Save six primitives in one signed JP8 continuation (no κ)

research/jp8-signed-continuation/README.md

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+# One signed JP8 continuation saves six scalar primitives
+
+This contribution was produced by Nick Petalas.
+
+Claim type: finite local circuit certificate with a scoped substitution proof.
+The historical PR626 JP8 forward fragment at zero-based event interval
+`[19709,19713)` has a shorter implementation than Ryan Haines's PR811
+positive-read compiler. Two cleared blocks cost 17 primitives per real
+component. One signed continuation costs 14. Applying it separately to the
+real and imaginary components saves exactly six real-component primitives.
+Every source read, shift, target update and boundary clear is counted.
+
+The recursive paid profile and productive targets are unchanged. This is a
+historical scalar-program improvement, with no new kappa or selected-frontier
+change. The search stopped at this first retained source-bound improvement;
+there is no wider census or optimality claim.
+
+## Exact fragment and construction
+
+The four consecutive full-frame cleanup events use source `s=L81` and distinct
+targets `a=L227`, `b=L230`, `c=L231`, `d=L232`:
+
+```text
+a += 3s/2
+b -= 3s/2
+c -= s/2
+d += 5s/2
+```
+
+The existing private work register is `w=L724`. Its initial value is arbitrary
+and its required exit value is zero. PR811's two blocks are
+`[19709,19711)` and `[19711,19713)`. The new literal program is:
+
+```text
+clear w
+w += s
+double w
+w += s
+halve w
+a += w
+b -= w
+w -= s
+c -= w
+halve w
+w += s
+double w
+d += w
+clear w
+```
+
+After the first five instructions, `w=3s/2`, independently of its initial
+value. The next two instructions perform the first two target updates. The
+new subtraction leaves `w=s/2`. After updating `c`, the inherited three-step
+positive route changes `s/2` to `5s/2`. Updating `d` and clearing `w` gives the
+stated complete map. Source and all other registers remain unchanged. This
+proves equality for arbitrary scalar inputs over the rationals or complexes,
+including arbitrary target and private-work inputs.
+
+The changed interface is the private-work clear between the two old blocks.
+The old four-instruction sequence `clear w; clear w; w += s; halve w`
+is replaced by `w -= s`, under the established entry value `w=3s/2`.
+The subsequent instructions are identical. There is no crossed child,
+adapter, phase or frame change, and no extra register. Equality at the
+fragment's complete boundary permits exact substitution into any unchanged
+surrounding scalar program. It does not establish a rounded physical caller.
+
+The exact work coefficient never exceeds three in absolute value in either
+program, and its finest intermediate dyadic denominator is four. Each target
+is updated once, by the same amount and in the same order. These exact prefix
+facts use cancellation. They do not imply that the predecessor's
+cancellation-free triangle majorant, whole-word precision receipt or rounding
+error bound transfers without a new calculation.
+
+## Evidence and reproduction
+
+Use CPython 3.12 and the standard library, from the worktree root:
+
+```sh
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -W error -B research/jp8-signed-continuation/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -I -O -W error -B research/jp8-signed-continuation/verify.py
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/research_package.py --package research/jp8-signed-continuation
+/Users/nick/git/integer-mult-bounds/.venv/bin/python3.12 -B scripts/check_research_commit.py --package research/jp8-signed-continuation --check-source-history
+```
+
+Substitute another CPython 3.12 executable elsewhere. Direct verification
+writes a generated hash-bound receipt to stdout, with marker
+`PASS_JP8_SIGNED_CONTINUATION`. It writes no files into the checkout.
+`WITNESS.json` is the circuit witness, not a claimed execution receipt.
+
+The verifier authenticates the three declared inputs, extracts exactly the
+four new application events, and uses only the parent constructor's two local
+lowerings. It runs no predecessor scientific verifier and does not recount
+the parent program. It checks the complete six-input matrix against a direct
+specification. A separate integer scalar interpreter executes both literal
+programs on all 15,625 fourfold-grid inputs per program. Seven semantic
+controls reject missing boundary clears, a missing or reversed subtraction,
+a wrong source, a wrong target sign and an endpoint-neutral work excursion.
+Normal and optimized execution use explicit checks.
+
+The matrix proof covers arbitrary inputs; the finite grid is corroboration.
+The interpreter does not execute native frame or phase operators. No whole
+supplier replay, selected cold replay, rounded induction, compiler, hosting,
+tape/storage pricing, stock proof, outer assembly, Lean or Docker run is
+included. All five selected framework assumptions remain. Independent human
+and formal proof-kernel review are unclaimed.
+
+## Sources and distinction
+
+The exact base is `7c49fe32c55de02c2c873655c804b16e4c3fef0a`, priority revision 8,
+selected PR6030. `SOURCES.json` pins the current catalogue and selected record
+as provenance, and the source program, PR811 constructor and README as live
+inputs. The task explicitly changes the scalar-to-moment card to this side
+result; it does not satisfy that card's moment-improvement acceptance gate.
+
+Ryan Haines's [PR811](https://github.com/CrocSwap/integer-mult-bounds/pull/811),
+head `b5c244c916dd0b30957332edad7ae7ae22b0eb9d`, supplies the positive-read
+compiler and this historical source application. Its positive transition
+search leaves signed reads outside scope. Its local code and credit are
+unchanged. Ryan's [PR830](https://github.com/CrocSwap/integer-mult-bounds/pull/830)
+supplies backward transposition context; this contribution makes no backward
+application claim.
+
+AmazedBot's [PR860](https://github.com/CrocSwap/integer-mult-bounds/pull/860)
+already studies signed continuation on CK. Signed shift/add arithmetic and
+that mechanism are predecessor work. The new result is the explicit shorter
+JP8 source fragment and its exact local application certificate. This is
+not a new general signed-digit method. Sagar Thakrar's PR696/723, Sebastien
+Taillieu's PR999, Philipp's PR882 and Michal Ciemiega's PR1223 change other
+standalone lowering menus. No superiority to every compiler or additive gain
+with those packages is claimed.
+
+Credit the retained Jeremy Kothe PR622/623, Chafik Boukhalfa PR626,
+icekylinx, Jeffrey Cox PR739, ellipsi2 PR722, Sagar Thakrar PR751 and the
+native/compiler/owner lineage recorded in the unchanged source README.
+New source, witness and prose are Apache-2.0. The public
+[advance claim](https://github.com/CrocSwap/integer-mult-bounds/discussions/1166#discussioncomment-19370136)
+states this investigation's boundary.
+
+## Implementation limits
+
+The verifier has no recursion and bounds words by 32 instructions, literal
+grid inputs by `5^6`, source events by 100,000 and JSON input sizes explicitly.
+Functions stay below 60 physical lines. Python and its exact arithmetic
+allocate dynamically; this is a managed-runtime deviation from Power of Ten
+rule 3. Source decompression and JSON parsing allocate before their payload
+size checks; the authenticated immutable input is the resource contract.
+The fixed, authenticated parent constructor is loaded through `runpy`; this
+is a bounded dynamic-code/dispatch deviation under rules 8 and 9 for replay
+only. It executes local lowering definitions, with no predecessor scientific
+entry point. The source-hash and direct replay commands above check these
+controls. A future untrusted-input service would need streaming/decompression
+caps and a declarative replacement for loading constructor definitions.
+No fixed-allocation or hard real-time verifier is claimed.
+
+## Open next questions
+
+Can a signed continuation be installed in one current complete scalar caller
+with a fully recomputed rounded prefix budget? It would connect an exact
+scalar saving to a current implementation. First extract one source-compatible
+boundary and its private-work contract, then charge every conversion and
+cleanup operation and derive its cancellation-free error bounds. Current
+source binding, native/private-work integration and a complete consumer bill
+remain blockers. This package reserves no follow-up.

research/jp8-signed-continuation/SOURCES.json

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+{
+  "schema_version": 1,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "files": [
+    {
+      "path": "certificates/selected-result.json",
+      "usage": "provenance",
+      "git_blob": "d59b5035e7b4cbaa9d688a1d32dd0d6eb79c466a",
+      "sha256": "9b8d0eea95b3bf0dfcb7938a732a6439b87a2685dec2a5ab9e525b3b34debbfa"
+    },
+    {
+      "path": "docs/research/agent-task-catalog.json",
+      "usage": "provenance",
+      "git_blob": "3404fbdd5e7529a0674eef26114b5071e4586cec",
+      "sha256": "ead6cdc9d0af6d58e8a49744d8ec8c7c15e13d2ba93c276c434bcf9b51b93a81"
+    },
+    {
+      "path": "research/community-k492-audit/pr626/replay/mixed-global/base/providers/jp8/LOCAL-PROGRAMS.json.gz",
+      "usage": "input",
+      "git_blob": "e22169a1633638213a5c63425a1919c7185f4c43",
+      "sha256": "fa0c196f65bd6ec1424fdf7d789f6972075c7bb02bf43f573ea85eafab31be98"
+    },
+    {
+      "path": "research/jp8-additive-coefficient-routes/README.md",
+      "usage": "input",
+      "git_blob": "adb9acc54157eb1ccd96cbac5836068fbc3fe5e3",
+      "sha256": "52fa53f25574f6b2b5e8c8a3c5acb225973693969d9b19fa812b7d9eb0ab2866"
+    },
+    {
+      "path": "research/jp8-additive-coefficient-routes/construct.py",
+      "usage": "input",
+      "git_blob": "0b996246d4ed3d86223fd45637952232284a88c0",
+      "sha256": "43b0fd819a8f8c02189aaa13c39b1c55f960c8b3c90cf4b8672499ead3cea3f0"
+    }
+  ]
+}

research/jp8-signed-continuation/TASK.json

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+{
+  "schema_version": 1,
+  "task_id": "scalar-to-moment",
+  "priority_revision": 8,
+  "base_commit": "7c49fe32c55de02c2c873655c804b16e4c3fef0a",
+  "original_card": {
+    "id": "scalar-to-moment",
+    "question": "Can a scalar/frame rewrite improve the complete signed moment through paid jobs, productive targets, or both?",
+    "starting_points": [
+      "docs/research/current-priorities.md",
+      "docs/research/research-family-status.md",
+      "certificates/selected-result.json",
+      "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md",
+      "docs/research/recursive-invoice-preflight.md"
+    ],
+    "methods": [
+      "Construct and independently check one source-bound instance of the stated first experiment.",
+      "Seek an exact counterexample or target-specific complete-budget obstruction to that same proposed change."
+    ],
+    "acceptance_gate": "Require a legal chronological rewrite and favorable complete signed target-minus-paid moment with all extra charges. Unchanged ADD counts or unchanged paid-call counts alone decide neither success nor failure. Compiler, native and outer admission remain separate obligations.",
+    "first_step": {
+      "command": [
+        "python3",
+        "-B",
+        "scripts/research_selected_baseline.py"
+      ],
+      "expected": "PASS_RESEARCH_BASELINE_BINDINGS_ONLY",
+      "inspect": "Read revision 8, the selected review and live exact-source handoffs. Then follow this card's bounded first_experiment.",
+      "scope": "Source-bound orientation only, not a supplier replay or theorem proof."
+    },
+    "first_experiment": "Construct one legal source-bound rewrite and compare complete before/after P and T. Charge restoration, source windows and owned helpers. A paid call need not disappear: a legal target split or rank redistribution may win. Stop if the signed moment is unchanged or the consumer repays the gain. Do not extend a scalar-only census on ADD counts.",
+    "bottleneck_link": "Judge the actual current supplier contract and complete signed target/paid bill; frozen-profile ceilings require an applicability proof.",
+    "allowed_variations": [
+      "One exact source head, helper/cut region or quantified proposition and changed hypothesis; check live handoffs first. Different seeds are not different scopes."
+    ],
+    "scope_change_triggers": [
+      "Changing source head, helper/cut domain, operation alphabet or caller boundary without recording the new scope.",
+      "Treating an archived proposal or local numerical pass as complete supplier admission."
+    ],
+    "overlap_terms": [
+      "signed moment",
+      "target split",
+      "rank exchange",
+      "scalar rewrite"
+    ],
+    "existing_checks": [
+      {
+        "scope": "PR #3998: consecutive A2 scalar contraction",
+        "evidence": "research/staged544-a2-graph-rewrite/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "389268a6b5e0373a3125d5c6fcd6995f4ea324f5",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4019: separated A2 sites with unchanged recursive histogram",
+        "evidence": "research/staged544-separated-a2/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "f408e09df300b575235f7f77f81948071397e16d",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4112: composition audit",
+        "evidence": "research/staged544-a2-composition-audit/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "205b7380656ba4b6316a8a493b1a3c679b8f7a0e",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "PR #4152: A1858 contraction audit",
+        "evidence": "research/staged544-a1858-contraction-audit/README.md",
+        "remaining": "A genuinely changed paid itinerary or a distinct independent audit; no default scalar-only expansion.",
+        "status": "author-checked",
+        "source_commit": "caaa14cde5962adc372fdca71f63d0f29e73c8b2",
+        "selected_record_sha256": "bb2eaa58647b353f88d0aec2eafb9d30df1be53589231b23e12ceef3e4bad129"
+      },
+      {
+        "scope": "Selected PR5599: complete helper-subspace construction and independent caller replay; five framework assumptions remain.",
+        "evidence": "docs/research/pr-intake-evidence/pr5599-completion/PROOF-REVIEW.md",
+        "remaining": "The next experiment must identify uncovered source-specific work. Successor archive intake does not transfer this admission.",
+        "status": "reviewed",
+        "source_commit": "09dd0965711ca7eeb169057a420abab1c9052137",
+        "selected_record_sha256": "2a0220e866417774606e0f991e41b9c1d26b1f43b97857238cf478dbc7d330b5"
+      }
+    ]
+  },
+  "scope_status": "changed",
+  "actual_scope": "Construct one shorter signed continuation for the fixed historical PR626 JP8 forward fragment [19709,19713), preserving its exact arbitrary-input map and private-work clearing.",
+  "scope_change_reason": "The first verified contribution is a local scalar-program improvement on PR811. It leaves the recursive moment unchanged and does not meet the original moment-improvement gate. No wider census follows it.",
+  "bottleneck_link": "Side result: reduces six charged real-component primitives in one exact historical scalar fragment. It does not improve the binding complex recursive bill or selected kappa.",
+  "budget_minutes": 60,
+  "stop_rule": "Stop at the first source-bound, exact signed continuation improvement; no route census or additional fragments.",
+  "outcome": "completed",
+  "evidence": "README.md gives the scoped substitution proof; verify.py regenerates the 17-to-14 per-component comparison from the pinned parent constructor, checks the new map, exact prefixes, literal grid executions and rejecting mutations.",
+  "author": "Nick Petalas",
+  "ai_assistance": "Independent human and formal proof-kernel review are unclaimed.",
+  "open_questions": [
+    {
+      "question": "Can a signed continuation be installed in one current complete scalar caller with a fully recomputed rounded prefix budget?",
+      "why_it_matters": "A historical exact scalar saving does not establish a usable current physical or precision improvement.",
+      "first_step": "Choose one current source-compatible same-source boundary, extract its private-work contract and price a single signed transition together with all conversion and cleanup operations.",
+      "blocked_by": "Current source binding, cancellation-free rounding/error budgets, native/private-work contract integration and a complete consumer bill are absent here."
+    }
+  ]
+}

research/jp8-signed-continuation/VERIFY.json

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+{
+  "schema_version": 1,
+  "status": "ready",
+  "python": "3.12",
+  "requirements": [],
+  "inputs": [
+    "research/community-k492-audit/pr626/replay/mixed-global/base/providers/jp8/LOCAL-PROGRAMS.json.gz",
+    "research/jp8-additive-coefficient-routes/README.md",
+    "research/jp8-additive-coefficient-routes/construct.py"
+  ],
+  "commands": [
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "Exact pinned fragment and parent lowering, six-column arbitrary-input matrix identity, literal integer-grid executions, scratch prefixes and rejection controls."
+    },
+    {
+      "argv": [
+        "{python}",
+        "-I",
+        "-O",
+        "-W",
+        "error",
+        "-B",
+        "{package}/verify.py"
+      ],
+      "timeout_seconds": 120,
+      "checks": "The same complete finite checks with Python assertions disabled."
+    }
+  ]
+}