Refreshed terminal-saturation audit + external-input sweep — iteration 12 (track B3)

Status: Active audit (the honest meta-track) · iteration 12 · track B3-external-input-sweep + saturation-refresh · Outcome CONFIRMS-SATURATION / AUDIT Last updated: 2026-06-19

One-line verdict. A fresh mid-2026 sweep of the carrier/net-naturality math, the Connes bicentralizer problem, reverse-WW phenomenology, the 2027 DESI w(z) program, and the empirical channels finds no new decidable lever that could move the verdict or the principal hedge by reasoning. The iter-11 A3 terminal-saturation diagnosis (referee-upheld) is UPHELD as of 2026-06. The one genuinely-new 2026 mathematics in the carrier circle — the Morinelli–Neeb–Olafsson Euler-pair Bisognano–Wichmann/Spin–Statistics theorems — is a cleaner statement of the encoding screen (the symmetry group is INPUT), not a carrier solution. Standing verdict unchanged, 11th consecutive confirmation; hedge unmoved in grade and condition; carrier-convergence count stays FIVE. INFERENCE, high

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1. Scope and method

This note re-runs the single external obligation the saturation diagnosis leaves open: has a NEW (2026) external development appeared that constitutes a decidable verdict-moving lever? It does not re-attack any gap. Every load-bearing reference below was web-verified live this session against the actual abstract/source. The sweep covers the four channels the mission named: (a) carrier / net-naturality / GMA-reconstruction math; (b) the Connes bicentralizer problem; (c) reverse-WW / distinguishing-test phenomenology; (d) the 2027 DESI five-year w(z) program + adjacent dark-energy probes (Euclid, Roman) and the empirical channels (BMV/QGEM, objective collapse, GQuEST/VZ, LIV/EP).

2. Sweep results — channel by channel

2a. Carrier / net-naturality / GMA-reconstruction math — one new 2026 result, encode-pattern

The genuinely-new 2026 item in the net-naturality/Euler-element/geometric-BW circle is the Morinelli–Neeb–Olafsson "Orthogonal pairs of Euler elements" program: Part I (arXiv:2508.10960, 14 Aug 2025 — classification, fundamental groups, twisted duality) and Part II (arXiv:2603.26390, 27 Mar 2026 — Geometric Bisognano–Wichmann and Spin–Statistics Theorems). Abstract read verbatim: AQFT models are generalized including Lie groups of symmetries whose Lie algebras admit an Euler element h, with ad h diagonalizable, eigenvalues in {−1,0,1}; from an orthogonal Euler pair the authors derive both a Bisognano–Wichmann Theorem and a Spin–Statistics Theorem for nets of standard subspaces and von Neumann algebras.

Adjudication — this is the encoding screen, not a carrier. The Euler element is the generator of the modular group in the symmetry Lie algebra (verified verbatim from the program's surrounding literature): the Lie group of symmetries is the INPUT, and the causal/wedge/Lorentzian structure is "output" only relative to that pre-installed symmetry. This is exactly the object the iter-11 A3 audit named as the irreducible smuggle — "forced to be signature-inherited from a pre-installed Euler-element/causal-index-set." The result is a stronger, cleaner statement of HYP-ENCODING-SCREEN (geometry recovered precisely where the symmetry is installed by hand), not a construction of Lorentzian structure from genuinely non-symmetric (algebra, state) data, and therefore not a carrier solution, not a reverse-WW inversion, and not a sixth convergence route. Count stays FIVE. [INFERENCE, high]

The broader GMA-reconstruction literature returns only the standing Buchholz–Summers / Brunetti–Guido–Longo / Neeb–Morinelli corpus already underwriting Lemma N1/N2. No net-naturality theorem (the verdict-bearing residual) has appeared.

2b. Connes' bicentralizer problem — confirmed OPEN in general (2026)

Verified live: the conjecture B(M,φ)=C1 for every type III_1 factor (separable predual) remains open in general as of 2026; settled only for special classes (amenable, Cartan, free products, semisolid, q-deformed Araki–Woods, tensor-III_1). The May-2026 model-theory paper arXiv:2605.12776 restates it as open via a "bicentralizer functor zeroset" reformulation — it is the same paper the iter-11 referee cited. No Houdayer–Marrakchi–Tomatsu general-resolution paper exists. This upholds the binding iter-11 referee correction in full. [OPEN]

2c. Reverse-WW / distinguishing-test phenomenology — still EVADE, not invert

The only 2026 item touching Weinberg–Witten is the "GR from RG" essay (Sheikh-Jabbari–Taghiloo, arXiv:2602.11806), which proposes to evade WW — boundary conditions flowing from rigid Dirichlet (UV) to mixed Dirichlet–Neumann (IR) to "unfreeze" the metric, or the energy-momentum tensor vanishing/non-conserved by construction. The background metric is Dirichlet-fixed in the UV (installed), confirming the iter-11 minor-correction (it confronts/evades, does not invert, WW). Evading WW by zeroing the T_munu matrix element is precisely the handle-erasing move HYP-ENCODING-SCREEN predicts; it produces no class-separating observable. The reverse-WW witness remains unattempted / OPEN, as of 2026-06, the empirical-side shadow of the carrier problem (iter-9 identity), carrying no registry ID. [OPEN]

2d. The 2027 DESI w(z) program + adjacent probes — unchanged, target not wager

• DESI: the dynamical-dark-energy preference persists in DR2 (~3–4σ for w0waCDM, w0>−1, wa<0, possible phantom crossing) but is dominated by low-redshift SN systematics — correcting low-z SN calibration reduces it to < 2σ (arXiv:2502.04212; cf. calibration-independent SN-systematics tests). The decisive five-year (DR3) w(z) verdict is still expected 2027 (DESI 3D map completed Apr 2026). [CONTESTED]
• Roman / Euclid: Roman launches 2026; Roman + Euclid joint dark-energy investigation by ~May 2027 (NASA/JPL). Adds multi-probe confrontation but no earlier decision point.
• All bear on Program A's correct TARGET (eternal dS vs metastable dS vs rolling quintessence), never the wager — status unchanged from the watchlist.

2e. Empirical channels — gate/core/target only, no wager bearing

• Objective collapse: NEW 2026 bounds — VIP collaboration analysis of XENONnT spontaneous-radiation data (Gran Sasso) improves CSL by ~2 orders of magnitude and tightens Diósi–Penrose by ~factor 5, no excess detected. Constrains a fixed CORE (exact linearity, A-3), not the wager. [ESTABLISHED]
• BMV / QGEM: ~6–8 orders below decisive mass/coherence; no funded milestone roadmap; 2026 work is decoherence/tripartite-entanglement modelling (Sci. Rep. s41598-026-44184-2), not a run. Bears on the gate.
• GQuEST / VZ: design in PRX 15 (2025) 011034; preliminary build at Caltech; no science data as of 2026-06. The Sharmila–Vermeulen–Datta mechanism-blind correlator taxonomy still governs any signal. Program-adjacent, not a wager test.
• GW strong-field nulls, LIV/EP nulls, matter-wave macroscopicity: continuing nulls/records harden cores and enablers; none bears on the wager.

3. Residual enumeration with decidability classification (refreshed)

Result. Of the verdict-bearing residuals, zero are reasoning-decidable in a way that could move the verdict or hedge. The two reasoning-decidable residuals stay headline-inert by their own scoping. Every verdict-bearing residual is external-math-gated (four collapse to the single carrier net-naturality breakthrough ⟺ commutant-gap closure ⟺ reverse-WW witness ⟺ HYP-CKV-VACUITY→unconditional HIGH) or external-experiment-gated (2027 DESI w(z), which bears on the target).

4. Adjudication — is the saturation diagnosis still correct?

YES — terminal saturation is upheld as of 2026-06. No purely-reasoning lever can move the verdict; only external input can. The classification:

• Reasoning-decidable-but-headline-inert: OP-44 R2 (higher-D / s^4 remnant coefficient), OP-49 (a/b/c′). Unchanged.
• External-math-gated: carrier net-naturality theorem; commutant-to-generated gap; reverse-WW witness; Connes bicentralizer (related vocabulary). The 2026 Euler-pair theorems and the model-theory bicentralizer paper are adjacent activity in the right circle but neither inverts the encoding screen nor closes the gap — they reconfirm it.
• External-experiment-gated: 2027 DESI five-year w(z) (target); objective-collapse coverage (core); BMV/QGEM gate; GQuEST/VZ program-adjacent. New 2026 results tighten cores/enablers, none touches the wager.

No genuine new decidable verdict-moving lever has appeared. The marginal-yield curve stays flat to second order (grade-derivative zero since iter 9; condition-derivative zero since iter 10; iter 11 added precision re-grounding only; iter 12 adds external confirmation only).

5. Conservative registry implication

NO new numeric ID; NO grade/condition change to any hedge; count stays FIVE; verdict unchanged (11th consecutive). Append-only watchlist/watch-item notes recording: Connes OPEN confirmed; the 2026 Euler-pair theorems flagged as an encode-pattern instance (explicitly NOT a sixth route, NOT a carrier); the 2026 objective-collapse core-tightening; the reaffirmed-2027 DESI w(z) verdict with strengthened SN-calibration caveat; the 'GR from RG' evade-not-invert instance.

See also

• ../CONCLUSION.md — the capstone verdict and its three hedges
• ../notes/2026-06-10-iter11-terminal-saturation-audit.md — the iter-11 A3 audit this note refreshes
• ../notes/2026-06-10-iter11-carrier-bicentralizer.md — the binding bicentralizer correction this sweep re-confirms
• ../EXPERIMENT_WATCHLIST.md — the channels and the 2027 DESI event
• ../HYPOTHESES.md — HYP-CKV-VACUITY-R6, HYP-FACTORIZATION-IS-GEOMETRY, HYP-ENCODING-SCREEN
• ../EPISTEMICS.md — the labeling discipline obeyed above

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Referee verdict — track B3 (external-input + experiment sweep / terminal-saturation refresh), iteration 12 (2026-06-19)

Adversarial referee, default stance REFUTE. Every load-bearing citation web-verified live this session against the actual abstract/source; the one genuinely-new mathematical result (Euler-pair Part II) fetched and read verbatim; the no-go red-team run against the binding iter-9/10/11 corrections and the standing five-route convergence count. Stance NOT sustained as a refutation — the submission survives with citation-precision corrections only; no fatal, major, or verdict-bearing defect.

Outcome: CONFIRMS-SATURATION — UPHELD WITH CITATION-PRECISION CORRECTION. Standing verdict UNCHANGED (11th consecutive). Carrier-convergence count FIVE. Hedge HYP-CKV-VACUITY stays -R6 (grade and condition). No new registry ID.

What is sound and verified (citations clean / faithful)

• Euler-pair Part II (arXiv:2603.26390) is the encoding screen, not a carrier — confirmed verbatim. I fetched the abstract directly. The Lie groups of symmetries / Euler element h are pre-installed as input; the Bisognano–Wichmann and Spin–Statistics theorems are derived FROM the Euler element; the paper makes no claim to construct causal/Lorentzian/metric structure from non-symmetric (algebra, state) data. This is exactly the pre-installed Euler-element/causal-index-set the iter-11 A3 audit named as the irreducible smuggle. The finder's adjudication — stronger/cleaner HYP-ENCODING-SCREEN instance, NOT a carrier, NOT a reverse-WW inversion, NOT a sixth route — is correct and survives the no-go red-team. Count stays FIVE. Part I (arXiv:2508.10960, Forum Math. 38(3) 2026) also verified.
• Connes' bicentralizer problem OPEN in general — confirmed (arXiv:2605.12776). Real, posted 12 May 2026; the 'bicentralizer functor zeroset' reformulation matches the finder's gloss. Upholds the binding iter-11 correction in full; no Houdayer–Marrakchi–Tomatsu general-resolution paper exists. The finder does not lean on the bicentralizer route to close the no-go — it correctly treats it as confirmed-open external vocabulary, respecting every binding iter-11 correction (trivial-centralizer ≠ trivial-bicentralizer; the no-go is not a reduction to Connes).
• 'GR from RG' (arXiv:2602.11806) — evade-not-invert, now CONFIRMABLE. Live search confirms the paper explicitly engages Weinberg–Witten and unfreezes a UV-Dirichlet-fixed (installed) metric (Dirichlet→mixed Dirichlet/Neumann under RG flow). This discharges the iter-11 A3 minor defect (where the WW gloss was flagged 'not confirmable'). Produces no class-separating observable; reverse-WW stays OPEN, 2026-06, the empirical-side shadow of the carrier problem, no registry ID. Correct.
• VIP/XENONnT objective-collapse bounds — numbers exact. CSL ~2 orders, DP ~factor 5, no excess; verified against the PRL March 2026 result. Constrains the A-3 CORE, not the wager. Correctly classified.
• QGEM tripartite-entanglement (Sci. Rep. 2026, s41598-026-44184-2) — verified; decoherence modelling, not a run; bears on the gate.
• Marginal-yield curve flat to second order; terminal saturation UPHELD. Every verdict-bearing residual is external-math-gated or external-experiment-gated; the two reasoning-decidable residuals (OP-44 R2; OP-49 a/b/c′) are headline-inert by their own scoping. No new decidable verdict-moving lever has appeared.

Citation-precision corrections (binding over the finder's claims; none verdict-bearing)

1. arXiv:2605.12776 authorship. Authors are Ando–Goldbring, not "I. Goldbring et al." Correct in any append.
2. arXiv:2502.04212 authorship. Huang–Cai–Wang (Efstathiou in acknowledgments only). Strike "Efstathiou-type ... analysis"; attribute correctly.
3. DESI residual magnitude. Source abstract states the preference reduces to "less than 2σ"; the finder's "~0.5–1.5σ" is sharper than the cited source supports. Soften to "< 2σ".
4. Primary VIP/XENONnT source. Name arXiv:2506.05507 (PRL March 2026) as the primary bound in any watchlist append; arXiv:2512.15393 and arXiv:2604.21705 (both verified real) are adjacent/auxiliary, not the primary result.

No-go / extraordinary-claim red-team — clean

No carrier solution, no metric smuggle, no generative (vs encoding) construction, no reverse-WW witness anywhere in the sweep. The one new mathematical result presupposes the symmetry group and outputs geometry only relative to it — encode-pattern, verified verbatim. The extraordinary-claim gate does not fire. No conflict with dS-cardinality, the iter-7 trichotomy / η_0 vacuity, the iter-8 net no-go, the iter-9 naturality obstruction / reverse-WW = carrier identity, the iter-10 commutant-gap null, or the binding iter-11 bicentralizer correction. Count stays FIVE; no RESOLVED-POSITIVE offered.

Registry implication (conservative)

NO new numeric ID; NO grade/condition change to any hedge; count FIVE; verdict unchanged (11th consecutive). Append-only watchlist/watch-item notes as the finder proposes, with corrections (1)–(4) applied: Connes OPEN confirmed (Ando–Goldbring, arXiv:2605.12776); the 2026 Euler-pair theorems flagged as an encode-pattern instance (explicitly NOT a sixth route, NOT a carrier); the objective-collapse core-tightening (primary arXiv:2506.05507); the reaffirmed-2027 DESI w(z) verdict with the SN-calibration caveat (Huang–Cai–Wang arXiv:2502.04212, preference < 2σ); the 'GR from RG' evade-not-invert instance (now confirmable, discharging the iter-11 minor defect).

Net

A verdict-neutral external sweep whose substance is correct and whose load-bearing citations are all real and faithfully characterized. The single genuinely-new mathematical result is correctly adjudicated as an encoding-screen instance rather than a carrier. The CONFIRMS-SATURATION outcome and every verdict-bearing claim are sustained; the only defects are four citation-precision items, none of which touches the verdict, the hedge, or the count. Terminal saturation upheld; the wager remains not-yet-physics; the object-level forecast unchanged.