Finite construction: selected X4 target forests save 47,690 primitives with an exact class floor (no new kappa)

research/complex-x4-target-forest/CLAIM.md

@@ -0,0 +1,37 @@
+# Sprint claim
+
+- Track: complex supplier; OS-random assignment seed **34**.
+- Base: `91a2094f2e022930069e8cfdc810a3ea1b81cd09`.
+- Claim recorded: 2026-10-14 Australia/Melbourne.
+- Expected finish: 2026-10-14 00:45 Australia/Melbourne (2026-10-13 13:45 UTC).
+- Object: the selected PR799 X4 zero-frame arbitrary-helper compensation matrix.
+- Method: restored signed target forests, extending the disjoint pair class of
+  PR901. Exact binary-Horner prices include both basis boundaries. Test whether
+  a minimum-spanning-tree formulation yields a cheaper complete circuit.
+  Seed 34 determines deterministic tie ordering, not mathematical coverage.
+- Deliverable: one source-pinned finite construction or scoped negative result,
+  exact reproduction, arbitrary-input replay and corruption controls.
+- Three candidates considered: X4 overlapping target forests (chosen); nonunit
+  target pairs (closed by PR909); JP8 coefficient-work sharing (substantial
+  existing coverage in PR722/739/751/755/811/830/839/882).
+- Overlap: PR901 disjoint X4 pairs; PR909 excludes nonunit disjoint pairs;
+  PR816 and PR917 use target forests in historical CK compensation. This
+  contribution will credit the mechanism and check a complete selected-X4
+  circuit, including the minimum-cost forest claim if justified.
+- Coordination: live pinnedIssues query returned no pinned issues; sprint issue
+  search returned none. Local claim used. Open PR metadata inspected through
+  PR925 immediately before this claim. No other issue opened.
+- Timing: orientation bounded to first 8 minutes of a 40-minute session;
+  final 10 minutes reserved for verification and handoff.
+
+## Completion
+
+Submitted one contribution: [PR932](https://github.com/CrocSwap/integer-mult-bounds/pull/932).
+The selected-X4 forest has 6 roots and 106 edges, reduces compensation from
+6,320 to 2,324 additions, and saves 47,690 real primitives per orientation.
+Its exact scoped floor is 10,883 primitives per real component. Full scalar
+replay, independent Prim/cycle/operator checks, nine package tests and selected
+record checks pass; VALIDATION.md records remaining integration obligations.
+No new kappa is claimed. Final overlap refresh reached #931, with #901/#816
+heads unchanged and no competing selected-X4 forest found. No pinned issue
+was available, so this is the single local claim update with the result link.

research/complex-x4-target-forest/EXPECTED.json

@@ -0,0 +1,168 @@
+{
+  "base": "91a2094f2e022930069e8cfdc810a3ea1b81cd09",
+  "census_edges": 12544,
+  "census_sha256": "0418c47ee4d11eabc6f5d070a78ed31ee03216f3b4b99569e31f6a5ebe07369d",
+  "compensation_new_additions": 2324,
+  "compensation_original_additions": 6320,
+  "complex_compensation_floor": 10883,
+  "controls": [
+    "missing_middle",
+    "missing_preparation",
+    "missing_restoration",
+    "wrong_coefficient_sign",
+    "wrong_order"
+  ],
+  "independent": {
+    "all_forest_registers_enter_in_zero_frame": true,
+    "arbitrary_input_columns": 328,
+    "component_primitive_baseline": 34728,
+    "component_primitive_optimum": 10883,
+    "cycle_inequalities_checked": 12544,
+    "forest_edges": 106,
+    "helpers": 216,
+    "method": "Fraction symbolic maps; explicit Horner lists; Prim; all-edge cycle property",
+    "negative_controls": [
+      "forward:omit_prepare",
+      "forward:omit_restore",
+      "forward:wrong_injection_sign",
+      "backward:omit_prepare",
+      "backward:omit_restore",
+      "backward:wrong_injection_sign",
+      "incorrect_edge_price"
+    ],
+    "orientations": [
+      "forward",
+      "backward"
+    ],
+    "real_primitive_baseline": 69456,
+    "real_primitive_optimum": 21766,
+    "real_primitive_savings_each_orientation": 47690,
+    "roots": 6,
+    "scalar_macros": 2324,
+    "scope": "Exact finite compensation operator and forest-class optimum only; no full theorem or kappa claim.",
+    "signed_graph_edges": 12544,
+    "status": "PASS_INDEPENDENT_X4_TARGET_FOREST",
+    "targets": 112,
+    "unique_microcircuit_coefficients": 8
+  },
+  "middle_additions": 2112,
+  "preparation_additions": 106,
+  "programs": {
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+        "exact_fractional_bits": 19,
+        "macros": 19197,
+        "paid_profile": {
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+          "2": 338,
+          "3": 430,
+          "4": 194,
+          "5": 56,
+          "8": 8
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+        "positive_prefix_upper": "48299247699832632898063/16",
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+        "primitive_counts": {
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+          "clear": 73424,
+          "double": 13892,
+          "halve": 28456,
+          "negate": 1296,
+          "subtract": 18930
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+        "program_sha256": "7915679ee305927463d19725360cc15132dd21ede18897d09a935dca1df0d55d",
+        "real_primitives": 193210
+      },
+      "candidate": {
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+        "exact_fractional_bits": 19,
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+        "positive_prefix_upper": "219829455967238186882729/16",
+        "prefix_bits": 74,
+        "primitive_counts": {
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+          "clear": 57440,
+          "double": 13872,
+          "halve": 12780,
+          "negate": 1296,
+          "subtract": 14728
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+        "primitive_sha256": "787082f54b7eb43f76b3dd859a128a31eb87491d9cb5449da9393e000f412f36",
+        "program_sha256": "574a8420cd769e5b0445e6f19b51a578a6e571a5e2057d24e330bb186a8caba5",
+        "real_primitives": 145520
+      },
+      "saved_real_primitives": 47690
+    },
+    "forward": {
+      "baseline": {
+        "arbitrary_input_columns": 737,
+        "exact_fractional_bits": 3,
+        "macros": 19197,
+        "paid_profile": {
+          "1": 2548,
+          "2": 338,
+          "3": 430,
+          "4": 194,
+          "5": 56,
+          "8": 8
+        },
+        "positive_prefix_upper": "6812058044968180837/256",
+        "prefix_bits": 55,
+        "primitive_counts": {
+          "add": 58568,
+          "clear": 73392,
+          "copy": 16,
+          "double": 13892,
+          "halve": 28456,
+          "negate": 1296,
+          "subtract": 17542
+        },
+        "primitive_sha256": "1a675754e424290dc81ef8672f6c7e66e8da5f0d4025314df0cea52306fe903a",
+        "program_sha256": "076a2d428f97abb30473df05110998efbe5ac809885bae4ceb1b8bd81329a1e6",
+        "real_primitives": 193162
+      },
+      "candidate": {
+        "arbitrary_input_columns": 737,
+        "exact_fractional_bits": 3,
+        "macros": 15201,
+        "paid_profile": {
+          "1": 2548,
+          "2": 338,
+          "3": 430,
+          "4": 194,
+          "5": 56,
+          "8": 8
+        },
+        "positive_prefix_upper": "6812058044968180837/256",
+        "prefix_bits": 55,
+        "primitive_counts": {
+          "add": 46348,
+          "clear": 57408,
+          "copy": 16,
+          "double": 13872,
+          "halve": 12780,
+          "negate": 1296,
+          "subtract": 13752
+        },
+        "primitive_sha256": "f4a17c8ae41ee40a1a235a765bbaff74f2cf9f35643d5c920a4ea26a2f4452a3",
+        "program_sha256": "bf0f10d672c3314eabf264e302d40d92926895e26f8bff91dfca17b8a3b908a2",
+        "real_primitives": 145472
+      },
+      "saved_real_primitives": 47690
+    }
+  },
+  "restoration_additions": 106,
+  "roots": 6,
+  "seed": 34,
+  "status": "PASS_X4_TARGET_FOREST"
+}