Conditional κ = 0.00300105 (+4.105e-5 over #4440): combine query thinning and helper retiming

docs/ci-verification.md

@@ -2,6 +2,18 @@
 
 ## Current selected-family replay
 
+Resolve the [selected record](../certificates/selected-result.json) before
+running a historical checkpoint. The current cold replay is
+`make frontier4359-verify`, using the
+[proof review](research/pr-intake-evidence/pr4359/PROOF-REVIEW.md),
+[validation](research/pr-intake-evidence/pr4359/VALIDATION.json) and
+[source manifest](../certificates/frontier4359-source.json).
+The [frontier4359 workflow](../.github/workflows/frontier4359.yml) provides
+hosted replay evidence. Metadata and source-pin checks are separate from
+operator replay and do not discharge the inherited theorem assumptions.
+
+## Historical frontier1094 replay
+
 Start with the [selected record](../certificates/selected-result.json). Its
 `reproduce`, `review`, `source_manifest` and `validation` fields identify the
 replay command, scoped assessment, source bindings and integration evidence.

docs/research/current-status.md

@@ -1,12 +1,14 @@
 # Current reviewed status
 
-Selected conditional κ: **0.0023 = 23/10000**, zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage.
+Selected conditional κ: **0.0023** (= 23/10000), zxv’s #4359 productive-helper construction, using Jacob Alan Sussman’s mixed-target recursion and the credited cumulative native/outer lineage.
 
 [Selected record](../../certificates/selected-result.json) · [Proof review](pr-intake-evidence/pr4359/PROOF-REVIEW.md) · [Integration receipt](pr-intake-evidence/pr4359/INTEGRATION.json) · [Contributors](community-productive4359-contributors.md).
 
 Cold replay: `make frontier4359-verify`. The fresh 23-stage replay and 59 normalized artifacts pass; the changed interfaces have an AI-assisted proof review under retained analytic/native/fixed-tape hypotheses. Winning uniform templates are not materialized. This is not a complete formal or independent human verification. #4404 independently checks a narrower arithmetic/flow scope.
 
-## Historical selected status through #1094
+All sections below are a historical snapshot; the selected-result.json record above is authoritative.
+
+## Historical checkpoint through #1094
 
 Historical selected conditional κ: **0.001672660197076918**, Rohan Arun's #1094 on Jeremy Kothe's #1087 packing and the cumulative k8/slot/T16 construction. The bit supplier remains #589 on #555.
 

research/d8-mixed-target-seeda97c8e/SOURCES.json

@@ -4,25 +4,25 @@
   "files": [
     {
       "path": "autoresearch.md",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "8d5403e0f10f68a61d0cb9294fa2e83e872d1d82",
       "sha256": "215b3222f6a943edc69422a28ac21ea1f397ddf54770f1d87ac4195385d73699"
     },
     {
       "path": "certificates/selected-result.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "ae6a99f28aa468649eb66a361e764d769363bf11",
       "sha256": "10b9e340fd8e354a37a0c4813c90e5de1dd42044b5f6aca4a3fc5a42b685fa32"
     },
     {
       "path": "docs/research/agent-task-catalog.json",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "06c96f5579bb67ed1b86d334e78fbed7da6945f1",
       "sha256": "6686ad58f1fbdbc87134a78901b60fd53a20d3984355e91defbbebc9e9fa8075"
     },
     {
       "path": "docs/research/current-status.md",
-      "usage": "input",
+      "usage": "provenance",
       "git_blob": "d73b4ff9da41f044e793422db4318be17e234a6c",
       "sha256": "adb54af005eb11edaf84d782fe729338680ff908f6d4fbf39ba1062d2e7d8a77"
     },

research/d8-mixed-target-seeda97c8e/VERIFY.json

@@ -4,10 +4,6 @@
   "python": "3.12",
   "requirements": [],
   "inputs": [
-    "autoresearch.md",
-    "certificates/selected-result.json",
-    "docs/research/agent-task-catalog.json",
-    "docs/research/current-status.md",
     "research/bit-three-register-lower-bound/README.md",
     "research/d8-mixed-target-seeda97c8e/verify.py"
   ],

research/fresh-helper-boundary/ARITHMETIC-RESULT.json

@@ -0,0 +1,219 @@
+{
+  "BIT": {
+    "admitted": "273/100000",
+    "gap": "118653797/10000000000000",
+    "inherited_unrelaxed_saving": "27418653797/10000000000000"
+  },
+  "compiler": {
+    "H": 349300000000,
+    "N": "2^349300000000",
+    "eta": {
+      "lower": "0.140815224484524968848722108625",
+      "upper": "0.140815224484524968848722108626"
+    },
+    "gap": "1/700000000",
+    "integer_test_exponent": 499,
+    "logarithm_power": 13,
+    "theta_upper": "6/7",
+    "uniform_saving": "952437/350000000",
+    "word_materialized": false
+  },
+  "fixed_profile_ceiling": {
+    "decreasing_C_interval": [
+      "0",
+      "1/20"
+    ],
+    "negative_derivative_upper": {
+      "lower": "-178315.972608883259749333049784629374",
+      "upper": "-178315.972608883259749333049784629373"
+    },
+    "negative_moment_upper": {
+      "lower": "-8137.901782546330185425252976230749",
+      "upper": "-8137.901782546330185425252976230748"
+    },
+    "remaining_C_interval": [
+      "1/20",
+      "1"
+    ]
+  },
+  "gain_over_PR4416": "3477/100000000",
+  "headroom_from_declared_to_root": [
+    "8051/400000000000",
+    "50319/2500000000000"
+  ],
+  "kappa": "68031/25000000",
+  "negative_controls": {
+    "closed_epsilon": [
+      "epsilon_below_one",
+      "global_gamma_power_slack",
+      "actual_logarithmic_gamma_guard",
+      "source_axis_superpolynomial",
+      "gaussian_above_main",
+      "new_semantic_guard_with_C1_one"
+    ],
+    "closed_uniform_gap": [
+      "new_complex_uniform_saving_above_b"
+    ],
+    "old_BIT_relaxation": [
+      "actual_bit_above_effective"
+    ],
+    "unfunded_outer": [
+      "main_transform_above_kappa",
+      "global_coordinate_router_above_kappa",
+      "fused_gaussian_above_kappa",
+      "group_bit_router_above_kappa",
+      "boundary_algebraic_matrix_above_kappa"
+    ]
+  },
+  "outer": {
+    "functional_checks": {
+      "fixed_halo_explicit_metadata_branch": "13475000001/175000000",
+      "new_BIT_row_stock_sublinear_in_active_group": "697899997009/700000000000",
+      "new_semantic_group_guard": "3/700000000"
+    },
+    "margins": {
+      "boundary_algebraic_matrix": "1333410398095129/490000000000000000",
+      "fused_gaussian": "1333410394285387/490000000000000000",
+      "global_coordinate_router": "238109/87500000",
+      "group_bit_router": "166676386785673/61250000000000000",
+      "group_scans": "349999999/350000000",
+      "main_transform": "1333409698095129/490000000000000000",
+      "microbox_face_corrections": "13475000001/175000000",
+      "polynomial_products": "699999999/700000000",
+      "sparse_union_movement": "200395910398095129/490000000000000000"
+    },
+    "parameters": {
+      "a": "238109/87500000",
+      "b": "1904873/700000000",
+      "beta": "699999997/700000000",
+      "bit_saving": "273/100000",
+      "cap_xi": "445395909698095129/490000000000000000",
+      "complex_uniform_saving": "952437/350000000",
+      "d": "1/700000000",
+      "epsilon": "699999999/700000000",
+      "kappa": "68031/25000000",
+      "lambda_": "199455751/200000000",
+      "lambda_prime": "698095129/700000000",
+      "layout": "1/700000000",
+      "q": "1904871/700000000",
+      "r0": "1/7000000000",
+      "stop": "1/700000000",
+      "tested_saving": "2177/800000"
+    },
+    "strict_checks": {
+      "actual_bit_above_effective": "383/43750000",
+      "actual_logarithmic_gamma_guard": "1/700000000",
+      "actual_logarithmic_group_guard": "44604091351904871/245000000000000000",
+      "alpha_logarithm_absorption": "1/7000000000",
+      "boundary_algebraic_matrix_above_kappa": "2798095129/490000000000000000",
+      "cap_above_band": "200395909698095129/490000000000000000",
+      "cap_below_cell": "44604089601904871/490000000000000000",
+      "cap_below_phase_cell_power": "534604090301904871/490000000000000000",
+      "complex_above_effective": "1/700000000",
+      "complex_below_one_over_32": "19970127/700000000",
+      "complex_endpoint": "1/350000000",
+      "epsilon_below_one": "1/700000000",
+      "epsilon_positive": "699999999/700000000",
+      "fine_prime_halo_umbrella": "7/2",
+      "fused_gaussian_above_kappa": "2794285387/490000000000000000",
+      "gaussian_above_main": "348095129/245000000000000000",
+      "global_coordinate_router_above_kappa": "1/175000000",
+      "global_gamma_power_slack": "9/7000000000",
+      "group_below_dimension": "1/350000000",
+      "group_bit_router_above_kappa": "436785673/61250000000000000",
+      "group_gauge_power_slack": "44604091316904871/245000000000000000",
+      "group_key_fits_record": "1/350000000",
+      "group_positive": "699999997/700000000",
+      "group_scans_above_kappa": "69809513/70000000",
+      "halo_covers_generic_inverse_radius": "5",
+      "improvement_over_user_baseline": "495134790400418148631/500000000000000000000000",
+      "lambda_above_internal": "1/1400000000",
+      "lambda_above_sigma": "3/1400000000",
+      "lambda_above_tau": "1/1400000000",
+      "lambda_prime_above_lambda": "1/1400000000",
+      "lambda_prime_above_leaf": "1398095127/490000000000000000",
+      "leaf_saving_above_effective": "698095127/490000000000000000",
+      "main_transform_above_kappa": "2098095129/490000000000000000",
+      "membership_arithmetic_fits_record": "1/700000000",
+      "microbox_face_corrections_above_kappa": "1684315473/21875000",
+      "microbox_halo_volume": "55300000003/700000000",
+      "new_complex_uniform_saving_above_b": "1/700000000",
+      "new_semantic_guard_with_C1_one": "1/700000000",
+      "polynomial_products_above_kappa": "698095131/700000000",
+      "positive_layout_slack": "1/700000000",
+      "q_below_effective": "1/700000000",
+      "q_below_internal": "1/700000000",
+      "q_below_leaf": "1398095127/490000000000000000",
+      "q_positive": "1904871/700000000",
+      "short_record_fallback": "698095127/700000000",
+      "source_axis_superpolynomial": "1/700000000",
+      "sparse_union_movement_above_kappa": "199062502798095129/490000000000000000",
+      "stop_below_one": "699999999/700000000",
+      "stop_positive": "1/700000000",
+      "strassen_integer_power_gap": "1951441519231",
+      "support_router_span": "3/700000000",
+      "theta_positive_polynomial_power": "2",
+      "union_header_fits_record": "3/700000000",
+      "union_tag_work_per_visit_fits_record": "3/700000000"
+    }
+  },
+  "paid": {
+    "1": 33795,
+    "16": 448,
+    "2": 7725,
+    "3": 6675,
+    "32": 448,
+    "4": 1530,
+    "48": 448,
+    "5": 600,
+    "8": 1464
+  },
+  "paid_calls": 53133,
+  "productive_fields": 7688,
+  "relative_gain_over_PR4416": "1159/89549",
+  "root_bracket": [
+    "1088504051/400000000000",
+    "6803150319/2500000000000"
+  ],
+  "status": "PASS_CHANGED_NATIVE_PROFILE_STRICTIFICATION_AND_COMPLETE_OUTER",
+  "strictification": {
+    "alpha": {
+      "lower": "0.999999983026163231936831206184",
+      "upper": "0.999999983026163231936831206185"
+    },
+    "cutoff_base": 10,
+    "delta": {
+      "lower": "0.864870069524004068270352709182",
+      "upper": "0.864870069524004068270352709183"
+    },
+    "gamma": {
+      "lower": "0.910935673068185945998089027910",
+      "upper": "0.910935673068185945998089027911"
+    },
+    "gap": {
+      "lower": "0.000000705775426641554341705594",
+      "upper": "0.000000705775426641554341705595"
+    },
+    "normalized_paid_upper": "312500529444649842944287051245464084985300648225953097729364854469515503029278664568874151635979493066877292627151728507225829268936433948299379518726558518343844530884174444838473561069623983608689185814338090148572417036912296673977860237369051387753314848294993638501683424262073636500572764166420861283708720335677094583332070847074689861555558356543552667138912721443073650953550760942655945597474686732201711464952735742366374988690440592748048891939/312500750000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000",
+    "rational_upper_limits": [
+      "62499999/62500000",
+      "911/1000",
+      "173/200"
+    ],
+    "tail_offset": "3/10",
+    "target_floor_base": 15,
+    "tensor_power": 150
+  },
+  "targets": {
+    "121": 224,
+    "25": 448,
+    "4": 390,
+    "41": 448,
+    "5": 30,
+    "57": 448,
+    "7": 435,
+    "8": 630,
+    "9": 4635
+  },
+  "tested_saving": "2177/800000"
+}

research/fresh-helper-boundary/ATTEMPTS.md

@@ -0,0 +1,44 @@
+# Scope of discovery
+
+The new contribution changes helper entrances and exits jointly with scalar
+contact frames. The old choice was optimized for a hosted owner fill. Once
+all helper fields are fresh independent inputs, that objective is different:
+price the paid moment minus the actual productive helper moment.
+
+Exploratory checks before this pivot (compiled C++ discovery, not registered
+proofs or global optimality certificates):
+
+- All 262,144 paired p7 masks: 256 modular candidates; none passes the numerical test C=.00268649.
+  The old rank profile and root were reproduced.
+- All 2,097,152 paired p8 masks: 576 modular candidates; none passes C=.00268649.
+- 2,391,496 masks within six individual-bank toggles of the selected p7 mask:
+  6,278 modular candidates; none passes the numerical test C=.00268649.
+- No untouched consecutive native transports fuse. Single common-frame
+  components, and alpha expansions over the 1,159 existing frame spaces with
+  all boundaries fixed, gave no improvement at C=.003.
+
+The rank-sum modular test is a discovery filter. If a polynomial matrix A has
+invertible A(1), a constant-basis diagonal monomial factorization implies that
+the sum of ranks of its nonzero coefficient matrices equals the dimension.
+A necessary mod-2 screen is particularly cheap here because A(1) stays
+invertible mod 2. Scientific acceptance of the selected word uses rational
+Laurent replay and full native replay, not this filter.
+
+Allowing helper boundary frames changes the result. A binary alpha-expansion
+cut changes a selected set of scalar contacts to one frame, while hard
+constraints preserve every nested chronological path and every warp contact.
+The energy is the complete paid moment minus productive helper moment. Entry
+and exit moves are optimized separately because their joint concave reward
+is not a submodular binary cost. The submitted finite choices are recorded
+explicitly in CHANGES.json; replay needs no optimizer or C++ compiler.
+
+The optimizer is a discovery aid. Passing every tested label does not prove
+global optimality. In particular, simultaneous different-label moves, changed
+scalar order, new operators, center sharing and new geometry remain open.
+
+A subsequent scan added all binary lines, all hyperplanes and all coordinate
+subspaces of F2^9: 1,264 new distinct labels, for 2,423 tested spaces. Separate
+entry and exit alpha-expansion sweeps from the submitted profile found no
+negative move at C=.003. The registered proof uses only the final finite
+choices and exact native/moment replay; no claim of global optimality or
+exact mathematical acceptance is drawn from floating discovery costs.