Coalesce a P104 owned copy: one fewer field and twelve fewer scalar units (no κ)

research/owned770-descent-pruning/PREDECESSOR.json

@@ -0,0 +1,12 @@
+{
+  "author": "DreamingOfClouds",
+  "credit": "The retained word is DreamingOfClouds' contribution, extending the PR6030/PR5907 words and Ali Romman's PR5827, Mason Hale's PR5811, and the credited P104 lineage. This export preserves the original bytes. Apache-2.0.",
+  "git_blob": "69b70ee50c697b185ebf585fbe69f2487af32d1d",
+  "head": "4f3b67e7c37ae270da9584033132866d0cf63e42",
+  "path": "research/p104-root-relay-descent-2/WORD.json.gz",
+  "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/6144",
+  "readme": "https://github.com/DreamingOfClouds/integer-mult-bounds/blob/4f3b67e7c37ae270da9584033132866d0cf63e42/research/p104-root-relay-descent-2/README.md",
+  "repository": "DreamingOfClouds/integer-mult-bounds",
+  "sha256": "c71985d96bf3d4a35aae111aaba87e376f7367efb4a5686278ef293732757533",
+  "size": 119901
+}

research/owned770-descent-pruning/PROOF.md

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+# Coalescing the last-read owned copy
+
+This contribution was produced by Nick Petalas. Apache-2.0.
+
+## Claim and source
+
+The claim is a finite exact circuit certificate and a scoped substitution
+proof. It does not assert a new exponent saving, a smaller peak-space bound,
+or a complete multiplication theorem.
+
+The input is DreamingOfClouds' PR6144 word at
+`4f3b67e7c37ae270da9584033132866d0cf63e42`. `PREDECESSOR.json` records the
+original path, Git blob, SHA256 and credit. The byte-identical exported word
+is retained in this branch's history. Ali Romman's PR5827 `local.py` is already
+on canonical main and is used unchanged. The source word's conditional
+supplier and framework claims are cited, not independently audited here.
+
+All event indices below are zero-based indices in the retained input.
+
+## General substitution
+
+Suppose an owned field S contains x, and an initialized owned field D receives
+COPY D,S followed by SCALE D,q. Suppose that after this COPY the old S has no
+use except a later CLEAR. Replace the COPY and D's initialization by SCALE S,q;
+execute D's continuation on S; clear S where D was cleared; delete the old
+S CLEAR. Require that S is available before the continuation starts, and that
+the continuation does not read the old S separately.
+
+Immediately after the scaling, the substituted S and old D have equal values
+and frames. Every subsequent continuation operation has the same coefficient,
+frame and value operands after renaming. Induction over the continuation proves
+equality of every other field and the substituted D value. The unread old S
+does not influence another field. Both constructions return all owned fields
+to the erased state. This is an exact linear argument over any coefficient
+field containing q. Its use here is over the dyadic rationals.
+
+The substituted lifetime starts at the old S initialization and ends at the
+old D erasure. While the two lifetimes previously overlapped, the new one
+occupies one field. Elsewhere it occupies at most their former union. Thus
+this substitution cannot increase live owned occupancy. This statement alone
+does not imply that the global peak falls strictly.
+
+## Literal application
+
+Old S is role 791, initialized at event 13473 in frame 549 and assigned the
+value x of role 173 by event 13474. Its only subsequent reads are
+
+```text
+13475  ADD 121,791,1/2,549
+13659  COPY 770,791,1,549
+```
+
+Its only remaining use is CLEAR at event 15591 in frame 549. There are no
+hidden reads or writes. `construct.py` checks this complete use list.
+
+Old D is role 770. The adjacent events at 13658 through 13661 initialize it,
+copy x, scale by 1/2 and start its descent from frame 549 to 553. Its
+continuation ends with CLEAR in frame 593 at event 15424. It has exactly one
+initialization and no use outside that lifetime. The continuation never reads
+old 791. Therefore the substitution lemma applies with q = 1/2. The new
+scaling occurs just before the old descent, after the retained read at 13475.
+
+The constructor removes old role 770 from the owned inventory. For every
+remaining old role r, the new label is r when r < 770 and r-1 when r > 770.
+Uses of old 770 first become old 791, then become new role 790. Only opcode
+role positions are renamed; frame IDs and coefficients are unchanged.
+
+All public initial and final frames, ports, productive outputs and arbitrary
+public input coordinates are identical. Initial arbitrary owned contents
+cannot affect the result because every reached owned lifetime initializes
+before use. The new source-owned lifetime is initialized once and cleared at
+the continuation's old endpoint. Both exact row replay and reverse-column
+replay check the resulting word in full.
+
+## Exact account
+
+The removed INIT costs 2 scalar units, COPY with coefficient 1 costs 8, and
+CLEAR costs 2. The same single SCALE by 1/2 remains and costs 2 in either
+program. Net savings are 12 scalar units and three events. The original
+source-owned CLEAR disappears, and the continuation CLEAR now clears the
+substituted field.
+
+Literal enumeration gives
+
+```text
+events                22818 -> 22815
+local scalar units   189658 -> 189646
+declared owned fields    29 -> 28
+owned lifetimes          31 -> 30
+peak live owned fields   13 -> 13
+```
+
+Every MOVE keeps its entry frame, exit frame and ownership flag. Its complete
+native operator is therefore the same prescribed operator after role
+renaming, including its scalar phase. No new native frame pair is introduced.
+Every public endpoint is retained, so every productive rank is retained.
+The complete local paid histogram is unchanged and equals
+`{1:2215, 2:457, 3:496, 4:99, 5:164, 6:8, 7:9, 8:1}`.
+Consequently this edit supplies no new signed-moment or kappa gain.
+
+## Verification boundary
+
+The finite checker verifies all 798 columns and 636804 matrix coefficients
+of the edited word using the retained sparse forward and dense reverse
+implementations. Nine mutation controls cover missing initialization, scaling,
+clear, descent and read; wrong scaling sign; hidden source use; a changed COPY;
+and incorrect source inventory. Normal and optimized runs retain the checks.
+
+The semantic native operator list is unchanged; no native operator replay,
+complete caller, compiler, outer ledger, rounded error analysis, Lean or Docker
+run is part of this result. In particular the retained caller's reserve is
+not changed to 28 by this package. All five framework assumptions remain.
+The rounded numerical equivalence of copying and subsequently scaling an
+existing field is a separate implementation obligation.

research/owned770-descent-pruning/README.md

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+# Coalesce an owned P104 copy and save twelve scalar units
+
+This contribution was produced by Nick Petalas. Apache-2.0.
+
+A new exact word coalesces owned register 770 with its source register 791 in
+DreamingOfClouds' [PR6144](https://github.com/CrocSwap/integer-mult-bounds/pull/6144)
+word. After its last frame-549 read, 791 performs 770's continuation itself.
+The duplicate INIT, COPY and CLEAR disappear. The public boundary and every
+paid and productive rank remain unchanged.
+
+```text
+Local scalar units   189658 -> 189646
+Events                22818 -> 22815
+Owned fields             29 -> 28
+Owned lifetimes          31 -> 30
+Peak live owned fields   13 -> 13
+```
+
+This is a **finite exact circuit certificate and scoped substitution proof**.
+There is no new kappa, strict peak-space reduction, supplier admission or
+complete multiplication theorem. [PROOF.md](PROOF.md) gives the all-input
+substitution argument, exact event anchors, prices and remaining obligations.
+
+The initial target was an interior descent-stage deletion, taking the
+read-rerouting question of JosieElliston's
+[PR6136](https://github.com/CrocSwap/integer-mult-bounds/pull/6136).
+No paid-profile stage deletion was obtained. The first smaller improvement
+was shipped instead. Frames 553 and 1047 remain in the substituted trajectory.
+This changes owned lifetime identity, rather than repeating PR6136's chart-only
+search or the earlier fixed-word scalar resynthesis. The complete cost profile
+and boundary are retained, so no dependent construction expansion is proposed.
+
+## Reproduction
+
+From the repository root, with CPython 3.12 and no third-party packages:
+
+```sh
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -I -B research/owned770-descent-pruning/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -W error -I -O -B research/owned770-descent-pruning/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/owned770-descent-pruning
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/owned770-descent-pruning --check-source-history
+```
+
+A clean `python3.12` may replace that local interpreter path. Direct output is
+`PASS_OWNED_LIFETIME_COALESCENCE columns=798 coefficients=636804 controls=9 scalar_saved=12`.
+The registered replay runs both ordinary and optimized checks.
+
+`construct.py` emits the complete word from the unchanged retained input.
+The verifier checks all arbitrary-input endpoint and ownership conditions with
+Ali Romman's unchanged main-branch checker, including a separate dense reverse
+check. It enumerates every literal scalar price and paid rank, compares native
+frame-boundary multisets, and rejects nine faults. `RESULT.json` is generated
+by this verifier and binds all package files by SHA256. To regenerate a receipt
+outside the checkout, pass `--receipt-out /absolute/scratch/RESULT.json`.
+
+The retained input is byte-identical to the PR6144 word at
+`4f3b67e7c37ae270da9584033132866d0cf63e42`.
+[PREDECESSOR.json](PREDECESSOR.json) records its original path, blob, size and
+hash. It is retained in publication ancestry, so replay does not fetch an
+unmerged commit or depend on a shared local object cache. The predecessor's
+supplier result is cited; its verifier stack is not rerun as this contribution.
+
+## Limitations
+
+The edited word has 798 logical input columns because one owned coordinate is
+removed; all 770 public inputs and their exact endpoints are retained. The
+existing physical caller's conservative owned reserve is not reduced. Peak
+occupancy remains thirteen. There are no new frame pairs, and the formal
+native operators are unchanged after renaming, but their actual implementation
+is not rerun. Caller/compiler/outer, rounded numerical analysis, the selected
+cold replay, Lean and Docker are unrun. The five framework assumptions remain.
+Independent human and formal proof-kernel review are unclaimed.
+
+This verifier uses bounded finite programs and managed Python allocation.
+The input has 22818 events and 799 original role coordinates. Its largest dense
+matrix has 798 by 798 entries. The one authenticated checker import is the only
+dynamic import. These are explicit Python allocation and import deviations
+from the Power of Ten rules. The existing frozen checker is unchanged.
+
+## Open next questions
+
+- Can a read-rerouting construction actually omit frame 553 or 1047 from this
+  trajectory? Start with the exact readers 169 and 206, preserve their other
+  meetings and price the complete changed route. Their current routes do not
+  permit a direct move to the neighboring owned frame.
+- Can the actual caller use the reduced declared inventory? First bind its
+  alias allocation and lifetime schedule to the 28-field word. The unchanged
+  global peak and caller reserve prevent claiming physical memory savings here.
+- Does a specified rounded implementation admit the same lifetime substitution
+  with a no-larger error budget? Bind actual COPY/SCALE and erasure semantics;
+  exact rational equality alone does not settle that numerical question.
+
+## Credit
+
+DreamingOfClouds supplies PR6144 and its owned-relay descent, extending that
+author's PR6143, PR6030 and PR5907 words. Ali Romman supplies PR5827 and the
+unchanged exact checker, building on Mason Hale's PR5811 and the P104 lineage
+back through Pierre-Loic Doulcet's PR5565. JosieElliston supplies PR6136's
+read-rerouting question. The native, helper, controller and framework
+predecessors retain their original credit and notices. Last-read register
+coalescence is a standard compiler technique. The contribution here is this
+literal legal P104 substitution and its exact complete-word certificate.

research/owned770-descent-pruning/RESULT.json

@@ -0,0 +1,110 @@
+{
+  "after": {
+    "events": {
+      "ADD": 18423,
+      "CLEAR": 30,
+      "COPY": 22,
+      "INIT": 30,
+      "MOVE": 3449,
+      "SCALE": 861
+    },
+    "paid": {
+      "1": 2215,
+      "2": 457,
+      "3": 496,
+      "4": 99,
+      "5": 164,
+      "6": 8,
+      "7": 9,
+      "8": 1
+    },
+    "scalar_units": 189646
+  },
+  "before": {
+    "events": {
+      "ADD": 18423,
+      "CLEAR": 31,
+      "COPY": 23,
+      "INIT": 31,
+      "MOVE": 3449,
+      "SCALE": 861
+    },
+    "paid": {
+      "1": 2215,
+      "2": 457,
+      "3": 496,
+      "4": 99,
+      "5": 164,
+      "6": 8,
+      "7": 9,
+      "8": 1
+    },
+    "scalar_units": 189658
+  },
+  "claim_type": "finite circuit certificate and scoped substitution proof",
+  "constructed_word_payload_sha256": "27039a0d408cafbe25b7b571dadcfb4f335faab8fab2d276aad1426530ef009a",
+  "edited_events": 22815,
+  "limits": [
+    "No new kappa or paid-profile improvement.",
+    "Peak owned occupancy remains thirteen.",
+    "Rounded, native, physical caller and all-size admission are not replayed."
+  ],
+  "local": {
+    "endpoint_coefficients": 636804,
+    "helpers": {
+      "1": 14,
+      "2": 8,
+      "3": 4,
+      "4": 107,
+      "5": 14,
+      "6": 2,
+      "7": 9,
+      "8": 19,
+      "9": 385
+    },
+    "owned_fields": 28,
+    "owned_lifetimes": 30,
+    "paid": {
+      "1": 2215,
+      "2": 457,
+      "3": 496,
+      "4": 99,
+      "5": 164,
+      "6": 8,
+      "7": 9,
+      "8": 1
+    },
+    "paid_rank_mass": 5952,
+    "peak_owned_fields": 13,
+    "public_inputs": 770,
+    "real_scalar_allowance": 189646
+  },
+  "rejection_controls": {
+    "hidden_source_use": true,
+    "missing_clear": true,
+    "missing_descent": true,
+    "missing_first_read": true,
+    "missing_half": true,
+    "missing_source_init": true,
+    "wrong_copy_anchor": true,
+    "wrong_half_sign": true,
+    "wrong_inventory": true
+  },
+  "source_hashes": {
+    "PREDECESSOR.json": "0e3124a5a565f9252c03bc0b66d890e20a4b93c8dd4f2214e50b47385fee7127",
+    "PROOF.md": "e0c32bcfa71ee2e21f258311935b5c7c243dd177f555f2ddc860fb2bcef2d105",
+    "README.md": "54776bf8039dfc2cb96e77cc5bde62d3eca8cbc0c6ac64f9a39d16a5813a5131",
+    "SOURCES.json": "d3790bfecd02d5d067ad4cae4d532e9e7f883944f12729c7dd0dbc11235cf31a",
+    "TASK.json": "75c1d3e8a0d98c4400c90b10caea28ae637069d73fde5f38117e6f8d935d913f",
+    "VERIFY.json": "3fd3ba5ce00eedc9a7377e0a773380068e9129e08ea0778f53bdae6ae825bb06",
+    "construct.py": "8f498c94e5ffd06b3a7aae5c36f7c47597ccf37ac9eba580ef998dbe905a1809",
+    "inputs/pr6144-WORD.json.gz": "c71985d96bf3d4a35aae111aaba87e376f7367efb4a5686278ef293732757533",
+    "verify.py": "df28f65652d4bf00ef7bd918b5a7cc10c2a6d3ef4e7a280875f42713112515e1"
+  },
+  "status": "PASS_OWNED_LIFETIME_COALESCENCE",
+  "transpose": {
+    "arithmetic": "Dense integer rows with binary denominators; reverse chronology",
+    "coefficients": 636804,
+    "columns": 798
+  }
+}

research/owned770-descent-pruning/SOURCES.json

@@ -0,0 +1,38 @@
+{
+  "base_commit": "721c03822c421b7f7fcbb2598993b947c4d88419",
+  "files": [
+    {
+      "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
+      "path": "certificates/selected-result.json",
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+      "usage": "provenance"
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+      "path": "docs/research/agent-task-catalog.json",
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+      "usage": "provenance"
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+    {
+      "git_blob": "b7be846b10c4c54a4e1558d7b563bc8c3a170223",
+      "path": "research/p104-unread-path-resynthesis/local.py",
+      "sha256": "7201df8e32f5c99f7403150e8664042322037906088bc754c67293a241368597",
+      "usage": "input"
+    },
+    {
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+      "path": "research/owned770-descent-pruning/inputs/pr6144-WORD.json.gz",
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+}