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.

Iteration 8 — 2026-06-10 (the net/family levers)

Theme: re-attack the standing analytical levers from the structurally-richer net/family angle the single-algebra levers had not covered — does the net upgrade (relative modular operators, {J_O}, HSMI, modular intersection, modular-Berry over a net) evade the iteration-7 carrier no-go (the verdict-flipper); push OP-44's R1/R2 to theorem-shape; scrutinize OP-49's cap-blindness / junction-additivity mechanism; promote the OP-48c X1 exit to a theorem. 4 attack tracks, all adversarially refereed (independent re-derivation, numerical replication, live citation audits; corrections binding — one submitted outcome label was overturned). Headline unchanged for the seventh consecutive iteration; the principal hedge HARDENS further toward HIGH on a narrowed condition (OP-46 / HYP-CKV-VACUITY: single-algebra → net/family no-go; MEDIUM-HIGH → MEDIUM-HIGH→HIGH, conditional on the net-constructibility ansatz). Synthesis: iteration-8 synthesis.

Net/family carrier no-go (attack — the verdict-flipper, re-attacked) — does net-modular data evade the iter-7 carrier no-go? Verdict: RESOLVED-NEGATIVE — the net upgrade relocates the carrier into the net's index set; net data adds operators but no localized indefinite form (covariance–locality obstruction; every modular-covariant pairing is positive-local, signature-free, or indefinite-nonlocal), and localization lives only in the net's parametrization, which IS the geometry (BGL isotony⟺positivity; Euler element as input; Lashkari et al. "insisting on a local representation"); hedge hardens toward HIGH on a narrowed (net-constructibility) condition; the carrier-convergence count STAYS FIVE — this is the net-level extension of the fifth route, not a sixth (binding referee correction).
OP-44 R1/R2 to theorem-shape (attack) — discharge or obstruct the named residues. Verdict: SHARPENED-OPEN — R1: the bare distributional worldline-clock Taub charge DIVERGES (ε^{2−d}); FMM/AMM/Hintz smooth-source framework does not apply; escape via Gralla–Wald / Pound puncture regularization (not mass renormalization — referee correction), conditional on the FMM cone condition. R2: all three cubic-divergence cancellations fail at leading order (smearing relocates the cutoff; KLS-II edge modes provably quadratic-order only; normal-ordering leaves the connected channel invariant); obstruction horn reinforced as INFERENCE, constrained-graviton tensor structure the sole escape. N and the ℓ_P floor untouched; encodes-not-generates reinforced.*
OP-49 junction additivity (attack) — is the bra/ket interface the transmissive defect, making cap-blindness exact? Verdict: SUBMITTED RESOLVED-POSITIVE → OVERTURNED to VERDICT-UNCHANGED, (c′) REFRAMED-AND-NARROWED, NOT CLOSED — the transmissive-orientation-reversal / dimension-zero-junction mechanism is INFERENCE-medium, extrapolated into the non-unitary imaginary-c regime where the unitary transmissivity bounds fail ("not rigorously excluded"); OP-49 stays NEAR-NO-GO with residuals (a)/(b)/(c′); the unconditional reality-mismatch pillar (S_SVD real ≥0 vs δ⟨K_A⟩ purely imaginary) is re-verified and untouched; no CONCLUSION hedge moves.
OP-48c X1 singular states (attack) — is the X1 exit a theorem, and does it collapse horn C? Verdict: RESOLVED-POSITIVE — X1-EXISTENCE is a theorem (singular product states on the III₁ Haag-dual pair exist: factor⇒Schlieder⇒C-independence⇒Roos⇒Hahn–Banach; non-normal by Takesaki, citation corrected from Florig–Summers); X1-DISQUALIFICATION sharper than posed (no axiom FAILS on a singular state — Hardy/CDP/MM quantify only over finite-dim σ-additive states, upstream of every axiom), so horn C STAYS theorem-conditional-on-framework, X1 a costed framework EXIT; X1-COST (theorem): relinquish density-matrix states + σ-additivity + finite tomographic dimension jointly. NOT-YET-PHYSICS untouched.*
Iteration-8 synthesis — per-track verdict table, hedge ledger before → after (OP-46 hardened toward HIGH on a narrowed condition; ENCODING-SCREEN inherits; OP-49 (c′) reframed-not-closed; the A3 overturn as evidence the referee discipline is binding), why the verdict stands a seventh time, and the residual map: the carrier problem as THE compressed analytical target (now a net/family no-go, count still five); OP-44's R1/R2; OP-49's (a)/(b)/(c′); OP-48c's X1 (theorem)/X2; experiment watchlist unchanged.

Iteration 9 — 2026-06-10 (the carrier no-go's naturality content)

Theme: attack the carrier no-go's residual naturality content and its single uncovered escape — replace the net-constructibility ansatz with a naturality theorem (A1); close the modular-Berry-holonomy escape (A2); decide whether reverse-Weinberg–Witten is independently provable or a free witness (A3); test whether the constrained-graviton TT structure cancels OP-44 R2's cubic divergence (A4). 4 attack tracks, all adversarially refereed (one outcome overturned — A4; one overclaim struck — A2). Headline unchanged, eighth consecutive confirmation; the principal hedge's grade is unchanged (MEDIUM-HIGH→HIGH conditional) and its condition sharpened; the modular-Berry obligation is discharged; reverse-WW is identified with the carrier problem. Synthesis: iteration-9 synthesis.

Carrier naturality (attack) — SHARPENED-OPEN: the ansatz is replaced by a naturality formulation (constructibility a theorem modulo a located commutant-to-generated gap; the boost-covariance engine promoted to a naturality obstruction), but "localized" is proven irreducible — it presupposes the index-set order, which is the geometry. Grade unchanged, condition sharpened; count stays five.
Modular-Berry holonomy (attack) — RESOLVED-NEGATIVE: the holonomy-natural form is the signature-free symplectic Kirillov–Kostant (Crofton) form; the only indefinite object (the kinematic-space dS $_2$ metric) is vacuum/symmetry-inherited. The "unconditional HIGH" claim was struck by the referee; one of the two iteration-8 obligations is discharged.
Reverse-Weinberg–Witten (attack) — SHARPENED-OPEN, the central identification: reverse-WW = the empirical-side shadow of the carrier problem. A1 ("net + vacuum is a complete invariant") is a conditional theorem (Weiner's algebraic Haag theorem) whose hypotheses are the geometry; so reverse-WW-theorem ⟺ carrier no-go, and a reverse-WW witness is strictly harder than a positive carrier solution. No witness, no flip.
OP-44 R2 graviton escape (attack) — SHARPENED-OPEN (overturned from RESOLVED-NEGATIVE): the submitted graviton cancellation was fatally wrong (the TT projector annihilates the leading divergence, $P_{ij}\hat n^j=0$ ); the surviving coefficient is uncomputed and dimension-dependent, so R2's escape stays OPEN and the failure-side foothold de-hardens (medium-high → medium).
Iteration-9 synthesis — per-track verdict table; hedge ledger (grade unchanged, condition sharpened; Berry obligation discharged; reverse-WW pinned; R2 de-hardened); why the verdict stands an eighth time; the residual map (the net-naturality theorem + commutant-to-generated gap as the sole gap between HIGH and a theorem on the verdict-flipper).

Iteration 10 — 2026-06-10 (the commutant-to-generated gap)

Theme: attack the two named obligations iteration 9 left between the principal hedge and a theorem — at the commutant-to-generated gap Lemma N1 located (the designated verdict-bearing lever: close the gap and the principal hedge goes to unconditional HIGH). Does the gap close, e.g. by ergodicity of the Bisognano–Wichmann vacuum (A1)? Does a carrier live in the gap (A2)? And the decidable OP-44 R2 D=4 cubic-coefficient sub-computation iteration 9 left uncomputed (A3). 3 attack tracks, all adversarially refereed (two outcomes corrected — A1's condition-shedding centerpiece struck as a major error; A3's RESOLVED-NEGATIVE refuted to SHARPENED-OPEN). Headline unchanged, ninth consecutive confirmation; the principal hedge moves in neither grade nor condition — the gap does not close, the hedge sheds no condition, and no carrier lives in the gap. Synthesis: iteration-10 synthesis.

Naturality / commutant-gap (attack) — verdict-neutral null result (submitted "gap closes / hedge sheds the commutant condition" STRUCK): ergodicity of the BW vacuum empties the modular centralizer $\mathcal M\cap\{\Delta^{it}\}'$ , not the representation-space multiplicity gap $\langle\Delta\rangle''\subsetneq\{\Delta^{it}\}'$ (Δ ∉ M), which stays non-empty and carries the indefinite $\eta_0$ . The gap does not close; HYP-CKV-VACUITY stays at -R6. Kept: the III₁ centralizer is genuinely large for degenerate spectrum (Popa math/0011084) and is a faithful-trace semifinite algebra (Takesaki).
Carrier-in-the-gap (attack) — RESOLVED-NEGATIVE: the gap is empty where geometry lives (Lebesgue spectrum, trivial centralizer — Shlyakhtenko structure theory) and geometry-void where it is non-empty (almost-periodic sector). The strongest-ever candidate $\mathrm{sgn}(h)\in\mathcal M$ clears the indefinite and algebra-compatible bars by an inner automorphism yet is geometry-void ( $\Delta_{\rm geo}=0$ ); its complete invariant is the finer per-modular-eigenspace signature (referee: NOT the global $(p,q)$ pair), localization failing via the inherited $n_1$ (the wedge-filling mechanism struck as sector-inconsistent). Combined with A1, the hedge narrows substantially toward but not provably to $n_1$ alone; count stays five.
OP-44 R2 D=4 coefficient (attack) — SHARPENED-OPEN (overturned from RESOLVED-NEGATIVE): the attempt to re-harden R2 at the physical $D=4$ by swapping iteration-9's radial-subtracting projector for a symmetric-traceless-on-full-cut one fails on the physics (the coincidence limit selects the radial-subtracting projector; the all-radial term is annihilated and the Hessian vanishes at $m=2$ ) and the arithmetic (the leading $s^2$ coefficient $(m-1)(m-2)/2$ vanishes at $m=2$ ). The $\ell_P$ floor in 4D is not re-established; R2 stays open, foothold at INFERENCE, medium.
Iteration-10 synthesis — per-track verdict table; hedge ledger (grade AND condition unchanged; the designated verdict-flipper executed and did not fire; the gap does not close; no carrier in the gap; R2 stays open); why the verdict stands a ninth time; the residual map (the net-naturality theorem + the still-open commutant-to-generated gap as the gap between HIGH and a theorem on the verdict-flipper).

Iteration 11 (2026-06-10) — the carrier reduction, net-completeness handles, and the terminal-saturation audit

Three-track iteration testing the verdict from three directions; verdict UNCHANGED for the tenth consecutive iteration; the principal hedge moved in neither grade, condition, nor count; terminal analytical saturation CONFIRMED. A1's submitted logical-equivalence reduction was MAJOR-CORRECTED by the referee.

2026-06-10-iter11-carrier-bicentralizer.md — A1. The algebra-internal carrier horn re-grounds on centralizer/bicentralizer structure theory and (loosely) Connes' bicentralizer problem, verified OPEN in general as of 2026 — the mission's "resolved-by-Houdayer–Marrakchi–Tomatsu" premise is FALSE. The submitted "carrier no-go REDUCES (logical equivalence) to the bicentralizer problem" is downgraded to a structural connection (the spine conflated trivial-centralizer with irreducible-centralizer, opposite conditions; Marrakchi–Vaes Thm A makes $M_\psi=\mathbb C1$ unconditionally achievable). Hedge UNCHANGED; count stays five; no closure to a theorem.
2026-06-10-iter11-net-completeness-handles.md — A2. Three independent handles on "is net+vacuum a complete invariant" all land on the existing carrier gate without flipping it: holography of information (STATE-completeness conditional on the gravitational Gauss law; its Dec-2025 failure mode arXiv:2512.18912 reproduces the carrier gap via an emergent localized observer installed by dressing), T-duality/mirror symmetry (net does not fix the target GEOMETRY, but class-symmetrically — no class-separating observable), MIP*=RE (underdetermines the split, not completeness). No reverse-WW witness; reverse-WW stays OPEN, NOT OP-50; new sub-question NQ-1 recorded.
2026-06-10-iter11-terminal-saturation-audit.md — A3. Terminal analytical saturation confirmed: every verdict-bearing residual is decidable only by external input; the two reasoning-decidable residuals are headline-inert; marginal-yield trend monotone to zero; live 2026-06 search found no decidable external lever. Recommendation: consolidate + watch-mode.
2026-06-10-iter11-synthesis.md — synthesis: tenth consecutive confirmation; hedge re-grounded on a named open problem (cleaner, not closed); terminal saturation; integration plan.

Iteration 12 — 2026-06-19

Theme: re-test the standing verdict from three external directions — the named "sharp next lever" iteration 11 left (physics-net relative-bicentralizer triviality), and two web-verified external-input sweeps (2023-2026 math; mid-2026 math + experiment). Coherence verdict unchanged at PARTIAL — 11th consecutive confirmation; principal hedge unmoved in grade, condition, and count (HYP-CKV-VACUITY-R6); carrier-convergence count stays FIVE; no new numeric IDs. Terminal analytical saturation re-confirmed. All three tracks adversarially refereed (UPHELD-WITH-CORRECTION).

iter12 physics-net bicentralizer lever — is the relative bicentralizer trivial for the physics-relevant BW local inclusions M(O) subset M(W), making the carrier no-go unconditional for physics nets? Verdict: RESOLVED-NEGATIVE-AS-A-LEVER / OA-question-OPEN. The triviality question is GENUINELY OPEN as pure operator algebra (AHHM's relative-bicentralizer theorem is discrete-inclusion-only; physics local inclusions are irreducible / infinite-index / non-discrete), AND it is non-load-bearing because trivial (relative) bicentralizer is the carrier-FRIENDLY condition (Marrakchi-Vaes Thm A unconditional trivial centralizer; Haagerup large-centralizer biconditional). The no-go for physics nets holds on the inherited geometry-void / non-localizability bars (iter-9 boost-no-fixed-locus engine). Iter-11 A1 §7.1 subquestion #1 retired as a lever. Citation repair: Marrakchi-Vaes Thm A is UNCONDITIONAL.
iter12 external-math sweep 2023-2026 — has any 2023-2026 result closed/refuted/addressed the net-naturality theorem or the commutant-to-generated gap? Verdict: CONFIRMS-SATURATION. Every cited paper presupposes geometry as input (Morinelli-Neeb-Olafsson Euler program; Liu notes; Weiner conditional on split+GMA), or is orthogonal (Naaijkens-Penneys-Wallick — Euclidean-side LTO reflection positivity, NOT a J-as-RP-carrier claim), or re-confirms an open external problem (Ando-Goldbring — Connes OPEN in general). Residual stays OPEN.
iter12 mid-2026 external-input sweep — any new decidable verdict-moving lever (math or experiment)? Verdict: CONFIRMS-SATURATION. The genuinely-new 2026 Euler-pair geometric-BW / Spin-Statistics mathematics is a cleaner statement of the encoding screen (symmetry = INPUT), not a carrier and not a sixth route. Connes' bicentralizer OPEN in general (Ando-Goldbring). Objective-collapse bounds (arXiv:2506.05507) tighten a CORE not the wager; DESI w(z) verdict reaffirmed 2027 (preference < 2 sigma), bears on target not wager; "GR from RG" (2602.11806) confirmed evade-not-invert WW.
iter12 indefinite-metric / Krein carrier route — CLOSED-NEGATIVE — does a non-self-adjoint / PT-symmetric / Krein-space modular structure furnish a carrier outside the bicentralizer framing (iter-11 A1 subquestion #3)? No — it collapses to encode-not-generate by a three-mechanism trichotomy (gauge artifact / installed-not-derived / η₀-equivalent). The same route-5 carrier problem in Krein vocabulary, not a sixth route; count stays FIVE.

Iteration 13 (2026-06-19) — new-angle frame/synthesis meta-audit (verdict unchanged, 12th consecutive; bottleneck map confirmed complete over the tracked set; triangulation yields an ontological leaning but no testable invariant; consolidation HOLDS)

A three-track structural/synthesis audit of the FRAME — explicitly NOT a carrier re-attack (that is terminally saturated). All three tracks verdict-NEUTRAL and referee-UPHELD-WITH-CORRECTION; principal hedge unmoved in grade and condition; carrier-convergence count stays FIVE; no new registry IDs.

2026-06-19-iter13-C1-unique-gate-audit.md — UNIQUE-GATE-CONFIRMED. The carrier problem is the unique analytical reasoning-decidable gate to the Program-A wager; measurement / Λ / OP-50 / BH-info / GC-1..17 are each downstream-or-orthogonal to the wager and themselves external-gated, never a neglected reasoning-decidable wager-gate. Rendered as an absence-over-the-tracked-set claim INFERENCE, not "provably complete." Scope clarification (annotation): unique to the wager, not to unification (AdS/CFT is an existence proof for §3A independently of the carrier).
2026-06-19-iter13-C2-cross-program-triangulation.md — TRIANGULATION-INVARIANT-FOUND (verdict-neutral). The one referee-survivable shared invariant is the area law S=A/4G — screen-PASSING, not class-SEPARATING (every program and every geometry-first description reproduces it). The geometry-is-emergent leaning fractures into incompatible substrates and is rejected by asymptotic safety. Citation repairs: detach the string/loop clause from arXiv:2208.09489; causal-set spectral-dimension is CQG 31, 125007 (2014) (arXiv:1311.2530).
2026-06-19-iter13-C3-how-close-calibration.md — CALIBRATION (verdict-neutral). "How close" is axis-dependent: framework-consistency largely won (AdS/CFT a strongly-evidenced worked example, NOT a theorem); derived theory math-gated at the carrier; experimental traction on the wager exactly zero; the axes are not independent and collapse to "how close is the carrier theorem" (external input, not reasoning). Citation repair: strike the "~7 orders" BMV figure misattributed to arXiv:2506.04300; restore "~6-8 orders below decisive."

Net: the audit STRENGTHENS the terminal-saturation diagnosis from the frame side — no neglected independent reasoning-decidable bottleneck, no referee-survivable testable shared constraint. Consolidation HOLDS; active mode stays consolidation + lightweight watch on the carrier mathematics and the 2027 DESI w(z) verdict.

Iteration 14 — maximal adversarial assault (2026-06-19)

notes/2026-06-19-iter14-D1-carrier-signature-assault.md — Pillar 1 assault: Fullwood–Vedral signature-as-output (arXiv:2604.07471) and cognates; FAILED-TO-FALSIFY (signature is carrier-installed, authors disclaim mechanism). Referee: ATTACK-FAILS-VERDICT-HOLDS.
notes/2026-06-19-iter14-D2-no-test-assault.md — Pillar 2 assault: GQuEST/geontropic as reverse-WW witness + Schneider global-content seam; FAILED-TO-FALSIFY (prong 1 screen-passing on authors' own words; prong 2 locates the seam without a witness). Referee: ATTACK-FAILS-VERDICT-HOLDS.
notes/2026-06-19-iter14-D3-saturation-assault.md — Pillar 3 assault: non-Hermitian/Krein cMERA dS (arXiv:2606.17983) + DESI completion + bicentralizer reformulation; FAILED-TO-FALSIFY + NO-NEW-INPUT (Krein route confirms iter-12 closure; DESI target-not-wager). Referee: ATTACK-FAILS-VERDICT-HOLDS.
notes/2026-06-19-iter14-synthesis.md — the maximal-assault synthesis: all three pillars survived; carrier count FIVE; hedges unmoved; verdict 13th consecutive, now earned by surviving the strongest attack rather than another lever-test. Strongest surviving crack: Schneider 2024 as an external corroboration of the screen's sole (un-breached) seam.

README note: iteration 14 changes the kind of confirmation, not the registry. Watch-mode continues; the standing verdict's two reopening channels remain a carrier/reverse-WW theorem (external math) and a generative readout (none exists). Mid-2026 literature swept; no carrier, no witness, no sixth route.

2026-06-19-iter15-three-new-frameworks-synthesis.md — Iteration 15 synthesis. Three refereed tracks attacked the net-naturality theorem (the one open gate) with frameworks never before applied in the wiki: (E1) factorization-algebra / functorial-QFT, (E2) Connes–Atiyah–Singer index / K-theory / coarse geometry, (E3) higher-categorical / homotopical / non-unitary tensor-categorical AQFT. All three REPRODUCE the encode-not-generate screen; no decidable handle found. Each smuggles the same geometric input (causal-disjointness/orthogonality order n₁, or a Dirac/Krein/metric datum η). The no-go is now robust across every modern mathematical framework tried. Verdict unchanged (14th consecutive); count FIVE; no ID consumed. Contains the iteration-15 dossier: the carrier problem as a self-contained open-problem statement for external solvers.

Watch mode — post-saturation (2026-07-02 →)

Dated external-input sweeps on the ROADMAP watch clocks. These are NOT analytical iterations: they carry no confirmation-counter change; the verdict moves only if a referee-surviving strong finding lands.

2026-07-02-watch-sweep-01.md — Watch-mode sweep #1 (window 2026-06-15 → 2026-07-02): DRY-AT-STRONG; clocks updated. Six channels, every gate-relevance claim adversarially refereed; zero strong survivors. Logged: Marrakchi arXiv:2606.23636 (unconditional bicentralizer-flow ergodicity — the tracked cluster is active; transfer blocked by the with-expectation hypothesis; watch target sharpened to expectation-free inclusions); Bateman–Turok arXiv:2607.00096 (one more installed-not-derived instance for the iter-12 Krein closure); Wakakuwa–…–Plenio arXiv:2606.31678 (first post-Newtonian frame-dragging GIE channel — BMV row); Euclid DR1 cosmology products slip to mid-2027 (verified); Roman NET 2026-08-30 (verified). Dossier echo: dry. (Correction addendum 2026-07-03: the sharpened watch target was ill-posed; superseded per iteration 16.)

Iteration 16 — 2026-07-03 (the clock-(1) iteration: the multi-wedge closure)

Theme: the first post-saturation analytical iteration, sanctioned by the ROADMAP clock rule (Marrakchi arXiv:2606.23636 = the genuinely new clock-(1) input). Four tracks (G1–G4), three binding adversarial referees (R1/R2/R3, default stance REFUTE); one pipeline fabrication caught and discarded. Verdict unchanged — 15th consecutive confirmation — but the principal hedge moves for the first time since iteration 9: HYP-CKV-VACUITY R6 → R7; the commutant-to-generated gap is CLASSIFIED (not closed) and the residual pinned to the single named open hypothesis (E_O). Synthesis: iteration-16 synthesis.

G1 — multi-wedge naturality assault (the verdict-bearing track) — PARTIAL, proof-grade negative hardening (R1: UPHELD-WITH-CORRECTIONS; R7 MINTED). The multi-wedge lever (all wedge flows at once — verified unused in iters 9–10) yields LEM-NET-NATURALITY-G: (G-loc) localized natural carriers are ±1 (written proof, independently re-derived); (G-glob) fully-natural non-localized algebra-compatible carriers are gauge-symmetry implementers, Δ_geo = 0 (proof-grade); the gap is NON-empty ((−1)^N) but exhaustively geometry-void. Residual = (E_O): vacuum ergodicity on massive double-cone algebras, OPEN. Bound down: DHR n₁-inheritance = framing; conformal closure = transport sketch.
G2 — constructive carrier attempt — all three untried constructions BLOCKED (R2: UPHELD-WITH-CORRECTIONS). State-family naturality (the real co-moving evasion of N2) closes via the section-rigidity trichotomy S2 (sketch-grade, an extension of the posed conjecture); the DL flip fails at an installed leg-identification η (Lemma PC); LEM-CORE-DESCENT (proof-grade corollary) exhausts core-built carriers. Repair found: Doplicher–Longo = Invent. Math. 75, not 73.
G3 — Marrakchi transfer audit — TRANSFER RESOLVED-NEGATIVE; watch target re-sharpened (R3: SUSTAINED). The expectation hypothesis is pervasive-and-definitional (flow undefined without it); no ambient state's modular flow preserves M(O); the sweep-#1 target was ill-posed. AHHM output: no carrier interaction. Repairs: "irreducible" false for local inclusions; HM 2511.11409 is an implication.
G4 — untried-readout sweep — 7 of 8 REPRODUCE-SCREEN; DCNG survives as a conditional watch item (R3: SUSTAINED-WITH-CORRECTIONS). Dirichlet forms, free probability, subfactor invariants, model theory, entropic order parameters, QRF crossed products, net cohomology, web sweep — closure reasons located. DCNG = the gap as a definability question (no-go direction only, gated on η₀-definability). Morinelli–Neeb (Adv. Math. 458 (2024) 109960): the two smuggle items are theorem-level interchangeable, BW-conditionally.
Iteration-16 synthesis — per-track verdict table; the R7 ledger with the verbatim condition string {n₁, (E_O)}; the standing-record repairs; the re-sharpened five-item watch state ((α)–(ε) with (E_O) principal); what could move the verdict from here.