED — Landmark proof that Minkowski space is nonlinearly stable; a benchmark global-existence result in GR PDE theory.
  • B. P. Abbott et al. (LIGO Scientific & Virgo Collaborations), "Observation of gravitational waves from a binary black hole merger," Phys. Rev. Lett. 116, 061102 (2016). ESTABLISHED — First direct detection (GW150914); confirmation of GR's dynamical, strong-field, radiative regime.
  • S. W. Hawking, "Particle creation by black holes," Commun. Math. Phys. 43, 199 (1975). ESTABLISHED (radiation) / OPEN (information fate) — Derivation of Hawking radiation; origin of the information paradox at the GR/QFT/thermodynamics interface. (Load-bearing across §5, §6, §7; primary listing here.)
  • C. M. Will, "The confrontation between general relativity and experiment," Living Reviews in Relativity 17, 4 (2014). ESTABLISHED — Authoritative, regularly updated review of the PPN formalism and the tests defining GR's domain of validity. [unverified] exact article number of the most recent revision; cite the current Living Reviews version.

4. Classical mechanics

Primary support for domains/classical-mechanics.md.

Textbooks

  • H. Goldstein, C. Poole, J. Safko, Classical Mechanics, 3rd ed. (Addison-Wesley, 2002). ESTABLISHED — Standard graduate text; canonical treatment of Lagrangian/Hamiltonian formalism, canonical transformations, Hamilton–Jacobi theory, rigid bodies, and chaos.
  • L. D. Landau and E. M. Lifshitz, Mechanics (Course of Theoretical Physics, Vol. 1), 3rd ed. (Pergamon, 1976). ESTABLISHED — Develops all of mechanics from the principle of least action with exceptional economy; authoritative on conservation laws, small oscillations, and the rigid body.
  • V. I. Arnold, Mathematical Methods of Classical Mechanics, 2nd ed. (Springer, GTM 60, 1989). ESTABLISHED — The definitive geometric/symplectic treatment: differential forms, symplectic manifolds, Liouville–Arnold integrability, action–angle variables, KAM; the bridge to modern mathematics (domains/mathematics.md).
  • J. E. Marsden and T. S. Ratiu, Introduction to Mechanics and Symmetry, 2nd ed. (Springer, 1999). ESTABLISHED — Authoritative on the geometry of symmetry: moment maps, Marsden–Weinstein symplectic reduction, Lie-group actions, and the modern form of Noether's theorem.
  • V. I. Arnold, V. V. Kozlov, A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics, 3rd ed. (Springer, 2006). ESTABLISHED — Comprehensive modern survey of integrable systems, perturbation theory, KAM, Arnold diffusion, and the rigorous state of celestial mechanics.
  • R. P. Feynman and A. R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, 1965). ESTABLISHED — The path-integral formulation ∝eiS/ℏ\propto e^{iS/\hbar} and the derivation of the classical least-action principle as its stationary-phase limit.

Landmark papers and original sources

  • E. Noether, "Invariante Variationsprobleme," Nachr. Ges. Wiss. Göttingen (1918). ESTABLISHED — The original paper establishing the symmetry–conservation correspondence (Noether's first and second theorems).
  • H. Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste, 3 vols. (Gauthier-Villars, 1892–1899). ESTABLISHED — Landmark origin of qualitative dynamics, the three-body problem, homoclinic tangles, and deterministic chaos / nonintegrability.
  • A. N. Kolmogorov (1954), V. I. Arnold (1963), J. Moser (1962) — the original KAM papers; synthesized in J. Moser, Stable and Random Motions in Dynamical Systems (Princeton Univ. Press, 1973). ESTABLISHED — Persistence of invariant tori under perturbation; foundational for the integrable–chaotic transition.
  • P. A. M. Dirac, Lectures on Quantum Mechanics (Belfer Graduate School, 1964); and "Generalized Hamiltonian dynamics" (1950). ESTABLISHED — Constraint analysis of singular Lagrangians (Dirac–Bergmann), Dirac brackets, and the bracket→commutator correspondence.
  • F. Bayen, M. Flato, C. Fronsdal, A. Lichnerowicz, D. Sternheimer, "Deformation theory and quantization, I & II," Ann. Phys. (NY) 111 (1978). ESTABLISHED (math) — Founding papers of deformation quantization and the star product, formalizing quantization as a deformation of the classical Poisson algebra.
  • Z. Xia, "The existence of noncollision singularities in Newtonian systems," Annals of Mathematics 135 (1992), 411–468. ESTABLISHED — Rigorous proof that finite-time noncollision singularities exist in the Newtonian NN-body problem (N≥5N \ge 5), bounding global determinism. See GAPS_AND_CONTRADICTIONS.md.
  • J. D. Norton, "The dome: an unexpectedly simple failure of determinism," Philosophy of Science 75 (2008). CONTESTED — Sharp articulation of the non-Lipschitz indeterminism debate internal to Newtonian mechanics.

5. Thermodynamics and statistical mechanics

Primary support for domains/thermodynamics.md and domains/statistical-mechanics.md.

Textbooks

  • H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed. (Wiley, 1985). ESTABLISHED — The canonical axiomatic (postulatory) treatment: fundamental relation, extremum principles, Legendre transforms, Maxwell relations, stability.
  • E. Fermi, Thermodynamics (Dover, 1956); M. W. Zemansky and R. H. Dittman, Heat and Thermodynamics (McGraw-Hill; multiple eds.). ESTABLISHED — Classic clear expositions of the four laws, Carnot's theorem, and the operational definition of absolute temperature. [unverified] exact edition/year of the Zemansky–Dittman volume in use.
  • L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1 (Course of Theoretical Physics, Vol. 5), 3rd ed. (Pergamon). ESTABLISHED — Authoritative bridge from statistical mechanics to thermodynamics: equilibrium ensembles, fluctuations, phase transitions, and the third law from quantum statistics.
  • K. Huang, Statistical Mechanics, 2nd ed. (Wiley, 1987). ESTABLISHED — Standard pedagogical text: Boltzmann equation and H-theorem, the ensembles, quantum gases, and the Ising model via the transfer matrix.
  • R. K. Pathria and P. D. Beale, Statistical Mechanics, 3rd ed. (Elsevier/Academic Press). ESTABLISHED — Comprehensive coverage of quantum statistics, the grand canonical ensemble, BEC, fluctuation–dissipation, and an introduction to critical phenomena and the RG.
  • L. E. Reichl, A Modern Course in Statistical Physics (Wiley; multiple eds.). ESTABLISHED — Strong on nonequilibrium statistical mechanics, kinetic theory, linear response, and the fluctuation–dissipation theorem.
  • N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Addison-Wesley, 1992). ESTABLISHED — Conceptually careful treatment of scaling, universality, and Wilsonian RG, including the ε\varepsilon-expansion.
  • A. I. Khinchin, Mathematical Foundations of Statistical Mechanics (Dover, 1949). ESTABLISHED — Rigorous demonstration that the equivalence of time and phase averages for macroscopic sum-functions rests on high dimensionality, not strict ergodicity — a cornerstone of the typicality viewpoint.

Historical origins

  • S. Carnot, Réflexions sur la puissance motrice du feu (1824); R. Clausius (1865, introduction of entropy); L. Boltzmann, Lectures on Gas Theory (1896–98). ESTABLISHED — Origins of the Carnot bound, the entropy concept, and the kinetic foundation of the second law.

Landmark papers — equilibrium, critical phenomena, foundations

  • L. Onsager, "Crystal statistics. I. A two-dimensional model with an order–disorder transition," Phys. Rev. 65, 117 (1944). ESTABLISHED — Exact solution of the 2D Ising model; the landmark demonstration of a genuine phase transition with non-mean-field critical exponents.
  • K. G. Wilson and J. Kogut, "The renormalization group and the ε\varepsilon expansion," Phys. Rep. 12, 75 (1974). ESTABLISHED — RG explanation of critical phenomena and universality (Wilson, Nobel 1982). (Primary entry; also load-bearing in §2.)
  • E. T. Jaynes, "Information theory and statistical mechanics," Phys. Rev. 106, 620 (1957). CONTESTED — The maximum-entropy / inferential reinterpretation of statistical mechanics; central to the disputed information-theoretic foundations. See domains/information-theory.md.
  • J. L. Lebowitz, "Boltzmann's entropy and time's arrow," Physics Today 46(9), 32 (1993). INFERENCE — Influential modern statement of the typicality/Boltzmann-entropy resolution of the irreversibility paradoxes (Loschmidt, Zermelo) and the role of the low-entropy past.
  • O. E. Lanford III, "Time evolution of large classical systems," in Dynamical Systems, Theory and Applications, Lecture Notes in Physics 38 (Springer, 1975). ESTABLISHED — Rigorous derivation of the Boltzmann equation from Hamiltonian dynamics (Boltzmann–Grad limit) for short times, clarifying the status of molecular chaos.

Landmark papers — nonequilibrium and fluctuation theorems

  • L. Onsager, Phys. Rev. 37, 405 and 38, 2265 (1931); S. R. de Groot and P. Mazur, Non-Equilibrium Thermodynamics (Dover, 1984). ESTABLISHED — Onsager reciprocal relations and linear irreversible thermodynamics; the near-equilibrium extension and connection to transport.
  • R. Kubo, "Statistical-mechanical theory of irreversible processes I," J. Phys. Soc. Jpn. 12, 570 (1957). ESTABLISHED — Linear-response theory and the fluctuation–dissipation theorem (Green–Kubo relations for transport coefficients).
  • C. Jarzynski, "Nonequilibrium equality for free energy differences," Phys. Rev. Lett. 78, 2690 (1997). ESTABLISHED — The Jarzynski equality ⟨e−βW⟩=e−βΔF\langle e^{-\beta W}\rangle = e^{-\beta \Delta F}, an exact nonequilibrium identity refining the second law.
  • G. E. Crooks, "Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences," Phys. Rev. E 60, 2721 (1999). ESTABLISHED — The Crooks fluctuation theorem relating forward/reverse work distributions; the detailed result from which Jarzynski follows.
  • U. Seifert, "Stochastic thermodynamics, fluctuation theorems and molecular machines," Rep. Prog. Phys. 75, 126001 (2012). ESTABLISHED — Comprehensive review of stochastic thermodynamics and trajectory-level entropy production.

Landmark papers — quantum thermalization

  • J. M. Deutsch, Phys. Rev. A 43, 2046 (1991); M. Srednicki, "Chaos and quantum thermalization," Phys. Rev. E 50, 888 (1994). INFERENCE (hypothesis, strongly supported) — The original formulations of the Eigenstate Thermalization Hypothesis (ETH) explaining thermalization in isolated quantum systems.
  • L. D'Alessio, Y. Kafri, A. Polkovnikov, M. Rigol, "From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics," Adv. Phys. 65, 239 (2016). INFERENCE — Comprehensive modern review tying ETH, quantum chaos, random-matrix theory, integrability/GGE, and the foundations of quantum statistical mechanics.

Black-hole thermodynamics (interface with §3, §6, §7)

  • J. D. Bekenstein, "Black holes and entropy," Phys. Rev. D 7, 2333 (1973). ESTABLISHED (within semiclassical gravity) — Black-hole entropy S=A/4S = A/4 (in G=ℏ=c=kB=1G=\hbar=c=k_B=1 units). (Primary entry; companion to Hawking 1975, §3.)
  • J. M. Bardeen, B. Carter, S. W. Hawking, "The four laws of black hole mechanics," Commun. Math. Phys. 31, 161 (1973). ESTABLISHED — The isomorphism between black-hole mechanics and the four laws of thermodynamics.
  • A. Strominger and C. Vafa, "Microscopic origin of the Bekenstein–Hawking entropy," Phys. Lett. B 379, 99 (1996). ESTABLISHED (for the specific BPS cases) / OPEN (general case) — String-theoretic microstate counting reproducing S=A/4S=A/4 for certain extremal black holes. See OPEN_PROBLEMS.md.

6. Cosmology

Primary support for domains/cosmology.md.

Textbooks

  • S. Weinberg, Cosmology (Oxford Univ. Press, 2008). ESTABLISHED — Authoritative graduate text; rigorous FLRW dynamics, the CMB and perturbation theory, and the anthropic bound on Λ\Lambda.
  • S. Dodelson and F. Schmidt, Modern Cosmology, 2nd ed. (Academic Press, 2020). ESTABLISHED — Standard reference for the Einstein–Boltzmann hierarchy, CMB and matter power spectra, and the formalism behind CAMB/CLASS.
  • V. Mukhanov, Physical Foundations of Cosmology (Cambridge Univ. Press, 2005). ESTABLISHED (formalism) — Rigorous cosmological perturbation theory and the inflationary generation of primordial fluctuations.
  • D. Baumann, Cosmology (Cambridge Univ. Press, 2022). ESTABLISHED — Modern pedagogical synthesis of background dynamics, inflation, and perturbations with current observational framing.
  • E. W. Kolb and M. S. Turner, The Early Universe (Addison-Wesley, 1990). ESTABLISHED — Classic reference on thermal history, freeze-out, BBN, and relics; standard source for the hot-Big-Bang formalism.
  • G. F. R. Ellis, R. Maartens, M. A. H. MacCallum, Relativistic Cosmology (Cambridge Univ. Press, 2012). ESTABLISHED — Careful treatment of the cosmological principle, averaging/backreaction (the fitting problem), and the foundations of the FLRW idealization.

Data reference

  • Planck Collaboration, "Planck 2018 results. VI. Cosmological parameters," Astron. Astrophys. 641, A6 (2020). ESTABLISHED — The definitive CMB determination of the six Λ\LambdaCDM parameters; baseline for the H0H_0-tension and curvature discussions. Use for numerical values (see CONSTANTS_AND_SCALES.md); the wiki states such values approximately by design.

Landmark papers and theorems

  • A. H. Guth, "Inflationary universe: a possible solution to the horizon and flatness problems," Phys. Rev. D 23, 347 (1981). INFERENCE (paradigm, strongly favored) — Foundational inflation paper articulating the horizon, flatness, and monopole problems.
  • A. Borde, A. H. Guth, A. Vilenkin, "Inflationary spacetimes are not past-complete," Phys. Rev. Lett. 90, 151301 (2003). ESTABLISHED (theorem) / SPECULATIVE (multiverse reading) — The BGV theorem: even eternally inflating spacetimes have a past boundary.
  • S. Weinberg, "The cosmological constant problem," Rev. Mod. Phys. 61, 1 (1989). OPEN — The canonical statement of the cosmological-constant problem and survey of attempted solutions; still the reference framing. See OPEN_PROBLEMS.md.
  • J. Martin, "Everything you always wanted to know about the cosmological constant problem (but were afraid to ask)," arXiv:1205.3365 C. R. Physique 13, 566–665 (2012), DOI 10.1016/j.crhy.2012.04.008. ESTABLISHED (pedagogy) — The standard regularization-aware treatment: dimensional regularization gives m4ln⁡μm^4\ln\mu structure, not Mcut4M_{\rm cut}^4.
  • C. P. Burgess, "The Cosmological Constant Problem: Why it's hard to get Dark Energy from Micro-physics," Les Houches lectures, arXiv:1309.4133. ESTABLISHED (pedagogy) — Naturalness / radiative-instability framing across EFT thresholds.
  • A. Padilla, "Lectures on the Cosmological Constant Problem," arXiv:1502.05296. ESTABLISHED (pedagogy) — Works Weinberg's no-go theorem through in detail; radiative instability; surveys sequestering and other exits.
  • N. Kaloper, A. Padilla, "Sequestering the Standard Model Vacuum Energy," Phys. Rev. Lett. 112, 091304 (2014) (arXiv:1309.6562); N. Kaloper, A. Padilla, D. Stefanyszyn, G. Zahariade, "A Manifestly Local Theory of Vacuum Energy Sequestering," Phys. Rev. Lett. 116, 051302 (2016) (arXiv:1505.01492). SPECULATIVE — Matter-loop vacuum-energy cancellation; the global version predicts transient dark energy and future collapse; graviton loops not covered by these versions.
  • R. Carballo-Rubio, L. J. Garay, G. García-Moreno, "Unimodular gravity vs general relativity: a status report," Class. Quantum Grav. 39, 243001 (2022) (arXiv:2207.08499). ESTABLISHED (review) — UG ≡ GR except Λ\Lambda-as-integration-constant; no further classical/semiclassical/quantum differences found; the "technically natural" reading is CONTESTED.
  • A. Salvio, "Unimodular Quadratic Gravity and the Cosmological Constant," Phys. Lett. B 856 (2024) 138920 (arXiv:2406.12958). ESTABLISHED (as literature verdict) — States explicitly that unimodular gravity does not solve the "new" CC problem (the observed value).
  • DESI Collaboration, "DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints," Phys. Rev. D 112, 083515 (2025) (arXiv:2503.14738); K. Lodha et al. (DESI), "Extended Dark Energy analysis using DESI DR2 BAO measurements," arXiv:2503.14743. ESTABLISHED (measurements) / CONTESTED (dynamical-DE interpretation) — The 3.1σ (BAO+CMB) / 2.8–4.2σ (+SNe) w0waw_0w_a preference; parameterization-robustness and phantom-crossing preference.
  • G. Efstathiou, "Evolving Dark Energy or Supernovae Systematics?," arXiv:2408.07175; D. D. Y. Ong, D. Yallup, W. Handley, "A Bayesian Perspective on Evidence for Evolving Dark Energy," arXiv:2511.10631. CONTESTED — The counter-analyses: the preference is SN-sample-driven; in Bayes-factor terms DESI DR2+CMB alone modestly favor Λ\LambdaCDM, and the signal largely vanishes with recalibrated DES-Dovekie SNe (ln B −0.57±0.26 → −0.30±0.19).
  • J. de Cruz Pérez, A. Gómez-Valent, J. Solà Peracaula, "Dynamical Dark Energy models in light of the latest observations," arXiv:2512.20616 (accepted 2026). CONTESTED — Running-vacuum variants vs DESI DR2 + Planck PR4 + SNe; evidence comparable to w0waw_0w_aCDM, strongest with DES-Y5.
  • L. A. Anchordoqui, I. Antoniadis, D. Lüst, "S-dual Quintessence, the Swampland, and the DESI DR2 Results," arXiv:2503.19428. SPECULATIVE — Swampland-consistent (distance/dS/TCC) quintessence matching the DESI-fitted potential.
  • R. Penrose, "Singularities and time-asymmetry," in General Relativity: An Einstein Centenary Survey, eds. S. W. Hawking and W. Israel (Cambridge Univ. Press, 1979); and The Road to Reality (Jonathan Cape, 2004). SPECULATIVE — Origin of the Weyl curvature hypothesis and the gravitational-entropy framing of the low-entropy past and the arrow of time. See HYPOTHESES.md.
  • S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge Univ. Press, 1973). ESTABLISHED — Singularity theorems and the rigorous geometric basis for the breakdown of FLRW at the initial singularity. (Primary listing in §3.)

7. Information theory and quantum information

Primary support for domains/information-theory.md.

Textbooks

  • T. M. Cover and J. A. Thomas, Elements of Information Theory, 2nd ed. (Wiley, 2006). ESTABLISHED — The canonical classical reference: AEP, data-processing inequality, capacity, rate–distortion, and the Kolmogorov-complexity chapter.
  • M. Li and P. Vitányi, An Introduction to Kolmogorov Complexity and Its Applications (Springer; multiple eds.). ESTABLISHED — Definitive treatment of algorithmic information theory: the invariance theorem, incomputability, relation to Shannon entropy, and Chaitin's results.
  • M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000/2010). ESTABLISHED — The standard quantum-information text: von Neumann entropy, no-cloning, teleportation, entanglement measures, channel capacities, error correction. (Primary listing in §1.)
  • M. M. Wilde, Quantum Information Theory, 2nd ed. (Cambridge Univ. Press, 2017). ESTABLISHED — Modern rigorous treatment of channels, entropies, and the information-theoretic structure underlying the operational generalization of the QM axioms.

Foundational papers — classical and quantum information

  • C. E. Shannon, "A mathematical theory of communication," Bell System Technical Journal 27, 379 & 623 (1948). ESTABLISHED — Founding paper: entropy, mutual information, source and channel coding theorems, channel capacity.
  • E. H. Lieb and M. B. Ruskai, "Proof of the strong subadditivity of quantum-mechanical entropy," J. Math. Phys. 14, 1938 (1973). ESTABLISHED — Proof of strong subadditivity, the single most important entropy inequality, underlying both quantum information and holographic entropy constraints.
  • J. A. Wheeler, "Information, physics, quantum: the search for links," in Complexity, Entropy and the Physics of Information (Addison-Wesley, 1990). SPECULATIVE — The "it from bit" manifesto framing physics as fundamentally informational; the conceptual lodestar of the domain. See UNIFYING_PRINCIPLES.md.

Thermodynamics of computation (interface with §5)

  • R. Landauer, "Irreversibility and heat generation in the computing process," IBM J. Res. Dev. 5, 183 (1961). ESTABLISHED — Landauer's principle: erasing one bit dissipates at least kBTln⁡2k_B T \ln 2 of heat.
  • C. H. Bennett, "The thermodynamics of computation — a review," Int. J. Theor. Phys. 21, 905 (1982). ESTABLISHED — Reversible computation and the resolution of the Maxwell-demon paradox via the cost of erasure.
  • N. Margolus and L. B. Levitin, "The maximum speed of dynamical evolution," Physica D 120, 188 (1998); S. Lloyd, "Ultimate physical limits to computation," Nature 406, 1047 (2000). ESTABLISHED (bounds) — The quantum speed limit / maximum operation rate and Lloyd's synthesis of physical bounds into computational ceilings.

Holography and "spacetime from entanglement"

  • J. D. Bekenstein, "Universal upper bound on the entropy-to-energy ratio for bounded systems," Phys. Rev. D 23, 287 (1981); G. 't Hooft (1993) and L. Susskind, "The world as a hologram," J. Math. Phys. 36, 6377 (1995); R. Bousso, "A covariant entropy conjecture," JHEP 07 (1999) 004, and "The holographic principle," Rev. Mod. Phys. 74, 825 (2002). INFERENCE (Bekenstein/Bousso bounds) / SPECULATIVE (holographic principle as fundamental) — The information-bound backbone of holography. [unverified] exact JHEP article number of Bousso 1999.
  • S. Ryu and T. Takayanagi, "Holographic derivation of entanglement entropy from AdS/CFT," Phys. Rev. Lett. 96, 181602 (2006); V. E. Hubeny, M. Rangamani, T. Takayanagi, JHEP 07 (2007) 062. INFERENCE (within AdS/CFT) — The RT formula and its covariant (HRT) generalization: entanglement entropy as a minimal/extremal bulk area.
  • A. Almheiri, X. Dong, D. Harlow, "Bulk locality and quantum error correction in AdS/CFT," JHEP 04 (2015) 163; F. Pastawski, B. Yoshida, D. Harlow, J. Preskill, "Holographic quantum error-correcting codes," JHEP 06 (2015) 149. SPECULATIVE — AdS/CFT as a quantum error-correcting code and the HaPPY tensor-network model.
  • T. Jacobson, "Thermodynamics of spacetime: the Einstein equation of state," Phys. Rev. Lett. 75, 1260 (1995); M. Van Raamsdonk, "Building up spacetime with quantum entanglement," Gen. Rel. Grav. 42, 2323 (2010); J. Maldacena and L. Susskind, "Cool horizons for entangled black holes," Fortsch. Phys. 61, 781 (2013). SPECULATIVE — Jacobson's thermodynamic derivation of Einstein's equations, the "spacetime from entanglement" thesis, and the ER=EPR conjecture. See UNIFICATION_LANDSCAPE.md.
  • D. N. Page, "Information in black hole radiation," Phys. Rev. Lett. 71, 3743 (1993). ESTABLISHED — The Page curve. Island/QES core (coordinates verified 2026-07-02, arXiv abs pages + journal records fetched): G. Penington, "Entanglement wedge reconstruction and the information paradox," arXiv:1905.08255, JHEP 09 (2020) 002; A. Almheiri, N. Engelhardt, D. Marolf, H. Maxfield, "The entropy of bulk quantum fields and the entanglement wedge of an evaporating black hole," arXiv:1905.08762, JHEP 12 (2019) 063; G. Penington, S. H. Shenker, D. Stanford, Z. Yang, "Replica wormholes and the black hole interior," arXiv:1911.11977, JHEP 03 (2022) 205; A. Almheiri, T. Hartman, J. Maldacena, E. Shaghoulian, A. Tajdini, "Replica wormholes and the entropy of Hawking radiation," arXiv:1911.12333, JHEP 05 (2020) 013. OPEN (paradox mechanism) / INFERENCE (island Page curve within controlled settings).
  • Islands — standing objections (all verified 2026-07-02): H. Geng, A. Karch, "Massive islands," arXiv:2006.02438, JHEP 09 (2020) 121; H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas, S. Shashi, "Information transfer with a gravitating bath," arXiv:2012.04671, SciPost Phys. 10, 103 (2021), and "Inconsistency of islands in theories with long-range gravity," arXiv:2107.03390, JHEP 01 (2022) 182; H. Geng, "Graviton mass and entanglement islands in low spacetime dimensions," arXiv:2312.13336, SciPost Phys. 19, 146 (2025); "Replica wormholes and entanglement islands in the Karch–Randall braneworld," arXiv:2405.14872, JHEP 01 (2025) 063; "Making the case for massive islands," arXiv:2509.22775 (no journal ref); S. Demulder, A. Gnecchi, I. Lavdas, D. Lüst, "Islands and light gravitons in type IIB string theory," arXiv:2204.03669, JHEP 02 (2023) 016. CONTESTED — the massive-graviton / gravitational-Gauss-law critique and its string-embedded refinements.
  • Ensemble-vs-single-theory (verified 2026-07-02): D. Marolf, H. Maxfield, "Transcending the ensemble: baby universes, spacetime wormholes, and the order and disorder of black hole information," arXiv:2002.08950, JHEP 08 (2020) 044; J.-M. Schlenker, E. Witten, "No ensemble averaging below the black hole threshold," arXiv:2202.01372, JHEP 07 (2022) 143. CONTESTED — whether replica-wormhole entropies are single-theory statements; see also arXiv:2510.06376 / 2605.15180 (OP-44 fourth option) and the OP-50 cluster.
  • Crossed-product founding trio (verified 2026-07-02): E. Witten, "Gravity and the crossed product," arXiv:2112.12828, JHEP 10 (2022) 008; V. Chandrasekaran, R. Longo, G. Penington, E. Witten, "An algebra of observables for de Sitter space," arXiv:2206.10780, JHEP 02 (2023) 082; V. Chandrasekaran, G. Penington, E. Witten, "Large N algebras and generalized entropy," arXiv:2209.10454, JHEP 04 (2023) 009; E. Witten, "A background independent algebra in quantum gravity," arXiv:2308.03663 (no journal ref listed). ESTABLISHED as mathematics / INFERENCE as physics — Type III1→_1\toII via the modular crossed product; vN entropy =Sgen=S_{\rm gen} up to an additive constant; the observer/clock is installed. (2024–2026 follow-ups on record in FINDINGS and the iteration-6 note: 2309.15897; 2306.01837; 2406.02116; 2406.01669; 2407.01695; 2501.01487; 2411.19931; 2601.07910; 2601.07915.)
  • C. Akers, N. Engelhardt, D. Harlow, G. Penington, S. Vardhan, "The black hole interior from non-isometric codes and complexity," arXiv:2207.06536 (no journal ref listed on arXiv). SPECULATIVE (leading proposal) — leading post-island account of interior reconstruction.
  • S. Raju, "Lessons from the information paradox," arXiv:2012.05770 [unverified journal-ref: Phys. Rept. (2022)]. — The holography-of-information counterpoint: exponentially small correlations + boundary completeness in massless gravity; companion cluster already on record at the A2 entries.

(Hawking 1975 — the origin of the information paradox — is listed in §3.)

8. Mathematical physics

Primary support for domains/mathematics.md.

Functional analysis and operator algebras

  • M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vols. I–IV (Academic Press, 1972–1979). ESTABLISHED — The canonical rigorous reference for functional analysis in physics: Hilbert spaces, self-adjointness and self-adjoint extensions (deficiency indices), the spectral theorem, Stone's theorem, and scattering. Vol. I (Functional Analysis), II (Self-Adjointness), III (Scattering), IV (Analysis of Operators). (Load-bearing for §1.)
  • M. Takesaki, Theory of Operator Algebras, Vols. I–III (Springer, 1979/2003). ESTABLISHED — The definitive treatise on C∗C^*- and von Neumann algebras, the Murray–von Neumann/Connes type classification, and Tomita–Takesaki modular theory with the KMS condition.
  • R. Haag, Local Quantum Physics: Fields, Particles, Algebras, 2nd ed. (Springer, 1996). ESTABLISHED — Algebraic QFT, the type-III nature of local algebras, modular theory in physics, DHR superselection. (Primary listing in §2.)

Geometry, topology, and representation theory

  • M. Nakahara, Geometry, Topology and Physics, 2nd ed. (IOP, 2003). ESTABLISHED — Widely used physicist's reference for manifolds, differential forms, fiber bundles, connections and curvature, characteristic classes, the Atiyah–Singer index theorem, and applications to gauge theory, anomalies, and instantons.
  • A. O. Barut and R. Rączka, Theory of Group Representations and Applications (PWN, 1977); M. E. Taylor, Noncommutative Harmonic Analysis (AMS, 1986). ESTABLISHED — Standard references for Lie groups, Lie algebras, and unitary representation theory in physics, including induced representations and Wigner's classification of Poincaré irreps. [unverified] exact year of the Taylor volume.

Rigorous QFT, constructive results, and modern frameworks

  • J. Glimm and A. Jaffe, Quantum Physics: A Functional Integral Point of View, 2nd ed. (Springer, 1987). ESTABLISHED — Constructive QFT and the rigorous Euclidean path integral, including the Osterwalder–Schrader axioms and the construction of P(ϕ)2P(\phi)_2 and ϕ34\phi^4_3. (Primary listing in §2.)
  • A. Jaffe and E. Witten, "Quantum Yang–Mills theory" (Clay Mathematics Institute Millennium Problem description, 2000). OPEN — The official statement of the Yang–Mills existence and mass-gap problem. See OPEN_PROBLEMS.md and GAPS_AND_CONTRADICTIONS.md.
  • M. Aizenman (Phys. Rev. Lett. 1981; Commun. Math. Phys. 1982) and M. Aizenman and H. Duminil-Copin, "Marginal triviality of the scaling limits of critical 4D Ising and ϕ44\phi^4_4 models," Annals of Mathematics 194 (2021), 163–235. ESTABLISHED — Rigorous proof of triviality of the continuum limit of ϕ4\phi^4 in four dimensions: some 4D theories exist only as cutoff effective theories. Central to the domain-of-validity discussion in domains/quantum-field-theory.md.
  • J. Lurie, "On the classification of topological field theories," Current Developments in Mathematics 2008 (2009), 129–280. INFERENCE (proof program/sketch) — The cobordism hypothesis; central result on fully extended TQFTs and higher-categorical structures.
  • K. Costello and O. Gwilliam, Factorization Algebras in Quantum Field Theory, Vols. 1–2 (Cambridge Univ. Press, 2017/2021). INFERENCE (perturbative scope) — Rigorous formulation of perturbative QFT via factorization algebras and the Batalin–Vilkovisky formalism; a leading bridge between physicists' QFT and rigorous mathematics.

Structural theorems and the meta-question

  • V. Bargmann, "On unitary ray representations of continuous groups," Ann. Math. 59 (1954); A. M. Gleason (1957, see §1); I. M. Gelfand and M. A. Naimark (1943) and I. E. Segal foundational C∗C^*-algebra papers. ESTABLISHED — Projective/ray representations (Bargmann–Wigner), the near-uniqueness of the Born rule (Gleason), and the representability of C∗C^*-algebras (Gelfand–Naimark–Segal).
  • E. P. Wigner, "The unreasonable effectiveness of mathematics in the natural sciences," Comm. Pure Appl. Math. 13 (1960), 1–14. OPEN (philosophical) — The original essay framing why mathematics is so effective in physics. See UNIFYING_PRINCIPLES.md.

9. Quantum gravity and unification

There is currently no experimentally confirmed theory of quantum gravity ESTABLISHED; accordingly every entry below is SPECULATIVE or OPEN as physics, even where the mathematics is rigorous. Many key results in this area are also load-bearing in §3 (Hawking 1975, Bardeen–Carter–Hawking), §5 (Bekenstein, Strominger–Vafa), and §7 (holography, RT/HRT, ER=EPR, islands) and are not repeated here. This section collects the additional canonical unification-program references. See UNIFICATION_LANDSCAPE.md, HYPOTHESES.md, and OPEN_PROBLEMS.md.

  • J. M. Maldacena, "The large-NN limit of superconformal field theories and supergravity," Adv. Theor. Math. Phys. 2, 231 (1998). SPECULATIVE (conjecture, very strongly supported within its regime) — The AdS/CFT correspondence; the most concrete realization of holography and the engine behind much of §7. [unverified] exact page; widely cited as Adv. Theor. Math. Phys. 2 (1998) 231 / Int. J. Theor. Phys. 38 (1999) 1113.
  • J. Polchinski, String Theory, Vols. I–II (Cambridge Univ. Press, 1998). ESTABLISHED (as exposition of the framework) — The standard graduate reference for perturbative string theory, D-branes, and dualities. The physical correctness of string theory as the theory of nature is OPEN.
  • C. Rovelli, Quantum Gravity (Cambridge Univ. Press, 2004); T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge Univ. Press, 2007). SPECULATIVE — Canonical references for loop quantum gravity (spin networks, the area/volume operators, spin foams). [unverified] exact year of the Thiemann volume.

Caution (per EPISTEMICS.md). The maturity of the mathematics in these programs must never be conflated with empirical confirmation of the physics. None of the candidate quantum-gravity frameworks has a confirmed prediction distinguishing it from the others or from semiclassical gravity ESTABLISHED. Treat all unification claims sourced from this section as SPECULATIVE unless a domain page demonstrates otherwise.

Maintenance conventions

  • Dedup rule. A source load-bearing in multiple domains is listed once under its primary section and cross-referenced (not re-quoted) elsewhere. When adding a reference, search this page first.
  • No fabrication. Add only sources you are confident exist. If unsure of a detail, supply author + title + approximate year and append [unverified]. Never invent a DOI, volume, page, or theorem name. This mirrors the cardinal rule of EPISTEMICS.md.
  • Numbers. All numerical constants and measured parameters trace to the Particle Data Group (§2) or Planck (§6); see CONSTANTS_AND_SCALES.md. Do not cite numbers from textbooks of memory.
  • Provenance. New entries should record which domain dossier or page motivated them; log additions in CHANGELOG.md.

See also

References

This is the references page. Other wiki pages should cite back here rather than maintaining parallel source lists. Cross-domain meta-pages — UNIFICATION_LANDSCAPE.md, UNIFYING_PRINCIPLES.md, FINDINGS.md, ROADMAP.md — should link individual entries above by author + short title.