[1337isnot1337]

Symmetric phase changes on the frozen PR4610 graph cannot improve its complete recursive moment, even when paid rank increases and compatible owned-center phases are allowed. For each helper, its added endpoint rank is bounded by its own added paid ranks; concavity prices that debt at least as highly as the helper reward for every 0 <= t <= 1. No higher K is claimed.

This extends #4665's unchanged-paid-rank, fixed-owned-contact rigidity question. The proof does not require all phase forms to vanish. It permits absorbing corrections into whole-job normalizers within a helper contact block. Exact reconstruction checks that each such block has at most one original paid call, so this does not artificially charge a separately fuseable correction. Main and adapter boundaries, subspaces, scalar graph/order/coefficients and field ownership stay fixed; shared multi-owner operations and fusion across scalar contacts remain outside scope.

Only research/phase-rank-debt/ is added. Read README.md and PROOF.md. The verifier authenticates Cao Yifan's original #4610 word, retains its exact bytes and source Git provenance, recounts both complete paid profiles including all eight center jobs, and checks all 632 paths and 408 helper endpoints. The phase grammar from Dugongue/#4654 is a premise; this is not a native all-column or outer theorem replay.

Validation: CPython 3.12 registered replay and isolated optimized replay pass; 512 exact symmetric-form triangles, rational concavity controls, four actual source mutation rejections and all frame-basis changes pass. Committed-byte/source-history preflight and official export integrity pass. The exported verifier passes with Git absent from PATH and leaves all exported files unchanged. Canonical base is b58ad9e; selected conditional K remains .00302015. The 16:12 UTC overlap snapshot completely paginated 461 open PR bodies and 3,620 Discussion records; sparse local note coverage remains incomplete.

Credit Dugongue/#4654, Cao Yifan/#4610, Cinna Davis/#4665 and #4470, zxv, Jacob Alan Sussman and the retained native/helper/compiler lineage. Prepared by Cinna Davis with substantial OpenAI Codex assistance; Apache-2.0. No independent human review or formal-kernel verification is claimed.