Research: transposed JP8 work saves 32,810 backward primitives (no new kappa)

[Ryan-Haines]

Transposing the cleared coefficient-work circuits from #811 gives their backward JP8 companions, including varying magnitudes and numerator-changing source reads. The historical #626 backward program drops 257,280 -> 224,470 real-component primitives, saving 32,810, or 13,122 beyond #751's equal-coefficient reverse-Horner construction.

Status: finite circuit construction / research result; no new kappa. The current selected #741/#589 frontier remains unchanged. This package explicitly studies the historical #626 word and makes no transport claim for #741.

The compiler reverses the primitive sequence, transposes unit updates and flips the sign of writes into the original common source. Clears are retained as self-transpose projections. Every read, accumulation, shift and clear is charged; every arbitrary private input is erased. Paired with the pinned #811 forward construction, complete counts are 224,422 / 224,470. The paired optimistic local invoice decreases by 32,810; using only the new backward circuit decreases its orientation maximum by just 48.

An important limitation is included: 377 isolated block prefixes increase, by as much as 40/9. A simple four-source quarter-coefficient counterexample grows from 2 to 4. Therefore the endpoint identity alone does not justify a prefix claim. Both literal complete programs and a separate integer/dyadic backward recurrence retain the exact original 64/101-bit full prefix bounds within the inherited 192-bit allowance.

Reproduce offline with standard-library Python 3.11+:

python3 -I -B research/jp8-transposed-coefficient-work/verify.py

Expected:

PASS_JP8_TRANSPOSED_WORK backward_saved=32810 blocks=1091 columns=725 controls=10

Validation:

• Both complete literal primitive projections on 716 native plus nine arbitrary private columns; all 492 dirty helpers restored, work erased, exact costs, paid children and non-scalar streams checked.
• Independent integer block matrices on 6,776 local input columns, original/companion isolated prefixes, and a complete backward dyadic prefix replay. No constructor/verifier code imported.
• Ten construction controls, four independent controls and 25 unchanged native frame/wrapper controls rejected.
• Windows Python 3.14 and Linux Python 3.12 pass. Five tests cover optimized Python, minimal relocation, read-only recompression, source/vendor/circuit corruption and undercharged receipts. Ruff, source Git-byte pins and current selected-record integrity pass.

Only research/jp8-transposed-coefficient-work/ is added. Exact base: c290b7b919790300e14004a75d8d24b55ca3c5b5; all six runtime inputs remain byte-identical on refreshed main 7ee02b7c96d85f22b38d28bd7ed49bb8c1aeb261. The #811 constructor is vendored verbatim from b5c244c916dd0b30957332edad7ae7ae22b0eb9d, so no sibling checkout or network is needed. Its forward work is a disclosed pending dependency, not silently treated as accepted upstream.

Credit Sagar Thakrar's #751 backward fan-in predecessor, Jeffrey Cox's #739 power-only continuation, @ellipsi2's #722, Ryan Haines's #811, Jeremy Kothe's #622/#623 providers, Chafik Boukhalfa's #626 allocation and the retained source/compiler/auditor lineage. #793 compensation ordering and #807/#816 CK basis changes are distinct and their savings are not combined here. OS seed 25, alternatives, overlap and local claim are recorded; no pinned sprint issue exists.

Production private-work contract integration, global invoices/admission and inherited all-size/compiler, realization, hosting, precision/tape and analytic obligations remain open. No full repository suite, selected cold rebuild, Lean or remote CI pass is claimed. Finite replay is not a formal multiplication theorem.

Prepared by Ryan Haines (@Ryan-Haines) with substantial OpenAI Codex assistance in research, implementation, verification and writing. Apache-2.0; no independent human review is claimed.

[Mister-Meeseeks]

100-PR batch review at 6a0b8d55bb8026f8b6d708ae07740453b41c872f.

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

Reviewed scope: Inverse-transpose companion to historical JP8 coefficient work, charging reads and private clears; complete finite scalar columns, no selected admission.

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.