Fuse P104 late delivery with residual cleanup for two actual consumers

research/p104-fused-late-cleanup/PROOF.md

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+# Fusing late FULL delivery with residual-based dirty cleanup
+
+## Result and predecessor boundary
+
+This is one explicit composition of two existing local constructions:
+PR3981's late FULL delivery (`cdb7dcf3f7e5f860714a1b12df4c7a5157d8ae3d`)
+and PR3943's compressed Q cleanup
+(`2cba526a4ebe0ef6c3c0143498adcf67dca97941`). The source-preserving variant also uses PR3940's frozen fused tail
+(`51ba88c007cfbcc3d9cf22dd321f5224be3a5bb1`). The encoded correction is PR3882's
+frozen builder (`9d56eeedbed5e3e9bbbc8c189d66f14cf15b6067`, publication head
+`d76586303e7036baa74f8deb2155038290174ffd`). The contribution is the source-bound
+fusion and its complete invoice, not a new discovery of either ingredient.
+
+The measurable target is fewer than 5472 unit ADDs with the same native mass
+2520 and exact old endpoint. The construction achieves **4704 unit ADDs**,
+with the same **2616 halves, 2616 doubles, and native mass 2520**. All 280
+independent input columns, all 72 arbitrary dirty helper returns, and the
+complete endpoint rows and formal frames are preserved. A second actual source-preserving consumer falls from5856 to5088 unit ADDs
+with2712 halves/doubles and the same native mass2520. This is a finite
+Gaussian-dyadic module identity, not a new multiplication theorem or kappa.
+
+## Literal source extraction and the fusion cut
+
+Use the original 4058-event native-channel witness. Its final 416 events,
+zero-based indices 3642 through 4057, are exactly
+
+    Q_k += D[k,i] X_i,
+
+with 52 nonzero coefficients per query, all ±2, at FULL. Extract D from these
+literal events. In the PR3882 pivot order
+`J=[0,1,3,6,22,31,93,103]`, set `T=D[:,J]`. The full exact matrix T is in
+RESULT.json; it has 32 nonzero entries, all ±2. For the actual Gram block
+`A=[[I,B],[B^t,B^t B]]`, direct exact multiplication gives
+
+    D = T [I B].
+
+This is checked against PR3943's unchanged T, but the cleanup coefficients
+are independently re-extracted from the main-branch witness. The verifier
+also checks the state produced by the actual PR3981 schedule, rather than
+assuming a possible query preparation.
+
+Remove the last 416 cleanup events from PR3981's generated word. Its remaining
+prefix includes all original public transports, its 104 retimed Y lifts, and
+all 416 late Q-to-Y deliveries. Each query was quartered for these unit reads
+and then doubled twice, restoring its value before the next step. At this
+precise cut all 280 roles are FULL and their normalized rows are
+
+    X=x,   Y=v=y+Ax,   Q=h-Dx,   G=h_G,   Dhelpers=h_D.
+
+Here h, h_G and h_D are independent arbitrary dirty inputs. They are not zero
+or source-dependent promises. The two meanings of D (cleanup matrix and
+register-family name) are distinguished above and in the verifier.
+
+## Chronology and reversible linear algebra
+
+Execute the actual PR3882 tail **without its initial 104 lifts**, because the
+prefix has already performed them. Its reads and writes are confined to X,Y.
+Writing `q=x_J+B x_N` and `w=x+y`, its endpoint is
+
+    X_J=q,   Y_J=w_J,   X_N=w_N,   Y_N=v_N.
+
+The residual donors X_J and query recipients Q remain FULL; X_N and Y_J
+occupy their indexed target hyperplanes. Q still equals h-Dx. Execute the
+actual PR3943 consumer: for each nonzero T[k,b], add the signed X_J donor to
+Q_k twice. This uses 64 unit ADDs, no scratch, no scaling, no transport, and
+leaves every donor unchanged. Since
+
+    Tq = T(x_J+B x_N) = Dx,
+
+it restores Q to h. The tail did not touch G or delivery helpers, so all 72
+dirty returns hold simultaneously. Every data endpoint equals PR3981 followed
+by the original correction after its old cleanup. The verifier compares all
+280 rows, including the retained residuals, rather than only the sum slots.
+
+The ordering is essential. Late Q-to-Y delivery must finish while the live
+queries still carry their source contribution; the quartered donors must be
+restored; the correction must then create the actual residual q before Tq is
+read. Running Tq cleanup earlier uses x_J rather than q. Running the old Dx
+cleanup after the correction attempts reads from consumed/non-FULL X_N.
+Neither incorrect reordering is silently admitted.
+
+## Source-preserving fusion at the actual PR3940 internal cut
+
+The unchanged `fused(J,N,B)` builder from PR3940 supplies a stronger matched
+source-preserving comparison than returning after the encoded exit. Its104
+initial Y lifts are again already present in the late-delivery prefix. Its
+remaining program is the actual sequence
+
+1. Pivot stream: X_J becomes q and Y_J becomes w_J; X_N remains x_N.
+2. Scatter `Y_N -= B^t q`, leaving Y_N=y_N. Each temporary half of a pivot
+   donor is restored by the builder's corresponding double.
+3. Inverse pivot stream: `X_J -= B x_N`, restoring x_J.
+4. `Y_N += X_N`, producing w_N; drop all104 Y to their indexed hyperplanes.
+
+Insert the same64-unit Tq cleanup **between steps2 and3**. Its exact internal
+cut is1360 tail operations after the removed104 lifts. The verifier compares
+the literal prefix against the frozen `pivot_stream + scatter` builders,
+checks every X_J donor equals the same exact q row as in the encoded variant,
+and checks all donors and Q recipients are FULL. It also checks Q still equals
+h−Dx. This excludes both reading a still-halved pivot and reading after the
+inverse stream has destroyed q. All X/Y operations otherwise remain unchanged.
+
+The matched baseline is the entire actual3981 word with its original Q cleanup,
+followed by this same3940 fused tail. The new whole word preserves its280 rows
+and frames, including every X_i=x_i at FULL, every Y_i=x_i+y_i in H_i, and all72
+dirty returns. Its chronological native subsequence is literally equal to
+that baseline's. The correction's scalar counts are1632 ADDs and200 each
+half/double:768 pivot-stream ADDs,384 scatter ADDs,384 inverse-stream ADDs,
+and96 sum ADDs. Therefore the complete matched invoices are
+
+| Source-preserving module | Unit ADDs | Halves | Doubles | Native mass |
+|---|---:|---:|---:|---:|
+| Late delivery + old cleanup + actual3940 fused tail |5856|2712|2712|2520|
+| Late delivery +3940 tail with internal Tq cleanup |5088|2712|2712|2520|
+
+This saves another768 ADDs under the same comparison convention, with no
+additional native work. Relative to the encoded fused result, source preservation
+costs384 additional ADDs and96 each half/double in these particular words.
+It does not require the192-native post-encoding return adapter. The later
+comparison with that adapter is context and an actual integration check;
+neither alternative is claimed optimal over all source-preserving programs.
+Moving the cleanup after step3 instead breaks all8 Q dirty returns, as an
+additional whole-word negative control confirms.
+
+## Physical contract and inherited native evidence
+
+Each new schedule has **exactly the same chronological native transport
+subsequence** as its matched reference (3981 plus3882 or plus3940), including every retimed lift and the
+correction's final drops. This is a literal ordered-event equality, not an
+inference from an equal histogram. No lift, descent, chart adapter, private
+register, or role change is added. The new 64 reads are scalar additions in
+a common FULL chart. The independent evaluator verifies every arithmetic
+entrance and every nested transport entrance and positive dimension tariff.
+
+With the inherited invariant `physical_r=Gamma_frame(r)*logical_row_r`,
+these scalar identities hold for arbitrary address functions over
+`Z[i,1/2]`. The old source and target chart operators retain exactly their
+existing meaning. In particular, equality of frame spans is not being used
+to donate an unproved physical basis change: the native event sequence itself
+is unchanged. PR3981's 104 lift recipes were bound to the ordered canonical
+bases from the native certificate and checked for signed Pauli action and
+exact phase. That phase evidence is inherited here, not freshly replayed.
+PR1991's full historical native realization and the final PR3882 physical,
+owner, global, precision and all-size qualifications remain as stated there.
+The PR3940 source-preserving tail likewise retains its stated native/admission
+qualifications. The present new verifier independently checks the complete scalar/frame
+composition; it does not claim a fresh native recipe audit.
+
+## Complete matched invoice
+
+Both sides use the same explicit scalar lowering: for an old coefficient
+p/2^s, halve its donor s times, perform |p| signed unit ADDs, then double it
+s times. New late-delivery batching and the correction's already batched
+scalings remain literal. This is a valid upper bound, not a scalar optimum.
+
+| Complete module | Unit ADDs | Halves | Doubles | Native mass |
+|---|---:|---:|---:|---:|
+| PR3981 + old cleanup + correction | 5472 | 2616 | 2616 | 2520 |
+| Fused prefix + early correction + Tq cleanup | 4704 | 2616 | 2616 | 2520 |
+| Difference | -768 | 0 | 0 | 0 |
+
+The removed 416 coefficients ±2 cost 832 unit ADDs and no scaling. Their
+replacement has 32 coefficients ±2, implemented by 64 unit ADDs. Thus the
+saving is exactly 832−64=768, with no unpriced return or donor restoration.
+All finite scalar counts are recounted from the actual joined event lists.
+The retained native profile is
+`{1:1282,2:58,3:86,4:104,5:48,6:24,8:8}`. Its rank sum is 2520.
+There is no private allocation, copy, or erase.
+
+For an actual source-preserving downstream contract, the verifier also
+appends PR3943's unchanged return adapter to the fused word. It restores
+all X_i=x_i at FULL and all Y_i=x_i+y_i in their indexed hyperplanes, with
+all 72 dirty helpers restored. This adapter adds its already-known 960 unit
+ADDs, 104 halves, 104 doubles and native mass192. The complete returned module
+therefore costs **5664 unit ADDs, 2720 halves, 2720 doubles and native mass2712**.
+This is an integration check of the actual inherited consumer, not a new
+192 lower bound or a claim that it is the cheapest source-preserving correction.
+The direct PR3894 I−A correction has a different consumer; its own complete
+matched scalar comparison and any optimality claim remain outside this result.
+The internal-cut3940 variant above is the actual source-preserving improvement
+proved here, with native2520 rather than this adapter route's2712.
+
+## Global gate and bounded stopping rule
+
+Under the unchanged favorable corrected two-axis contract of PR3954, calls
+number208, per-call endpoint progress is2312, and the anchor allowance is10816.
+Scalar fusion changes none of those native quantities. The necessary gate
+remains
+
+    208*(2520-2312)-10816 = 32448 > 0.
+
+Thus the retained complete native bill remains2997696 over denominator2965248.
+This local scalar improvement does not reopen that native gate or justify
+further dependent kappa optimization. Newly proposed one-axis/global completion
+contracts are separate research tasks; this package neither prices nor admits
+them. No selected-frontier change, universal obstruction, global owner theorem,
+or all-size admission is claimed.
+
+## Verification and controls
+
+The frozen PR3981, PR3943, PR3882 and PR3940 source exports are byte-identical to their
+recorded original Git blobs, with explicit source-head and SHA256 metadata.
+Only their named schedule/geometry builders are reused. A new sparse Fraction
+interpreter evaluates the actual joined words and formal frames on all 280
+independent columns. It separately checks cut states, actual residual donors,
+D=T[I B], data outputs, dirty returns, scalar lowering, and native subsequence.
+
+Eight semantic mutants reject: omitted compressed cleanup, cleanup before q
+exists, reuse of old cleanup after source consumption, double cleanup, omission
+of one unit update, failure to restore a quartered dirty donor, and correction
+before late delivery, plus source-preserving cleanup after q has been
+restored to x_J. Separate actual optimized CLI processes first validate
+each private fixture and then reject Boolean/float receipt types, duplicate
+keys, false savings, changed/missing source, or changed frozen tail bytes.
+Read-only official exports are preserved; only private test copies become
+writable. Assertions removable by Python optimization are not used to enforce
+these checks.

research/p104-fused-late-cleanup/README.md

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+# P104 fused late delivery and compressed query cleanup
+
+Combine the actual PR3981 copy-free late FULL delivery with PR3943's early
+correction and compressed Q cleanup. The source-bound composed word preserves
+all 280 input columns, every endpoint row/frame, and all 72 arbitrary dirty
+helper returns. **Unit ADDs fall from5472 to4704; native mass stays2520**, with
+2616 halves and2616 doubles unchanged. No private storage is introduced.
+
+The point is an executable fusion of already credited ingredients. The
+correction now creates residual `q=x_J+B x_N` while Q still equals `h-Dx`;
+the actual extracted factorization `D=T[I B]` permits64 unit ADDs to restore Q
+instead of the old832. The ordering and donor restoration are checked explicitly.
+An actual source-preserving variant inserts the cleanup inside PR3940's fused
+tail while q still exists:5856→5088 ADDs,2712 halves/doubles and native2520.
+This preserves all X=x FULL and Y=x+y in their hyperplanes. The inherited
+post-encoding return adapter also composes, costing5664 ADDs,2720 halves/doubles
+and native2712; this is contextual integration, not a new optimality claim.
+
+See [PROOF.md](PROOF.md), [RESULT.json](RESULT.json), [VERIFY.json](VERIFY.json).
+Run `python3.12 -B research/p104-fused-late-cleanup/verify.py` or the registered
+package launcher. Native transport events are literally unchanged; prior phase
+checks are inherited, not freshly replayed here. The old conditional two-axis
+gate still fails32448. No supplier, all-size result or selected-frontier claim.
+
+## Provenance and overlap
+
+Canonical main20ecf2891d80b5acf18d980b2164fb44ea7faa90, priority6, fetched and
+read at entry. The explicitly assigned task is this bounded composition; no
+new dependent native/kappa search follows the failed global gate. The overlap
+helper used702 open PR bodies including drafts, complete at08:30:14UTC on
+2026-10-19, with49 possible matches. It had no Discussion cache; the root
+coordinator separately checked live boards and posted the canonical scoped
+claim at https://github.com/CrocSwap/integer-mult-bounds/pull/3954#issuecomment-6263112891 .
+This is bounded overlap coverage, not a novelty certificate. The optional
+selected-frontier orientation command could not run in this sparse checkout
+because its unrelated selected ASSEMBLY archive is omitted; no full selected
+replay or successful baseline command is claimed.
+
+Credit Chris R / Clear1nsight's PR3981 late delivery, PR3943 residual cleanup
+and return adapter, PR3882 encoded correction, and PR3940's actual fused source-preserving tail. Unchanged builder exports record
+original heads, Git blobs and hashes; they require no unavailable unmerged
+commit in a main-only source export. Credit Rohan Arun's PR1972 witness,
+Chafik Boukhalfa's PR1991 native realization, Adam Gall's PR1940 delivery,
+icekylinx PR531 compiler and PR1862 interpreter lineage, and Josie Elliston,
+Sagar Thakrar, Douglas Colkitt and Dominik Scholz's E8/P104 work. PR3954's gate,
+PR3965's fixed-consumer audit, and PR3961/3962/3966's distinct boundary/coverage/
+gauge constraints remain credited. PR3956's adapter comparison is not repeated
+as a new result. Prepared with substantial OpenAI Codex assistance. Apache-2.0.
+
+## Open next questions
+
+An independently proposed changed global caller needs its own physical,
+entrance, ownership, coverage, precision and all-size invoice. First test that
+caller's full gate with the exact native profile before optimizing scalar
+cleanup further. The present result changes no native cost, so another local
+scalar tweak cannot resolve the retained two-axis obstruction by itself.