[Clear1nsight]

Change and mathematical scope

Independently validate Ali Romman's direct backward caller in #5398 at exact head 174fb211493b43a42210434083e9702b4fb7a2ce, under exactly the five selected #4610/#5241 framework assumptions. The accepted conditional endpoint is κ = 302728823/100000000000 = 0.00302728823.

Comparison	Conditional κ gain
Previously independently validated #5387/#5396 point .003026674765	.000000613465 = 122693/200000000000
Frozen selected #4610 point .0030217758	.00000551243
#5392 transpose point .00302725	.00000003823, from compiler headroom on the same recursive profile

The new contribution is independent admission of the distinct direct caller, its complete invoice and funded endpoint. Ali retains construction credit. The wrapper F_s = R B_s R^-1, with R = [[0,1],[-Q^-2,0]], carries the unchanged completed #5383 backward supplier into both forward sites. Equality with #5392's profile supplies no automatic caller acceptance or additive saving.

Fresh independent engines check all 32 exact Laurent output rows, the actual stage-0 and stage-32 native interfaces, 896 boundary contacts and 114,688 literal central-square columns. All 400 helpers preserve their actual backward conjugate maps and required signed two-sided positive-child normalizers. The 17 arbitrary owned returns of the unchanged supplier are authenticated reuse of #5396's exact #5383 review.

The complete event-derived invoice is 64,116 paid calls / 10,784 productive fields, rank surplus 752. Query and idle bills, boundary programs and all lost productive helper credit remain charged. Our conservative route allowance includes ten phase groups absent from the author's displayed subtotal: 4,828,000 + 158,744 scalar units = 4,986,744 < 10^7 per full local call. The complete reserved raw allowance remains 181,586,816 < 10^9.

Directed rational arithmetic independently funds tested saving .00302728824, reserve 10^-12, both tails, completion/rounding, compiler j=55099, H=38569300000000000, and all 54 strict plus four functional outer predicates with compatible ordinary BIT. The fixed-profile crossing lies in (.00302728824993,.00302728824994); it is a scoped necessary moment ceiling, with no global-optimality claim.

The fresh written all-integer-rank precision/stock proof defines expanded W/P/U/O/R/G, E/B/C0 and eventual thresholds. It includes all 306 raw LOCAL owned banks, distinct recursively suspended banks, signed helper adapters and the three-ADD signed swap's intermediate norms [2,2,1]. The raw allowance is not an expanded storage/precision cap. Complex and actual updated BIT stock reservations multiply.

Task and overlap

Donor-assigned price-plane continuation with gpt-6.1-sol high agents. Task independent-moment, priority revision 7, explicitly changed to complete independent direct-caller admission. Canonical base 1ec1119972c9aefe42525172d07b332fcff81cb4 was freshly fetched before this round and submission. Only research/direct-backward-independent-validation/ is added.

The parallel contribution chat owns #5392's independent transpose admission. This packet does not rerun its author pair or duplicate its transpose engines. #5395 and #5396 corroborate the preceding point; gains are not added. The unchanged supplier is bound to exact #5383 native code, witness and payload through authenticated public #5396 proof and separately labelled frozen execution evidence. Prior raw algebra/ownership results were external execution artifacts, not committed #5396 files.

Live targeted PR and canonical Discussion5125 reads found #5398's construction scope released for independent review. Ali's paid-history/chart/relation discovery and Dillon's query/decoder work retain their scopes.

Validation

Python 3.12, standard library only:

python3 -B scripts/research_package.py --package research/direct-backward-independent-validation
python3 -B scripts/check_research_commit.py --package research/direct-backward-independent-validation --check-source-history
python3 -B scripts/export_research_package.py export --package research/direct-backward-independent-validation --ref HEAD --output /tmp/direct-backward-validation.tar
python3 -B scripts/export_research_package.py check /tmp/direct-backward-validation.tar

Publication head 7ea72fb692cbfd64fea556de84327bbf88555986, tree 7b4b5597365bb3f26fa482a4bbf6790240c2a17e: 156 committed files, 154 local bindings plus the manifest and pinned verifier. Committed and working bytes match. Source-history preflight uses canonical history; pending candidate and prior-review origins have offline Git membership proofs.

Fresh registered normal/optimized independent replay PASS:75.526s,197,083,136bytes sampled peak descendant RSS under serial240s/512MiB guard. All four mathematical engine files retain reviewed hashes. Actual caller/invoice/numerical mutants reject corrupted operators, normalizers, credit, reserves, grids and outer conditions. Seven precision controls are explicitly algebraic/grammar sentinels. Thirty-six cheap normal/optimized wrapper and receipt controls reject aliases, shadows, stale bytecode, rehashed false claims and incomplete scientific coverage.

The separate exact unmodified #5398 author registered normal/optimized pair PASS:137.752s,166,567,936bytes sampled peak RSS,22scientific+2provenance files unchanged. Its raw evidence is frozen; package CI freshly runs our independent engines and does not repeat the author pair.

Official committed export and read-only Git-free normal/optimized replays PASS:37.950/37.833s, files0444/directories0555, PATH without Git. All156 package bytes still match the committed tree; source bytes and modes remain unchanged. Export SHA256 dcedbbafabfc3be204416ceb2ce492f5251026b6eb867b8c1810dda6cbc6b089.

Hosted CI run40032592511 passed both planning and the registered independent package replay, including the unchanged committed-input check, at this exact published head. Hosted execution and local scientific acceptance are separately recorded. The same five inherited assumptions remain. Selection/merging are separate maintainer decisions; no independent human or proof-kernel approval, unconditional theorem, or practical speedup is claimed.

Credit

Ali Romman supplies #5398's direct caller and #5383/#5377's owned relations. Cao Yifan supplies final #4610. Chris R / Clear1nsight supplies #5241, #5396 and this independent review, with substantial OpenAI Codex assistance through a gpt-6.1-sol high swarm. Retain Cinna Davis, zxv, Dugongue, Jacob Alan Sussman, ToikY and all native, Clifford, BIT, compiler, precision and analytic predecessor attribution. Exact source notices are preserved; Apache-2.0.

Open next questions

An improved recursive price plane now needs a distinct completed supplier or changed fully priced interface beyond this frozen profile. The direct wrapper can transfer a stronger backward supplier only after its full main/helper/owned contract, phases, lost productive credit and fresh precision/compiler funding are checked. Active discovery scopes remain with their authors. Separately, a named inherited premise can receive a source-bound all-size proof audit.