[aliromman]

The complete frozen PR4948/4978 p2 caller requires at least 225 new same-capacity linear returns at every width f>=72. A construction with 240 arbitrary linear-oracle returns gives an upper bound in the enlarged model. This binds all four original banks and strengthens the previous 104-column obstruction. It is not a native 240-call word or a kappa improvement.

Scope, proof, exact checks, source pins, registered replay. Base: canonical main 5e0052ca0aa3036a3afa8b0438927377c8d97d53, priority revision 7. Contribution head: 49811a9a37cc1b71bcbe851dd20da3cbf479ff35.

All 39 observations, nine macro cuts, three paid responses and 448 original input columns are bound to the source. The full-column grade test gives 208 missing columns. Coupled left-coset separation excludes all 224 negative targets, and the nonzero last positive-bank leakage forces one more return. The source code has rank-eight minus eigenspaces; their factorization supplies the 16 repair rows in the 240-return oracle construction. Canonical Discussion #5583 takes PR5570's unreserved source-binding handoff. The selected frontier and active construction scopes are unchanged.

Python 3.12 registered normal and optimized replays pass. All 156 bank coefficients agree between D-right and credited D-left arithmetic. All 112 signed normalizers and 5,832 supported native pairs are checked; binary matrix grades agree with the retained phase interpreter. The exact full-history certificate checks distinct cosets, one off-diagonal witness per row, every high-layer observation, leakage identity coefficient -143 and all nine concave-order hinges. The cheapest 225-H1 repair has rank-mass deficit 129 and loses for every power tariff. Controls include the full uncoded endpoint, selected diagonal terms, a missing bridge, false homogeneous frames and a row with no witness.

python3.12 -B scripts/research_package.py --package research/p2-full-history-deficit

Python 3.12 and the standard library suffice. Committed-byte checks pass. The exact regular-module rank and minimum cyclic-generator count remain open, so the [225,240] gap is explicit. The pointwise Clifford/history theorem is a credited written premise. The quantitative error bound uses 208 grade-separated columns; no 224-column angle bound is inferred. The full native word, precision/tape, compiler and outer budgets are not re-proved. Full source-history ancestry was not checked in the shallow checkout. Hosted status is unconfirmed at publication.

Credit Dugongue / PR4948, exact native source 86e4740; Chris R / Clear1nsight / PR4978, its D-left audit and both mandatory source clarifications; aliromman PR5526/5449; and josecarlosgonzalezroque-design / PR5570. Retain Cao Yifan, Cinna Davis, DLamdata, zxv and the native/controller/Clifford/interval lineage. Imported source files are unchanged and pinned in INPUTS.json.

Next: compute the regular-module rank of I-C3 C1 with its phase cocycle and cyclic-generator count, or bind a literal changed paid-input caller and its complete invoice. A width-one rank is not the missing regular-module rank.

Prepared by Ali Romman with substantial OpenAI Codex assistance; Apache-2.0.