Finite complex construction: two-sided Markowitz LPR cleanup refactorization on U8 (-2,580 macros, -37,320 real prims per orientation, seed 30, no new kappa)

research/u8-cleanup-markowitz-lpr-seed30/CLAIM.json

@@ -0,0 +1,54 @@
+{
+  "track": "20-39: Complex supplier: improve one specific circuit, frame schedule, decoder, or paid recursive profile",
+  "assignment_seed": 30,
+  "base_commit": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "status": "completed",
+  "pr_url": "https://github.com/CrocSwap/integer-mult-bounds/pull/1119",
+  "selected_frontier_certificate": {
+    "path": "certificates/selected-result.json",
+    "sha256": "a1324455ccdf7261df660e3748374a6680fdbe15c97a7161cf30c9d0ab49cd8f",
+    "kappa": "1661960547713947/1000000000000000000"
+  },
+  "candidate_tasks_evaluated": [
+    {
+      "id": 1,
+      "title": "Partial E4 -> E5 entrance-promotion reversion inside one 4-helper group [659, 661, 662, 663] of U8 to fill T37 rank-1 idle gaps",
+      "status": "scoped_negative_finding_recorded",
+      "summary": "Reverting m in {1, 2, 3} helpers of [659, 661, 662, 663] from E5 (dim 5) to E4 (dim 4) forces the 12 bipartite delivery gates B[420..431] into {656, 657, 658, 660} to split between frames E4 and E5, splitting the single rank-4 climb (1 -> 5) on {656, 657, 658, 660} into (1 -> 4 -> 5) and yielding local profile deltas {1:+2, 2:+1, 3:+3, 4:-3} (m=1) and {1:+2, 2:+2, 3:+4, 4:-4} (m=2), which strictly worsen the complex moment."
+    },
+    {
+      "id": 2,
+      "title": "Frame-0 premix refactorization at the head of section A in U8",
+      "status": "ruled_out_in_favorable_budget_check",
+      "summary": "The frame-0 premix prefix of section A in U8 comprises only 57 scalar macros (482 real primitives per orientation) with small coefficients (max_num = 2, max_den = 2), offering negligible circuit savings."
+    },
+    {
+      "id": 3,
+      "title": "Two-sided Markowitz LPR (R^{-1} P L^{-1}) Schur-complement refactorization with Weyl-group signed cycles for full_frame_cleanup on the selected U8 complex supplier word",
+      "status": "completed_positive_circuit_improvement",
+      "summary": "Replaces the 6,105-macro one-sided dyadic Gauss-Jordan high_inverse in U8 full_frame_cleanup with a 3,525-macro two-sided Markowitz R^{-1} P L^{-1} factorization with Weyl-group signed cycles (seed=30, trial=16, swap_pen=6, scale_pen=0), cutting cleanup macros by 2,580 (-42.26%), cleanup real primitives by 37,320 per orientation (-54.31%, or -74,640 across the forward+backward pair), maximum cleanup numerator from 131,646 to 8, and backward prefix L1 bit bound from 72 bits to 54 bits (-18 bits, 210,704x reduction) while preserving all 728 exact columns, native frames, paid recursive profile, and residual adapter recipes."
+    }
+  ],
+  "search_domain": {
+    "rng": "random.Random(30)",
+    "trials": 40,
+    "swap_penalty_grid": [3, 4, 5, 6],
+    "scale_penalty_grid": [0, 1],
+    "stopping_rule": "Evaluate exactly 40 deterministic trials seeded by assignment seed 30 (plus deterministic grid sp in {2,3,4,5,6}, scp in {0,1} without tie-breaking noise) and select the word minimizing lexicographically (real_component_primitives, scalar_macros).",
+    "completed_coverage": "All 10 deterministic grid points and all 40 seed-30 trials completed; minimum attained at seed=30 trial=16 (swap_pen=6, scale_pen=0) with 3,525 scalar macros and 31,394 real-component primitives per orientation."
+  },
+  "deliverables": [
+    "research/u8-cleanup-markowitz-lpr-seed30/CLAIM.json",
+    "research/u8-cleanup-markowitz-lpr-seed30/CLAIM.md",
+    "research/u8-cleanup-markowitz-lpr-seed30/PROOF.md",
+    "research/u8-cleanup-markowitz-lpr-seed30/RECIPE.json",
+    "research/u8-cleanup-markowitz-lpr-seed30/SOURCES.json",
+    "research/u8-cleanup-markowitz-lpr-seed30/EXPECTED.json",
+    "research/u8-cleanup-markowitz-lpr-seed30/verify.py",
+    "research/u8-cleanup-markowitz-lpr-seed30/independent.py",
+    "research/u8-cleanup-markowitz-lpr-seed30/test_package.py",
+    "research/u8-cleanup-markowitz-lpr-seed30/VALIDATION.md",
+    "research/u8-cleanup-markowitz-lpr-seed30/NOTICE.md",
+    "research/u8-cleanup-markowitz-lpr-seed30/README.md"
+  ]
+}

research/u8-cleanup-markowitz-lpr-seed30/CLAIM.md

@@ -0,0 +1,26 @@
+# Sprint Claim — Seed 30 (Track 20–39: Complex Supplier)
+
+- **Track & Seed:** `20–39: Complex supplier: improve one specific circuit, frame schedule, decoder, or paid recursive profile` (OS random seed: **`30`**)
+- **Base Commit:** `abdc6a7002abdbcd9e21bfc5e1a795784deacfdf`
+- **Submitted PR:** [`CrocSwap/integer-mult-bounds#1119`](https://github.com/CrocSwap/integer-mult-bounds/pull/1119)
+- **Selected Frontier Certificate:** `certificates/selected-result.json` (conditional $\kappa = 1661960547713947 / 10^{18} = 0.001661960547713947$, PR #942 on PR #869/#870 and PR #890 / PR #858)
+- **Coordination Note:** No pinned sprint coordination issue exists on `CrocSwap/integer-mult-bounds` (open issues are `#913` and `#650`). This claim is recorded locally in `CLAIM.json` and `CLAIM.md` and checked against all open PRs through `#1118` for non-overlap.
+
+## Three Narrow Candidate Tasks Evaluated
+
+1. **Candidate 1 (Partial $E_4 \to E_5$ entrance-promotion reversion inside one 4-helper group `[659, 661, 662, 663]` of U8 to fill T37 rank-1 idle gaps):**
+   - **Hypothesis:** In PR #869 (`PROOF-NOTE-PROMO.md`), two 4-helper groups (`659, 661, 662, 663` and `666, 669, 672, 673`) had their entrance frames promoted from $E_4 = [298, 170, 102, 30]$ (dim 4) to $E_5 = [298, 170, 102, 30, 1]$ (dim 5), changing the local paid profile by $\Delta = \{2:-4, 3:-2, 4:+2\}$ per group. Since T37 (`research/complex-t37-owners`) has 2 remaining rank-1 idle slots (examined via $J$-pair unpromotion in PR #1072), we tested reverting $m \in \{1, 2, 3\}$ helpers of `[659, 661, 662, 663]` back to $E_4$.
+   - **Outcome (Scoped Negative Finding):** In U8 (`native/barch/FULL-WORD.json.gz`), the 12 bipartite delivery gates `B[420..431]` (`dst in {656, 657, 658, 660}`, `src in {659, 661, 662, 663}`) find the destination helpers `656, 657, 658, 660` at frame dimension $1$. When $1 \le m \le 3$ helpers in `{659, 661, 662, 663}` are reverted to $E_4$ (dim 4) and $4-m$ remain at $E_5$ (dim 5), each of `656, 657, 658, 660` must first climb $1 \to 4$ (rank 3) for the $E_4$ sources and then climb $4 \to 5$ (rank 1) for the $E_5$ sources, splitting 4 rank-4 climbs into 4 rank-3 climbs plus 4 rank-1 climbs. This produces local profile deltas $\Delta_{\text{local}}(m=1) = \{1:+2, 2:+1, 3:+3, 4:-3\}$ and $\Delta_{\text{local}}(m=2) = \{1:+2, 2:+2, 3:+4, 4:-4\}$, strictly worsening the complex moment at $b_{\text{front}}$. Recorded and verified in `PROOF.md` and `verify.py`.
+
+2. **Candidate 2 (Frame-0 `premix` refactorization at the head of section `A` in U8):**
+   - **Outcome:** Ruled out during the Step 4 favorable-budget check because the frame-0 `premix` prefix of `A` in U8 contains only 57 scalar macros (482 real primitives per orientation) with small coefficients ($\max |\text{num}| = 2$, $\max \text{den} = 2$).
+
+3. **Candidate 3 (Selected — Two-sided Markowitz $R^{-1} P L^{-1}$ Schur-complement refactorization with Weyl-group signed cycles for `full_frame_cleanup` on the selected U8 complex supplier word):**
+   - **Object:** `cleanup` (`full_frame_cleanup` at frame `1` = `FULL`) in the selected U8 complex supplier word (`native/barch/FULL-WORD.json.gz` content sha256 `090fd574...`, `native/local/CANONICAL-WORD.json.gz` content sha256 `48b532f1...`).
+   - **Mechanism & Result:** Replaces the 6,105-macro one-sided dyadic Gauss-Jordan elimination (`high_inverse = "dyadic_sparse_Gauss_Jordan"`, which suffers severe fill-in and coefficient explosion up to `131,646`) with a 3,525-macro two-sided Markowitz $R^{-1} P L^{-1}$ Schur-complement factorization with Weyl-group signed cycles (`seed = 30`, `trial = 16`, `swap_pen = 6`, `scale_pen = 0`):
+     - Cuts `full_frame_cleanup` scalar macros from **6,105 to 3,525** (**$-2,580$ macros per orientation, $-42.26\%$**).
+     - Cuts `full_frame_cleanup` real-component primitives from **68,714 to 31,394** per orientation (**$-37,320$ real primitives per orientation, $-54.31\%$**).
+     - Cuts full U8 local program real-component primitives from **193,306 to 155,986** (forward) and **193,354 to 156,034** (backward), saving **74,640 real primitives per forward+backward invocation pair** (**$-19.30\%$** of the entire U8 local program).
+     - Cuts maximum `cleanup` numerator magnitude from **131,646 to 8** ($16,455.75\times$ reduction) and maximum denominator from **64 to 8**.
+     - Cuts the backward orientation's peak prefix $L_1$ coefficient norm (`prefix_l1_upper`) from `48299247708521178587951/16` (`72` bits) to **`57316408753392281/4`** (**`54` bits**, **$-18$ bits**, a **$210,704\times$ reduction**), and the forward peak prefix $L_1$ norm from `6812058044968180837/256` (`55` bits) to **`1938756620440273`** (**`51` bits**, **$-4$ bits**, a **$13.7\times$ reduction**).
+     - Preserves all 728 exact columns in both orientations, all 1,005 native frames, all 2,949 directed frame edges, the paid recursive child profile `{1: 2548, 2: 338, 3: 446, 4: 162, 5: 72, 8: 8}`, and byte-identical `RESIDUAL-ADAPTERS.json` (`8b06181f...`). Does not claim a new $\kappa$.

research/u8-cleanup-markowitz-lpr-seed30/EXPECTED.json

@@ -0,0 +1,157 @@
+{
+  "package": "u8-cleanup-markowitz-lpr-seed30",
+  "seed": 30,
+  "track": "20-39: Complex supplier",
+  "base_commit": "abdc6a7002abdbcd9e21bfc5e1a795784deacfdf",
+  "status": "PASS_U8_CLEANUP_MARKOWITZ_LPR_REFACTORIZATION",
+  "changes_kappa": false,
+  "selected_kappa": {
+    "numerator": 1661960547713947,
+    "denominator": 1000000000000000000,
+    "decimal": "0.001661960547713947"
+  },
+  "cleanup_section_comparison": {
+    "baseline_u8": {
+      "method": "dyadic_sparse_Gauss_Jordan",
+      "scalar_macros": 6105,
+      "add_macros": 6005,
+      "scale_macros": 100,
+      "real_component_primitives_per_orientation": 68714,
+      "max_abs_numerator": 131646,
+      "max_denominator": 64
+    },
+    "refactored_lpr_seed30": {
+      "method": "two_sided_Markowitz_LPR_Weyl_seed30",
+      "scalar_macros": 3525,
+      "add_macros": 3355,
+      "scale_macros": 170,
+      "R_inv_macros": 1744,
+      "P_macros": 406,
+      "L_inv_macros": 1375,
+      "disjoint_cycles": 61,
+      "real_component_primitives_per_orientation": 31394,
+      "max_abs_numerator": 8,
+      "max_denominator": 8
+    },
+    "deltas_per_orientation": {
+      "scalar_macros": -2580,
+      "scalar_macros_pct": -42.26044226044226,
+      "real_component_primitives": -37320,
+      "real_component_primitives_pct": -54.31207614168874
+    }
+  },
+  "full_local_program_comparison": {
+    "baseline_u8": {
+      "scalar_operations_audit": 19189,
+      "refactored_cleanup_gates_total": 6276,
+      "early_cleanup_gates": 171,
+      "events_per_orientation": 24415,
+      "scalar_macros_per_orientation": 19213,
+      "forward_real_component_primitive_bound": 193306,
+      "backward_real_component_primitive_bound": 193354,
+      "pair_real_component_primitive_bound": 386660,
+      "forward_prefix_l1_upper": "6812058044968180837/256",
+      "forward_prefix_bits_upper": 55,
+      "backward_prefix_l1_upper": "48299247708521178587951/16",
+      "backward_prefix_bits_upper": 72
+    },
+    "refactored_lpr_seed30": {
+      "scalar_operations_audit": 16609,
+      "refactored_cleanup_gates_total": 3696,
+      "early_cleanup_gates": 171,
+      "events_per_orientation": 21835,
+      "scalar_macros_per_orientation": 16633,
+      "forward_real_component_primitive_bound": 155986,
+      "backward_real_component_primitive_bound": 156034,
+      "pair_real_component_primitive_bound": 312020,
+      "forward_prefix_l1_upper": "1938756620440273",
+      "forward_prefix_bits_upper": 51,
+      "backward_prefix_l1_upper": "57316408753392281/4",
+      "backward_prefix_bits_upper": 54,
+      "raw_full_word_content_sha256": "2fcbb16c5a87553f4b4cfff7bfd75b7900a99ce66f9ff9fa47e971d53f5ebd30",
+      "canonical_word_content_sha256": "e9152741730bf34f4cdff694d38dace6b624d643d7bf53e7d492822101eebe8f",
+      "forward_program_sha256": "268751349882fba3e5f7834a6676ad545042a7d634a585334594cd1f433afc4e",
+      "backward_program_sha256": "0bfe1e727bfafca2f573caa862a6fe7308b5cea28c91df6ce2d36df226f2a45f",
+      "residual_adapters_sha256": "8b06181f69832da05e3bffab0737598013e20de6f1f48aad43617fbfe62df615",
+      "wrapper_checks_sha256": "75510637de1a14c5d37e2fe95d4c11aabc5cf3d2f1508dfb04f9795972629865"
+    },
+    "deltas": {
+      "events_per_orientation": -2580,
+      "events_pair": -5160,
+      "scalar_macros_per_orientation": -2580,
+      "scalar_macros_pair": -5160,
+      "real_component_primitives_per_orientation": -37320,
+      "real_component_primitives_pair": -74640,
+      "forward_prefix_bits_delta": -4,
+      "backward_prefix_bits_delta": -18
+    }
+  },
+  "preserved_invariants": {
+    "all_columns_each_orientation": 728,
+    "helpers": 504,
+    "frames": 1005,
+    "directed_edges": 2949,
+    "paid_profile": {
+      "1": 2548,
+      "2": 338,
+      "3": 446,
+      "4": 162,
+      "5": 72,
+      "8": 8
+    },
+    "local_rank_mass": 5634,
+    "upstream_local_negative_controls_rejected": 25,
+    "upstream_wrapper_negative_controls_rejected": 17,
+    "package_negative_controls_rejected": 12
+  },
+  "scoped_negative_finding_candidate1": {
+    "object": "Partial E4 entrance-promotion reversion inside 4-helper group [659, 661, 662, 663] of U8",
+    "entrance_e5_vectors": [
+      298,
+      170,
+      102,
+      30,
+      1
+    ],
+    "entrance_e4_vectors": [
+      298,
+      170,
+      102,
+      30
+    ],
+    "coupled_delivery_registers": [
+      656,
+      657,
+      658,
+      660
+    ],
+    "local_profile_deltas_by_m": {
+      "0": {},
+      "1": {
+        "1": 2,
+        "2": 1,
+        "3": 3,
+        "4": -3
+      },
+      "2": {
+        "1": 2,
+        "2": 2,
+        "3": 4,
+        "4": -4
+      },
+      "3": {
+        "1": -1,
+        "2": 4,
+        "3": 4,
+        "4": -4
+      },
+      "4": {
+        "1": -8,
+        "2": 8,
+        "3": 4,
+        "4": -4
+      }
+    },
+    "mechanism": "When 1 <= m <= 3 helpers in {659, 661, 662, 663} are reverted to E4, the 12 bipartite delivery gates B[420..431] into {656, 657, 658, 660} split between frame E4 (dim 4) and frame E5 (dim 5), splitting the single rank-4 climb (1 -> 5) on each of {656, 657, 658, 660} into a rank-3 climb (1 -> 4) plus a rank-1 climb (4 -> 5)."
+  }
+}

research/u8-cleanup-markowitz-lpr-seed30/NOTICE.md

@@ -0,0 +1,19 @@
+# Notice and Attribution
+
+**Package:** `research/u8-cleanup-markowitz-lpr-seed30`  
+**License:** Apache-2.0 (following the repository license at the root of `CrocSwap/integer-mult-bounds`).
+
+## Contributor Attribution and AI Disclosure
+
+- **Contributor:** `steph4n-gh`
+- **AI Assistance Disclosure:** Substantial AI assistance from **Gemini 4 Argon** (Google DeepMind / Antigravity) was used in the mathematical formulation of the two-sided Markowitz $R^{-1} P L^{-1}$ Schur-complement cleanup factorization and Weyl-group signed cycle realization, the analysis of the partial-$E_4$ entrance-promotion climb-splitting lemma, and the implementation of `verify.py`, `independent.py`, and `test_package.py`.
+
+## Credit to Predecessor Work
+
+This package builds directly on and credits the following predecessor contributions in `CrocSwap/integer-mult-bounds`:
+
+- **Jonathan Capalbo (`jon314159`, PR #942):** Selected frontier certificate (`certificates/selected-result.json`, $\kappa = 1661960547713947 / 10^{18}$), T37 owner-allocation proof (`research/complex-t37-owners/`), and the PR #942 audit bundle (`research/community-frontier942-audit/t37-replay.tar.gz`).
+- **Jeremy Kothe (`jeremykothe2`, PR #869 / PR #870):** The U8 complex supplier word (`research/gauge44-barch/construction/barch/RECIPE-U8.json`, `LOCAL-PINS-barch-U8.json`) and the `gauge44-barch` pipeline (`PROOF-NOTE-BARCH.md`, `PROOF-NOTE-FRAMES-X4.md`, `PROOF-NOTE-PROMO.md`, `PROOF-NOTE-LAYERS.md`, `PROOF-NOTE-NOTRI.md`).
+- **Chafik Boukhalfa (`chafreaky`, PR #890) and Hao Yan (`icekylinx`, PR #858, PR #704, PR #635, PR #571, PR #558, PR #552, PR #531, PR #514, PR #433, PR #425):** The hyperplane-ended (`HPE`) and cold-hyperplane-ended (`COLD-HPE`) local compiler and verification suite (`hpe_audit_and_transport.py`, `hpe_emit_local.py`, `hpe_audit_local.py`, `hpe_adapters_local.py`), the `cold44x.py` refactored-cleanup architecture, and the multi-cold global assembly pipeline.
+- **DreamingOfClouds (PR #484, PR #593, PR #589, PR #555):** Entrance-frame residual wrapper theorems ($L_{E,U}^{-1} S_{E,U} R_{E,U}^{-1} = C_{[w]} \otimes I$), arbitrary-dirt local compensation audits, and the selected bit-side supplier (`PR #589` on `PR #555`).
+- **`steph4n-gh` (PR #1072):** Analysis of the remaining rank-1 idle slots in T37 under $J$-pair unpromotion (`research/complex-t37-jpair-unpromotion-seed24/`).