Research Notes

Dated, deep-dive investigation logs. Each note records one focused research question pursued in an iteration, with full epistemic tagging and an adversarial referee verdict on every new claim. Notes are the long-form working memory of the wiki; their distilled conclusions are folded into FINDINGS.md and the registries (OPEN_PROBLEMS.md, ASSUMPTIONS_LEDGER.md, HYPOTHESES.md).

Iteration 2 — 2026-06-08

Theme: stress-test the central wager (causal/algebraic/entanglement structure is more fundamental than metric geometry) and the foundations of the quantum framework. 38 agents; recent (2020–2026) literature web-verified; 0/25 new claims flagged unsound.

de Sitter & emergent spacetime — can holography/entanglement→geometry reach our Λ>0 universe? Verdict: structural barrier; CLPW Type II₁ is a genuine Λ>0 entropy foothold, but no dS RT surface and no dS dynamics-from-entanglement.
Born rule & quantum linearity — is Born derivable; is linearity fundamental? Verdict: form forced (Gleason + Busch); quantitative meaning OPEN; deterministic nonlinearity excluded by no-signaling, stochastic collapse the live untested exception.
Tabletop quantum gravity (BMV) — would gravitationally-induced entanglement prove gravity is quantum? Verdict: valid but premise-dependent; falsifies a class of classical theories, does not prove graviton quantization.
Entropic & emergent gravity — derivation or analogy? Verdict: one theorem (Jacobson, given inputs) + a rewriting (Padmanabhan) + a mechanism (Sakharov); Verlinde dark matter contested→disfavored. Corrects an iteration-1 lensing inversion.
Algebraic background-independence — does the modular/crossed-product program derive geometry? Verdict: rigorous reorganization of semiclassical gravity on a fixed background; encodes, does not generate, geometry.
Unified-program synthesis — does it all cohere? Verdict: PARTIAL — two coherent programs (geometry-from-algebra; is-the-quantum-framework-final) joined by thin bridges (no-signaling/causal-order + BMV as a logical gate); the "it's all information" fusion is refused.

Iteration 3 — 2026-06-08

Theme: shift from surveying to attempting — try to derive the dS first law, formalize encode-vs-generate, attempt to merge Programs A & B, and red-team our own posture. Coherence verdict unchanged at PARTIAL; progress real but negative/structural.

Attempt: de Sitter entanglement first law (OP-41) — located the exact obstruction: dS supplies one Killing vector / one region, so δS_gen=δ⟨K⟩ gives only the ξ-integrated Hamiltonian constraint (the dS GSL), not the tensor δG_μν; plus a sign-reversed maximization (empty dS maximizes S_gen). Jacobson-2015 already gives the local Einstein equation at any Λ but is non-holographic. One un-foreclosed escape: an SO(d+1,1) modular-Hamiltonian family. OPEN, not a no-go.
Formalize: encode-vs-generate criterion (OP-46) — a decision-usable criterion (graded axes Δ_geo, κ_Φ + a 5-item smuggling checklist); six constructions graded; none generates Lorentzian spacetime from factorization-free, region-free, symmetric-state-free data — the encode/generate frontier coincides with the Type III₁ no-factorization fact.
Attempt: merge Programs A & B — succeeded narrowly, failed deeply: one (M, ω) substrate non-circularly co-derives the Born form + thermal/entropic structure, but the GPT framework-fixing axioms (composition, purification, reversibility) have no Type III₁ formulation (candidate-no-go OP-48) — and fail precisely in the no-observer cosmological regime.
Red-team: the demotion-and-derivation posture — 0 fatal, 4 serious cracks: the "fixed cores" are heterogeneous, three conditional (Type III₁ not fixed once gravity is on — Giddings); "demotion-and-derivation" is a heuristic, not a falsifiable program; the six-lens "convergence" partly a shared-input streetlight effect; CLPW II₁ is a bounded-area feature, not Λ-diagnostic (KLS: Schwarzschild–dS is II∞×II∞).
Iteration-3 synthesis — verdict + the empirical falsifiability portfolio (BMV ~10–20+ yr; objective-collapse decisive by ~2035; DESI w(z) 2–7 yr; LIV/EP null anchors; matter-wave the shared enabling tech). None of the live channels tests the geometry-from-algebra wager itself — by the wiki's own standard, still not yet physics.

Iteration 4 — 2026-06-08

Theme: attack the three named decidable problems, web-verify the literature, and audit distance-to-conclusion. Verdict unchanged at PARTIAL (third consecutive); trend diminishing.

Attempt: dS first-law SO(d+1,1) escape (OP-41) (+ raw attempt) — executed and failed: a finite isometry orbit gives ≤10 global Killing-charge constraints, no Radon inversion to the local δG_μν; promoted toward a scoped near-no-go (HYP-dS-NOMIN-R3, HYP-dS-CARDINALITY). Corroborated by Chen–Xu 2511.00622.
Resolve OP-48 (GPT on Type III₁) — sharp disjunction: no-go for exact composition on a single III₁ factor; split-property qualified yes that relocates the BW/CHM circularity (HYP-SPLIT-GEOM).
Break the modular circularity (OP-46) — near-vacuous under the standard readout (Borchers/Wiesbrock + Caminiti et al.; Connes gives only a Riemannian metric — GAP-NCG-LORENTZIAN-SIGNATURE); a non-CKV Lorentzian readout is the live target.
Literature refresh — muon g−2 now SM-consistent (WP2025, arXiv:2505.21476); the three flagged 2026 preprints all real / web-confirmed; collapse bounds tighter, not closed.
Convergence audit — analytical saturation ≈1–3 iterations away; object-level confirmation non-forecastable; recommendation HYBRID.
Iteration-4 synthesis — consolidated verdict + next targets.

Iteration 5 — 2026-06-08 (closing push → saturation)

The closing analytical push. Executed the one designated verdict-flipping move (OP-46 Lorentzian non-CKV readout) — it did not flip. Named list settled; analytical saturation reached; capstone ../CONCLUSION.md written.

OP-48(c) collar-free composition — conditional no-go: "collar-free + state-independent" and "singles out QM" mutually exclusive on a single III₁ factor (van Luijk embezzlement κ_max).
OP-44 nonperturbative crossed-product — regime-dependent (boundary N*); Type III₁-for-any-Λ is a leading-order input, not a fixed nonperturbative core.
OP-46 Lorentzian non-CKV readout — the verdict-flipper: produced the first emergent Lorentzian metric (Huang–Ma dS₂) but signature inherited from symmetry → did not flip; obstruction now readout-independent.
Surviving dS routes — pseudo-entropy inherits non-unitarity; Jacobson-in-CLPW re-imports η. Root: the area-entropy coefficient is an input, not an output, everywhere (HYP-dS-CARDINALITY-R1).
Iteration-5 synthesis — saturation reached; capstone recommended and written.

Iteration 6 — 2026-06-10 (new-input iteration)

Theme: the first post-saturation iteration — inject new 2023–2026 input (6 research + 4 attack tracks, 22 agents, all adversarially refereed; ~90 findings kept, 0 fatal) and test whether the saturated verdict survives contact with the field. It does: headline unchanged for the fifth consecutive iteration; hedges restructured (OP-48c shrunk; OP-49 closed-negative; HYP-ENCODING-SCREEN added; obstruction now four readout families). Synthesis: iteration-6 synthesis.

Distinguishing-prediction hunt (attack) — can ANY published channel distinguish the wager even in principle? Verdict: no — and the no-test fact is now a corollary of encode-not-generate (ENCODING-SCREEN), inheriting the OP-46 MEDIUM hedge; a class test would need a "reverse Weinberg–Witten" theorem (none exists); GQuEST added as a decision-grade EFT-breakdown channel, not a wager test.
Generation-construction survey (attack) — does any construction generate Lorentzian signature? Verdict: no — causal fermion systems are a fourth readout family closing at the same signature-installation step ((≤n,≤n) axiom = relocated Krein η); new selection-type pattern (Lee 2020) generates only the choice; HYP-CKV-VACUITY-R3; target compresses to deriving the indefinite pairing from modular data.
OP-44 / OP-48c levers (attack) — move the two residual analytical levers. Verdict: both moved, neither flips — JRS no-commutant + crossed-product rigidity; order-G_N² obligation located (quadratic boost constraints); horn C partially discharged (theorem-shaped under the full-pair reading; residue = formalization choice + III₁-embezzlement alternative).
OP-49 pseudo-entropy reality (attack) — can Im S be nulled keeping nontrivial δG? Verdict: NEAR-NO-GO (resolved-negative, conditional) — the Einstein content lives entirely in the imaginary channel; reality forces triviality; three named residuals; corrects the iter-5 Re/Im parenthetical.
Closed universe & dS holography — the 2024–26 dim H_closed = 1 debate. Verdict: real, live, CONTESTED → new OP-50; the observer rescue independently corroborates OP-48(c)'s structure (analogy, not derivation); HYP-dS-CARDINALITY-R1 extended — η input or absent, never output.
Algebraic frontier — 2024–26 operator-algebra sweep. Verdict: survival side theorem-hardened perturbatively (KLS II; CF: non-stationary GSL + QFC proof); failure side acquires algebraic replacements (stringy split breakdown; survives-after-averaging); N unmoved; encode-direction evidence (Engelhardt–Liu).*
Amplitudes & positive geometry — surfaceology/zeros/cosmohedra. Verdict: H5 scope expands (confidence low → low-to-medium), but no positive geometry for gravity (structural) and all kinematic data presuppose flat space — encodes; verdict untouched.
Background-independent programs — landscape refresh. Verdict: two new entries warranted (Oppenheim CQ; dark dimension — both genuinely testable, sharpening the wager's demotion by contrast); six stale-fixes; no program supplies a new signature readout.
QG phenomenology — 2022–26 sweep. Verdict: GQuEST/VZ is Program-A-adjacent, not a wager test (chain re-imports η=1/4G); CQ gate may close from the classical side before BMV; DSW deflated (Biggs–Maldacena); dead-end ledger (Hogan dead; Aziz–Howl dying).
Experiment refresh — mid-2026 numbers. Verdict: all standing numbers hold; w(z) decision point compresses to 2027; four watchlist rows change (GW nulls incl. area-law confirmation; neutrino-mass; matter-wave 1.7×10⁵ Da; LHCb ~4σ); nothing touches the wager.
Iteration-6 synthesis — hedge-accounting table (2 hedges → 3, one shrunk), registry deltas, why the verdict stands, and what could move it next (only new input: 2027 w(z); GQuEST; CQ falsification; the order-G_N² obligation; the compressed OP-46 target).

Iteration 7 — 2026-06-10 (the decidable levers)

Theme: execute the four named decidable levers iteration 6 left on the table — the compressed OP-46 target (the designated verdict-flipper), OP-44's order-G_N² obligation, OP-49's SVD residual, and OP-48c's formalization-choice residue. 9 agents; 4 attack tracks, all adversarially refereed (independent re-derivation, numerical replication, live citation audits; corrections binding). Headline unchanged for the sixth consecutive iteration; the principal hedge HARDENS (OP-46 MEDIUM → MEDIUM-HIGH conditional; OP-49's SVD residual closed-negative; OP-48c's definitional residue resolved; OP-44 split P1a/P1b/P1c with the first failure-side perturbative foothold). Synthesis: iteration-7 synthesis.

Indefinite pairing from modular data (attack — the verdict-flipper) — can the Krein η be derived from (M, Ω) modular data? Verdict: RESOLVED-NEGATIVE in the most informative way — η₀ = sgn(ln Δ) IS a canonical smuggle-free Krein fundamental symmetry (one of an infinite J-odd family, per referee), but provably geometry-void (unitarily universal ⟹ Δ_geo = 0; algebra-incompatible; non-localizable); new modular-form trichotomy lemma (ansatz-scoped); g₃ upgraded structural (J carries reflection positivity via cone self-duality); OP-46 hedge hardens MEDIUM → MEDIUM-HIGH; target re-compresses to the carrier problem (HYP-FACTORIZATION-IS-GEOMETRY, fifth route to converge there).
OP-44 order-G_N² descent (attack) — discharge or obstruct the named obligation. Verdict: SHARPENED-OPEN — P1 splits P1a/P1b/P1c: quadratic descent of the full global-dS constraint set to the CLPW crossed product discharged at inference grade (stabilizer/coset frame; DEHK+FJLRW+AKL); residues R1 (footnote-12 classical sufficiency with worldline clocks — distributional sources exit FMM/AMM) and R2 (cubic-constraint horizon non-splittability, δ^{-2(d-1)} divergence, Planck-length collar floor δ ≳ ℓ_P — the first perturbative failure-side foothold, at order κ³; parallel to OP-48's stringy ℓ_s floor). N* untouched.
OP-49 SVD computation (attack) — perform the iter-6 stated decidable computation. Verdict: RESOLVED-NEGATIVE (conditional, referee-narrowed) — the SVD first law fails on the dS₃ hemisphere: S_SVD real by construction vs the purely-imaginary verified carrier (unconditional); the c+c* = 0 cap-blindness mechanism conditional on heterogeneous-cover junction additivity (new residual c′); OP-49 stays NEAR-NO-GO with residuals (a)/(b)/(c′); byproduct S_SVD = S_dS/2 dropped to SPECULATIVE.
OP-48c full-pair forcing (attack) — settle the full-pair vs subsystem reading; run the OP-50 watch. Verdict: RESOLVED-POSITIVE (forced-modulo-rejecting-the-question) — all three GPT reconstructions quantify composition over THE designated pair; LT-separation HOLDS on the III₁ pair, so the failure locus is the normal-product-preparation primitive; horn C → theorem-conditional-on-framework; residue = normal-state postulate + exits X1 (singular states, corrected Schlieder/Roos+Hahn–Banach route) / X2 (non-OPT composition). OP-50 now three-cornered (polynomial-dim II₁ sector, arXiv:2606.04575).
Iteration-7 synthesis — per-track verdict table, hedge ledger before → after (OP-46 hardened; ENCODING-SCREEN inherits), why the verdict stands a sixth time, and the residual map: the carrier problem as THE compressed analytical target; OP-44's R1/R2; OP-49's (a)/(b)/(c′); OP-48c's X1/X2; experiment watchlist unchanged.