[Clear1nsight]

Change and mathematical scope

Save eight paid H1 calls per direction in the named balanced-J source-query interface, under the retained native ABI. Remove the eight old-h queries and their copied-query lifetimes, retain the actual native/alias/scalar segments, pay all120 queries on the current returned source bank, and apply K -= 3 Z_s E_p + 13 E_h before destination encoding. The ordered main endpoint is unchanged: (Du-Rv, JRv). E remains unchanged at every correction primitive; the existing owned c0 is cleared before use and returned zero.

The comparison is original fused T followed by the same full current-source Q120 layer. H1 changes2321→2313, with all other paid ranks and392 independent helper jobs unchanged:

Pnew={1:2313,2:412,3:510,4:127,5:40}.

This is a validated local recursive saving with an explicit ordinary bill. It supplies no new canonical main targets, thin-query reuse, complete caller or funded κ. The 392 helper transforms are positive in both directions; they are not asserted to compose as inverses.

ECONOMICS.md supplies the accompanying scoped limit. Even granting120 D8 outputs,120 R9 outputs and all392 helpers with remaining work free, the displayed standalone FULL120 profile has negative target-minus-paid moment for every 0<C<1. At C=.00330007, a change consisting only of additional H1 deletions/reuses needs at least28 further actual paid occurrences removed, with all targets and other calls fixed. The eight calls saved here are already absent. This is necessary only, and does not govern a different caller or changed paid/target profile.

Task and overlap

Explicit donor assignment refines priority-revision7 independent-moment to a source-bound occurrence overlay; TASK.json declares scope_status: changed and its connection to the cost bottleneck. Canonical base is 1a3ced60b2f7a46bc70280a04f2eeb8ca027c700, selected conditional κ .003027288235 under the same five assumptions.

The peer retains original fused-T derivation/implementation and the separate complete-caller search. This complementary overlay and unchanged dependency vendoring have explicit coordination clearance. The preserved sources are labelled LOCAL generated evidence; filenames containing PUBLIC are not a claim of public Git ancestry. Public predecessors include native #5402 (3348fccea855082786d5f0fc5558b73d4974e745), actual inverse #5411 (123ffa6aa7c1866ac60c67739841f71d95b3edf7) and consumer #5419 (d94f60b3b603782fce40f1911b3b094847d0f45a). #5418/#5420 supply separate scoped economic support.

The all-author PR feed was refreshed through06:04UTC, including #5422's old-#4610 scalar-pair negative; that scope does not cover this changed interface. Newest handoffs in #1166 were also read before submission, including the unreplied Rohan source request and the current replay-maintenance notices. These are bounded checks, not exhaustive novelty certification or ownership of another contributor's decoder.

The publication also reuses the exact #5420 CI-navigation repair because canonical main still pointed its current CI section at the historical4610 command. The sole extra file is docs/ci-verification.md; no scientific package or test is changed by that successor.

Validation

The emitted packet is 9f4578a8d85a16f1d19b4fe759a2d5aa17c9d84d4028f48940e85c9843f3ce8e. Independent checker v2 is dae704de19122deed696cfcdc6fb1479faac66cd42aa4d87d9c0285a30d38600. It interprets the new correction on129 independent inputs, preserves all120 source rows at every primitive, joins the retained main240+9owned contract, checks both main inverse products, and checks the ordered algebraic MAIN raw inverse transpose with J^T retained. A literal full helper/owned physical dual remains open.

The current query is bare positive C1 on physical central axis0, uniquely fixed by Q=R D^-1 in the actual phase-bound native output equations. An analytical counterexample from an actual mode word rejects the proposed K-conjugated route; full-R intertwining does not imply separate q or D commutation. The inverse uses120 positive central calls plus120 ordinary central translations. Twelve controls reject wrong versions/order, omitted calls/correction, extra query phase, wrong source phase/stage, source writes and missing cleanup.

The external bill per direction is1952 unit/half ADDs,136 COPY,24 SWAP,272 CLEAR,272 zero-retags and120 paid Q calls, plus one unchanged native provider. Monomial maps are1168 forward and1288 inverse, including800 inherited aliases. Native internal work remains inherited and charged. No ordinary instruction is converted into a recursive-rank credit.

The sole peer's first independent normal/O pair passed in0.704941994/0.807483174 seconds, sampled peaks54,849,536/52,019,200 bytes. Their full15,698-byte results match, SHA256 15bdc61d48d082224865f212ea8471d3f323b511bf1af1afd18c16895b0a5db9, with zero JSON exclusions. All38 pre/post byte/mode records stayed unchanged (34 at0664, four at0444); these two runs were not a filesystem-readonly test.

After the74-file package freeze, three further serial guarded requests passed: registered normal/O pair 2.923508826s,103,223,296B, portable normal 1.207998975s,71,475,200B, portable optimized 1.410404486s,80,482,304B. All four complete scientific receipts are byte-identical and JSON-identical to the accepted result, with zero scientific field exclusions. All155 source/tool records and42 readonly directory modes remained unchanged. Portable files were0444/directories0555, with empty PATH, no Git metadata inside the copy and explicit Git-discovery ceiling; ancestor Git metadata was preserved and discovery under the ceiling returned exit128. These are four additional checker executions, separate from the original two.

The official canonical signed-invoice comparator separately ran once: uniformly_better, delta_paid={"1":-8}, delta_targets={}, strict negative new-minus-old power cost for 0<t<1, using only the392 unchanged actual helper credits and no hypothetical main reward. Runtime0.101276681s; this integer concave-order screen validates the declared relative invoice, not absolute profitability or source admission. The source tool is canonical scripts/compare_recursive_invoices.py, Git blob fda2a852e9937e42fe40df0707694465ca7c1b48.

The standalone proof cancels28H4, leaving equal residual rank masses5263 with target ranks7/8/9 above6 and paid ranks1..5 below6. Exact rational logarithm/Taylor bounds give paid-minus-target deficit greater than 13559903132446535673/500000000000000000 >27 at the named C. This written economic support is outside the registered component replay; no fractional powers, new price point or Powers engine ran.

Scientific commit: 122d42143d1f3eca582240a095eec9e0591044a4, direct parent canonical1a3. Publication head: bb81dd1f8aa34d5ee89a43f3c19d4b50606d6287, whose only extra delta is the unchanged #5420 documentation repair. All74 package blobs match the reviewed/requested/executed working source, science/publication commits, actual readonly copy and official archive. Committed-byte and declared-source-history checks pass; the publisher fetched canonical commit metadata (7507 reachable canonical commits), not the complete file corpus. LOCAL generated premises are not presented as canonical ancestors.

Official export/check passes: SHA256 b217332b48a0ea87e2c78871e95dfb79b838ecf115cab71e0d06d08f2095d8a0,29,276,160 bytes,75 members (74 payloads plus transport receipt). Its payloads are byte-bridged to the executed copy; the final official archive was not separately rerun. Working0644/0664, readonly0444, Git100644 and export0644 are distinct, documented representation modes.

python3 -B scripts/research_package.py --package research/deferred-k-query-sharing-component
python3 -B scripts/check_research_commit.py --package research/deferred-k-query-sharing-component --check-source-history

Direct portable command: /usr/bin/python3 -I -Werror -B verify.py, add -O for optimized mode. The wrapper invokes only the independent component checker and compares the complete scientific result. It does not execute the producer, original T checker, native/phase engine, economic certificate, compiler or complete caller. The first hosted run40070147658, attempt1, passed at this exact publication head: plan/onboarding/selection, registered bounded replay and committed-inputs-unchanged. These hosted executions are separate from the six local checks; they do not validate the written economics certificate, native/source-phase premises, complete caller or κ admission.

Credit

Retain peer original fused-T/balanced-J placement and implementation; root deferred-K identity/order audit; Astra actual-Q source/frame audit; independent literal checker and conservative28-call economic gate; occurrence-overlay/custody packaging; Dillon Amburgey/dillona #5402, Ali Romman #5411, zxv #5419, Dugongue's completion/coded normalizers, Cao Yifan, Cinna Davis, Jacob Alan Sussman and the retained native/Clifford/helper/BIT/analytic/compiler/precision/recovery lineage. The official comparator credits mightyOil's classical concave-order lineage and zxv's shared interface. Contribution by Chris R/Clear1nsight, with substantial OpenAI Codex assistance; Apache-2.0 and retained source-specific notices. No independent human or formal-kernel acceptance is claimed.

Open next questions

The useful next economic object is an actual global occurrence/owner ledger: prove each response reuse has the same chronological input, physical map, chart, phase, axes and lifetime; debit displaced helpers once; then test the complete changed paid/target profile. The fixed standalone H1-only profile cannot pass with at most27 additional deletions at the target C. A different caller needs its own bound.

A complete physical raw dual, canonical independent outputs, ordinary/precision/stock/tape/geometry application, compiler reserve and separate outer transfer remain open. Main functional inversion does not prove helper inversion. κ>=.0033 remains an unfunded research goal; selected metadata is unchanged. The peer's separately owned changed caller work continues.

Scientific handoff

HANDOFF

Research discussion / PR / artifact: This PR, research/deferred-k-query-sharing-component, PROOF.md, ECONOMICS.md and source-complete independent checker. Complementary local optimization/support; original T and global caller remain peer-owned.

Exact commit: Scientific 122d42143d1f3eca582240a095eec9e0591044a4; publication bb81dd1f8aa34d5ee89a43f3c19d4b50606d6287; canonical parent1a3. Export SHA256 b217332b48a0ea87e2c78871e95dfb79b838ecf115cab71e0d06d08f2095d8a0. LOCAL source, execution, committed and exported bytes are explicitly bridged; no unproved public ancestry is inferred.

What is established: Exact eight-H1 saving against T+sameQ120, unchanged392helpers, strict source-preserving correction, main endpoint/inverse and scoped algebraic main rawIT under retained premises; two original checks plus four package checks agree with no exclusions. Official relative-invoice preflight passes. Standalone all-C negative moment and restricted28-further-H1 necessary gate are separate written economic results.

What remains uncertain: Global reuse/caller and independent main targets, full physical helper/owned dual, ordinary/precision/stock/tapes, compiler/outer funding and κ. Native/source-phase premises are reused, not freshly replayed. The archive is byte-checked transport, not a new execution. Hosted CI remains separate.

Smallest useful next task: Independently review the new literal correction/Q-placement and exact cost delta, then bind an actual changed global ledger. Do not spend another construction round polishing the losing fixed standalone invoice.

Reproduction command and expected runtime: Registered command above, measured2.924s; direct portable normal/optimized1.208/1.410s, each under30s/256MiB. Declared-source-history check requires canonical commit history. Optional official comparator compares2321→2313H1 with the same392helper target profile; it performs no construction or root search.

Predecessor credit: Peer original T/placement; root/source-frame/independent-check/economic/packaging lanes; #5402/#5411/#5419 and full native/helper/Clifford/compiler/precision lineage above. Exact CI-navigation repair reused from #5420. Substantial OpenAI Codex assistance; no new selected κ or complete theorem claim.

[Clear1nsight]

The first hosted run passed at publication head bb81dd1f8aa34d5ee89a43f3c19d4b50606d6287: run40070147658, attempt1. Plan/onboarding/selection, registered bounded replay and committed-inputs-unchanged all passed. This hosted evidence is separate from the six local component checks and does not replay native/source-phase, economic, price or complete-caller engines, or establish a new κ.

Official signed-invoice preflight — exact relative saving, no new κ.

Research discussion / PR / artifact: This PR and the public seven-label handoff. The official comparator was run separately from the registered component checker; its input declarations are reproduced below.

Exact commit: Publication bb81dd1f8aa34d5ee89a43f3c19d4b50606d6287, scientific source 122d42143d1f3eca582240a095eec9e0591044a4. Comparator from canonical 1a3ced60b2f7a46bc70280a04f2eeb8ca027c700, scripts/compare_recursive_invoices.py, Git blob fda2a852e9937e42fe40df0707694465ca7c1b48.

What is established: One exact integer-only run returns uniformly_better for the declared same-interface comparison, delta paid −8H1 and zero target delta. Only392 unchanged actual helper outputs are credited; coded main fields receive no productive reward. For r^t,0<t<1, the relative net-cost change is exactly−8. Complete original input JSONs:

OLD.json:

{
  "schema": "integer-mult-recursive-invoice/v1",
  "contract": {
    "model": "same-current-source-Q120-balanced-J-local-component/v1",
    "rank_semantics": "H_r costs r^(1-C); only392 unchanged independent helper jobs credited; codedmain has no productive credit; ordinary work separate",
    "ambient_rank": 25,
    "boundary": "Same632original+9owned per-direction local endpoint (Du-Rv,JRv), with120currentqueries; conditional nativeABI, not complete compiler/caller funding"
  },
  "paid": {
    "1": 2321,
    "2": 412,
    "3": 510,
    "4": 127,
    "5": 40
  },
  "targets": {
    "4": 28,
    "7": 7,
    "8": 39,
    "9": 318
  }
}

NEW.json:

{
  "schema": "integer-mult-recursive-invoice/v1",
  "contract": {
    "model": "same-current-source-Q120-balanced-J-local-component/v1",
    "rank_semantics": "H_r costs r^(1-C); only392 unchanged independent helper jobs credited; codedmain has no productive credit; ordinary work separate",
    "ambient_rank": 25,
    "boundary": "Same632original+9owned per-direction local endpoint (Du-Rv,JRv), with120currentqueries; conditional nativeABI, not complete compiler/caller funding"
  },
  "paid": {
    "1": 2313,
    "2": 412,
    "3": 510,
    "4": 127,
    "5": 40
  },
  "targets": {
    "4": 28,
    "7": 7,
    "8": 39,
    "9": 318
  }
}

Relevant fields from the actual complete CLI report:

{
  "classification": "uniformly_better",
  "delta_paid": {
    "1": -8
  },
  "delta_targets": {},
  "signed_net_delta": {
    "1": -8
  },
  "hinges": [
    {
      "rank": 0,
      "value": 0
    },
    {
      "rank": 1,
      "value": -8
    }
  ],
  "rank_mass": {
    "delta": {
      "paid": -8,
      "paid_minus_targets": -8,
      "targets": 0
    },
    "new": {
      "paid": 5375,
      "paid_minus_targets": 2040,
      "targets": 3335
    },
    "old": {
      "paid": 5383,
      "paid_minus_targets": 2048,
      "targets": 3335
    }
  },
  "power_moment": {
    "exponent": "0 < t < 1",
    "new_minus_old_sign": "strictly_negative",
    "tariff": "r^t"
  }
}

What remains uncertain: The comparator authenticates input bytes and proves declared histogram order; it does not derive the source invoice, prove circuit legality/phase/ownership, price ordinary work, establish absolute profitability, or close compiler/outer transfer. Those boundaries remain as stated in the reviewed component. No new target, thin-response reuse or κ is inferred. The separate optimistic standalone ceiling is unchanged.

Smallest useful next task: Apply the new component only to an actual version/owner-correct complete caller invoice, and derive that caller's paid and target profiles before claiming funding. This relative−8 comparison does not fund an unrelated profile.

Reproduction command and expected runtime: python3 -B scripts/compare_recursive_invoices.py OLD.json NEW.json. Actual one-off guarded runtime0.101276681s,1,294,336B sampled peak,30s/128MiB limit, exit0/no termination; log SHA256 8ce5658dec21180c2240916ab41d6cb76e620e1ea2e8e38ddca26053b5bf8bd8. All four script/input/request byte+mode records stayed unchanged. Original input files were646 bytes each, old SHA256 d9e20d03403ccac0457d51faf915853bd226d3660a9fc6608006f54cb05f78d0, new ae9c07a153ccafeedd5db212bc854ce51f18f98a62699bf523a6d6e1da76074f. No normal/O duplicate, root search, Powers, native, phase, compiler or complete-caller execution was performed for this preflight.

Predecessor credit: Official shared comparator retains zxv's interface and mightyOil's classical concave-order lineage; exact component source retains peer original T, Dillon/Ali/native/helper/Clifford/analytic/compiler/precision lineage. Chris R/Clear1nsight with substantial OpenAI Codex assistance. This comment adds reproducible arithmetic evidence, not a new construction priority or selected-frontier claim.