Iteration 9 synthesis — the carrier no-go's naturality content, executed

Date: 2026-06-10 · Type: lever-execution iteration (4 adversarially-refereed attack tracks) · Headline movement: none (8th consecutive confirmation) · Hedge movement: principal hedge sharpened in condition, not grade; one of its two outstanding obligations discharged negative.

Per-track verdict table

Track	Target	Submitted	Referee	Net effect
A1 carrier-naturality	Replace the net-constructibility ansatz by a naturality theorem	SHARPENED-OPEN	UPHELD-WITH-CORRECTION	Constructibility half → naturality theorem (Lemma N1) modulo a commutant-to-generated gap; boost engine → naturality obstruction (Lemma N2); localization half irreducible (= index-set order = $n_1$ ). Hedge grade unchanged, condition sharpened. Count stays 5.
A2 modular-Berry-holonomy	Does the holonomy escape yield a localized indefinite form?	RESOLVED-NEGATIVE (+ "unconditional HIGH")	UPHOLD-OUTCOME / DOWNGRADE-HEDGE	Escape closes: (a) holonomy form is signature-free symplectic (KKS/Crofton); (d) the indefinite kinematic metric is vacuum-inherited from the $SO(d,2)$ orbit. "Unconditional HIGH" struck — stays CONDITIONAL. Obligation (ii) discharged. Ground (b) false (not needed). Count stays 5.
A3 reverse-Weinberg–Witten	Is reverse-WW independently provable or a free witness?	SHARPENED-OPEN	KEEP-ALL, UPHELD	A1-concrete is a conditional theorem (Weiner 1006.4726); its hypotheses ARE the geometry. reverse-WW-theorem ≡ carrier no-go; witness strictly harder. Target pinned to §8 reopening condition. No witness; no flip. Count stays 5.
A4 OP-44 R2 graviton escape	Does the TT tensor structure cancel the cubic horizon divergence?	RESOLVED-NEGATIVE	OVERTURNED → SHARPENED-OPEN	Step-3 contraction $\Pi:\hat n\hat n\hat n\hat n=0$ (not $(d-2)/(d-1)$ ): TT structure annihilates the naive leading term; residual coefficient uncomputed, zero in $D=4$ . Escape stays OPEN; foothold de-hardened to INFERENCE-medium.

Hedge ledger: before → after

Hedge 1 (OP-46 residual / carrier no-go). Before: MEDIUM-HIGH→HIGH, conditional on the net-constructibility ansatz, two named obligations outstanding (net-naturality theorem; modular-Berry-holonomy escape). After: MEDIUM-HIGH→HIGH (grade unchanged), condition sharpened — the ansatz replaced by a naturality formulation (constructibility a theorem modulo a located commutant-to-generated gap; localization proven irreducible), and the modular-Berry-holonomy obligation discharged RESOLVED-NEGATIVE. Sole residual between HIGH and a theorem: the net-naturality theorem itself plus the new commutant-to-generated gap.
Hedge 3 (HYP-ENCODING-SCREEN / §7 no-test). Inherits unchanged grade and the sharpened condition. The reverse-WW target is now pinned to the §8 reopening condition (A3) rather than free-floating.
OP-44 R2 (not a CONCLUSION hedge). Failure-side foothold de-hardened (medium-high → medium); escape OPEN.

Why the verdict stands an eighth time

The two named obligations iteration 8 placed between the hedge and a theorem were the entire iteration-9 agenda. One (the Berry escape) closed against the evader; the other (the net-naturality theorem) was advanced to a theorem-modulo-a-located-gap but not completed — and A3 independently showed why it cannot be free: the naturality/A1 theorem is Weiner's algebraic Haag theorem, whose hypotheses are exactly the geometric inputs the carrier problem isolates. Every route to closing the hedge unconditionally runs back through the same $n_1$ smuggle (the index-set order). No new degree of freedom entered the problem; the A4 overturn even removed a previously-claimed failure-side foothold. This is the signature of saturation: the marginal yield of further reasoning is sharper obstructions and self-corrections, not new structure.

The residual map after iteration 9

The carrier problem (HYP-FACTORIZATION-IS-GEOMETRY) — still THE compressed analytical reopening target; five routes converge there; the net-naturality theorem (plus the commutant-to-generated gap) is what stands between the hedge and a theorem.
reverse-WW — OPEN, as of 2026-06, pinned to the carrier problem; un-registered; strictly harder than a positive carrier solution.
OP-44 — R2 escape OPEN (residual same-power coefficient uncomputed, dimension-dependent); $N_\ast$ theorem-free both sides; R1 a regularization-conditional failure-side result; $\ell_P$ floor in-principle status untouched.
OP-48c — X1 a theorem-with-a-price-tag; horn C theorem-conditional-on-framework. OP-49 — NEAR-NO-GO, residuals (a)/(b)/(c′). Both untouched this iteration.
Experiment watchlist — unchanged; 2027 $w(z)$ the nearest-dated external event.

Binding discipline notes (carried)

One submitted outcome label overturned (A4) and one verdict-bearing overclaim struck (A2) — the referee discipline is binding, not rubber-stamping. Carrier-convergence count is five (A1/A2/A3 all fold into route (5); none is a sixth route). reverse-WW is not OP-50 (OP-50 is the closed-universe Hilbert-space problem). math/0304340 is Bisch, not Jones. No new OP/GC/A/H numeric IDs consumed (next free: OP-51, A-24, GC-18, H9).