[RossRichardson]

Summary

The selected P112 cut is a destination-first scatter d <- d + S p, so a target basis change requires U S. The inverse-transpose reader law remains valid as an abstract identity but does not implement this scatter. This package supplies an exact reachable coefficient witness and a corrected U; scatter(U S); U^-1 word with complete dirty restoration.

The three-/fourteen-tetrad words add 185/878 scalar operations and leave the entire recursive histogram unchanged. No new κ or recursive saving is claimed. This preserves a concrete correction for PR3604 at 9a56309846c262238de04138d14d8bc32ec83d77; its relevant consumer verifier matches the initially audited 30968c83f160011b5f435380746f0e57e64517d0.

The later head 7156bb98f78b7492002010e8729d59fe38b92e60 adds a separate
abstract co-delivery screen and leaves these audited literal consumer bytes
unchanged. That screen is outside this correction's conclusions.

Scope and limits

The replay binds all 176 canonical/native cut events, every one of 14 tetrads, and all 704 normalized ordinary scalar columns for both corrected words. It checks common scalar frames, final ordinary labels, private zero endpoints and the full recursive profile. The 512-address statement is an exact all-vector boundary identity; unchanged Clifford recipes are authenticated reuse, not freshly reexecuted native compiler checks. Rounded execution, magnitude/storage bounds, unchanged precision admission, scalar optimality and all-size transfer are not established.

Pending basis/port-map definitions and source-specific credit are retained as exact original Git blobs with SHA256 identities. The selected main archive and geometry are declared inputs. Runtime needs no pending Git history or network. New files are confined to this package; the selected record and frozen predecessors are unchanged.

Test plan

• Exact original source identity with GIT_NO_REPLACE_OBJECTS=1, including the unchanged consumer verifier at both audited heads.
• Registered metadata and all declared live pins.
• Optimized-parent fresh replay in 4.38 seconds: 176 bindings; 14 tetrads; 704 columns per corrected word; complete scalar bill and zero recursive delta.
• Independent reversed-operand event control, wrong scatter coefficient, two missing-dirty-entrance full-word controls and two hybrid-scatter full-word controls.
• Exact committed-byte/strict source-history preflight: all 21 exported files. Committed Git-free optimized replay passed in 5.70 seconds; all source bytes remained unchanged.
• Automatic hosted CI passed at exact head 7e7a889cbf6da2c4461af806fe52a888c621a7e7, including the registered replay and unchanged-input check.

Sources and credit

Gonzalo Mier's P112 consumer, integer tetrad basis and selected port-map work, and the credited P112 geometry, gauge44 and native-lift predecessors. Original source READMEs and Apache-2.0 license are retained. Ross Richardson with substantial OpenAI Codex assistance, including separate AI-agent proof review and an independently written cut parser; no independent human or formal-kernel proof is claimed. This follows the concrete orientation review.