P104 #5718 cache delivery cannot save the tested centre charges

research/p104-cross-call-paid-reuse/README.md

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+# Earlier P104 answers do not fund these eight separately delivered centre replacements
+
+**Local-only checked result; no new κ.** This binds the internal paid outputs
+of PR5718's first two actual LOCAL invocations, at caller events **0 and 3**,
+instead of testing only their input rows. All 3,426 local paid outputs have
+exact coefficient rows, instruction versions, frames and owned epochs. The
+two invocations use **536 different independent helper columns each**. Their
+main inputs are expanded into all 32 original raw caller columns, with the
+actual stage-1 routes and native operators.
+
+The named initial target is call-event3, local-event13609:
+`MOVE owned744, frame559 -> frame593`, of rank seven. Its last logical write
+is SCALE13607, following COPY13606 from the current version of173. A difference
+in **call3 helper173 alone** leaves every call0 answer zero and every available
+destination-frame observation zero, but changes this answer by
+`(1/2) S1 Phi593 phi`. This is a nonzero full native field. It cannot be replaced
+by combinations of old-call answers and those destination-frame values.
+
+The adjacent bounded domain is the other seven rank-seven owned queries in
+the same invocation. A complete optimistic cost screen additionally allows
+**any subset of earlier paid outputs in call3**, provided each retained value
+is separately transported to the requested output chart before recombination.
+No such subset improves the H7 charge, for any tariff `Hr=r^t`, `0<t<1`.
+This is a restriction on that explicit delivery protocol, not on joint
+transport, arbitrary native recombination or every changed consumer.
+
+## Exact maps and observation contract
+
+`results/QUERY-MAPS.json.gz` is a factorized exact map certificate, not a list
+of query signatures. Its 3,426 complete local rows are instantiated twice using
+machine-readable `native_input_bindings`. Every paid output records its source
+version, output version, last logical write, INIT epoch, rank, old/new frame and
+every nonzero public coefficient. Source names retain invocation and owner.
+Owned entrance values are initially arbitrary and are removed only by the
+literal owned INIT/CLEAR contract. The independent literal walk verifies every
+one of753 public/owned endpoint columns and all scalar coframes and lifetimes.
+
+Write `Phi_f` for the pinned canonical nine-axis frame, `Cq` for the translation
+root at portq and `S1=C_e9 ... C_e16`. If the literal right-boundary rows0,1 give
+raw inputs `A,B`, call0 logical main inputs are `X=Cq^-1 A`, `Y=B`.
+The actual resident outputs and wrapper are
+
+```
+U = H9 X
+V = Cq^-1 H9 (Y+X)
+second raw input = (V, -Cq^-2 U).
+```
+
+The literal stage-1 contacts then give logical main inputs
+`P_rho(q) Cq^-1 (X+Y)` and `-P_rho(q) Cq^-1 X` at the routed physical owner.
+The104 actual involutive routes swap the pinned eight orthonormal
+q-perpendicular axes with fresh axes9..16 and fixq. The verifier checks416
+exact Fourier phase-polynomial identities, including the translations and
+wrapper signs. Scalar coefficients stay outside tensor powers.
+
+Consequently a query row with main coefficients `c_r,c_(r+112)` has, for each
+raw caller columnj, the stage-1 operator terms
+
+```
+(c_r-c_(r+112))*right[0,j] * S1 Phi_f P_rho(q) Cq^-2
+             + c_r*right[1,j] * S1 Phi_f P_rho(q) Cq^-1.
+```
+
+Its helper term is `c_h S1 Phi_f h1(h,I)`, where the normalized helper is
+`h_s(h)=(S_s Phi_initial(h))^-1 H_s_raw(h)`. The machine substitution includes
+this inverse source gauge, so raw helper columns are explicit too. Call0 uses
+`H0_raw(h,g)`, a different independent input even when the register number agrees. Before a MOVE use
+`f=old`; after it use `f=new`. These rules, the complete right boundary,
+input substitutions and source-bound Clifford circuits specify the full
+maps without materializing enormous dense265-axis matrices. Other axes are
+spectators under the retained caller contract.
+
+## Exact quotient and complete delivery screen
+
+First grant every call0 answer, at every owner, with unlimited retention and
+even free transport. Grant all main information at the requested output chart.
+Also retain every earlier call3 paid output already in that chart and every
+current field there. On differences supported only on fresh call3 helpers,
+all call0 answers and all granted main information vanish.
+
+After removing the common invertible native prefix, ordinary recombination
+is an exact rational row-span question. The kernel witnesses below annihilate
+every remaining ordinary observation. They remain witnesses even if arbitrary
+linear actions on the available destination-frame fields are allowed: zero
+fields stay zero. No distinction-of-functions assumption is used.
+
+| Local event | Owned role | Frames | Fresh-helper difference | Nonzero response |
+| ---: | ---: | --- | --- | --- |
+|13609|744|559→593|`e173`|`1/2`|
+|13620|745|543→594|`e151`|`1/2`|
+|13631|746|531→595|`e146-e34`|`-1/2`|
+|13640|747|591→597|`e133`|`-1/2`|
+|13660|748|518→598|`e21`|`-1/4`|
+|13673|749|267→599|`e34`|`1/4`|
+|13688|750|517→600|`e21`|`1/4`|
+|13703|751|477→601|`e21`|`-1/4`|
+
+Each scalar response is multiplied by its full `S1 Phi_new` operator. The
+eight centre maps are independently checked with the retained native compiler
+and Gaussian interpreter, including absolute phases. The first map is also
+checked on all512 central basis columns. Independent interpretation also checks
+7,976 nine-axis cache-cost tableaux and997 actual17-axis alignment tableaux.
+This witnesses actual query outputs,
+not only source INPUT continuity.
+
+For the stronger screen, a retained prefix answer at frameF is delivered by
+the exact canonical operator `Phi_new Phi_F^-1`. Its Gaussian rank is computed
+from the full signed tableau. Any ordinary monomial normalizers are included
+in that native map. All acquisition, retention, normalizers, scalar arithmetic,
+main corrections and cleanup are optimistically free. Thus a failure cannot
+be repaired merely by pricing those obligations more carefully.
+
+There are1,195–1,228 actual earlier paid outputs at the eight cuts. Every
+strict improvement over H7 necessarily satisfies `sum r_i <= 6`, because
+`sum r_i^t >= (sum r_i)^t` for `0<t<1`. Zero-rank alignments are exactly the
+literal output frame and are already in the ordinary quotient. At each cut
+there are at most two rank-one alignments. This reduces the entire subset
+question to:
+
+- One or two other answers: exact projective residual grouping tests all
+  possibilities with rational coefficients, including non-dyadic coefficients.
+  No survivor. This grants more coefficients than a legal dyadic word permits.
+- Three rank-two answers with no rank-one answer: for the first four queries,
+  the target is outside the span of **all** rank-two answers. For the last four,
+  exact basis-coordinate support bounds give74,45,25,17 uncovered target
+  coordinates, while one answer covers at most2,2,2,3. Even three cannot cover
+  the target. Dense earlier-centre coordinate vectors are granted free before
+  forming this support bound.
+- One or both rank-one answers, plus at most two rank≥2 answers: condition on
+  each of the three possible nonempty rank-one subsets, grant its whole span,
+  debit its rank, and repeat the exact two-answer test. No survivor.
+
+Four rank≥2 jobs already cost more than H7. Repeated copies of one snapshot
+do not add an information direction. These cases exhaust separately aligned
+snapshot subsets under the necessary rank budget. The receipts retain every
+coordinate map and every conditioning choice.
+
+This does **not** cover mixing different snapshots in an intermediate chart
+before a shared paid job, noncanonical matrix-valued recombination, new
+ordinary reads from other frames, source-consuming changes, changed helper
+contracts or a weaker terminal consumer. It is not a physical lower bound for
+all P104 implementations.
+
+## Positive relaxation, controls and adjacent main query
+
+The full call0 paid history has scalar rank744. Erasing native maps makes
+the main-only `X0+Y0` target reconstructible from earlier paid answers. The
+receipt supplies and rechecks the exact combination; distinct answers are
+therefore not presumed independent. Illegally identifying H1 with H0 makes
+the first centre appear reconstructible too, with a393-answer combination.
+The actual namespace binding rejects that stale identification.
+
+A real two-version identity also passes:
+`703(after13610)-703(before13610) = owned744(after13609)`.
+The future13610 value is rejected as an input to the13609 replacement.
+A synthetic sum of two actual low-rank paid outputs is discovered by the
+two-cache generator, so the search has a constructive discovery control.
+Wrong global phase and an unpaid nonzero frame retag are rejected.
+
+As a distinct adjacent candidate, call3 local9733 is the pure-main
+`MOVE role0, frame0 -> frame249`, rank one. Grant the entire desired logical
+`X0+Y0` snapshot in every one of997 earlier paid-output frames, ignoring the
+cost of reconstructing it. Exact17-axis native alignment still costs at
+least H1; frame128 attains that minimum. Thus one-snapshot or typed cache-tree
+delivery cannot improve the removed H1 job, even before retention/read costs.
+This says nothing about a jointly shared job serving several changed outputs.
+
+## Complete invoice and obligations
+
+The complete source invoice is independently rebuilt from the local word and
+literal18-call controller and compared with PR5718's RESULT:
+
+```
+66,348 paid jobs; 12,976 productive fields; rank surplus760.
+local paid:    2184 H1 +459 H2 +495 H3 +92 H4 +159 H5 +22 H6 +15 H7
+local targets: 2 H1 +5 H2 +91 H4 +6 H5 +6 H7 +15 H8 +411 H9
+```
+
+Deleting one named call3 centre would grant `Delta paid=-H7`, `Delta targets=0`.
+The tested protocols cannot earn that allowance. **Realized paid and target
+deltas are both zero.** Every original/helper target, owned clear and caller
+job remains required. No cache program was emitted or given productive credit.
+The adjacent main cache's best possible recursive saving is zero.
+
+The pinned source reports221,474 local scalar units and a184,647,552 complete
+ordinary upper bound under10^9. Those are source figures, not new replayed
+ordinary tariffs. Actual new COPY/retention, every read, route, dirty return,
+restoration, cleanup, hosting, compiler and outer obligations are **unknown or
+unrun** because no improving candidate survived. Unknown costs are not zero.
+No new κ or full multiplication theorem is claimed. No selected cold replay,
+Lean, Docker, heavy full native replay or compiler/outer replay was run.
+
+## Reproduction and source status
+
+From the repository root, Python3.12 standard library:
+
+```sh
+python3.12 -B scripts/research_package.py --package research/p104-cross-call-paid-reuse
+```
+
+The registered serial normal and optimized commands rederive all maps,
+quotients, native ranks, support certificates, invoices and controls and compare
+the entire decompressed JSON receipts. Direct command:
+
+```sh
+python3.12 -I -B research/p104-cross-call-paid-reuse/experiment.py
+```
+
+`--write` regenerates only this package's two result files. It never edits
+frozen sources. CPython3.12.8/macOS arm64 was used for the registered replay;
+initial exploration used3.14.5. Timings are not proof fields.
+
+Canonical main was refreshed to `de5ec2e7a6074068452f45b1a191b5c72832df4a`,
+priority8; selected κ remains `.00310045`. PR5718's exact head is
+`a1534ac45401c9a9c80c07aa65c89e00e33594f8`, claiming `.00311024570`.
+It was archive-merged at15:22:41Z on October26; that does not select or admit
+its claim. Live Discussion5600 additionally reports an unpublished
+`.00311301600` construction; it was read as provisional overlap, not executed.
+The checkpoint searched312 open PRs with complete pagination and25 most
+recently updated Discussions with three recent comments each. Cached complete
+overlap is older and explicitly labelled. Unpublished work and arbitrary diffs
+remain outside that coverage.
+
+The managed latest-main checkout failed twice on missing promisor blobs.
+This clean managed branch therefore starts at `df0137efd35e11b4445734bf612bdd4c7ebc330c`;
+latest guidance was read through Git and the exact scientific inputs remain
+the specified PR5718 source. Every consumed byte is pinned in `SOURCES.json`.
+No shared checkout or predecessor artifact was edited. No public post or PR
+was made.
+
+## Open next questions
+
+The next reuse experiment must change the delivery protocol. At call3
+local13660, specify one intermediate frame, actual earlier paid-answer
+versions, a chronological gather and **one shared final native job** to
+frame598. Compare its full paid bill against H7 before implementing scalar
+cleanup. First test exact fresh-helper availability, including helper21, and
+then all original/main columns. Separately delivering more snapshots is closed
+by the certificate above; another larger separate-cache census is not useful.
+Shared transport, retention, every read and final clears need a concrete
+allowance. A favorable scalar span alone does not justify an implementation
+campaign. `TASK.json` records this scoped handoff and stop rule.
+
+## Significance for researchers
+
+The missing internal-output extraction is now available. Earlier paid
+answers can have full scalar information while failing a later versioned
+obligation or its actual native delivery price. The result closes one natural
+source-specific completion protocol and identifies the changed transport
+premise needed to reopen it. It does not turn finite failed searches into a
+universal obstruction.
+
+Credit [flyingviper](https://github.com/flyingviper)'s
+[PR5718](https://github.com/CrocSwap/integer-mult-bounds/pull/5718),
+[Ali Romman](https://github.com/aliromman)'s
+[PR5713](https://github.com/CrocSwap/integer-mult-bounds/pull/5713), and the full
+native/P104/caller/compiler lineage retained in `inputs/NOTICE5718`.
+The completed predecessor at local commit
+`1f51164a1dba5b9cb7639d3b760d2a0660931f63`, both earlier information-reuse reports
+and the controller input ledger are credited in `SOURCES.json` and unchanged.
+The existing paid-history-quotient, centre-history-innovation and
+gaussian-cache-reuse packages supply the scope and classical module/transport
+principles. [PR5647](https://github.com/CrocSwap/integer-mult-bounds/pull/5647)
+is constructive precedent, not transferred proof. New source binding and finite
+checks prepared for [zxv](https://github.com/zxv) with substantial OpenAI Codex
+assistance; no subagents, independent human review or formal-kernel proof.
+Apache-2.0.