OP-44 literature delta (2024–2026): the survival side hardens perturbatively; the failure side turns out algebraic; no theorem on either side of $N_\ast$

Status: Research sweep executed (iteration 6, track R2-algebraic) — 17 abstracts individually fetched and verified this session; OP-44/OP-CP1 verdict UNCHANGED (regime-dependent, no theorem on either side of $N_\ast$ ) but its interior structure is refined: perturbative survival is now theorem-grade including non-stationary cuts and the QFC; all published post-breakdown candidates remain algebraic; a fourth verdict option ("survives-after-averaging over $N$ ") enters the literature. Two orchestrator leads corrected. Last updated: 2026-06-10 Iteration: 6

This note is the iteration-6 literature delta for OP-44/OP-CP1, relative to the iteration-5 baseline 2026-06-08-iter5-op44-nonperturbative-crossed-product.md and the Program-A verdict note 2026-06-08-algebraic-background-independence.md. Everything below is new input: no paper cited here (except baseline anchors) appears in the wiki with a fetched abstract.

1. Baseline being updated

Iteration 5 left OP-44/OP-CP1 as the sole residual analytical lever: the von Neumann-algebraic subregion description survives under dynamical gravity only as an approximate / QRF-relational Type II structure below the (author-estimated) boundary $N_\ast \sim R/2GE_f$ , degenerates above it (Giddings' algebraic spacetime disruption), with no theorem on either side and three admissible verdicts (survives / fails / regime-dependent). The live downside was open subquestion #1: does the $O(\kappa)$ spacelike noncommutativity already destroy the conditional-expectation / split structure the crossed product silently requires? The live upside was subquestion #2: a controlled all-orders dressing. [baseline]

Headline of this sweep [INFERENCE, medium-high]: nothing published in 2024–2026 supplies either theorem; OP-44 stays open and regime-dependent. But the open problem's interior moved in three specific ways, each below.

2. The survival side hardens to theorem-grade at linearized order

2.1 The complete constraint group: KLS II (Jan 2026)

Klinger–Kudler-Flam–Satishchandran, Generalized Entropy is von Neumann Entropy II: The complete symmetry group and edge modes (arXiv:2601.07910, 12 Jan 2026, 104 pp) impose, for the exterior of a stationary black hole and the dS static patch, the complete family of constraints of perturbative quantum gravity — not the single boost generator of KLS I (arXiv:2309.15897, PRD 111, 025013). Gravitational backreaction produces angle-dependent horizon-area perturbations encoded in edge modes tied to boost supertranslation symmetries; the complete observable algebra satisfies infinitely many constraints and is still Type II with a universal trace; the entropy is $S \;=\; S_{\rm gen} + S_{\rm edge} + \text{const},$ with Type II $_\infty$ (black hole, no max-entropy state) and Type II $_1$ (dS, max-entropy state exists once observer properties such as rotational kinetic energy are included). [ESTABLISHED — abstract verified; ESTABLISHED as mathematics / INFERENCE as physics, per house convention]

Delta: the iteration-4 literature refresh (2026-06-08-iter4-literature-refresh.md) listed 2601.07910 as "incremental follow-up, action=none, abstract not fetched." That gloss is superseded: surviving the full infinite-dimensional constraint group, with a computed edge-mode correction to $S_{\rm gen}$ , is a nontrivial robustness theorem for the survival side. It also bears on iter5 open subquestion #4: the dS II $_1$ structure tolerates the complete perturbative constraint family. [INFERENCE]

2.2 GSL for non-stationary perturbations + the QFC becomes a perturbative theorem: Chandrasekaran–Flanagan (Jan 2026)

Chandrasekaran–Flanagan, Subregion algebras in classical and quantum gravity (arXiv:2601.07915, 12 Jan 2026, 111 pp) study subregion algebras for portions of null surfaces — event horizons and finite causal diamonds. The inference chain, from the verbatim abstract [ESTABLISHED]:

Extend the subregion phase space by doubled corner edge modes (relative boosts and null translations of the corners), carrying a corner symplectic form;
these generate canonical charges for half-sided boosts and translations acting nontrivially on gravitationally dressed horizon observables, so the horizon subalgebra "naturally takes the form of a crossed product by the associated automorphism group";
quantizing around a black-hole background: for each horizon cut a Type II $_\infty$ algebra with trace, vN entropy $=S_{\rm gen}$ of that cut;
the half-sided null translation generator lifts to a self-adjoint operator implementing null time evolution on the cut algebras; the area operator is the bulk implementation of Connes cocycle flow for one-sided observables in excited states;
nesting of the one-parameter family of cut algebras $\mathcal A(s')\subseteq\mathcal A(s)$ , $s'\ge s$ , implies "a generalized second law for non-stationary linearized perturbations of Killing horizons";
gravitational half-sided modular inclusions are used to "prove the quantum focusing conjecture in the perturbative quantum gravity regime" (verbatim).

Delta: this is the strongest movement on the wiki's algebraic-GSL ledger since Faulkner–Speranza (arXiv:2405.00847, Killing-horizon cuts, semiclassical): the GSL now covers non-stationary linearized perturbations, and the QFC — listed in the wiki only as a conjecture — is a theorem within the linearized regime. [ESTABLISHED for the results as scoped] Scope honesty [INFERENCE]: a fixed black-hole background to linearize around, the null-surface structure, and the edge-mode extension are inputs; this hardens the sub- $N_\ast$ regime and is silent on the nonperturbative one. It does not derive geometry — the crossed product's automorphism group is built from a pre-installed corner symmetry, exactly the pattern of A-CP-KILLING, now at the corner-symmetry level.

2.3 Physical clocks replace external observers; non-stationary backgrounds

Chen–Penington, A clock is just a way to tell the time: gravitational algebras in cosmological spacetimes (arXiv:2406.02116): in slow-roll inflation and evaporating Schwarzschild–de Sitter black holes — out-of-equilibrium, non-stationary — diff-invariant observables exist without external clocks or asymptotic charges (the inflaton / the evaporating hole is the clock); algebras are Type II $_\infty$ ; Type II entropy $=S_{\rm gen}$ . [ESTABLISHED — abstract verified]
Kudler-Flam–Leutheusser–Satishchandran, Algebraic Observational Cosmology (arXiv:2406.01669): the dressed algebra of a comoving FLRW observer (inflationary origin); all accessible states are mixed with vN entropy $=S_{\rm gen}$ of the observer's causal diamond. [ESTABLISHED — abstract verified]
Background fill (2023, absent from wiki): Jensen–Sorce–Speranza, Generalized entropy for general subregions in quantum gravity (arXiv:2306.01837, JHEP 12 (2023) 020) — Type II for general subregions without isometries in the $G_N\to 0$ limit (observer model for compact regions, ADM Hamiltonian for asymptotic ones); compact case II $_1$ with the max-entropy state realizing Jacobson's entanglement-equilibrium hypothesis. [ESTABLISHED — abstract verified] Cross-link: this is directly relevant to route (b) of 2026-06-08-iter5-surviving-dS-routes.md.
Ali Ahmad–Klinger–Lin, Semifinite von Neumann algebras in gauge theory and gravity (arXiv:2407.01695, PRD 111, 045006): sufficient conditions for semifiniteness of crossed products by any locally compact group containing the modular flow (centrality of modular flow in the symmetry group), with evidence of necessity — the structural theorem behind "which constraint groups still give a trace." [ESTABLISHED — abstract verified]

2.4 Beyond subleading order, and state-independence

Ali Ahmad–Jefferson, Algebraic perturbation theory: traversable wormholes and generalized entropy beyond subleading order (arXiv:2501.01487): perturbative crossed products from unitary deformations; new contributions to $S_{\rm gen}$ beyond subleading order; black-hole information transfer to radiation modeled "by passing to a perturbative crossed product exhibiting a degree of non-locality in its modular structure." [ESTABLISHED — abstract verified] This is the first published machinery past the order at which iter5 froze the expansion — the upside lever (subq. #2) moved from "nothing exists" to "order-by-order constructible, no remainder bound"; note the price is modular non-locality, consonant with Giddings' leading-order noncommutativity. [INFERENCE]
Krishnan–Mohan, State-independent Black Hole Interiors from the Crossed Product (arXiv:2310.05912, JHEP 05 (2024) 278): via extended half-sided modular translations and the Connes cocycle, the crossed-product Type II $_\infty$ algebra is independent of the cyclic-separating vector (and other choices); with an interior observer it can be Type I or II $_1$ depending on whether the light cone contains a full Cauchy slice. [ESTABLISHED — abstract verified] Sharper than the additive-constant state-independence the wiki records. [INFERENCE]

3. The failure side becomes concrete — and stays algebraic

3.1 The split property DOES fail — but from strings, not dressing

Herderschee–Kudler-Flam, Stringy algebras, stretched horizons, and quantum-connected wormholes (arXiv:2510.01556, v2 Dec 2025), verbatim: in the $g_s\to 0$ limit with excited string modes as free particles, "the resulting Hagedorn spectrum leads to the breakdown of the split property, a strengthening of the locality principle, for regions that are within a string length of each other"; this gives "a precise algebraic definition of stretched horizons and stretched quantum extremal surfaces"; where stretched horizons exist there is "an associated nontrivial horizon ★-algebra"; the algebraic ER=EPR proposal then yields Type III von Neumann factors characterizing quantum Einstein–Rosen bridges between geometrically disjoint regions. [ESTABLISHED — verbatim abstract]

Mechanism (standard AQFT + the paper's application): split follows from Buchholz–Wichmann-type nuclearity, which requires $\mathrm{Tr}\,e^{-\beta H}<\infty$ for all $\beta>0$ ; a Hagedorn density $\rho(m)\sim e^{m/T_H}$ makes the partition function diverge for $\beta < 1/T_H$ , so nuclearity — and with it the standard route to split — fails below string-length separations. [ESTABLISHED inputs; the application is the paper's]

Bearing on OP-44 [INFERENCE — mine]: iter5's "genuinely live downside" (subq. #1) was that loss of the conditional-expectation/split structure would kill even the approximate subalgebra. The split does fail — but (i) from the string tower, not from $O(\kappa)$ dressing; (ii) only below $\ell_s$ separations; (iii) the replacement is still an algebraic object. So the downside is realized in a controlled form that does not propagate to macroscopic separations, and the $O(\kappa)$ -dressing version of subq. #1 remains open.

Wiki-internal corollary [INFERENCE — mine, for referee]: the iter4 GPT-composition resolution (2026-06-08-iter4-gpt-type3-resolution.md) used a split-property collar with an intermediate Type I factor; in stringy completions that collar acquires a minimal width $\ell_s$ — it cannot be shrunk to zero, sharpening the iter5 OP-48(c) conditional no-go from the dynamical side. [SPECULATIVE rider: whether the stringy breakdown scale and the Giddings dressing boundary $N_\ast\sim R/2GE_f$ meet at a Horowitz–Polchinski-type correspondence point is untested.]

3.2 A fourth verdict option: survives-after-averaging over $N$

Kudler-Flam–Witten, Emergent Mixed States for Baby Universes and Black Holes (arXiv:2510.06376), verbatim: large- $N$ sequences of states "generally fail to converge as pure states"; with diverging coarse-grained entropy they converge to mixed states for the large- $N$ algebra (black holes); for Euclidean preparations producing baby universes "the sequences do not converge, due to wormhole contributions, and so these states cannot admit large $N$ limits" — yet "appropriate averaging over $N$ can lead to convergence to a mixed state," the associated algebras having "nontrivial commutants, which can possibly be interpreted as operators in the baby universe." Companion: Wormholes and Averaging over N (arXiv:2605.15180, May 2026) — Mellin averaging over $N$ defines asymptotic averages reproducing apparent wormhole randomness, given analytic continuation in $N$ and superpolynomially small fluctuations. [ESTABLISHED — abstracts verified]

Bearing on OP-44 [INFERENCE — mine]: iter5 admitted three verdicts (survives / fails / regime-dependent). This line publishes a fourth: survives-after-averaging — at fixed $N$ a nonperturbative vN-subregion description may simply not exist for wormhole/baby-universe sectors, while an $N$ -ensemble-averaged algebra does. This is the most concrete published proposal for what "the algebra" could mean past the perturbative regime, and it is — again — algebraic.

3.3 Even at infinite $N$ , the vN property is dynamical: Engelhardt–Liu

Engelhardt–Liu, The Making of von Neumann Algebras from Bulk Focusing (arXiv:2509.05413): whether single-trace (infinite- $N$ ) boundary subregion algebras close into von Neumann algebras at all is GNS-sector-dependent, and the bulk dual of the sector-dependence is null geodesic focusing ("the well-known difference between null congruences fired from the bulk and those fired from the boundary"); causal wedge reconstruction is rigorously formulated and proven for subregions whose single-trace algebras do support vN algebras. [ESTABLISHED — abstract verified]

Bearing [INFERENCE]: this sharpens OP-44's framing question — the vN property is not free even before $1/N$ corrections; it is a dynamical, geometry-correlated property. For the headline verdict this cuts in the ENCODE direction: the algebra's existence is read off pre-installed bulk geometry (focusing), not conversely. Related: Leutheusser–Liu's subregion-subalgebra duality (arXiv:2212.13266) is now published as Phys. Rev. D 111, 066021 (2025) — the wiki cites only their 2112.12156; the duality paper defines entanglement wedges without entropy and assigns duals to bulk regions not touching the boundary. A mathematically rigorous instance: Crann–Kang, Algebraic approach to spacetime bulk reconstruction (arXiv:2412.00298), operator-algebraic subregion-subregion duality for Klein–Gordon fields with type III $_1$ bulk/boundary correspondence. [ESTABLISHED — abstracts/publication verified]

3.4 Multi-region structure: two areas, generalized wedges

Cao–Faulkner–Wang, Gravitational Algebras with Two Areas (arXiv:2512.04435): long-wormhole model with two compact extremal surfaces; via the split property, Type II algebras from crossed products in the left/right/middle regions; microcanonical treatments keeping only the area sum or difference yield Type II or Type III; the area-difference crossed product gives a weight restricting to a trace on the middle region, with relative-entropy differences $=$ variations of $S_{\rm gen}$ — an algebraic order parameter for entanglement-wedge phase transitions. [ESTABLISHED — abstract verified] (Supersedes iter4's "abstract not fetched" status for this ID.)
Sahu–van der Heijden–Van Raamsdonk–Zibakhsh, Algebras for generalized entanglement wedges (arXiv:2511.21852, v2 May 2026): conjectural assignment of algebras to generalized entanglement wedges in non-asymptotically-AdS spacetimes, with a proposed RT generalization; inclusion monotonicity and SSA would follow from algebraic entropy inequalities. Explicitly conjectural. [ESTABLISHED that the proposal exists; the proposal itself SPECULATIVE/OPEN]

4. The universal additive constant: demonstrated in JT

Blommaert–Kudler-Flam–Urbach, Absolute entropy and the observer's no-boundary state (arXiv:2505.14771, JHEP 11 (2025) 113): for closed universes with an observer, "the observer's no-boundary state is the identity operator on the physical Hilbert space, i.e., the maximum entropy state," demonstrated in JT gravity; geometrically a bra-ket wormhole; expectation values in it furnish a trace for the observer's algebra, so cross-universe vN entropies are relative entropies against the no-boundary state. [ESTABLISHED — abstract verified]

Delta: 2026-06-08-algebraic-background-independence.md open subquestion #1 recorded Witten's Hartle–Hawking universal-constant proposal as "speculative ... demonstrated only for de Sitter vacua." Upgrade: worked construction in a solvable model; absolute gravitational entropy is well-posed in JT. Beyond JT: [OPEN].

5. Lead corrections (binding-rule 3 items)

No Kudler-Flam–Leutheusser–Satishchandran review exists (orchestrator lead garbled). Kudler-Flam's complete recent arXiv listing (API-checked this session) contains only research papers with that trio (2309.15897; 2312.07646; 2406.01669). The actual synthesis is Hong Liu, Lectures on entanglement, von Neumann algebras, and emergence of spacetime, arXiv:2510.07017 (Oct 2025, 119 pp): vN-algebra fundamentals, modular flow and emergent time, algebraic large- $N$ AdS/CFT, subregion-subalgebra duality, operator-algebraic gravitational entropy, firewall diagnostics, islands. [ESTABLISHED — abstract verified] New results inside it relative to the wiki: none claim-moving; it is consolidation (its firewall-diagnostic and island sections are presentation of the Leutheusser–Liu / Engelhardt–Liu line covered above). [INFERENCE from abstract; full-text not audited]
No Giddings follow-up, rebuttal, or sharpening post-2510.24833. His hep-th listing ends (as of this sweep) at 2510.24833 v3 (Jan 9, 2026 — already in the wiki) and 2507.13351 (Jul 2025, unitary-evolution pictures, not on this thread). Targeted searches found no published response to "algebraic spacetime disruption." The $N_\ast$ boundary is exactly where iteration 5 left it. [ESTABLISHED-negative — API listing + searches this session]

6. Explicit judgment on OP-44 (mission deliverable)

Does anything published move OP-44 from "no theorem on either side"? NO. [INFERENCE, high confidence as a literature judgment]

No all-orders survival proof: 2501.01487 is order-by-order with no remainder bound; 2601.07910/2601.07915 are linearized-regime theorems.
No no-go: 2510.01556's split breakdown is stringy and confined below $\ell_s$ ; 2510.06376's non-convergence concerns baby-universe sectors and is cured by $N$ -averaging; neither derives a finite- $N$ commutant collapse at $N_\ast$ .

What DID move [INFERENCE]:

Survival side, sub- $N_\ast$ : from "approximate / QRF-relational, no theorem" to theorem-grade at linearized order — complete constraint group with edge modes (II survives), GSL for non-stationary perturbations, QFC proven perturbatively, state-independence of the algebra, physical clocks replacing external observers, first beyond-subleading entropy contributions.
Failure side, post-breakdown: every published candidate replacement structure is algebraic — stretched-horizon ★-algebras, Type III ER=EPR factors, $N$ -averaged algebras with nontrivial commutants — weakening (not refuting) Giddings' "beyond algebras" horn.
Verdict space: add a fourth admissible verdict, survives-after-averaging over $N$ .
Even-at- $N=\infty$ subtlety: the vN property is GNS-sector-dependent and dual to bulk focusing (Engelhardt–Liu) — the framing question "does a vN algebra survive" must now be asked per-sector even before $1/N$ corrections.

Headline impact: none. All constructions import a background (stationary exterior, FLRW, AdS, JT); KLS II installs an infinite-dimensional pre-given corner symmetry; Engelhardt–Liu read algebra-existence off geometry. Encodes-not-generates is reinforced, not challenged. [INFERENCE]

Proposed registry updates

[OP-44/OP-CP1 wording] Keep "regime-dependent, no theorem on either side of $N_\ast$ "; append: (a) the sub- $N_\ast$ survival is now theorem-grade at linearized order including non-stationary cuts (GSL) and the QFC (2601.07915), for the complete constraint group with edge-mode-corrected entropy (2601.07910); (b) admissible verdicts now include "survives-after-averaging over $N$ " (2510.06376, 2605.15180); (c) published post-breakdown candidates are all algebraic (2510.01556), weakening the "beyond algebras" horn.
[Subq. #1 update] Split-property strain: realized in the stringy regime via Hagedorn/nuclearity failure below $\ell_s$ (2510.01556); the $O(\kappa)$ -dressing version remains [OPEN].
[Subq. #2 update] Beyond-subleading machinery now exists with modular non-locality as the price (2501.01487); still no bounded remainder. [OPEN]
[Subq. #4 update] dS II $_1$ survives the complete perturbative constraint group (2601.07910). [OPEN beyond perturbative]
[A-23 / A-CP-KILLING annotation] The geometric input has migrated from "Killing horizon" to "pre-installed corner symmetry group (boost supertranslations + null translations)" — same circularity, finer resolution.
[Algebraic-background-independence note] Open subquestion #1 (universal constant): upgraded from "speculative, dS-only" to "demonstrated in JT (2505.14771); OPEN beyond."
[iter4-literature-refresh correction] The "incremental, action=none" gloss on 2601.07910 / 2512.04435 is superseded by the verified abstracts above.

7. Open subquestions (updated)

Does the $O(\kappa)$ gravitational dressing (as opposed to the string tower) strain the split/conditional-expectation structure at macroscopic separations, or is gravitational split-failure also confined to a microscopic collar? [OPEN — the surviving form of the iter5 downside]
Can the Ali Ahmad–Jefferson perturbative crossed product be given a bounded remainder below $N_\ast$ — and does its modular non-locality grow with order in a way that locates $N_\ast$ intrinsically? [OPEN — the surviving form of the iter5 upside]
Is the Kudler-Flam–Witten $N$ -averaged algebra a subregion algebra (does it admit localized subalgebras with commutants), or only a global structure — i.e., does "survives-after-averaging" extend to OP-44's subregion question? [OPEN]
Does the Engelhardt–Liu focusing criterion have a finite- $N$ analog — and if vN-ness is sector-dependent at $N=\infty$ , what replaces "the" subregion algebra in sectors where it fails? [OPEN]
Do the Chandrasekaran–Flanagan half-sided modular inclusion methods extend off Killing-horizon backgrounds (not just non-stationary perturbations of them), closing the gap to fully dynamical horizons? [OPEN]

References

All entries below were individually verified this session by fetching the arXiv abstract page (or the arXiv API listing), except where marked.

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 (12 Jan 2026, 104 pp).
V. Chandrasekaran, É. É. Flanagan, Subregion algebras in classical and quantum gravity, arXiv:2601.07915 (12 Jan 2026, 111 pp).
C.-H. Chen, G. Penington, A clock is just a way to tell the time: gravitational algebras in cosmological spacetimes, arXiv:2406.02116 (2024).
J. Kudler-Flam, S. Leutheusser, G. Satishchandran, Algebraic Observational Cosmology, arXiv:2406.01669 (2024).
K. Jensen, J. Sorce, A. Speranza, Generalized entropy for general subregions in quantum gravity, arXiv:2306.01837, JHEP 12 (2023) 020.
S. Ali Ahmad, M. S. Klinger, S. Lin, Semifinite von Neumann algebras in gauge theory and gravity, arXiv:2407.01695, Phys. Rev. D 111, 045006 (2025).
S. Ali Ahmad, R. Jefferson, Algebraic perturbation theory: traversable wormholes and generalized entropy beyond subleading order, arXiv:2501.01487 (v2 Dec 2025).
C. Krishnan, V. Mohan, State-independent Black Hole Interiors from the Crossed Product, arXiv:2310.05912, JHEP 05 (2024) 278.
A. Herderschee, J. Kudler-Flam, Stringy algebras, stretched horizons, and quantum-connected wormholes, arXiv:2510.01556 (v2 Dec 2025).
J. Kudler-Flam, E. Witten, Emergent Mixed States for Baby Universes and Black Holes, arXiv:2510.06376 (2025).
J. Kudler-Flam, E. Witten, Wormholes and Averaging over N, arXiv:2605.15180 (May 2026).
N. Engelhardt, H. Liu, The Making of von Neumann Algebras from Bulk Focusing, arXiv:2509.05413 (2025).
S. Leutheusser, H. Liu, Subregion-subalgebra duality: emergence of space and time in holography, arXiv:2212.13266, Phys. Rev. D 111, 066021 (2025). [publication verified via APS record]
J. Crann, M. J. Kang, Algebraic approach to spacetime bulk reconstruction, arXiv:2412.00298 (2024).
X. Cao, T. Faulkner, Z. Wang, Gravitational Algebras with Two Areas, arXiv:2512.04435 (Dec 2025).
A. Sahu, J. van der Heijden, M. Van Raamsdonk, R. Zibakhsh, Algebras for generalized entanglement wedges, arXiv:2511.21852 (v2 May 2026).
A. Blommaert, J. Kudler-Flam, E. Y. Urbach, Absolute entropy and the observer's no-boundary state, arXiv:2505.14771, JHEP 11 (2025) 113.
H. Liu, Lectures on entanglement, von Neumann algebras, and emergence of spacetime, arXiv:2510.07017 (Oct 2025, 119 pp).
S. B. Giddings, arXiv:2510.24833 (v3, 9 Jan 2026) and arXiv:2505.22708 — baseline anchors, previously wiki-verified; v3 date re-confirmed this session via search.
T. Faulkner, A. J. Speranza, arXiv:2405.00847, JHEP 11 (2024) 099 — baseline anchor. [not re-fetched this session — previously wiki-verified]
Engelhardt–Liu algebraic ER=EPR proposal — cited within 2510.01556; exact arXiv ID not independently verified this session. unverified

Binding note. Where a correction in the referee verdict below conflicts with the body above, the referee correction governs; the body is the pre-referee submission, retained for the audit trail per house convention.

Referee verdict

Track R2-algebraic, iteration 6. All ten findings kept; zero major or fatal. Every citation web-verified this session (arXiv abs pages fetched; PRD/JHEP records independently confirmed). The standing PARTIAL verdict and the encodes-not-generates headline are untouched; OP-44 remains "no theorem on either side of $N_\ast$ " with a restructured interior.

R2-F1 (KLS II, 2601.07910) — KEEP, severity MINOR. Paper verified (Klinger–Kudler-Flam–Satishchandran, 12 Jan 2026, 104 pp); the supersession of iter4's "incremental, action=none" gloss is confirmed against the iter4 literature-refresh note (the abstract was never fetched there). Two fixes: the entropy is $S_{\rm gen}$ + edge-mode contribution + a constant term (the dropped constant feeds the wiki's standing Obs-4 additive-constant caveat — do not drop it); the dS-observer example is "multipole moments and kinetic energy" per the abstract, not "rotational kinetic energy." Perturbative-only strengthening of iter5 subquestion #4 is correctly scoped.

R2-F2 (Chandrasekaran–Flanagan, 2601.07915) — KEEP, severity MINOR. Verified (12 Jan 2026, 111 pp); the chain edge modes → crossed product → Type II $_\infty$ per cut → GSL for non-stationary linearized perturbations → QFC proven perturbatively is verbatim-supported. Correction to the proposed action: decisive-progress item 5 has two legs (interacting QFT; genuinely non-Killing horizons) and CF discharge neither fully — they cover linearized perturbations of Killing horizons. Write "one leg partially addressed at linearized order"; QFC status is always "theorem within the linearized/perturbative regime," never bare "theorem."

R2-F3 (Chen–Penington 2406.02116; KLS cosmology 2406.01669) — KEEP, severity MINOR. Both verified. Fixes: 2406.02116's abstract claims a "connection" between Type II entropy and generalized entropies — verify the bare equality against the full text before wiki entry; 2406.01669 is "FLRW spacetimes that are asymptotically de Sitter" (not "with inflationary origin"), with entropy $=S_{\rm gen}$ for semiclassical states. The widening of the survival regime beyond Killing/stationary settings (same perturbative order, metric still input) is a fair, properly-tagged delta.

R2-F4 (Ali Ahmad–Jefferson 2501.01487) — KEEP, severity NONE. Verified. Exemplary scoping: order-by-order, no bounded remainder, explicitly not the all-orders theorem; partial movement on iter5 subquestion #2 only. Keep the information-transfer mechanism in quotation marks (authors' proposal).

R2-F5 (Herderschee–Kudler-Flam 2510.01556) — KEEP, severity MINOR. Verbatim abstract verified. Headline overclaim corrected: this does not "realize the iter5 live downside risk" — subquestion #1 concerns $O(\kappa)$ gravitational-dressing strain on the split/conditional-expectation structure, which remains open; this is a parallel stringy (Hagedorn) realization at sub-string-length separations in the $g_s\to0$ free-string model. Wiki-internal catch: the iter4 GPT-composition note already cites Hagedorn/ $T\bar T$ split failure (arXiv:2005.08972) in a referee addendum — the minimal-collar-width- $\geq\ell_s$ corollary sharpens that addendum and must cross-cite it. Horowitz–Polchinski correspondence-point speculation stays note-level SPECULATIVE, out of any registry statement. Strengthens (does not contradict) the OP-48c collar leg.

R2-F6 (Leutheusser–Liu PRD 111, 066021; Engelhardt–Liu 2509.05413; Crann–Kang 2412.00298) — KEEP, severity NONE. All three verified; PRD publication (March 28, 2025) confirmed via APS though the arXiv page lacks the journal ref — cite the DOI in BIBLIOGRAPHY. The Engelhardt–Liu focusing criterion (vN-algebra existence read off from bulk null focusing, GNS-sector-dependent) is correctly read as encode-direction evidence; endorsed for citation in CONCLUSION §2.

R2-F7 (Kudler-Flam–Witten 2510.06376 + 2605.15180) — KEEP, severity MINOR. Both verified, including the May 2026 Mellin-averaging companion. The "survives-after-averaging" fourth option is admitted into the OP-44 verdict list with two riders: (i) KW analyze global large- $N$ algebras and state-sequence convergence, not subregion crossed products — the transfer to OP-44 is the track's INFERENCE; (ii) averaging cures the non-convergence only conditionally (analytic continuation in $N$ ; superpolynomially small fluctuations). Does not locate or move $N_\ast$ .

R2-F8 (Krishnan–Mohan 2310.05912, JHEP 05 (2024) 278) — KEEP, severity NONE. Verified including the JHEP record. Algebra-level choice-independence (Connes cocycle) at perturbative order; a genuine sharpening of the wiki's state-independence record; correctly silent on the nonperturbative regime.

R2-F9 (Blommaert–Kudler-Flam–Urbach 2505.14771, JHEP 11 (2025) 113) — KEEP, severity MINOR. Verified including the JHEP record. Retag precisely: the universal max-entropy-state proposal now has a worked closed-universe JT realization (no-boundary state = identity = trace) — but it retains the universal-state postulate, so it does not discharge decisive-progress item #4's request for a route avoiding one, and the cross-spacetime constant beyond JT (different $\Lambda$ , higher-D, non-topological) stays OPEN.

R2-F10 (lead corrections; Giddings status; mission judgment) — KEEP, severity MINOR. Verified: no KLS-trio review exists (the orchestrator lead was garbled); Hong Liu's lectures (2510.07017, 119 pp, Oct 2025) are the synthesis; Giddings' latest are 2507.13351 (Giddings–Perkins, Jul 2025 — note: a unitary-evolution-pictures paper, not an algebraic-disruption follow-up) and 2510.24833 v3 (Jan 9, 2026); no follow-up or rebuttal surfaced. Tag correction: absence claims are INFERENCE, high — negative-after-search, as of 2026-06, not ESTABLISHED-negative. The judgment stands: no all-orders survival proof, no no-go, $N_\ast$ unmoved; the "all published post-breakdown candidates remain algebraic, weakening Giddings' beyond-algebras horn" gloss is kept with a selection-effect guard (publication bias toward algebraic structures makes this weak evidence).

No-go red-team (track-wide): all results are perturbative / fixed-background / strict-large- $N$ , so Weinberg–Witten, Coleman–Mandula/HLS, Haag, Reeh–Schlieder, spin-statistics, and the singularity theorems are not engaged; the perturbative QFC claim makes no nonperturbative assertion. No finding contradicts the wiki's closures: the dS cardinality no-go, HYP-CKV-VACUITY (every new construction installs its symmetry/foliation input — boost supertranslations, corner edge modes, comoving frames), and the OP-48c conditional no-go (F5 strengthens its collar leg) are all untouched. No candidate reopenings.

OP-44 literature delta (2024–2026): the survival side hardens perturbatively; the failure side turns out algebraic; no theorem on either side of N∗N_\astN∗​