Implement eight-child identity transfers and centre-query codes

[aliromman]

This construction changes the historical complex supplier's local target operation from X-JY to the exact subtraction X-Y, while an invertible source code stores the full eight-coordinate centre query in eight existing fields. A forward companion performs (G^-1X,Y+G^-1X). Each complete word restores all 480 arbitrary helpers and adds eight rank-one native children and no array field.

The complete kappa bound is unchanged. This is a local construction and an enabling theorem. It resolves the identity-target and full-query encoding requirements at the actual native cuts. A complete supplier must still close the changing-chart controller, remove the source code, and pay all address, precision, storage, hosting, and recursive costs.

Evidence: ordered proof and scope, exact certificate, cold replay receipt, and independent package review.

For J=I-KR, the theorem assumes RP=LK=I and LP=0 over a unital coefficient ring. With ordered products,

Z=K-P(RK-I), Q=R-L,
G=(I-PL)(I+ZQ), G^-1=I+PL-ZR,
LG=R, RG=Q, JG-I=-P[R+(RK-I)Q], G^6=I.

The target correction is supported on P. The source code fixes a 96-dimensional complement and rotates two eight-dimensional sections with matrix [[0,-I],[I,I]]. No inverse of 13, scalar Gram assumption, or commutation assumption is used. Order six applies to a fixed chart; products of changing charts need not have order six.

For the actual dyadic supplier, a modulo-13 rank argument proves that every identity-target preparation needs at least eight target repair rows. The construction attains eight. This optimum covers the stated source-preparation/target-row interface, not arbitrary native circuits. The proof also gives a conditional full-query transport law between compatible selected-coordinate routes, without inverting the cross-chart query matrix. Full source restoration does not follow from that law.

Complete word	Data map	Scalar allowance
Backward	(X-Y,GY)	217898
Forward	(G^-1X,Y+G^-1X)	217898

Both words have complete original-rank profile {1:2420,2:418,3:432,4:142,5:82}, of mass 5530 versus retained mass 5522. Each uses 16 explicit address maps for its eight new children. The scalar total is 202138+9056+6704; it counts real primitives per array coordinate and is not a full recursive or precision bill. All eight owned private outputs are zero. The new work uses only existing C0. These words are companions, not inverse calls.

The four original source-group examples remain byte-exact and are replayed in the same command. Their complete scalar allowances remain 218794, 218794, 222846, and 225794. They preserve the clean-J target while changing the source.

The exact base is bce54fb3f895cbe5cd4c0eb477c3afeed100190f. Inputs come from the frozen PR #1042 source archive, also used by the historical PR #1094 assembly. All consumed source and credit objects remain in SOURCES.json. This PR does not require an unmerged PR implementation.

With Python 3.10 or later, Git, and that base object in the local database, run from the repository root with a new output directory:

python3 -I -O -B research/native-source-codes/replay_unit_transfers.py \
  --repo . --out /tmp/native-unit-transfer-review

Expected output:

PASS_UNIT_TRANSFER_EXTENSION
Four published examples and both unit transfers passed all 712 formal input columns.
The eight positive and eight inverse native recipes passed all 8192 Gaussian columns.
The complete supplier and kappa calculation are unchanged.

Root and isolated independent cold replays passed and produced byte-identical receipts. A separate reviewer reconstructed both new words directly from the pinned source archive without importing the producer, verifier, or campaign modules. All six complete words pass 712 input columns, arbitrary helper restoration, and private-output checks. The added positive and inverse recipes pass 8192 exact Gaussian columns, including scalar phases. Checks cover both source inverse orders, serial query reads, order six, noncentral coefficient examples, native cuts, scalar costs, and formal prefix bounds. Negative controls reject early source/target updates, wrong factor order, missing compensation, positive lines at inverse exits, wrong phases, and missing private clears. Global routing/decoding, complete supplier pricing, and a new kappa calculation were not established. No complete supplier or repository-wide suite was run for this local addition.

Related corroboration is Chafik Boukhalfa's (@chafreaky) PR #1877. Its pinned proof proves an endpoint-support tradeoff and an unchanged-frame obstruction for the original clean-J-preserving logger. It leaves changed codes and paid or later native transitions open. This package consumes none of that code or certificate.

The retained gauge notice credits @icekylinx. The t16 notice credits Hao Yan (@FanPUYen) for integration, Jeremy Kothe (@jeremykothe2) for the PR #799 local supplier, and Chafik Boukhalfa (@chafreaky) for the PR #741 frame work. The slot-word source credits @rohanarun for PR #987 and NewBArch for PR #869; no account is inferred for NewBArch. Exact notices and further lineage remain in NOTICE.md. The loader and replay tools share the campaign's source work with PR #1719, without requiring that PR to merge.

Related mutable-source work is Hanson Sun’s (@bbMisk) PR #1522. Its pinned proof and scope share a restored source-query tour across distinct BIT outputs under an exclusive mutable-source contract. This package uses the complex input interface, fixed-support source codes, and identity-target transfers. It consumes none of that package’s code or certificate.

New research, implementation, and independent agent review used substantial OpenAI Codex assistance under the user's direction. No independent human review is claimed. New material uses Apache-2.0. The open next questions specify the remaining restoration and chart-transition constructions.

[woklerx]

Independently check dyadic source-code inversion and ordered composition

Intentional independent review of PR1862 at 7649d9ceecec949541bec4bbde5929344166ba59, starting from main 0b1cccf86e2f5132ed286a26ef0a681a495740ea.

An exact Fraction implementation checks 1,728 distinct low-dimensional parameter cases for logger, fixed-support, inverse and ordered prelude-composition equations. It includes singular RK and RK-I, 384 singular G cases, and 1,104 cases with dyadic inverses. It explicitly distinguishes rational invertibility from a dyadic unit: inverse(3)=1/3 is outside the allowed ring. Dropping RP=I breaks the construction. The pinned complete local cold replay independently executes on this machine: all 712 formal input columns and 4,096 new native Gaussian columns pass.

The low-dimensional census corroborates the general written proof; it is not that proof. The 112-field cold replay uses the predecessor implementation. Global chart restoration, recursive hosting and complete supplier pricing remain unverified here.

Reproduce: python -O -B research/source-code-group-independent-audit/audit.py. Source head: 7649d9ceecec949541bec4bbde5929344166ba59.

Ali Romman, PR1862. Native/source lineage and license notices are retained by reference to the exact original package; no source is copied or relicensed.

Prepared by woklerx with substantial OpenAI Codex assistance.

Exact committed audit artifact. Commit 88ed0cf6e8e5b8047af0d8ffc536cc8dbd9ab7c1; base 0b1cccf86e2f5132ed286a26ef0a681a495740ea. Coordinated batch, round 18.

This audit is frozen at 7649d9ceecec949541bec4bbde5929344166ba59. The final overlap snapshot reports newer source head bb29ea73ad9be9a0c3d53cdcb1d22b2ee9ffe42f; this report does not certify those later changes.

A direct Git comparison confirms that PROOF.md and the original local replay code/certificate are unchanged in that newer head. Its added unit-transfer construction is outside this audit.

[Mister-Meeseeks]

Batch review at bb29ea73ad9be9a0c3d53cdcb1d22b2ee9ffe42f.

Merged to main, preserving the original contributor commits and package attribution.

Reviewed scope: Fixed-chart ordered-ring source code and eight-row identity-target repair: exact forward/adjoint 712-column checks for six words and8192 native Gaussian checks pass. All480 arbitrary helpers restore; eight extra rank-one children and217898 scalar additions are charged. Source transport, global controller/hosting and full supplier admission remain open; no kappa claim.

The pinned scoped command passed; the batch ledger contains its command, input hashes, environment and log. This incorporates the research/tooling contribution and does not change the selected κ or discharge the inherited multiplication-theorem assumptions.

Batch review, attribution and evidence. Thank you for the contribution.