[aliromman]

This closes the actual-word/boundary verification gap in the existing forward balanced-J component. It reconstructs all 21,473 coupled native records, computes their transfer on 632 independent original fields and nine arbitrary owned inputs, and then composes every literal source and balanced-J boundary. The direct physical comparison uses the exact nine-axis, one-column operators in the retained source convention. No new construction or complete kappa improvement is claimed.

The proof, exact receipt, source pins and validation record state the result and limits.

The verified endpoint is T_s(u,v)=(D_s u-R_s v,D_s J_s v) on two 120-field banks, with J_s=[[I-W_s Z_s,-4W_s],[3Z_s,13I]]. All 392 other original fields have their positive normalized helper transforms, and all nine owned outputs are zero. The main 240-field result remains a joint coded endpoint. Its promoted H8 fields do not retain a second autonomous target credit.

The audit retains absolute Clifford phase and keeps extracted operator signs separate from exterior rational coefficients. It also compares the complete formal operator dictionaries in both odd and even digit-column sign classes. This gives the field identity under the prescribed columnwise tensor implementation: operator signs are raised to the column count, while scalar ADD/SCALE coefficients stay fixed. No sum is tensor-powered. Native phase/adapter/residual annotations and the normalized-row implementation remain inherited premises; this is not a new fully flattened physical implementation or all-width machine compiler.

The complete existing paid profile is {1:2201,2:412,3:510,4:127,5:40}. It includes all native calls and eight external H1 calls. The receipt derives the native, provider-boundary and external ordinary counts from the actual records and loops, including all eight zero-cache clears. The autonomous helper profile is {4:28,7:7,8:39,9:318}. No paid request is removed and no new independent main target is admitted, so these checks cannot be inserted as a new exponent gain.

Base: 32890bc5de034ab8fc93ac88ead7279a6a416d04, priority revision 7. Every live source is already present at that base. Its selected conditional kappa remains 0.003027288235 under the same inherited assumptions. Python 3.12 or later and the standard library suffice:

python3 -B scripts/research_package.py --package research/balanced-j-native-word-join
python3 -I -O -B research/balanced-j-native-word-join/verify.py

Expected token: PASS_BALANCED_J_ACTUAL_NATIVE_WORD_JOIN. Registered normal and optimized checks passed in 420.859 seconds total, within the 600-second limit for each command. Both modes also passed from a fresh read-only, Git-free export with empty PATH and unchanged source hashes. A changed Clifford source failed before import. The six semantic controls reject a wrong native rank, deleted owned-entry CLEAR, reversed native warp, missing final half, phase-only k0 post-alias error and added spectator translation. Committed-byte and official export-integrity checks passed for all 16 files. The final export adds validation records and clarifies README credit; its scientific and live-input bytes are unchanged from the cold replay. The strict source-history gate stopped because the checkout is shallow; full-history ancestry remains unverified.

A separate campaign worker reviewed the phase/exterior-scalar argument, ownership and invoice, reran the cheap raw native interpreter and reconstructed the counts directly. That worker did not repeat the expensive Clifford join. These are author-side AI checks. No independent human acceptance, selected cold replay, inverse audit, Lean proof, new compiler, precision/stock bill, global caller or outer admission is claimed. Hosted CI is unconfirmed at publication.

Credit Dillon Amburgey (@dillona) and his PR #5402 for the coupled provider and its source boundary. The retained balanced-J packet credits zxv's PR #5419 for the cross-chart consumer and gauge, Dugongue (@mdumitrean) through PR #4935 for the involutive completion, and the Dillon/Ali/native/helper/Clifford/compiler lineage. Chris R (@Clear1nsight) supplied the deferred-K overlay in PR #5423 and retained the packet and budget in PR #5424. The original fused-T construction keeps its separate credit. Those roles are preserved; emitter authorship is not inferred from a submitter account. The retained author notices bind the Cao Yifan/intqwq, Cinna Davis/1337isnot1337 and Dugongue/mdumitrean credit.

Related PR #5467 serializes the centre-free and uncoded native units. PR #5526 and PR #5529 address general tensor faithfulness and cutoffs. They are not consumed executable dependencies, and this fixed-component coefficient check claims no general faithfulness theorem. The inverse in PR #5411 is not republished. Retain Cao Yifan (@intqwq), Cinna Davis (@1337isnot1337), Dugongue, zxv, Jacob Alan Sussman, PR #589, and the source geometry/COPY/compiler/precision/analytic notices in the source proof and physical interface.

Prepared for Ali Romman (@aliromman) with substantial OpenAI Codex assistance; Apache-2.0. This is a bounded verification contribution and closeout of saved research, not a new caller campaign.