Research: lower selected complex scalar primitives by 22–25% (no new kappa)

research/complex-dyadic-lowering/CLAIM.json

@@ -0,0 +1,24 @@
+{
+  "track": "Complex supplier: scalar coefficient circuit",
+  "assignment_seed": 22,
+  "randomness": "Python secrets.randbelow(100), operating-system randomness",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "claimed_at_utc": "2026-10-13T04:10:00Z",
+  "expected_finish_utc": "2026-10-13T04:36:37Z",
+  "coordination": "No pinned issue exists; only open issue #650 requests Discussions. Scope recorded locally.",
+  "object": "Dyadic scalar-add primitive lowering in the selected PR626 CK and JP8 local programs, both orientations",
+  "method": "Replace clear plus leading-bit addition by copy; specialize unit coefficients to signed accumulation plus work clear. Exact rational symbolic replay and primitive recount, without changing scalar macros or frame events.",
+  "deliverable": "Executable lowering, finite verification receipt, proof of unchanged boundaries and prefix envelope, meaningful negative controls; no new kappa",
+  "candidates": [
+    {"task": "Invertible factory coordinate-total resynthesis", "disposition": "Rejected overlap with PR681 at 80d4edbc2d53f058787cb5c43bd0fc22c7e7fdff"},
+    {"task": "Selected butterfly pivot/frame scheduling", "disposition": "Rejected overlap with pivot-swap and entrance work in PR641/655"},
+    {"task": "Dyadic coefficient primitive lowering", "disposition": "Selected; changes the scalar implementation underneath fixed macro/frame words"}
+  ],
+  "prior_work_checked": [651, 679, 681, 683, 687, 667],
+  "prior_negative_results": "research/structural-gain/factory/README.md and research/experiment-log/README.md. No closed packet, hosting, or retiming search is reopened.",
+  "seed_use": "Seed 22 selects CK first and the 22nd distinct nonunit coefficient for mutation controls. All coefficients and all four programs are covered, with no randomized search.",
+  "status": "completed",
+  "result": "All four 716-column primitive replays and all 686 coefficient checks pass; 10 negative controls rejected. Saved real primitives: CK forward 55320/backward 55352, JP8 forward 56852/backward 56884. Paid profiles and kappa unchanged.",
+  "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/696",
+  "final_overlap_check": "513 open PRs through #693; no matching selected-word coefficient-lowering scope. Historical #411 credited; PR681 changes a factory scalar word. origin/main still equals the exact base."
+}

research/complex-dyadic-lowering/EXPECTED.json

@@ -0,0 +1,145 @@
+{
+  "controls": {
+    "coefficient": "-8403008",
+    "rejected": [
+      "missing_cleanup",
+      "missing_source_copy",
+      "wrong_sign",
+      "redundant_work",
+      "endpoint_neutral_prefix_growth",
+      "unit_dirty_work_not_cleared",
+      "nondyadic",
+      "zero_coefficient",
+      "source_alias",
+      "work_alias"
+    ]
+  },
+  "distinct_coefficients": 686,
+  "programs": {
+    "ck/backward": {
+      "additions": 21451,
+      "all_input_columns": 716,
+      "baseline_real_primitives": 224986,
+      "charged_payload_bits": 192,
+      "dirty_helper_columns_restored": 492,
+      "new_real_primitives": 169634,
+      "paid_profile": {
+        "1": 2596,
+        "2": 552,
+        "3": 304,
+        "4": 160,
+        "5": 70,
+        "6": 8,
+        "8": 8
+      },
+      "primitive_tags": {
+        "add": 24236,
+        "clear": 42934,
+        "copy": 30452,
+        "double": 11170,
+        "halve": 38998,
+        "negate": 696,
+        "subtract": 21148
+      },
+      "primitive_word_sha256": "e342c630489789aa7e2aa938d8740ffc63d267d2420994be902893e7d9b50bf4",
+      "retained_prefix_l1_upper": "146068000389976309073/32",
+      "saved_real_primitives": 55352,
+      "scalar_macros": 21936,
+      "unit_additions": 6225
+    },
+    "ck/forward": {
+      "additions": 21443,
+      "all_input_columns": 716,
+      "baseline_real_primitives": 224938,
+      "charged_payload_bits": 192,
+      "dirty_helper_columns_restored": 492,
+      "new_real_primitives": 169618,
+      "paid_profile": {
+        "1": 2596,
+        "2": 552,
+        "3": 304,
+        "4": 160,
+        "5": 70,
+        "6": 8,
+        "8": 8
+      },
+      "primitive_tags": {
+        "add": 23838,
+        "clear": 42918,
+        "copy": 30468,
+        "double": 11170,
+        "halve": 38998,
+        "negate": 696,
+        "subtract": 21530
+      },
+      "primitive_word_sha256": "16ae874e3352c4df265026f62db95359a30399f1edc4c1b151d564d71902380c",
+      "retained_prefix_l1_upper": "920709848294",
+      "saved_real_primitives": 55320,
+      "scalar_macros": 21936,
+      "unit_additions": 6217
+    },
+    "jp8/backward": {
+      "additions": 22219,
+      "all_input_columns": 716,
+      "baseline_real_primitives": 257280,
+      "charged_payload_bits": 192,
+      "dirty_helper_columns_restored": 492,
+      "new_real_primitives": 200396,
+      "paid_profile": {
+        "1": 2512,
+        "2": 400,
+        "3": 448,
+        "4": 160,
+        "5": 70,
+        "6": 8,
+        "8": 8
+      },
+      "primitive_tags": {
+        "add": 29176,
+        "clear": 44470,
+        "copy": 31992,
+        "double": 32576,
+        "halve": 39438,
+        "negate": 692,
+        "subtract": 22052
+      },
+      "primitive_word_sha256": "c71f7fd2d52031e730f3ed42e56e38878e5746c053d990aad9d6e5c0d55d2bbd",
+      "retained_prefix_l1_upper": "16753412757380464429924108070201913461/8388608",
+      "saved_real_primitives": 56884,
+      "scalar_macros": 22693,
+      "unit_additions": 6223
+    },
+    "jp8/forward": {
+      "additions": 22211,
+      "all_input_columns": 716,
+      "baseline_real_primitives": 257232,
+      "charged_payload_bits": 192,
+      "dirty_helper_columns_restored": 492,
+      "new_real_primitives": 200380,
+      "paid_profile": {
+        "1": 2512,
+        "2": 400,
+        "3": 448,
+        "4": 160,
+        "5": 70,
+        "6": 8,
+        "8": 8
+      },
+      "primitive_tags": {
+        "add": 29050,
+        "clear": 44454,
+        "copy": 32008,
+        "double": 32576,
+        "halve": 39438,
+        "negate": 692,
+        "subtract": 22162
+      },
+      "primitive_word_sha256": "21bdebedaf5ef43d0a9149e56d15e6287c87d5031bcfaad13973fb5c24a662fe",
+      "retained_prefix_l1_upper": "4536094588619580433782972610869617/281474976710656",
+      "saved_real_primitives": 56852,
+      "scalar_macros": 22693,
+      "unit_additions": 6215
+    }
+  },
+  "status": "PASS_COMPLEX_DYADIC_LOWERING"
+}

research/complex-dyadic-lowering/README.md

@@ -0,0 +1,165 @@
+# Smaller dyadic circuits for the selected complex suppliers
+
+This finite circuit improvement reduces the scalar primitive bill of the
+selected PR626 complex programs by 22.1–24.6%. It replaces coefficient work
+inside each scalar macro, preserving the exact macro, its frame and its source
+and target registers. It does not claim a new κ or a measured runtime speedup.
+
+| Provider | Orientation | Original real primitives | Replacement | Saved |
+| --- | --- | ---: | ---: | ---: |
+| CK | Forward | 224,938 | 169,618 | 55,320 |
+| CK | Backward | 224,986 | 169,634 | 55,352 |
+| JP8 | Forward | 257,232 | 200,380 | 56,852 |
+| JP8 | Backward | 257,280 | 200,396 | 56,884 |
+
+These counts include all scalar macros in each complete emitted local program,
+including preconditions, compensation, centers and cleanup. They count both real
+components of the complex streams. They exclude the unchanged recursive children,
+frame adapters and residual wrappers, exactly as the original
+`real_component_primitive_bound` field does.
+
+## Reproduce
+
+From a checkout containing this contribution, with Python 3.11+ and no external
+dependencies:
+
+```sh
+python3 -B research/complex-dyadic-lowering/verify.py
+```
+
+Expected:
+
+```text
+PASS_COMPLEX_DYADIC_LOWERING programs=4 columns=716 savings=55320,55352,56852,56884 controls=10
+```
+
+The command is offline and writes no files. `--json` prints the deterministic
+receipt after checking it against [EXPECTED.json](EXPECTED.json). It verifies
+source hashes before replaying; gzip pins cover decompressed payload bytes.
+It can be run from another working directory by using the script's absolute path.
+
+## Circuit and cost
+
+For a nonzero dyadic coefficient `q = ±a/2^k` in reduced form, a scalar macro
+updates `T ← T + qS`. The existing binary Horner implementation first clears
+private work `W`, then adds `S` for the leading binary digit of `a`. Both
+instructions together set `W = S`, even for arbitrary initial `W`. The
+replacement uses one copy instruction for that assignment and retains every
+remaining binary digit, halving, signed accumulation and final work clear.
+
+For `q = ±1`, the replacement is simply `T ← T ± S; W ← 0`. The clear is still
+charged, so this circuit does not assume a clean private input. Both replacements
+have the complete three-register map
+
+```text
+(T, S, W) → (T + qS, S, 0).
+```
+
+The original cost per real component is
+`3 + floor(log2(a)) + popcount(a) + k`. Copy initialization saves one primitive
+for every nonunit coefficient. The unit replacement costs two primitives,
+instead of four. Thus a program with `A` additions, of which `U` have unit
+coefficients, saves exactly `2(A + U)` real-component primitives.
+
+The executable replacement is [lower.py](lower.py). Its primitive vocabulary is
+clear, copy, doubling, halving, negation and signed addition. Scale macros retain
+their original signed-power-of-two lowering. Each primitive stays at the scalar
+macro's frame. No source is temporarily modified; no helper, source access,
+frame change, center copy, restoration or recursive child is added or omitted.
+The existing two real coefficient-work streams suffice.
+
+## Prefix bound and substitution argument
+
+For a nonunit coefficient, the new copy reaches precisely the old state after
+the leading addition. The rest of the instruction sequence is identical. Each
+new register value therefore occurs in the old prefix trace, including the
+arbitrary initial private-work value.
+
+For a unit coefficient, the target reaches its old final value directly. The
+source remains unchanged. Work retains its initial value until the clear.
+Each of these register values also occurs in the original trace. This proves
+containment of the maximum over prefixes and registers; it does not assert
+entrywise domination of simultaneous transfer matrices.
+
+The argument holds for arbitrary real or complex inputs and correlated input
+values. In particular, it preserves the inherited maximum-row norm bound.
+The verifier also reconstructs the original nonnegative scalar/Horner envelope
+from the full macro stream and matches the pinned independent replay's exact
+`prefix_l1_upper`. Its existing 192-bit charged payload allowance is retained.
+This is an exact-arithmetic circuit argument. The all-size rounding and tape
+interfaces remain inherited, as they are in the selected result.
+
+Replacing a macro by a circuit with the same source, target and cleared-work
+boundary preserves every following macro's inputs. Induction over the fixed
+event stream then preserves the complete scalar program. Frame events,
+normalization wrappers, center lifetimes and recursive calls are unchanged.
+The existing geometric and physical admission is inherited from the pinned
+selected supplier; this package does not independently prove it.
+
+## Evidence and limits
+
+[verify.py](verify.py) expands every scalar macro into primitives and executes
+those primitives with exact rational sparse rows. Each of the four programs
+checks all 716 input columns, including 492 arbitrary dirty helper columns,
+plus an arbitrary coefficient-work input column. It verifies the required
+forward or backward shear, restored helpers, and cleared private registers.
+The imaginary component uses the same real-coefficient circuit, so the exact
+linear identity applies separately to it.
+
+For all 686 distinct addition coefficients, a separate three-register check
+compares every candidate register row with the complete reference Horner trace.
+This includes the initial state. It checks the full boundary and exact primitive
+count. The receipt records hashes of the expanded primitive words, their
+operation counts, unchanged paid profiles and inherited prefix bounds.
+
+Ten controls reject missing cleanup, missing initialization, a wrong sign,
+unnecessary work, excessive intermediate growth with a restored endpoint,
+uncleared private dirt for a unit coefficient, a nondyadic coefficient, zero,
+and source/target or source/work aliasing. The growth control must fail the
+prefix check specifically; the unnecessary-work control must fail the count.
+
+This is deterministic complete coverage of these four frozen programs and their
+686 coefficients. There is no randomized circuit search and no optimality claim.
+Seed 22 selects the first provider and a coefficient for mutation controls; it
+does not stand in for coverage. The general leading-bit proof above is distinct
+from the finite replay and does not formalize the multiplication theorem.
+
+The paid profiles and assembly parameters are unchanged, so the accepted
+conditional κ remains `51110230636731/31250000000000000`, or
+`0.001635527380375392`. This package supplies an executable local lowering and
+an independently reviewable receipt. It does not replace the selected emitter,
+regenerate its certificates, or change the accepted frontier.
+
+## Provenance and sprint scope
+
+Base commit: `66849e1475c930fd7732b1a0067ffee7e1e95f60`.
+[SOURCE-PINS.json](SOURCE-PINS.json) pins every consumed source, the original
+lowering and invoice code, and the selected record. The selected PR626 head is
+`660de893d27bb7abd1d5b01b1640207528a5c851`; its construction descends from PR622
+at `f69477f4f6d3c7eb1f740b166881bffed4ffa9f6`.
+
+Credit goes to icekylinx for the scalar operation and coefficient-work lineage
+through PR425/433/531, Jeremy Kothe for the K492 construction and schedules,
+Chafik Boukhalfa for the selected PR626 packing, and the predecessors retained in
+the [maintainer review](../../docs/research/community-k492-review.md), including
+DreamingOfClouds' cold-helper construction and Rohan Arun's recurrence correction.
+The retained bit supplier is eumemic's PR543.
+
+Eumemic's historical [PR411](https://github.com/CrocSwap/integer-mult-bounds/pull/411)
+at `f58d95f2c5da03445e704ea9c72cc55df9e68190` already used paid copy, halving,
+accumulation and clear for quarter/eighth coefficients. It is related prior work,
+not a code dependency. This contribution specializes the fixed selected macro
+streams and covers all their coefficients, arbitrary private dirt and prefix
+containment. It makes no priority claim for copy-based coefficient preparation.
+
+Current [PR681](https://github.com/CrocSwap/integer-mult-bounds/pull/681), reviewed
+for overlap at `80d4edbc2d53f058787cb5c43bd0fc22c7e7fdff`, resynthesizes an
+87-operation factory window into 35 scalar operations. That changes a scalar
+word. This contribution reduces the primitive cost inside unchanged macros and
+does not depend on PR681. PR667 concerns exact logarithm evaluation. Raw-face
+sharing, cold-end scheduling and closed packet-factory searches are not reopened.
+
+The [local claim](CLAIM.json) records seed 22, the three candidate tasks and the
+absence of a pinned sprint issue. Contribution by Sagar Thakrar / `thakrarsagar`,
+with substantial OpenAI Codex assistance in research, implementation, proof
+writing and review. New files are under the repository's Apache-2.0 license.

research/complex-dyadic-lowering/SOURCE-PINS.json

@@ -0,0 +1,16 @@
+{
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "selected_source_head": "660de893d27bb7abd1d5b01b1640207528a5c851",
+  "hash_semantics": "SHA256 of decompressed payload for gzip; exact bytes otherwise",
+  "files": {
+    "certificates/selected-result.json": "b3bf402f31a69bde0629936a9b569bed48281568d7b16d5fba120b5311ea1f53",
+    "research/complex-k492-owner-repair/code/hpe_emit_local.py": "7e4a6fbc38c8228157b6311457d1496bf460291393043932d2c365f004f77805",
+    "research/complex-k492-owner-repair/code/invoice_allcold.py": "141bd2fd58bbfb5b8d0fc8f56f61c45586d5608a5af3487c6b883dd987f998ec",
+    "research/community-k492-audit/pr626/replay/mixed-global/base/providers/ck/LOCAL-PROGRAMS.json.gz": "854f17274092263dc25e60367f4cd0d29f60a8446becd17cc1883ebed7a97900",
+    "research/community-k492-audit/pr626/replay/mixed-global/base/providers/ck/LOCAL-CHECKS.json": "059c4e59142bdf5c19dc7c0afebcddfec28e6e60cbc7299b8bdcc624afbc0cbe",
+    "research/community-k492-audit/pr626/replay/mixed-global/base/providers/ck/INDEPENDENT-LOCAL-REPLAY.json": "ecefb9e661301d8081522be68bbe6640e175c011eb1177f643383d193c6fb2f0",
+    "research/community-k492-audit/pr626/replay/mixed-global/base/providers/jp8/LOCAL-PROGRAMS.json.gz": "efe45ce7fb025a6f53cc9eb54e951ac2211a5ed927e689a049e4f68ca680654b",
+    "research/community-k492-audit/pr626/replay/mixed-global/base/providers/jp8/LOCAL-CHECKS.json": "0fad744aa863eedb288a9f87b1c23225a36b316b6275cc3b1bcedd42afe28a67",
+    "research/community-k492-audit/pr626/replay/mixed-global/base/providers/jp8/INDEPENDENT-LOCAL-REPLAY.json": "cb2f99ed351925dd35434b73de16f4085884fe81a35a69e1c7ce2d5e96cb975b"
+  }
+}

research/complex-dyadic-lowering/VALIDATION.md

@@ -0,0 +1,41 @@
+# Validation receipt
+
+Validated locally on macOS on 2026-10-13, based on
+`66849e1475c930fd7732b1a0067ffee7e1e95f60`.
+
+| Command | Result |
+| --- | --- |
+| `python3 -B research/complex-dyadic-lowering/verify.py` | PASS on Python 3.14.8 |
+| `python3.11 -B -O research/complex-dyadic-lowering/verify.py` | PASS on Python 3.11.15, all checks remain active without assertions |
+| `make selected-record-check` | PASS, selected source inventory and exact κ unchanged |
+| `git diff --cached --check` | PASS, only this research package is added |
+
+The deterministic evidence is in [EXPECTED.json](EXPECTED.json). Both Python
+runs match it, including all four primitive-word hashes. The package makes no
+wall-clock performance claim. The original and replacement primitive counts
+refer to the same pinned complete scalar inputs.
+
+A minimal committed archive of the seven package files and nine pinned source
+files also passes under Python 3.11.15 with `-O`, invoked by absolute script path
+from an unrelated working directory. This checks that no untracked file, local
+dependency, repository import or original checkout path is required.
+
+An additional scoped AI worker reviewed the algebra, operation vocabulary,
+source binding and written scope. That review identified the need to compare
+prefixes per register, including the initial dirty-work row. The implementation
+now performs that exact comparison. This is AI review, not independent human
+peer review or a formal proof assistant result.
+
+The final overlap refresh inspected 513 open PRs through #693 and fetched
+`origin/main`, which remained at the base commit. PR681 changes a factory's
+scalar word; this package changes primitive lowering beneath unchanged scalar
+words. Historical PR411 is credited for its coefficient microcircuits. PR667
+checks logarithm intervals, PR688 composes bit circuits, and PR693 audits signed
+block extraction. None is a dependency of this result. No pinned sprint issue
+was present at either coordination check.
+
+Not run: repository-wide `make verify`, cold selected-construction replay,
+Linux CI or Lean. This standalone research package does not modify generators
+or selected certificates. The focused primitive replay and selected-record
+check cover its changed behavior without regenerating unrelated artifacts.
+The geometric, compiler, hosting, rounding and tape contracts remain inherited.