d6g8k5htny-coder · Oct 18, 2026 · Oct 18, 2026 · Oct 18, 2026
@@ -0,0 +1,28 @@
+# Compact Morse torus geometry for one ordinary H0 interval
+
+This packet derives the geometric premises of the existing ordinary-H0 interval construction for a supplied nonessential nondegenerate maximum of a fixed smooth periodic Morse function. It constructs the closed domain as the closure of the maximum's strict-superlevel path component at the literal C263 death, proves its height and frontier bounds, and obtains an actual path to a strictly older maximum at that closed death level.
+
+The conclusion is one interval direct summand on `[-g(M), -death(M))`, over any fixed coefficient field, for each supplied maximum. The proof uses finite critical-point geometry to retain one older endpoint while approaching death; compact connected intersections and the local Morse form then establish closed-level path attainment. It consumes the existing `elderBoundaryDirectSummand` instead of changing or reimplementing it.
+
+## Evidence and status
+
+- [Complete frozen author proof](PROOF.md): conventional mathematical composition with explicitly named classical imports. Its draft frontmatter records its author-time status; the separately bound review and root acceptance determine the later delivery status.
+- [Fresh nonauthor mathematical review](reviews/NONAUTHOR_REVIEW.md): substantive reconstruction and failure-mode analysis of the exact proof, with source exposure disclosed.
+- [Root acceptance](ROOT_ACCEPTANCE.json): exact proof/review bindings and retained limits.
+- [Exact source identities](SOURCE_IDENTITIES.json): 23 immutable input bodies, with repository, cut, path, length, SHA-256 and Git blob identity. `inputs/` contains those unchanged public source bytes, including the literal Field/Lifetime definitions and the formal consumer.
+
+Actual proof author: OpenAI Codex `/root/adapter_feasibility_c292`. Actual nonauthor reviewer: OpenAI Codex `/root/c292_geometry_review`. Coordinator/internal mathematical check and custody: OpenAI Codex `/root`, chat `01a0bbb5-2fcb-77f0-b78b-4d220ddd7ab2`. All work is delegated AI work for Dylan Roy. Organizational independence 0; human review 0; scientific effect NONE. Neither source identity nor agreement proves the result by itself.
+
+## Exact scope
+
+Inputs retain `n >= 1`, fixed `L > 0`, literal smoothness, periodicity, `IsMorseDistinct`, a supplied `IsNondegMax` and the literal nonessentiality predicate. No death equality, selected saddle, elder relation, attained closed path, bar count or interval decomposition is an input. The local Morse lemma, inverse function theorem, smooth lattice-quotient atlas and elementary compact topology are explicit conventional imports. No novelty or new audit of those classical theorems is claimed.
+
+This packet contains no new Lean implementation or compiler/kernel execution. The copied formal modules retain only their existing historical evidence. Hosted repository checks, if observed on this PR, verify their own registered targets and repository contracts; they do not formalize this new conventional proof.
+
+C291 supplies the literal smooth periodic Gaussian field interface. Applying the result almost surely to its `smoothLaw` still requires Morse admission for that exact law. Simultaneous coherent splitting, exhaustive once-counting, a unique saddle partner, measurability of choices, all-small-bars converse, regional shrinking-collision estimates and finite-window/sampler/count/confidence transfer remain separate. The auxiliary level sequence approaches one fixed deterministic death; it is not a field-law, small-lifetime, period or cutoff limit.
+
+## Next useful task
+
+Under a fresh claim and current owner check, formalize the first missing deterministic geometric prerequisites on the existing quotient: transport the literal complementary-sign Hessian predicate to a genuine Morse local form, derive finite critical points and local path connectivity of closed superlevels, then implement the source-bound trap construction in this proof. Keep companion, component-kernel and hosted-registration owners intact. A record assuming finite Morse events or the target closed path would move the gap into a premise and does not complete this task.
+
+No merge, Release, permission change, source deletion, scientific-status update or transfer of another owner's claim is part of this delivery. The broader C261 program and project-wide audit remain active and incomplete.
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+{
+  "accepted_boundary": "Fixed n>=1,L>0 smooth periodic literal MorseDistinct nonessential maximum -> closed trap and older closed path at literal death -> one actual ordinary H0 interval",
+  "accepted_utc": "2026-10-18T01:26:25.819299+00:00",
+  "author": "OpenAI Codex /root/adapter_feasibility_c292",
+  "exposure": "Fresh nonauthor; task/design and exact source exposure; actual full proof reconstruction; root internal check is not another peer vote",
+  "human_review_credit": 0,
+  "new_formal_execution": "NOT_IMPLEMENTED_NOT_RUN",
+  "nonauthor_reviewer": "OpenAI Codex /root/c292_geometry_review",
+  "organizational_independence_credit": 0,
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+  "proof_sha256": "39f92734da35aa4c3ad97ea9d8e194cea4ee3a0b23054a8a412f331294d74762",
+  "retained_obligations": [
+    "formal local Morse quotient geometry and adapter",
+    "almost-sure Morse under literal smoothLaw",
+    "measurable choices",
+    "simultaneous exhaustive barcode and once-counting",
+    "unique saddle pairing",
+    "all-small-bars converse",
+    "regional shrinking collisions",
+    "finite-window sampler count and confidence transfer"
+  ],
+  "review_bytes": 16983,
+  "review_sha256": "ab8ab0084449e676f0466510e31f8e0a84b36616d1d4f7488f470c47a30a4ede",
+  "root_internal_check": "evidence/ROOT_MATHEMATICAL_CHECK.md",
+  "scientific_effect": "NONE",
+  "source_count": 23,
+  "source_manifest_sha256": "8b0fc8892a1936ad6a37c49b45e5fcf987154068fb7107e07b0b48d55c9f5d44",
+  "verdict": "ACCEPT_SCOPED_CONVENTIONAL"
+}
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