Fuse full QQ16 recovery from 336 to 224 native calls

[Clear1nsight]

The full PR #2707 recovery word transports every future-logger field into and out of its query frame, although the logger reads 104 ports and writes only eight. This contribution replaces that block with an owned rectangular correction and preserves all 224 original outputs in F17.

The complete local bill changes from 336 to 224 H1 children, from 672 to 448 native wrappers, and from 464 to 352 cover maps. It adds 1,344 scalar allowance (27,184 total) and 112 owned full-cover temporary arrays, all returned zero in identity frame. All 224 current X/Y fields stay borrowed and unchanged. Owner-private peak remains 16. The literal removals are the 104 query-source return transports and eight response-entry transports; the original predecessor and F0-inverse suffix remain intact.

PROOF.md gives the ordered operator identity and exact ownership/lifetime bill. WORD.json contains the complete 3,935-event replacement word. The verifier authenticates 22 canonical inputs before reusing the credited source algebra, replays the whole word on both original and independent-current routed symbols, checks all 73 frame coordinates at each ADD, and verifies both signed native kernels on 114,688 basis columns with all 224 occurrences bound to their recipes. Eight semantic failure controls cover native offset, maps, sign, ownership, dirty initialization and zero return.

Validation: normal and optimized read-only replay; Git-free export with no executable search path; source corruption rejected before inherited execution; full-word and type-sensitive receipt mutation controls; generation refuses overwrite. Independent AI code/proof review by the coordinating agent and a separate proof/native review found no blocker; their exact scope and file hashes are recorded. This is substantial OpenAI Codex-assisted work, not independent human or formal-kernel review.

This is a local same-output improvement, not a complete physical supplier. Storage, movement, precise outer invocation and productive-family coverage, changed numerical defects, and both all-depth supplier caps remain open. The old one-consumer-per-pair fixed-coverage screen rejects 224 H1, but that rate is hypothetical and differs from the actual first-cut frequency; this is explicitly not a global rejection or a 224-H1 lower bound. The separate incidence contribution is not an executable dependency.

Canonical main: 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision 6. Assigned parallel follow-up of #3963; shared claim and progress. Main was fetched and the binding baseline rechecked before publication. No frontier or selected science changes.

Predecessor credit: ywz65 / #2707 for the full F17 decoder and native normalization; Arham Tahir / #2681 for ordered inverse algebra; retained QQ16/native/geometry lineage; #3952 and #3963 for the motivating demand and boundary audits; Nick Petalas / #3339 for the conditional consumer-budget accounting boundary. Exact source heads and adapted code are recorded in PREDECESSORS.json and SOURCES.json.

One bounded follow-up was rejected before publication: replacing the 104 corrected W query copies by borrowed current Y gives a nominal 120-H1 word, but the full routed replay fails at Z0. All 104 W ports have already received inverse-prefix corrections (the eight T ports also receive Z); the bypass loses their future-query contribution. The 120-H1 nominal bill is not an implementation. The published 224-H1 word and receipt remain unchanged.

Registered local replay also passed: PASS_REGISTERED_RESEARCH_PACKAGE outcome=completed. After replay, one extra EOF blank line in budget.py was removed with parsed-AST equality checked; the complete scientific word and receipt are unchanged. Final byte/source-history preflight is recorded below.

Final published head: 400df7fca8f60c19bf163c77564fe3fbe9154b04, created through GitHub. PASS_RESEARCH_COMMIT_BYTES checked all 37 package/input paths against this head and confirmed canonical source-history ancestry; the base-to-head whitespace check passed. Final metadata/source-pin validation passed after the EOF-only cleanup.

Hosted verification passed in run 39219936311 for head 400df7fca8f60c19bf163c77564fe3fbe9154b04. Completed logs confirm the synthetic merge cba74ef20f825a22eb229daaea2f9440b6259999 into canonical base 20ecf2891d80b5acf18d980b2164fb44ea7faa90, CPython 3.12.15, the complete primary verifier, normal/optimized and Git-free replay, all word/receipt/source/overwrite controls, and PASS_REGISTERED_RESEARCH_PACKAGE. The final committed-input check passed with no diff. Workflow conclusion: success at 08:09:05 UTC. This verifies the registered local contract and evidence; physical hosting, numerical-error and all-depth supplier obligations remain open.

[Clear1nsight]

PUBLISHED / DONE — complete terminal-band QQ16 cost exclusion: #4177, head 4cdda81 (20 October 2026). Class B decision-changing comparison; no selected frontier change.

Frozen #4166 D uses strictly MORE reads, writes and unit moves than strongest compatible original-arithmetic B* on the explicitly admitted terminal-child domain. Scientific main 12fa8c5 / priority7; #4172 59b4662; #4167 6749e45. These pins and prior attribution remain frozen.

New result: source monomial/gate coupling plus a quantified O(73,2) tail-completion theorem matches the old736 wrapper gates into7150 new fixed gates and paid owner words. Complete source-derived terminal C bounds, removed B external shells/copies, disjoint extra bank gathers/scatters, retained headers, B* adoption once, and startup/retirement yield a strictly positive complete signed lower bound in EACH R/W/M coordinate. All510646 Gamma retained bodies, including6972 changed-core and493097 later calls, use inherited #4172 equality. The703-write marker potential cancels once globally; Gamma and adoption are not counted twice. Acquisition/compiler/service/setup/cleanup work retained nonnegative is explicitly identified, not treated as free.

Domain: actual admitted fast RootPlan, post-remainder e=73lambda, genuine C8 terminal predicate 8lambda<73 OR (8lambda)^1000<d, H_b>=L^4, complete v>=2685, compatible q/profile/program/capacities and certified positive-slope threshold. Forty exact production-descriptor certificates at p=2^8500 cover lambda5..44; payloads were NOT executed. lambda<=4 fails actual fast-entry reachability; width>=73 alone does not imply recursion. Preserve original successful-input, numerical, hosting, stock/depth and long-record hypotheses.

Verification: full registered ordinary/optimised and six boundary groups PASS (95.511s for boundary groups); committed-byte/source-history and official export checks PASS108files. Actual committed read-only Git-free scientific replays PASS ordinary50.928s / optimised58.403s with empty stderr and unchanged bytes/modes/mtimes/inodes. Frozen16-file assisted adversarial review PASS with no blocking defect. Hosted run39407419960 was in progress at publication verification; hosted CI is separate from scientific acceptance. PR remains open/unmerged. Sources, exact formula, complete resource/control limits and predecessor credit are in PROOF.md, CBODY.md, GATE-COVER.md, NONCHILD.md, RESOURCES.md and REUSE.json.

Decision: stop fixed-mechanism recovery expansion in this proved band. Next cheapest discriminator is a genuinely nonterminal C8 after the actual height cutoff, pricing complete embedded descendant parking and candidate local/native work. No universal QQ16 impossibility, arbitrary compiled-step/runtime or historical-space verdict, all-node supplier, bootstrap or kappa improvement follows. Selected kappa remains0.001672660197076918. Search coverage remains capped/partial; no novelty guarantee. Chris R / Clear1nsight with substantial coordinated OpenAI Codex assistance; earlier publications and predecessor credit preserved below.

Preserved #4172 publication and earlier handoffs

PUBLISHED — native-history action coupling and complete QQ16 reduction, #4172, 20 October 2026. Head 59b46625a8b2f0dfff3e38ba0949b4247423938a; one integrated Class-C enabling context result. Main 12fa8c5c844be21bfefb38a19503fbd867a11244, priority 7. The source-bound six-arena/codec relation and successful-payload action proof remove the complete C-body residual on all 510,646 Gamma retained calls, including 6,972 changed-core calls and the full later suffix. No reset, new engine or tape. Remaining header cost is 14,298,088 Gamma actions. Total QQ16 advantage over B/B remains unknown; fixed-mechanism recovery expansion stops until the remaining necessary comparison is priced.* Registered checks, committed-byte/source-history and both committed read-only export replays passed. Selected kappa is unchanged.

#4172 result, evidence, limits and next discriminating test

The action relation pairs logical handles, values, widths, heads and free stacks by position, suspends the parent map during actual native recursion, and restores original parent slot bindings. It is phase-dependent, not one global slot permutation. All 490 literal parking transitions pass binary-counterpart closure and collapse to 360 action-shape classes; missing-counterpart and bit-dependent-movement controls reject. This is a source R/W/unit-move theorem on paired successful admitted execution, not an unrestricted runtime or equal-space theorem.

Legal completed fallback/fitted histories reach five different allocator queues before the same actual fitted Ordinary call. Both calls use (79543744,23380814,82873286) reads/writes/moves; a nonconstant complement has the same counts. All six arenas are inventoried, with the remainder arena unused in this zero-remainder fixture. This reduced declared grammar uses execute_plan, not production select admission. A separate actual width-four native root reaches a real width-two child return, preserving original parent slots/bytes/heads, PC, mode/root and borrowed input. The parent is deliberately stopped, with explicit disposal separately charged; no completed nonleaf root is claimed. The inherited reduced prefix/both-bridge-legs/suffix fixture is replayed separately.

Actual warm-erased output markers require a one-write BLANK/LEFT correction. The original child-controller cold potential is 703 writes once per nonempty successful epoch, not per call or Gamma; B and D each retain one child backend, so the potentials cancel globally. Empty live sets do not exclude escaped PhysicalWord references: source ownership remains an explicit premise. Codec/head/live-lease/template/queue mutations, a sealed 1,200-tape inventory and historical per-role backing controls reject. Erasure does not reclaim high-water storage.

The exact reduced comparison is:

T_D - T_B = Delta_N + Delta_shell + 14298088 Gamma
              + 368 Gamma E_1(g) - 16 Gamma E_8(g).

E_r is the complete external C call at actual packet geometry and marker class, descendants once. Delta_N retains acquisition/compiler, scalar/maps, all bank movement, service nonchild work, publication/disposal, constructors/startup/cleanup. Delta_shell retains unmatched preparation/return shells. Frozen D versus B* additionally owes B* its proved return saving. A hypothetical both-adopt D* is stated separately and is not credited to frozen D. Generic parking, child-return exchange and #4166 bank-publication credits are retained once. Finite-control tariffs and per-role historical backing remain separate.

Verification: CPython 3.12.3 fresh ordinary/optimised scientific registered replays and all six boundary groups PASS (47.948s final boundary run). Committed preflight/source ancestry and official export/check PASS for 108 payload files plus manifest. Actual Git-free, no-search-PATH, read-only committed replays PASS in 274.784/270.929s, empty stderr and unchanged bytes/modes/mtimes/inodes. Archive SHA256 79dbd35b8ea69d1b307f044b23b1fa9c380a720cd7f78319b14d3926a15a9be4. Frozen assisted adversarial review found no unresolved blocker in this Class-C scope; shared sources/checkers are disclosed, not human or formal-kernel acceptance. Hosted registered run 39394824899 was in progress at publication check.

Frozen #4167 6749e458800f461535d64cc91c017552d9f55e5f and #4166 0b082d22a0e9a442d264ab0633e35ef26c790630 are preserved. Dependency heads/reviews, main and bounded PR/Discussion overlap were refreshed; capped/cache-limited/unavailable coverage is recorded and is not a novelty certificate. Credit Jose Manuel/#2899/#3385, ywz65, Sagar/#3464, Tekalign/#3380 and prior adaptations, Ross/#2831, Nick/#2923/#2982/#2951, commdata2338/#3233, Wentao Li/#3993, Ali Romman/Arham and the retained QQ16 lineage. Exact reuse limits are in REUSE.json. Substantial coordinated OpenAI Codex assistance is disclosed.

Production O73, complete RootLayer.run, completed nonleaf native root, all-node substitution and supplier/bootstrap/exponent consequences are not established. Original native/Ordinary/Compact success, width/grid/range, stock/depth, hosting and long-record hypotheses remain. Kappa stays 836330098538459/500000000000000000.

Next: derive geometry-sensitive complete E_1/E_8 prices and the full Delta_N/Delta_shell bill against B*. No further reset study or fixed decoder expansion follows from this theorem. A changed source-compatible demand is a separate premise.

Preserved #4167 publication and earlier handoffs

PUBLISHED — shared-engine protocol and fair QQ16 comparison, #4167, 20 October 2026. Head 6749e458800f461535d64cc91c017552d9f55e5f; one integrated class-C enabling mechanism. Original arithmetic can avoid parent parking with the same closed numerical bundle and 1,023 additional controller tapes, rather than a second Ordinary engine. The complete-root source-action comparison covers all 510,662Γ calls, including the 493,097Γ later suffix; setup/terminal retirement is bounded by 66,496 actions. This is a generic protocol gain, not a QQ16-specific gain. Recovery’s incremental context/service/nonchild bill remains open; selected κ is unchanged. Registered, committed-source/history, ordinary/optimised read-only export and assisted adversarial checks passed. Hosted registered-package CI is in progress at publication; human acceptance remains separate. Submission main 12fa8c5c844be21bfefb38a19503fbd867a11244, live priority revision 7, was read; scientific base e40a7b454da6a0df53e358aa3265b9c1c39de2c8 and frozen sources remain unchanged.

#4167 result, evidence, limits and next discriminating test

A is original embedded arithmetic; B is original arithmetic with shared closed primitives and a separate controller; C/D remain #4166 fixed/adopted publication at 0b082d22a0e9a442d264ab0633e35ef26c790630. Protocol action formulas include loop tests, append checks, rewinds, markers, unmatched return and constructor/retirement work. The proved capsule injection C<=S yields A_IO-B_IO >= 510662 Γ (52 B_bank+18214)-66496 >0; B_bank already contains Γ. Separate read/write/move bounds are positive. Compiled finite-control cost retains an explicit threshold, so this is not an unrestricted Turing-step or elapsed-time theorem. A new guarded internal child-return adoption saves 11n+4 actions less finite rebinding control, with every relevant alias updated and public ports fixed. It is available fairly to compatible variants and is not #4166’s already credited whole-bank saving.

Closed native arenas retain free-slot order and encoded slot IDs. Sharing the same primitive bundle preserves their literal invocation/history sequence for B. The formerly proposed isolated-engine cancellation is withdrawn as unproved, not disproved. Of 510646Γ retained calls, 503674Γ have matching payloads, while 6972Γ are changed core. The exact matching-payload header component adds 14,102,872Γ actions (13,806,716Γ in the suffix), but nonheader context residuals, complete service, changed/add/remove children, nonchild work and finite control remain explicit. No sign is inferred for D-B.

Verification: authenticated sources before execution; 60 primitive calibrations; complete nonconstant direct runs over two generations; a real nonleaf child with ten grandchildren and next source ADD; both bridge forms, later calls, prefixes/spectators/coefficient data; borrowed/head/public-identity preservation; allocator queues/leases, PC/target/root, active engine/reentry, alias/generation and cleanup controls. The same-output zero-child losing case is retained. Production O73 and complete RootLayer.run were not executed. All-size claims use the written source refinement and inherited backend/ordinary/Compact/source-entry/hosting/row-stock/long-record hypotheses; descendants remain original C. Extra high-water backing remains charged after erasure.

Registered primary plus all six boundary groups PASS (252.471s); committed-byte/source-history PASS for 106 files; official committed export/check PASS for 106 payload files plus manifest. Actual committed ordinary/optimised read-only Git-free replays PASS in 124.643/122.214s, empty stderr, unchanged bytes/modes/mtimes/inodes. Archive SHA256 b9ffc464b72905fa1f789782ebab06269e1e0bff9d7342eed19903f4d51a4518. Frozen assisted review found no unresolved blocking defect within the stated scope, with shared checker/source dependencies disclosed. It is not formal-kernel or independent human acceptance.

Credit Jose Manuel/#3385, Sagar Thakrar/#3464, Tekalign/#3380, Ali Romman/QQ16, Arham Tahir, ywz65, retained numerical/physical/Compact/ordinary authors, and #3985/#4015/#4106/#4109/#4129/#4166. Ownership exchange is adapted at a new site with a new bill; predecessor savings are not added. Chris R/Clear1nsight with substantial coordinated OpenAI Codex assistance. Searches refreshed named heads/reviews and bounded open/closed PR/Discussion results; caps, cached coverage and unavailable helper remote searches do not establish novelty.

Next discriminating test: execute fitted Ordinary calls from two legal closed free-slot orders, then implement and price a canonical reset of all six arenas on explicitly named fair B/D variants, or prove literal codec equivariance. Preserve borrowed bytes/heads and charge validation/finite control. Only then price the 6972Γ changed-core calls plus complete recovery service/nonchild difference. Do not expand the decoder on the generic parking gain alone.

Preserved #4166 result and earlier handoffs

DONE — actual QQ16 caller installation published as PR #4166, head 0b082d22a0e9a442d264ab0633e35ef26c790630 (20 October 2026). One integrated conditional class-B contribution, built on frozen #3985/#4015/#4106/#4109/#4129. Scientific main remains bb4bccbf42844d2801487450727c2f63e10d1d0f, priority6; final main/overlap refresh found no drift. No new supplier or kappa claim.

Installed connection: actual first source events0/4 -> complete QQ16 B fence573 -> paid whole-family acquisition and encoded448-family service -> all224 recovered/current G outputs in the actual owner-dependent F17/negative-Y frames -> exclusive output publication/retirement -> idle5 and both bridge6 legs. The original C endpoint remains a distinct closed backend, with unchanged original descendants. Fine q_s and actual H_b are retained under the new sufficient full-interval admission argument. Auxiliary PΓ validation descriptors are explicitly distinct from actual P-prefix per-owner native capsules.

Cost decision: the isolated native-component tariff loses (368 C1 versus16 C8, ratio at least23/8), but this does not reject total physical affordability. The adapter changes every root child protocol:510662Γ baseline root calls versus510678Γ installed plus336Γ service, including493097Γ later calls. Original parent parking and embedded return are not cancelled against external-run copying/return. The complete context-indexed operation sum and retained-call threshold are recorded. Internal bank adoption constructively saves11B+4 cell actions less separate finite control compared with this installation’s fixed-copy publication; B is the complete bank length.

Evidence: full selected finite compilation, all336signed73D recipes, both complete selected shadows, actual46-body range/debt and exact all-parameter sufficient inequality; two continuous reduced native generations, nonsymmetric O3 routing and both signed owner conjugations, full224-field storage/packing, borrowed and dirty-state controls. Registered Python3.12 replay and four boundary tests PASS; committed-byte/source-history and official Git-free read-only ordinary/optimized export PASS with unchanged content. Hash-bound assisted adversarial review has no unresolved blocking scientific/composition defect. Hosted registered CI is running at publication; it is distinct from local verification. Production O73 payload/full RootLayer.run, inherited native/common-label/hosting/ordinary/Compact/long-record premises, complete runtime dominance and all-node supplier/bootstrap admission remain outside the established result.

Next discriminating test: price paired actual parent parking/restoration versus external Machine.run copying/protected return at complete bank/packet geometry, retaining every later-root call and descendant context; compare the measured/derived credit against added maps, bank scans and service work. A smaller demand/fused recovery remains a separate way to improve the native profile. Do not conclude full D must be retired from the isolated component screen.

Compatibility and credit: Jose Manuel/source physical C and Compact; Sagar Thakrar #3464/#3607; Tekalign #3380 with new all-binding proof/bill; #3619 fast support rates not imported; unpaidmoon #4114/#4123 and Victor Li #3993 as scoped regression evidence; Ali Romman/QQ16, Arham Tahir, ywz65 and recovery/selected-source lineage. Chris R/Clear1nsight with substantial coordinated OpenAI Codex assistance; shared-source review is not human/formal acceptance. Overlap remains bounded: all-stateQQ16top25, quoted4129query, named heads/comments and Discussions1163/1166/index; helper remote corpus unavailable, so no exhaustive novelty claim.

Preserved active checkpoint and all predecessor handoffs

ACTIVE — actual QQ16 caller installation beyond #4129 (20 October 2026). Assigned continuation on canonical main bb4bccbf42844d2801487450727c2f63e10d1d0f, priority 6; frozen scientific inputs retained. One coordinated package and at most one PR, after the significance and verification gate.

Selected connection: replace actual source events0/4 by full-cover QQ16 F_0/B_1_2, retain events1–3, acquire224 whole families at completed B fence573, run a separate encoded448-family recovery/current-return service using the original exact C backend, then resume idle5 and both bridge6 legs. New selected G reconstruction is (-y,x+y) in its required frames. Actual reduced continuous execution has passed twice on the same engines; production O73 compilation and proof are distinct evidence.

Current decision: a substantial enabling caller mechanism is being verified, not an affordable supplier. The complete explicit route adds368 C1 against16 C8; even free post-D repair leaves256 C1 versus at most128 C1 credit in the stated homogeneous charge. The internal whole-bank publication adaptation saves exactly11B+4 cell actions less separately charged finite control, relative to this installation’s fixed-copy alternative. No global runtime or kappa gain. Final integrated adversarial, committed-byte, registered and read-only export checks are pending.

Overlap refreshed: bounded all-stateQQ16 top25 includes new #4162 adjacent ADD/frame audit and #4149 ADDRESS tariff, neither a turnkey caller installation; named dependency heads/comments and Discussion1163/1166/index inspected. Helper remote coverage unavailable; capped searches do not establish novelty. Credit the retained QQ16/recovery/native lineage, Jose Manuel, Sagar Thakrar, Tekalign, Victor Li and unpaidmoon; exact compatibility limits are in the integrated package.

Preserved previous completed handoff and history

DONE — substantial integrated native contract published as #4129, head e708f02, canonical base bb4bccb (priority6). Claim released. One coherent PR; no selected frontier/kappa change.

New implication (outcome B): paid finite-state promotion/projection now connects the frozen #4106/#4109 native interface to the actual retained recursive Machine C endpoint on its admitted prepared physical ABI. All224 signed73D recipes bind; all-depth row-stock/whole-array-height arguments retain the source refinement/native/ordinary/Compact/hosting hypotheses. Keep actual admitted H_b and require H_b>=W_c+2a+1. Checked exact return gives conditional completed native error0 and reusable reserve. This is an implementation contract, not actual QQ16 caller or whole-supplier admission.

Local evidence:53 canonical inputs authenticate before inherited execution; actual recursive fixture10child entries/10returns and both signed MonomialPackets/Machine fixtures; metered conversion with seven rejection controls; final registered primary/all4boundary groups PASS (135.818s); frozen assisted adversarial review no unresolved blocker; committed/source-history and86-file export checks; ordinary/optimized Git-free read-only committed export identical. Upstream publication bytes match. Hosted run39361206396 completed successfully. Planning passed270tests/11platformskips and selected only this package. Replayjob118428048388 logs bind merge95d1804fd5fce26c9429368624661bdca042224e to exact head e708f02 and basebb4bccbf42844d2801487450727c2f63e10d1d0f, CPython3.12.15. Primary PASS, all4boundary groups PASS (111.868s), registered completed result and committed-input preservation PASS. Hosted reproduction/integrity success is not supplier, human or formal acceptance. Scientific bytes unchanged.

Complete ledger retains224 native calls/448wrappers/352maps and paid precision/copies/control/cleanup/inventories. Same signed multiset/common width preserves the100-unitADD/800-localallowance difference; no full runtime dominance. Actual caller acquisition, descriptor arithmetic/compiler, output lease, current-value owner/frame reconnection, retirement and recursive usage remain explicit obligations. Internal seven-tape/direct-seek and shallow7-lane pooling alternatives keep narrow scopes. Source #4123 one-round normalizedH0/rounded return inspected at499427578245cbd3d2b07680945a94f6e927d020: complementary, not this exact recursive-C lifecycle. Overlap/Discussion coverage bounded, not novelty proof.

Next discriminating test: pin one actual QQ16 F0/B1 cut, check both currentX/Y owner/frame observations and parent rows/L-stock/K/guards/passives/H_b, obtain exclusive224-output/16-private leases plus disjoint closed engines, then price the complete same-boundary continuation against named source work removed. Stop at the first failed admission or budget inequality without claiming a universal barrier.

Credit Jose Manuel/jmbarrancoml and retained physical/selected Gaussian, monomial, scalar, Compact, ordinary and parking lineage; Ali Romman/QQ16, ywz65, Arham Tahir, #3985/#4015/#4106/#4109 and distinct producer/query/frame work. New integration by Chris R/Clear1nsight with substantial coordinated OpenAI Codex assistance; review shares inherited context and is not human/formal acceptance.

Preserved integrated decision record and completed predecessor handoffs

ACTIVE / substantial integrated QQ16 native implementation assignment, started02:08:57UTC, advisory claim expires04:10UTC. One package and at most one PR after significance/verification gate. Mainbb4bccbf42844d2801487450727c2f63e10d1d0f/priority6 and selectedκ unchanged; frozen4106head48529915d50bb59b53db53686c4add1cf53429dd and4109head30dcf52a7722d0919e125f77a4fb921094578242 refreshed. Live3985handoff/4109reviews and new4113/4114distinct scopes checked; helperremote corpus unavailable, boundedPR/Discussioncoveragepartial.

Decision:4109's ideal precision certificate lacks an actual recursive interior/scratch/physical contract. Trace the firstreal event4 W0/port0/q11/+1 and all224 variants (120positive/104negative); no scalarpercentage target. Borrowed224XY preserved, owned224outputsF17, private16, actualparent row/spacing/compactguard and terminalobligations explicit. Logical26144/224H1/448wrappers/352maps known; actualconversion/scratch/physicalusage and globalQQ16currentbridge/idle/suppliercharges remain separate.

Primary constructive experiment: use the actual canonical physical-complex-controller Machine C endpoint, not the normalized/truncating root. An admitted e=73lambda parent supplies child widthlambda, rowsR/L and after+=72lambdaK with all existing passives/guards; monotoneD0 proves stock reuse across224sequentialcalls. Promote the coarse integer stream onto q_w=q_c2^-a with a from the real recursive height bound; checklowzero/signreturn then returnexactlytoq_c. Minimum workingwidthW_c+2a+1 includesGaussianmodulusheadroom. Keep the actualadmittedparent componentwidthH unchanged and requireH>=minimum, so no unproved Compact-width substitution. One separatelyclosedbackend and its completeexclusivework/return/conversionpasses mustbepaid. Actualselectedinsertion/outputlease/currentendpoint remains unestablished; this is an enablingcallbackcontract underintegration, not supplieradmission.

Closest alternatives kept internal: seven-fieldpooling fixesonlyonelevel's oddrowdivisor andcannotreplaceall-depthstock; a metered tagged/rawsix-window axisadapter closesrepresentationmismatch but its directseek schedule canbequadratic. No freecoordinateGaussian atrecursiveprice. Root plusconstruction/cost/physicalworkers, boundedbatchalternative andread-onlyadversary. Successrequiresimplementedpaidstreambridge, actualsourceMachinefixture, quantifiedproof+fullledger andadversarialreview; stop/pivotonfalseprecisionreturn, unsupportedcapsule orsignificancefailure. No intermediatePR, merge, closure, frontierchange or newκ.

Preserved completed QQ16 handoffs and evidence

DONE / assigned range and rounding audit of #4106: published PR #4109, head30dcf52a7722d0919e125f77a4fb921094578242. Mainbb4bccbf42844d2801487450727c2f63e10d1d0f, priority6; frozen4106head48529915d50bb59b53db53686c4add1cf53429dd and4015head0fff81d8997cef646538bcd4f60d7d455cf93b8e unchanged. Assigned joint-query-controller scope5423eef254a4943f6bf1. This scoped audit is complete; no exclusive claim remains.

Result: both complete frozen words admit the same sufficient all-depth component format q=h2^(-9-3t), W=P+28+6t, t=lambda-1>=0, under the stated borrowed-entry lattice/range and exact pair-first Gaussian reference. The800 logical allowance saving survives at common width. A fully declared fixed-bank numerical reference, including both permutation copy legs, saves200N real additions: (12352+2240lambda)N versus(12152+2240lambda)N, N=2^(73lambda). These units differ, and the reference is not a free recursive H1 implementation.

Independent component/lattice induction and shifted-positive-polynomial certificate cover all tensor depths. All224 endpoint error polynomials agree without independence assumptions. Literal source/response/suffix binding proves relative fixed-point bit identity only under exact nonoverflowing unitADDs and common deterministic isolated bank-independent callbacks. Actual query-cut precision2 floating rounding gives Q0=4 versus6, so arbitrary floating bit transfer fails; no full rounded-caller reachability is claimed. Approximate native interiors, absolute errors, scratch cleanup and the actual recursive tariff remain separate contracts.

Evidence: new standalone analyzers import no predecessor executable; five canonical and five retained inputs authenticated. CPython3.12 registered replay and all four boundary groups PASS, including normal/optimized Git-free read-only equality and meaningful corruption/semantic controls. Official committed-byte/source-history/export checks PASS for33 package/input files; committed PATH-free read-only replay leaves all34 exported files unchanged. Assisted adversarial review found no blocker within scope; not human/formal approval. Hosted run39354072941 completed successfully. Replayjob118405325093 binds mergea99b40e032e92debfe6b0b05c6e6362c550d7461 to exact published head30dcf52a7722d0919e125f77a4fb921094578242 and basebb4, CPython3.12.15. Primary audit, all four boundary groups (18.077s), registered completed result and committed-input preservation PASS. Planning270tests/11platformskips selected only this package. Scientific bytes unchanged; reproduction/integrity success is not supplier or human/formal acceptance.

Next viable step: pin one actual recursive H1 child and caller entry grid/range, output nu(W,lambda), native-interior bounds, scratch return and tariff/layout; apply the91101 B2^(3t) logical error margin and the stated width/tariff break-even inequality, paying conversion and physical costs. Stop at a missing/failing contract. Concurrent #4108 is a distinct actual-query native-acquisition obstruction, not a dependency or verified physical connection here. Selectedκ remains0.001672660197076918; no supplier admission, merge, closure or frontier change. Main/predecessor heads refreshed before submission; local helper39records/21matches lacks remote snapshots, supplemented by bounded live PR/Discussion reads (coverage partial).

Credit #3985 native reduction, #4015 streaming/hosting, #4106 pairing, #4003 residual, ywz65/#2707, ArhamTahir/#2681, AliRomman and retained native/compiler/geometry lineage, NickPetalas/#3303, ToikY/#3652, Tekalign/tekuuu/#4030. ChrisR/Clear1nsight with substantial OpenAI Codex assistance: separate range, rounding/cost and adversarial agents; root integration. Earlier completed handoffs preserved below.

Preserved paired-recovery and earlier caller handoffs

DONE / released — actual-pair query factor and native acquisition obstruction #4108 is published and open. Publication head edd6426abf8341daee53d898d81d709d8c7680bd; scientific base bb4bccbf42844d2801487450727c2f63e10d1d0f, priority6. This caller task releases its claim. The separate #4106 range/rounding investigation above, now published as #4109, is preserved. No paid supplier admission, merge, selected-frontier or κ change.

Exact scope. This changes #4105's selected-only write restriction by allowing ordinary U updates. For actual replica0/pair0 F0/B1 calls[0]/[4], a five-query correction H acquired entirely from current Q outputs matches selected G on all224 original and all224 independent current fields over the full actual noncommuting73D owner algebra, at constant payload. An explicit ordered persistent-data inverse establishes H=GQ^-1; no private-clearing712 transition is inverted and D_4015 is not substituted for G. The literal word uses33 declared owned fields (n/c lifetime reuse plus one selected-X delta),6,112 ADD-view and104 CLEARs. All33 arbitrary dirty owned inputs are erased before use and outputs return zero. No pair1/helper accesses; ordinary X is unchanged. Both X0+=X1 and Y1-=Y0 therefore agree before/after the actual execution6/source-event3 bridge on this checked domain, with arbitrary preserved pair1 inputs. Intervening idle/replica/helper obligations remain inherited from the pinned #4105 comparison. Its delta-owner ordinary-Y1 residual is corrected logically; a physical all-payload implementation remains unadmitted.

Precise obstruction. Actual event32 q0 += Y0 through rho1_0 has source phase0 versus F17 targetphase1 at ownerI/e0; payload translation adds only even phase. Raw owner-view+ADD cannot implement it. An independently written probe binds events32/50: Y0/Y25 phases0/3 exclude any one fixed query carrier with those prescribed routes and translation-only compensation. Paid native operations, dynamic carriers and producer/query fusion remain open. The old-chart current-Y query is outside the legal future-Y alignment premise. Per-gate phase-polar ranks0/1/16/17 occur2240/1632/1824/416times; these are carrier-specific obligations, not additive native-call lower bounds.

Same-boundary ledger. No accepted selected source work disappears in this PR; REMOVALS records the proposed16H8 deletion and32H1 insertion with exact source indices/hashes. Known counts are exact literal censuses or inherited compiler allowances, reproduced here; they are not physical prices.

Resource	Selected G pair	QQ16 Q	Q plus logical H	Status / provenance
Native calls	6988	7004	7004+unknown lift	Exact literal count, reproduced
Native rank sum	11172	11076	11076+unknown	Exact count; not exponent/cost
Scalar allowance	397580	426196	493028	Exact inherited dyadic-compiler allowance, independently invoiced
Increment vs G	—	28616	95448	Known arithmetic subtotal; complete saving unknown
Added explicit owner maps	—	528	528+unknown lowering	Logical4736routedADDreads are not paid map/tape calls
Added line wrappers	—	64	64+unknown	Include once, in tariff or separately
Repair ADD-view / CLEAR	—	—	6112 /104	Exact emitted logical word
Declared owned stock	—	—	33, all returnedzero	Logical lifetime checked; exclusive physical/native-scratch lease unknown
Bridge, idle, borrowed state	Retained	Retained	Both current banks match in checked domain	Full native implementation remains open
Representation/movement/control, widths/error, usage/coverage/idle and both supplier caps	Selected obligations	Unestablished replacement	Unknown	No complete physical saving or recurrence claim

The symbolic screen is 16C8 > 32C1 + 95448S + all remaining native/frame/storage/restoration/movement/precision/control costs. All3486common native climb events per orientation retain exact order/arguments. Under explicitly comparable normalized tariffs C_r(lambda)=K(lambda)(r lambda)^(1-a), K>0,0<=a<=1, the sixteen removed centres credit at most128H1units. QQ already adds32H1; normalize112Y on ingress and restore112Y on egress adds224H1/448wrappers, giving optimistic saving at most -128H1units, even granting every other added cost zero. Ingress alone exceeds credit by16. This rejects that specified route under the stated tariff; actual recursive supplier correspondence remains a premise. No #3976 usage/headroom is borrowed, no universal query-repair lower bound is claimed, and #3985/#4015/#4106 savings are not credited again.

Evidence and publication. Proof, cost, native audit, exact source/review ledger. Local CPython3.12.3 registered four-command replay PASS outcome=partial; all224original/current owner-ring factor checks, dirty-owned erasure, independent one-source query availability/invoice/lifetime and16384signedrecipe columns. Independent native probe, missing future-n/initial-CLEAR and route/native-sign controls; normal/optimized Git-free read-only exports, word/source/vendor/manifest/type/overwrite boundaries PASS. All270 onboarding tests PASS with11platformskips. Official committed-byte/source-history/export/check PASS for35 package/input files; actual committed read-only no-Git/PATH-free replay PASS with all36 bundle files unchanged. ArchiveSHA256 3be0dd7bb89903c0bb6cbc22f49ab87d8d82fc7f43e6e7469e3e8f64bb329ce8. Three4105data blobs and4030proof match their exact original Git heads. RESULTSHA256 66277267959f01bc01b30bb2def6380a81c1449b8c2e337aa9f779ad9636b6d7. Scientific review binds frozen hashes, then official publication bytes; no human/formal-kernel acceptance. Hosted verification completed successfully in run39353352561, replay job118403064469. Decoded logs bind synthetic merge d63d5d57b1ad35ce92080bd7068ef2838e85751e to exact published head edd6426abf8341daee53d898d81d709d8c7680bd and canonical base bb4bccbf42844d2801487450727c2f63e10d1d0f, CPython3.12.15. Planning passed270 helper tests with11 platform skips and selected only this package. The primary passed at01:29:44UTC; normal/optimized Git-free export and source/word/typed/overwrite controls at01:33:26; source-event and independent native probe checks followed, registered outcome=partial at01:33:28UTC. Committed-input preservation passed. Hosted reproduction/integrity success is not supplier or mathematical acceptance. Scientific bytes remain unchanged. No scientific bytes changed after publication.

Entry/submission canonical fetches remain bb4; guidance, priority6 and selectedκ0.001672660197076918 unchanged. Overlaphelper at01:15:37UTC covered37localrecords/19matches but no usable remotePR/Discussion corpus (gh unavailable). Targeted live all-state QQ16 and Discussion/canonical reads supplement partial coverage, not novelty proof. The separate rounding investigation and its source claims are preserved separately.

Remaining obligations and next single experiment. Compile producer-coordinated acquisition of current a=R1Y in a carrier sharing paid phase work. Start with event32 and Y0/Y25 relative-phase controls plus old/future-chart distinction, using emitted signed native/map/scalar operations and a removal record. Then require all-payload action, actual exclusive33-field/native-scratch lease, both bridge legs, full restoration, physical access, finite formats/error and favorable complete cost at justified recursive usage. Stop at a separating state, incompatible carrier or sound optimistic screen that repays the16H8 deletion. Native phase sharing/dynamic carriers change the rejected hypothesis; merely renaming uniform normalization does not. General paid repair remains open.

Credit4105 actual boundary;3985 native reduction;4015 streaming;4044/4047/4043/4042 distinct audits;4003 and Tekalign/tekuuu4030 within their stated domains; separately reported4106 pairing; Ali Romman, ywz65/2707, Arham Tahir/2681, Douglas Colkitt, commdata2338/2651, Nick Petalas and retained native/compiler/geometry/hosting/controller lineage. Chris R/Clear1nsight with substantial OpenAI Codex orchestration, construction, separately implemented query/cost and native analysis, and read-only adversarial assistance. Shared source context and adapted4105helpers disclosed; independent probe is distinct from rerunning worker implementations. Apache-2.0.

Preserved completed recovery and actual-caller handoffs

DONE / released — paired-source recovery PR #4106 is published and open. Exact head48529915d50bb59b53db53686c4add1cf53429dd, basebb4bccbf42844d2801487450727c2f63e10d1d0f, priority6. No continuing exclusive claim, supplier admission, merge or κ change.

The unchanged224-output F17 recovery interface now has a fully emitted3713-event word costing26144 scalar allowance versus26944 in #4015 and27184 in #3985. The new contribution removes100 paid unitADDs (800 allowance, about2.97% of4015's scalar bill), with224H1/448wrappers/352maps and privatepeak16 unchanged. All104 correctedW sources including T/prefix contributions remain acquired and separately normalized. Eight query accumulators and two source roles use ten existing Z_U outputs; all ten paid CLEAR/X-copy definitions are restored before the exact suffix. All224 borrowed current X/Y values/frames remain unchanged; all224 owned outputs remain required. The saving is800, not802.

Full original/checkpoint and arbitrary-current rational routed replay, complete phase frames/borrowed return, nonconstant residual/attainability/response witness,114688 signed-native basis columns, separate two-symbol identity and acquisition/invoice checks PASS. Normal/optimized read-only Git-free export and source/copied-executable/manifest/vendor/whole-word/type/duplicate/overwrite controls PASS. The registered Python3.12.3 wrapper reports outcome partial. Five original-head predecessor blobs match; official committed-byte/source-history and export/check PASS for46 package/input files. Published PR head was fetched back and exact46-file check repeated successfully. Hosted run39350712039 completed successfully. Replay job118394540764 binds merge c980b84 to exact head48529915d50bb59b53db53686c4add1cf53429dd and basebb4, CPython3.12.15. Primary, normal/optimized export114.825s, remaining3groups116.164s, registered partial result and committed-input preservation all PASS. Planning passed270 helper tests (11platformskips), selecting only this package. The actual committed export also passed an optimized read-only no-Git/PATH=/nonexistent replay; all47 bundle files including its manifest stayed unchanged. Hosted reproduction/integrity success is not supplier acceptance. Scientific bytes remain frozen.

This is a changed scalar DAG. #4043's identical-trace precision transfer does not apply. Physical movement/control, tag ABI/native exclusivity, numerical range/error, actual invocation/coverage/idle credits, weighted recurrence and both supplier caps remain unknown. The selected κ stays0.001672660197076918. #4105's selected-only actual-bridge obstruction remains a separate limitation; this local recovery word does not provide its missing outer connection. #4030's fixed-owner/common-frame gate is respected because all normalizers remain paid.

Next bounded experiment: derive exact intermediate norms and output-error propagation on the frozen paired WORD, under a stated numerical/bit-cost model. Determine whether extra precision preserves the800 allowance advantage or identify the precise repaid budget. Actual physical/caller connection remains a separate prerequisite forκ. No further census or exclusive claim is opened.

Credit3985's336→224 native reduction;4015 streaming/nine-output hosting;4003 ordered residual; ywz65/2707, Arham Tahir/2681, Ali Romman, Douglas Colkitt, commdata2338/2651, Nick Petalas and retained native/compiler/geometry/supplier lineage. Tekalign/tekuuu4030 is distinct. Chris R/Clear1nsight with substantial OpenAI orchestration, construction, independent accounting and read-only adversarial assistance; shared canonical/replay engines disclosed, no human/formal acceptance. Current-main and targeted live overlap were refreshed; broader remote corpus coverage remains partial.

Preserved actual-caller and predecessor handoff

DONE / released — QQ16 actual-pair obstruction PR #4105 is published and open. Scientific/publication head f0c9a602d1c82b326917e87397dc7fab8750534b; canonical base bb4bccbf42844d2801487450727c2f63e10d1d0f, priority revision6. No continuing exclusive claim, paid supplier admission, merge or κ change.

Exact new result. Bind selected replica0 F0/B1 calls[0]/calls[4], intervening replicas8/1/9 and their helper returns, pair1 idle, and actual execution6/source-event3 full signed bridge. The retained #4015 decoder is distinct from both selected G and QQ16 Q: its actual WORD inverts Q on the 224-data constant-cover specialization, but DG differs from identity at rank32. Original recovered Y does not provide current bridge Y. Only 224 data coordinates are inverted; the private-clearing712 transition is not. F0/B1 physical helper sets intersect40 and have union920, rather than being one identical704 bank.

The sole pivot tests a post-pair patch suggested by constant-owner localization at16 selected ports. On the permitted independent-cover module input X0(d,z)=delta[d=I73], payload constant, ordinary current Y1 is0 under G and -1/2 under Q. Actual full73D routes give
(Y_Q-Y_G)_1=[D_(rho1 rho76)+D_(rho1 rho81)]X0/4-X0/2.
Both translated owners are nonidentity, so the next bridge returns0 versus+1/2. This excludes adapters whose persistent writes are confined to selected pair0 X/Y while preserving ordinary pair0 fields, pair1 bridge inputs and other persistent bridge inputs. Nonconstant intermediate operations cannot evade that same support/domain restriction.

This is an all-permitted-module-state obstruction. Outer integer-multiplication reachability of this particular delta state is unestablished; neither reachability nor unreachability is claimed. Earlier producer changes, repairs writing U, different proved endpoints and separately justified reachable-state restrictions remain open. It is distinct from #4003's future-query transfer and #4030's separately normalized fixed-owner/shared-frame tariff.

Same-boundary ledger. The accepted comparison retains current X/Y, borrowed productive state, idle preparation, both full bridge legs and restoration. No source operation disappears from the accepted selected construction in this PR. The attempted patch fails; complete saving remains unknown.

Resource	Selected pair	Raw QQ16 pair plus D_4015	Status/provenance
Native calls	6988	7228	Exact literal census, newly reproduced; different ranks have different prices
Native rank sum	11172	11300	Exact count, not native cost/exponent
Scalar real-primitive allowance	397580	453140	Exact under inherited dyadic compiler tariff, reproduced
Candidate centre substitution	16 H8	32 new H1 plus224 decoder H1	Every event/index/hash recorded; candidate unintegrated
Explicit QQ owner maps	0 added	528	Literal count; physical tariff unknown
Added line wrappers	0 added	64 plus448 decoder	Literal count; charge exactly once
Decoder owner maps/CLEARs	0 added	352/416	Actual retained WORD census
Decoder stock	0 added	224 owned outputs,0 extra query fields, privatepeak16	Inherited #4015 module contract; no caller lease supplied
Actual bridge	224 complex ADDs	Common only after correct connection	Signed inherited controller bound; endpoint mismatch shown
Repair, physical access, precision, cleanup and usage	selected obligations retained	unknown complete added cost	No matched supplier or recursive incidence
Terminal zero return	boundary dependent	+224 CLEARs/+448 scalar if #4047's erasure contract applies	Conditional, after legitimate last use; not universal
Complete saving old-new	—	unknown	Raw subtotal is not a valid replacement

The raw delta is +240 native calls, +128 native rank sum and +55,560 scalar allowance. #3985's 336→224 saving is already inherited and is not credited again. The counts supply no new κ and no numerical affordable adapter allowance without comparable tariffs and an applicable recursive model.

Evidence and publication. Proof, literal ledger, source pins, assisted review with11 frozen hashes. Actual pending #4015 head0fff81d8 and #4044 heada8c75dd7 bytes are retained, SHA/blob authenticated before new code execution and separately compared to their exact original-head files. No predecessor module imported; only the pinned pure signed-controller recipe is AST-extracted and executed. All18 preterminal events match; exchange/terminal spelling differs and is explicit.

Local Python3.12.3 registered isolated exact replay PASS; independently implemented cost/owner replay; emitted-coefficient mutation, reversed/identified owner-route controls; normal/optimized read-only Git-free export; source/vendor/manifest/type rejection and overwrite refusal. All270 onboarding tests PASS(11platformskips). The official committed-byte/source-ancestry preflight and exporter/checker PASS for24 package/input files. Hosted registered workflow 39349478363 completed successfully. Planning job118390011846 passed270 tests(11platformskips) and selected only this package. Replay job118390715884 passed the registered exact replay, normal/optimized Git-free export and rejection controls, and committed-input preservation. Decoded checkout logs bind synthetic merge ad31fe1b0e382ef7b63a0984e8a94dbc40ab8c04 to scientific/publication head f0c9a602d1c82b326917e87397dc7fab8750534b and base bb4bccbf42844d2801487450727c2f63e10d1d0f, CPython3.12.15. Hosted success is a reproduction/integrity result, not supplier or mathematical acceptance. The24-file committed exporter/checker and a fresh read-only optimized Git-free extraction passed; payload hashes stayed unchanged. Export archive SHA256 310d5e779c0456a98488e5fc965c877ba557a0dd6329fe72c25a534178114592. No scientific bytes changed after publication. Assisted review shares source context and is not independent human or formal-kernel acceptance.

Entry/submission overlap helper coverage is37 local records/19 matches; refreshed remote open/closed PR and Discussions corpus is missing because gh is unavailable. Bounded authenticated PR searches/targeted comments supplement that partial coverage, not a novelty certificate. Canonical main remained unchanged at the prepublication refresh. Frozen sources, selected manifest and selected conditional κ=0.001672660197076918 are unchanged.

Remaining obligations. General current-endpoint repair; full nonconstant payload/native recipes and arbitrary dirty restoration; implementation-bound exclusive224-output/16-scratch lease; signed formats/ranges/rounding and decoder certificate; complete tape/head/control movement; actual invocation/coverage/idle and both all-depth supplier caps. Neither #4043's conditional transfer nor #4042's local copy bill supplies these missing producer/adapter contracts.

Single next viable experiment. Build one paid query-factor correction that may write ordinary U, coordinated with the producer so query normalization is fused into original work actually removed. Pin its eight actual query channels, retained selected records, ordered owner/payload action and native recipes at this exact pair/bridge, rather than automatically appending all224 recovery outputs. Check #4003/#4030's stated hypotheses before adopting a route. First test: eliminate the delta_I ordinary-Y residual with an explicit emitted word, preserving both bridge inputs and borrowed state. Success then requires all required X/Y observations and restoration on every permitted state, plus a favorable complete same-boundary bill at justified recursive usage. Stop at a permitted separating state, a repair that repays the proposed deletion, or a sound optimistic complete-cost failure; preserve that evidence rather than infer a global barrier.

Credit #3985/#4015/#4044 and separate #4047/#4043/#4042 audits; ywz65/#2707, Arham Tahir/#2681, Ali Romman, Douglas Colkitt and retained QQ16/native/hosting/controller authors; Tekalign/tekuuu's distinct ordered-query/common-frame work. New scoped analysis by Chris R/Clear1nsight with substantial OpenAI Codex assistance: root orchestration, primary construction, independent implementation of supporting owner/cost audit, and read-only adversarial review.

Preserved predecessor handoff and validation history

DONE / released — four distinct caller-audit PRs published; all exact-head hosted registered workflows PASS. No continuing reservation, supplier admission or improved K. Canonical main 20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority revision6 and selected 836330098538459/500000000000000000 refreshed unchanged at11:28:18UTC. Frozen inputs and selected frontier are unchanged.

1. Provider binding #4044, a8c75dd7c964855cc9b03c210575be27c65467e4: actual first gauge44 F0 specializes to G=(X,Y+X); QQ16 persistent trace600 versus704 excludes fixed invertible role conjugacy preserving this subspace. Exact correction rank24; scalar211210 versus198766 (+12444) before repair. Different paid entrance/exit maps remain open; no matched B1 input is assumed. Hosted39243930355, full12-file input/export checks PASS.
2. Actual stock #4047, ac6a248e221b91f4ab08bba84e76a5e1a3cc4277: first224 helper-owner candidate has0 eligible banks under fixed-owner/no-evacuation/retirement premises. Existing480-field reserve admits a concrete224-output+16-scratch address injection with zero conflicts across482 explicit events. Native/map/wrapper exclusive lease remains unknown; distinct-target clobber witness proves macro absence insufficient. Eventual output erasure costs224CLEAR/448scalar after a legitimate last consumer. Hosted39244196214, full18-file input/export checks PASS.
3. Physical transition #4042, 403c741e700ea8c21334954b4927de77dde3b685: actual event1708 is a source-preserving zero-target copy. Its explicit local window protocol pays every seek/return and removes P=2SW redundant destination reads in that protocol. The quadratic shuttle is a reference, not a favorable global layout. Concrete header/stride/head witnesses block direct3394 tagged-router to3884 raw-axis composition; negativeq19 wrappers remain paid. The cell bill excludes physical CLEAR1697/map/native provision. Hosted39243745563, full16-file input/export checks PASS.
4. Rounded transfer #4043, aeeca9ffb50203b56924ee3f1325deab4029f4d9: all3392 value-producing operation occurrences,224 outputs, checkpoint and native sequence match between3985/4015. Under identical deterministic finite primitives, persistent formats and isolated scratch, one valid decoder range/error certificate transfers. This removes duplicate analysis, not arithmetic sites;3303/3652 producer bounds do not certify the decoder. Hosted39243839930, full16-file input/export checks PASS.

Each separate agent delivered proof/source-bound controls, registered local replay, read-only Git-free export and reciprocal review; root read the proofs/code and independently ran optimized warning-strict primaries. Hosted CPython3.12.15 logs bind every exact head to canonical20ec, select only its package and confirm committed inputs unchanged. No human or formal-kernel acceptance claimed.

Next viable step: derive distinct paid boundary maps at the FULL actual owner/frame operator level (start with E=GQ^-1), then test whether a named B1/bridge continuation absorbs them. Invoice adapters, scalar delta, helpers, native wrappers, storage/movement and returns before claiming displaced work or K. The rank24 specialization is a necessary obstruction, not a physical native-child lower bound. Stop if the correction restores the proposed saving or a complete favorable screen fails. Next independent obligations are the240-field native exclusion contract, a real final output consumer, actual tagged/raw q19 layout adapter and one finite decoder certificate on the shared DAG. Unknown costs are not zero;3976 conditional553-H1 headroom is not a paid budget.

Credit retained selected hosting/invoice contributors; Ali Romman/QQ16; ywz65/2707; ArhamTahir/2681; NickPetalas/2965/3303/3339; ToikY/3652; commdata2338/merged2651; Dugongue/3394;3884;2722/2794.3985 owns336→224native reduction;4015 owns nine-output streaming/26944scalar;4007 materialized hosting is separate. Tekalign/tekuuu4030 common-frame formal-tariff gate was inspected and excluded from these domains; ToikY4002 phase tags were tested for relevance, not transplanted. Broader Discussion/closed/code overlap coverage remains partial. Chris R/Clear1nsight with substantial OpenAI Codex assistance; Apache-2.0. No merge/closure/frontier change.

Completed claims, prior results and original bounded decision

CLAIM / next bounded caller audit; expires2026-10-19 11:50UTC. Round start10:49:47UTC, canonical main20ecf2891d80b5acf18d980b2164fb44ea7faa90 refreshed, priority6 and selected K unchanged. Four separately owned agents pair representation theory/bisimulation with actual gauge44 provider binding; linear resource/lifetime analysis with reserved-family output stock; tape complexity with first literal streamed query access/return; and compiler trace equivalence with finite-format numerical transfer. Exact boundaries remain224F17 outputs, borrowed224XY unchanged, owned scratch restored, actual outer continuation. Prior #4015 has224H1/26944scalar and no extra decoder banks in its stated model. Complete provider/physical/precision/global supplier costs remain UNKNOWN, not zero. Each item gets one discriminating source-bound test and at most one bounded pivot, stopping at a precise obstruction or paid local connection. Science freeze~11:20, finalquarter11:34+ for verification. No selected-frontier change. Fresh #4030 by Tekalign/tekuuu inspected: its separately normalized common-frame tariff obstruction is excluded from these distinct scopes. #4002 phase tags inspected for actual applicability; no free primitive transplant. Repository overlap helper has local coverage only (gh unavailable); connector QQ16 PR-body searches and recent Discussion1166 checked, broader remote/diff coverage partial. Full five-point decision retained with task metadata. This is a user-assigned next round, not another inverse census. Clear1nsight with substantial OpenAI Codex assistance; separate focused PRs if useful.

DONE prior round: #4003 (restricted Schur residual), #4007 (materialized output hosting), #4013 (costed dirty-workspace stop), #4015 (nine-output streaming) all have exact-head successful hosted registered replays. #3985 retains credit for336→224native children; #4007/#4015 improve storage/scalar counts only. #4015 hosted run39227131409 completed, and its description is corrected. These do not admit a supplier or improve K.

Prior round claim and predecessor credit

COMPLETED / bounded expansion decision — four contrasting QQ16 successor tests; expires 2026-10-19 09:26 UTC.

Canonical main 20ecf28 / priority revision 6 fetched and guidance reread at round start; selected κ remains 836330098538459/500000000000000000. Predecessor #3985 head400df7fca8f60c19bf163c77564fe3fbe9154b04 has author/coordinating-AI replay plus successful hosted registered replay, not human/kernel admission. #3976 and #3977 are likewise checked local scope. Prior completed claim/results: #3963 comment6262031944.

Boundary: all224 original QQ16 X/Y outputs in F17 from224 borrowed current fields, unchanged borrowed values/frames, zero-return owned workspace, owner-private scratch cleared before native calls. Actual gauge44 supplier mapping and arbitrary productive-family allocation are still missing. This round asks which temporary/source obligations can disappear at that exact local boundary, not whether a free decoder or physical supplier exists.

Four separately owned mechanisms/packages, each with a separate focused PR only if useful:

1. Graph pebbling/register allocation: derive exact output read sets and deferrable output initializations; test hosting the rectangular query/response lifetimes in already-owned output slots, including reuse at last query use.
2. Streaming linear algebra/external-memory scheduling: eight persistent full-cover owned F16 query accumulators plus one reusable conjugation buffer in place of112 simultaneous copies. Explicitly price scalar/clear/native/map events and expose traversal/control obligations.
3. Reversible computation/dirty ancilla: exact before/after commutator on borrowed dirty buffers with content/frame restoration; compare the strict source-preserving version and one bounded aligned-owned-source pivot against existing2707 rather than call a dominated reversion a saving.
4. Representation theory/noncommutative harmonic analysis: derive the actual lost inverse-prefix correction in the failed nominal120-H1 shortcut; test one structured routed Schur factorization, with owner-order constraints and a literal paid word or a scoped obstruction.

Ledger: predecessor224H1/448wrappers/352maps/27184scalar and112extraowned fields are constructively upper-bounded for its local exact word. New event/ownership bills will be proved or constructively upper-bounded by literal replay; physical traversal, global hosting/coverage, numerical precision, opposite orientation and both all-depth supplier caps remain UNKNOWN and are not zero. Conditional553-H1 module headroom from3976 is only an optimistic screen, not an admitted budget.

Decision: narrow expansion to these distinct lifetime/contract/source-saving tests for one hour, reserving finalquarter for verification. Each must name real eliminated work and show it does not reappear at consumer/cleanup. Stop after one bounded pivot if exact replay fails, favorable complete screen fails, or the construction is dominated with no changed obligation; preserve a discriminating fixture/handoff instead of expanding a census. A κ improvement requires the missing supplier mapping and complete global bill, not local counts. No selected frontier change, merge or closure.

Overlap: repository helper and targeted live open-PR searches for QQ16 streaming/dirty/Schur/pebbling, current Discussions/start-here/newest handoffs checked; broader remote Discussion/closed-diff coverage remains partial. Distinct predecessors2794/2722 fixed streaming scratch,2651/2617 early output capture,1969 Schur centre transfer,3422 dirty helper and3339 existing count/budget lineage will be credited where used. New local data/proofs remain independent of siblings. Clear1nsight with substantial OpenAI Codex assistance from four research agents and coordinating review; Apache-2.0.