Finite construction: two-sided CK compensation saves 8,798 beyond target forests (no new kappa)

research/complex-ck-two-sided/CLAIM.md

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+# Sprint claim: CK two-sided compensation (seed 38)
+
+- Track: complex supplier; OS-random assignment seed **38** (`secrets.randbelow(100)`).
+- Start: 2026-10-13 12:01:59 UTC. Expected finish: **2026-10-13 12:42 UTC** (23:42 Melbourne).
+- Exact base: `f567884aeb8851b6e794af1184119a3bfbe1e631`.
+- Selected record at base: reviewed conditional PR799, kappa `0.001661634653669567`.
+- Object: historical PR626 CK provider's frame-zero arbitrary-helper compensation.
+- Hypothesis: after a signed target-forest transform, disjoint signed helper shears
+  can reduce the complete compensation bill further. Reprice the transformed
+  matrix; do not add independent savings from PR807 and PR816.
+- Method: exact dyadic matrix arithmetic, a signed target forest, then a bounded
+  all-ordered-helper-pair/sign census and deterministic disjoint greedy selection.
+  Seed 38 diversifies forest/pair tie breaks. Charge preparation and restoration
+  on both sides, literal coefficient work, source reads, and unchanged children.
+- Expected deliverable: one executable finite circuit with exact replay and pins,
+  or a scoped negative result if the complete budget fails. No new kappa.
+- Candidates considered: X4 helper pairs (obvious follow-up to PR901); this
+  two-sided CK compensation (selected); JP8 coefficient routes (crowded by
+  PR793/811/837/839/882). This changes the search class, not only its seed.
+- Coordination: GitHub returned zero pinned issues. Local claim used. Refreshed
+  703 open PRs through #912 before claiming; read PR807/816/901/909 and relevant
+  accepted ledger/review. PR807 changes helpers alone; PR816 targets alone.
+  No pending source code is imported. Credit and exact predecessor pins will
+  accompany the result. Delegated work stays within this compensation scope.
+- Budget: at most first 8 minutes for orientation; final 10 minutes reserved
+  for verification and handoff.
+
+## Completed result (single claim update)
+
+Completed finite circuit construction: 106 target-forest edges and 112 disjoint
+helper pairs reduce the complete compensation bill from 49,624 to 11,965
+component primitives. Both full orientations save 75,318 real primitives,
+including 8,798 beyond the target-only forest. All 725 arbitrary input columns,
+both arithmetic engines, native frame/wrapper checks, 10 new and 25 inherited
+controls pass. Prefixes are 41/65 bits; denominator budgets remain 3/8 bits.
+No new kappa and no claim of joint optimality or global admission.
+
+Result: [exact receipt](EXPECTED.json), [construction proof](PROOF.md), and
+[validation/handoff](VALIDATION.md). Branch: `research/complex-seed38`.
+The final refresh found no pinned issue and 705 open PRs through #915; no
+overlapping two-sided CK contribution was found. PR807/816 are credited as
+precursors, with complete repricing rather than an additive savings claim.

research/complex-ck-two-sided/EXPECTED.json

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+{
+  "status": "FINITE_CK_TWO_SIDED_COMPENSATION_NO_NEW_KAPPA",
+  "base_commit": "f567884aeb8851b6e794af1184119a3bfbe1e631",
+  "seed": 38,
+  "source_pins_sha256": "5db1688947b52af69d4670c159b994e6ceb927f7a1fce0656d2459ad7dab9c2d",
+  "recipe_sha256": "a77b4cc1bdf70b52fb000cc75040afd253a63beb72139616232ebbfd58cbd437",
+  "columns": {
+    "logical": 716,
+    "private": 9
+  },
+  "search": {
+    "target_edges": 12544,
+    "helper_cases": 128524,
+    "profitable_helper_cases": 1525,
+    "target_basis_edges": 106,
+    "helper_pairs": 112
+  },
+  "panel_component_prices": {
+    "baseline": 49624,
+    "target_only": 16364,
+    "two_sided": 11965
+  },
+  "programs": {
+    "forward": {
+      "baseline": {
+        "real_primitives": 224938,
+        "prefix_l1": "920709848294",
+        "prefix_bits": 40,
+        "maximum_denominator_power": 3,
+        "program_sha256": "24d4fdd9641278242add4c3ed9843e138e04f6a54d067cf6b755f6bcba84978f",
+        "primitive_word_sha256": "76f540eb9b679eb33a9b22c7f1ad96063c70dd1e84171e5c42eb3e7f824da8ef",
+        "scalar_macros": 21936,
+        "primitive_counts": {
+          "add": 44127,
+          "clear": 42902,
+          "copy": 8,
+          "double": 5585,
+          "halve": 19499,
+          "negate": 348
+        }
+      },
+      "candidate": {
+        "real_primitives": 149620,
+        "prefix_l1": "1200150150114",
+        "prefix_bits": 41,
+        "maximum_denominator_power": 3,
+        "program_sha256": "46cbc67d4bf6768e7531a2c31f7a5105ef2f572d25045f0ce8877b41d8e30356",
+        "primitive_word_sha256": "228baefc17e57c5d499b4118af5f1d3336ce4a102eca82f2a8d7e43a65ab182b",
+        "scalar_macros": 15773,
+        "primitive_counts": {
+          "add": 31582,
+          "clear": 30576,
+          "copy": 8,
+          "double": 5374,
+          "halve": 6922,
+          "negate": 348
+        }
+      },
+      "real_saved": 75318,
+      "additional_real_saved_vs_target_forest": 8798
+    },
+    "backward": {
+      "baseline": {
+        "real_primitives": 224986,
+        "prefix_l1": "146068000389976309073/32",
+        "prefix_bits": 62,
+        "maximum_denominator_power": 8,
+        "program_sha256": "314b814a33d1339c7862112a4c927c19af0aee03dead0f841c983814a9f24d58",
+        "primitive_word_sha256": "ae56e8b527f88897d4b8be72f142666f5e159c424a567e61adfebd643a0260b8",
+        "scalar_macros": 21936,
+        "primitive_counts": {
+          "add": 44143,
+          "clear": 42918,
+          "double": 5585,
+          "halve": 19499,
+          "negate": 348
+        }
+      },
+      "candidate": {
+        "real_primitives": 149668,
+        "prefix_l1": "626977768061479717259/32",
+        "prefix_bits": 65,
+        "maximum_denominator_power": 8,
+        "program_sha256": "326571ffa80b1fc7c60a2c5316396cccfbac75e83913da9f0d5132f9da264f95",
+        "primitive_word_sha256": "60df568ec2923dfac35c53ca86135dcead61c33bd167fe69a8a94a1a709415e3",
+        "scalar_macros": 15773,
+        "primitive_counts": {
+          "add": 31598,
+          "clear": 30592,
+          "double": 5374,
+          "halve": 6922,
+          "negate": 348
+        }
+      },
+      "real_saved": 75318,
+      "additional_real_saved_vs_target_forest": 8798
+    }
+  },
+  "independent_recipe": {
+    "method": "Prim signed-forest minimum; exhaustive ordered signed helper-pair census",
+    "baseline_panel_price": 49624,
+    "target_minimum": 16364,
+    "helper_search": {
+      "cases": 128524,
+      "profitable": 1525,
+      "census_sha256": "7969fdd428e83a60a965c02b94ee906357ed53683fd705933f224214c0e069bf",
+      "gain": 4399
+    },
+    "complete_panel_price": 11965
+  },
+  "native": {
+    "checks": {
+      "forward": {
+        "sha256": "46cbc67d4bf6768e7531a2c31f7a5105ef2f572d25045f0ce8877b41d8e30356",
+        "events": 21093,
+        "scalar_macros": 15773,
+        "real_component_primitive_bound": 149620,
+        "paid_profile": {
+          "1": 2596,
+          "2": 552,
+          "3": 304,
+          "4": 160,
+          "5": 70,
+          "6": 8,
+          "8": 8
+        },
+        "all_columns": 716,
+        "private_centers_cleared": true,
+        "private_coefficient_stream_cleared_after_each_macro": true
+      },
+      "backward": {
+        "sha256": "326571ffa80b1fc7c60a2c5316396cccfbac75e83913da9f0d5132f9da264f95",
+        "events": 21093,
+        "scalar_macros": 15773,
+        "real_component_primitive_bound": 149668,
+        "paid_profile": {
+          "1": 2596,
+          "2": 552,
+          "3": 304,
+          "4": 160,
+          "5": 70,
+          "6": 8,
+          "8": 8
+        },
+        "all_columns": 716,
+        "private_centers_cleared": true,
+        "private_coefficient_stream_cleared_after_each_macro": true
+      }
+    },
+    "local": {
+      "forward": {
+        "all_exact_columns": 716,
+        "prefix_l1_upper": "1200150150114",
+        "prefix_bits_upper": 41,
+        "charged_payload_bits": 192,
+        "private_work_erased": true
+      },
+      "backward": {
+        "all_exact_columns": 716,
+        "prefix_l1_upper": "626977768061479717259/32",
+        "prefix_bits_upper": 65,
+        "charged_payload_bits": 192,
+        "private_work_erased": true
+      }
+    },
+    "paid_profiles": {
+      "forward": {
+        "1": 2596,
+        "2": 552,
+        "4": 160,
+        "8": 8,
+        "3": 304,
+        "5": 70,
+        "6": 8
+      },
+      "backward": {
+        "1": 2596,
+        "2": 552,
+        "4": 160,
+        "8": 8,
+        "3": 304,
+        "5": 70,
+        "6": 8
+      }
+    },
+    "negative_controls_rejected": [
+      "wrong_scale",
+      "missing_center",
+      "wrong_common_frame",
+      "wrong_child_rank",
+      "missing_pre_wrapper",
+      "missing_post_wrapper",
+      "wrapper_with_wrong_frame",
+      "wrapper_in_wrong_phase",
+      "wrapper_on_a_data_register",
+      "wrapper_on_a_target_register",
+      "wrapper_on_a_centre_register",
+      "hpe_pre_wrapper_resolved_to_full_recipe",
+      "hpe_post_wrapper_without_terminal_frame",
+      "hpe_post_wrapper_wrong_terminal_frame",
+      "hpe_tail_gate_at_full_frame",
+      "hpe_tail_climb_dropped",
+      "hpe_helper_exit_adapter_to_full",
+      "hpe_tail_gate_moved_into_full_cleanup",
+      "cold_hpe_pre_wrapper_replaced_by_identity_entry_adapter",
+      "cold_hpe_pre_wrapper_dropped",
+      "cold_hpe_post_wrapper_replaced_by_exit_adapter",
+      "cold_hpe_pre_wrapper_resolved_to_cold_full_convention",
+      "cold_hpe_wrapper_with_nonzero_entrance",
+      "cold_hpe_post_wrapper_wrong_terminal_frame",
+      "cold_hpe_premix_gate_before_pre_wrapper"
+    ],
+    "logs": {
+      "hpe_emit_local.py": [
+        "PASS emitted forward 21093 events",
+        "PASS emitted backward 21093 events"
+      ],
+      "hpe_audit_local.py": [
+        "independent emitted replay PASS forward",
+        "independent emitted replay PASS backward",
+        "PASS_INDEPENDENT_LOCAL_SCALAR_FRAME_AND_WRAPPER_REPLAY 25 controls rejected"
+      ]
+    }
+  },
+  "controls": {
+    "rejected": [
+      "omitted_target_preparation",
+      "omitted_helper_preparation",
+      "omitted_helper_restoration",
+      "omitted_target_restoration",
+      "reversed_target_preparation",
+      "reversed_target_restoration",
+      "wrong_helper_preparation_sign",
+      "wrong_residual_sign",
+      "cold_wrapped_helper_access",
+      "omitted_initial_work_clear"
+    ],
+    "omitted_target_preparation_passes_helper_only": true
+  }
+}

research/complex-ck-two-sided/NOTICE.md

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+# Attribution and license
+
+New contribution by **Ross Richardson (@RossRichardson)**, with substantial
+**OpenAI Codex assistance** for research selection, construction, code, proofs,
+verification and writing. A separate AI worker implemented the integer-dyadic
+checker and Prim/census check without importing the construction algorithm;
+another reviewed the two-sided identity and native interface. This is not
+independent human peer review. New files use the repository's **Apache-2.0**
+license; see `../../LICENSE`.
+
+The mechanism combines and reprices ideas from:
+
+- **David Awad, PR807**, restored CK helper pairs,
+  `b1a5c533a22c2665600102d872f6a84e0664a70d`.
+- **@dd-hemant, PR816**, signed CK target forests,
+  `133735a2cc2319c12ba5d786214b2217e083e7da`.
+- **Sricharan Vagvala, PR749**, rational JP8 restored target pairs; and
+  **Oscar Fennell, PR759**, binary target forests and superroot reduction,
+  as credited by PR816.
+
+No pending implementation is copied or vendored. The new construction and
+checker are written for this experiment. No additive combination of predecessor
+savings is assumed, and no priority claim is made for either individual basis
+mechanism.
+
+The unchanged retained inputs and native scripts carry their existing notices:
+**icekylinx**'s PR425/433 scalar/compiler lineage, **DreamingOfClouds**' framed
+extensions, **Jeremy Kothe**'s PR622 supplier and **Chafik Boukhalfa**'s PR626
+owner-repair package, with the earlier cold-end, frame, residual, source-gauge,
+physical-owner, bit-supplier and recurrence contributors recorded in the
+repository's `CONTRIBUTORS.md`. Those notices and source files remain unchanged.