[1337isnot1337]

The unchanged-paid-rank symmetric-phase mechanism proposed in #4654 has only the zero solution on the frozen PR4610 round-three word, under its fixed main/adapter/owned boundary conditions. Both boundaries of all 408 independent helpers may vary. Exact reconstruction gives 310,640 free binary form coordinates and 559,016 homogeneous equations; equality substitution forces every coordinate to zero and discharges all 80 nontrivial helper difference functionals.

This is a scoped exact obstruction, not a higher kappa or a universal phase ceiling. Paid phase changes, changed subspaces/maps or scalar order, and redesigned center interfaces remain outside scope. It supplies the concrete missing decision before expanding the new grammar into unchanged-cost helper searches.

Only research/symmetric-phase-rigidity/ is added. It retains exact source bytes from #4610 at 1eb8da6 with original commit/path/blob provenance, an ancestor-bound pin for the retained copy, a standalone standard-library verifier and the complete result.

Validation: CPython 3.12 registered and isolated optimized replays pass; changing every frame basis preserves the entire result; exact free/forced direction and higher-arity substitution controls pass. The reconstructed contact graph reproduces the source paid profile and shared G actions. Committed-byte/source-history preflight and export integrity pass; the final exported verifier passes without Git on PATH. Native all-column endpoints, absolute phases, compiler, BIT, precision and outer/theorem replay are explicitly outside this no-solution certificate. Canonical base b58ad9e; selected conditional kappa remains 0.00302015.

Credit Dugongue/#4654 for the phase-form grammar, Cao Yifan/#4610 for the round-three word, Cinna Davis/#4470 and its controller lineage, zxv, Jacob Alan Sussman and all retained E8/scalar/Clifford/native/compiler contributors. Prepared by Cinna Davis with substantial OpenAI Codex assistance, Apache-2.0.