Bind QQ16 recovery to an actual recursive C precision and return contract

[Clear1nsight]

What changes

PR #4109 leaves the actual recursive child's interior precision, completed error and scratch return unspecified. This package implements a paid finite-state bit-stream bridge to the retained physical-complex-controller.Machine C endpoint on its admitted prepared-packet ABI. It supplies a source-relative implementation contract for that previously unsupported stage (assignment outcome B).

For every one of #4106's 224 signed native events, the package binds the actual monomial recipe and physical child descriptors. It derives the all-depth row-stock inheritance and whole-array Gaussian height reserve, promotes to a finer working quantum while keeping the unchanged admitted component width, and checks low-zero/sign-extension conditions before exact projection back to #4109's coarse format. The reserve is reused after each completed callback. Exact completed native error is zero conditional on the retained exact backend refinement and admission.

The new bridge executes actual tape reads, writes and unit moves; encoded-count-to-unary setup, copies, erasure, return markers and separate exclusive backend/wrapper inventories are charged. Its conversion body has the explicit bound 64[m H_b + H_b + W_c + a + b + 1] cell actions, plus separately paid descriptor setup. The complete symbolic invoice retains all 224 native calls, 448 wrappers, 352 maps and coarse operations. The same signed child multiset and common width preserve the local 100-unit-ADD / 800-allowance difference between #4015 and #4106; no total physical runtime dominance is inferred.

Boundary and significance

This enables actual recursive C execution and exact representation return given a prepared packet, disjoint engine inventory and valid encoded descriptors. It does not install the QQ16 caller, supply its output lease or descriptor compiler, identify original inputs with current bridge endpoints, or establish an affordable whole supplier. Actual acquisition, current-value/owner/frame reconnection, retirement and recursive usage remain explicit cost obligations. Source all-size/refinement, native/ordinary, Compact, long-record and hosting hypotheses remain inherited. No selected frontier or kappa changes.

Two closest alternatives stay inside this package: a metered seven-tape signed tagged/raw adapter with its direct-seek cost, and shallow seven-lane batching with a quantified deeper-stock obstruction for its fixed pooling class. Neither is presented as a universal barrier or an affordable substitute.

Evidence

• Authenticate 53 canonical inputs and retained Research: metered QQ16 Gaussian axis on six bit tapes #3884/Stream full QQ16 recovery in nine existing output banks #4015/Pair QQ16 recovery sources to remove 100 paid unit additions #4106/Verify QQ16 paired recovery preserves scalar saving at common precision #4109 bytes before inherited execution; all 224 signed 73-dimensional recipes bound.
• Actual unchanged Machine fixture on nonconstant complex data: ten recursive child entries and ten returns; active-backend re-entry rejected. Both signed monomial/Machine compositions run on reduced geometry.
• Seven conversion rejection controls, semantic lifetime/route controls, source/word/typed-receipt corruption, exclusive generation, and ordinary/optimized Git-free read-only replay.
• Registered package replay passed (all4 boundary groups,135.818seconds), committed-byte/source-history preflight passed (86files), committed export inventory passed, and ordinary/optimized Git-free read-only committed-export replays passed with identical contents/modes. Reduced fixtures are distinct from all-depth proof and do not execute production O73/GL64 payloads.
• Frozen integrated AI-assisted adversarial review found no unresolved blocking defect within the stated domain; shared inherited context and no human/formal-kernel approval claimed.

Assigned task joint-query-controller, scope key 5423eef254a4943f6bf1, priority revision6; scope changed by the integrated assignment to actual native implementation/precision return. The retained task and decision record are in TASK.json. Canonical investigation: #3985 (comment).

Publication head: e708f02bf78c3ed6d770cedf00724ebc5ce928d1. Canonical base: bb4bccbf42844d2801487450727c2f63e10d1d0f. Frozen dependencies: #4106 48529915d50bb59b53db53686c4add1cf53429dd, #4109 30dcf52a7722d0919e125f77a4fb921094578242. New #4123's source-bound one-round normalized H0/rounded return is complementary and does not supply this recursive-C lifecycle.

Reproduce: python3.12 -B scripts/research_package.py --package research/qq16-recursive-binding.

The next discriminating test is one actual QQ16 F0/B1 cut: verify current values/owners/frames, row/spacing/guard/width descriptors and an exclusive 224-output/16-private lease, then price the complete continuation against named source work removed.

Credit Jose Manuel/jmbarrancoml and the physical/selected Gaussian, monomial, scalar, Compact, ordinary and parking lineage; Ali Romman/QQ16, ywz65, Arham Tahir, #3985/#4015/#4106/#4109 and the distinct producer/query/frame investigations. New integration by Chris R/Clear1nsight with substantial OpenAI Codex assistance from coordinated construction, cost, physical, alternative and read-only adversarial agents. Exact attribution and scope are in the package.