[aliromman]

The actual restricted C Gaussian supplier now has six identity coframes, 201 fewer positive recursive calls, and all 408 independent helpers. This improves Dugongue's two-line proposal and closes the entire compatible binary coframe class at C=.00351: the certified remaining objective headroom is at most 1.604e-21. No complete caller, ordinary saving or new kappa is claimed.

Proof, cut certificates, physical program, exact evidence, verification, source pins, scope and next questions. Exact head 024e43cdd1b942059c87446a76235c3f0b681c34.

The complete profiles are P=1618 H1+619 H2+418 H3+139 H4+12 H6+8 H7 and T=26 H3+2 H4+12 H7+368 H8. Frames 59 through64 are folded. The four new folds give -192 H1+96 H2 with no target change. The full signed-moment gain is .876907816598408238338... at C=.00351, compared with .410349854119189300479... for the two-line proposal. The full-interval gain exceeds 206 C for 0<C<=.00351. The local rank deficit remains 1680.

The source has 423 active unprotected binary coframe choices. Main boundaries, native warp endpoints, ground and centre frames are fixed; every helper endpoint change is debited. Four exact integral flow/cut certificates cover the full 2^423 class. Three output branches violate the rank-seven child cap at named source events. Replay verifies flow conservation, capacities and flow=cut rather than trusting or rerunning the optimizer. Rational power enclosures prove the stated real-objective headroom.

The emitted plan includes both complete 21,166-record chronological programs, the actual 56 A / 56 C interface and all four source retimings. The source free-group replay checks all 632 persistent inputs and the arbitrary owned entrance in each orientation. Independent stored-recipe decoding checks 4268 oriented Clifford maps, including absolute phases, and 24 distinct helper normalizers covering every helper. Source main adapters remain byte-exact. All ordinary dispatch, scalar, COPY/CLEAR, main/helper adapter and inherited working-stock obligations are retained. The ordinary ledger gives 7333 monomial field passes per orientation and a conservative scalar prefix/suffix envelope 2^18446; this is not a complete machine invoice.

The charged higher-moment proof includes all twelve new H6 queries and every target change. For a supplied compatible complete caller with the stated old guards, cutoff c>=17 and u=1/5, it gives gamma_new<49/50 and strictly lowers delta. A named funded caller, refreshed ordinary fees, uniform native/ROW implementation, precision, tape/stock and finite compiler thresholds remain open.

python3.12 -B scripts/research_package.py --package research/restricted-gaussian-coframe-mincut

Expected: PASS_RESTRICTED_GAUSSIAN_COFRAME_MINCUT and PASS_REGISTERED_RESEARCH_PACKAGE. Python 3.12 and the standard library suffice. Registered normal and optimized replay pass. All four cut certificates, 256 separate literal/network objectives, full physical reconstruction, real power/tail bounds and eleven semantic rejection controls pass. Actual damaged frozen source is rejected before import. Exact committed-byte checks cover all 32 package files. Official export integrity and a sealed read-only Git-free optimized replay with empty PATH pass without changing exported bytes or modes. Full-history ancestry preflight is unavailable in the shallow checkout. Hosted CI, independent human review and proof-kernel acceptance are separate; the main planner's navigation regression is not repaired here.

Base and final refresh: df0137efd35e11b4445734bf612bdd4c7ebc330c, priority revision 7; selected conditional .00310045 is unchanged. Canonical claim. The paginated final overlap refresh covered 380 open PRs and 5019 Discussion records, with sparse local omissions disclosed. The parallel PR5693 gives general cut/native-specialization proof handoffs; this result is the separate executed restricted-source optimum and physical certificate. Changed native words, arbitrary coframes and that handoff's broader implementations are outside this result.

Credit Dugongue PR5687, the native-dual-supplier source, Cao Yifan PR4610/4470, Cinna Davis and the native/frame/ROW/controller lineage, DaysSky, Nick Petalas, Ryanson Jonathan, zxv, Jacob Alan Sussman and all retained notices. Seventeen source files are byte-exact. Dinic's algorithm and the submodular cut method are classical. New optimization, four added folds, physical evidence and charged gain/tail proof: Ali Romman with substantial OpenAI Codex assistance; no subagents. Apache-2.0. No global literature-priority claim.