Verify QQ16 paired recovery preserves scalar saving at common precision

[Clear1nsight]

PR #4106 changes the query arithmetic DAG to save100 unit ADDs /800 logical scalar allowance against #4015. This independent audit proves that the saving survives in a common sufficient finite format: for every lambda>=1, t=lambda-1, both complete frozen words admit q=h2^(-9-3t) and W=P+28+6t signed component bits, provided all borrowed entry components are in hZ with magnitude<2^P h. This is a sufficient uniform format, not a minimum-width or actual recursive-supplier claim.

The new D+=E intermediate doubles one local envelope230 to460, but remains inside the agreeing completed-query bound11864. Whole-word component/lattice induction includes quarter halvings, all Gaussian interiors, dirty initialization and the deferred tenth host. A separately implemented positive-polynomial certificate F(u)=445+28230u+96u^2+142272u^3, u=2^(lambda-1), dominates3932 candidate/4032 baseline observations for every u>=1. Both have maximum171043<2^18 and identical224 endpoint envelopes.

Rounding and cost results.

• The specified exact pair-first numerical reference incurs zero arithmetic rounding/overflow at the common q/W.
• A literal source/response/suffix binding plus integer associativity establishes relative fixed-point bit identity under exact nonoverflowing unit additions and common deterministic, bank-independent, isolated callbacks. Approximate native interiors, absolute accuracy and scratch restoration remain separate contracts.
• A new correlated-error interpreter gives equal224 endpoint polynomials and equal conservative logical-cut enclosures. No error independence is assumed. The logical-cut error headroom is91101 B2^(3t), B=2^P h; actual error-versus-width and native-interior guarantees remain unknown.
• Floating reassociation is not automatic: the actual query scalar subsequences with supplied normalized components v76=4,v87=v92=1 give Q0=4 versus6 at binary precision2, ties-to-even. This is a query-cut countermodel, not a full rounded-caller reachability claim.
• A declared fixed-bank numerical reference costs (12352+2240lambda)N versus (12152+2240lambda)N, N=2^(73lambda) complex coordinates per owner. It pays shifts, Gaussian interiors, zero stores, signs and both permutation copy legs. The difference is 200N real additions, a different unit from800 logical allowance. Common width preserves both comparisons. The proof states an explicit tariff/extra-width break-even inequality.

The inherited #3303 producer format can be algebraically substituted to give conditional joint q=h2^(-80-22t), W=P+242+44t. This does not establish a selected producer/caller connection or pay conversions. The coordinate Gaussian reference is not a free replacement for a charged recursive H1 implementation. Physical addressing/movement/placement, actual recursive workspace, usage and supplier caps remain open. No kappa improvement or physical supplier admission is claimed. Selected conditional kappa remains0.001672660197076918.

Scope, pins and overlap. Assigned changed scope of joint-query-controller, scope key5423eef254a4943f6bf1. Canonical basebb4bccbf42844d2801487450727c2f63e10d1d0f, priority6. Frozen #4106 head48529915d50bb59b53db53686c4add1cf53429dd and #4015 head0fff81d8997cef646538bcd4f60d7d455cf93b8e. Five canonical semantic/proof inputs and five retained word/construction/proof files are SHA/Git-blob authenticated before new analysis; no predecessor executable is imported. Endpoint/frame identity is inherited rather than re-executed. Main and predecessor heads remained unchanged at the submission checkpoint. Local overlap helper lacks gh/remote PR and Discussion data; bounded live all-state QQ16 precision/range/rounding searches and current Discussion/canonical reads supplement partial coverage. Concurrent #4108 addresses a distinct actual caller/query native-acquisition obstruction and is not an executable dependency here.

Validation. CPython3.12.3 registered isolated replay PASS; four boundary groups PASS, including normal/optimized Git-free read-only content equality, source-first authentication, manifest/vendor corruption, type-sensitive whole receipts, duplicate-key rejection and overwrite refusal. Elementary Gaussian1250 cases,104 source basis plus2 mixed query regressions, independent all-depth certificate and semantic controls pass. Source-before-analysis, changed shared sum/captured recipe, missing native/tenth restoration and illegal private/native overlap reject. Assisted adversarial review found no blocker within the declared scope. Finite checks supplement the written all-depth induction; no human/formal approval or selected cold replay is claimed.

Publication head 30dcf52. Official committed-byte/source-history and export/check PASS for33 package/input files; whitespace PASS. The committed Git-free/PATH-free read-only replay also passes with all34 exported files including the manifest unchanged. Hosted registered verification passed in run39354072941, replay job118405325093. Completed logs bind synthetic merge a99b40e to head30dcf52a7722d0919e125f77a4fb921094578242 and basebb4bccbf42844d2801487450727c2f63e10d1d0f, CPython3.12.15. Primary audit, four boundary groups (18.077seconds), registered completed result and committed-input preservation all PASS. Planning passed270 tests (11 platform skips) and selected only this package. No scientific bytes changed; hosted reproduction is not supplier/human/formal admission.

python3.12 -B scripts/research_package.py --package research/qq16-paired-precision

PROOF.md, range/rounding/cost notes, complete typed receipts, REVIEWS and TASK document assumptions and evidence. Next useful experiment: pin one actual recursive H1 child and its caller entry grid/range; obtain nu(W,lambda), native-interior range, scratch return and full tariff/layout. Test the stated logical margin, all interiors and width-tariff break-even threshold. Stop at the first missing or failing contract; another decoder precision constant does not fill it.

Credit #3985 native reduction, #4015 streaming/hosting, #4106 scalar pairing, #4003 residual; ywz65/#2707, Arham Tahir/#2681, Ali Romman and retained native/compiler/geometry lineage; NickPetalas/#3303 producer grid, ToikY/#3652 independent review, Tekalign/tekuuu/#4030 distinct frame gate. Chris R/Clear1nsight with substantial OpenAI Codex assistance: separate range, rounding/cost and adversarial agents, root integration. New work Apache-2.0, retained notices preserved. Canonical investigation. No merge, closure or selected-frontier change.