κ = 9.98243154231047e-4: nine-stage complex E8 (≈2^-9.9683; complex +14.036%, bit side pending)

Makefile

@@ -547,3 +547,8 @@ recycled-bit-full-verify:
 
 verify-recycled-bit: recycled-bit-full-verify
 	python3 -m unittest discover -s tests -p 'test_recycled_bit_integration.py' -v
+
+.PHONY: complex-nine-verify
+complex-nine-verify:
+	@work=$$(mktemp -d "$${TMPDIR:-/tmp}/integer-mult-complex-nine.XXXXXX"); \
+	python3 -B research/nine-stage-complex-e8/verify.py --work "$$work/replay"

research/nine-stage-complex-e8-validation/CLIFFORD-REVIEW.json

@@ -0,0 +1,47 @@
+{
+  "status": "PASS_EXACT_GAUSSIAN_CLIFFORD_LOCAL_FRAMES_AND_CHILDREN",
+  "frames": 946,
+  "distinct_directed_edges": 3120,
+  "ranks": {
+    "9": 2,
+    "1": 1519,
+    "8": 24,
+    "2": 465,
+    "3": 484,
+    "4": 113,
+    "6": 292,
+    "5": 178,
+    "7": 43
+  },
+  "endpoint_adapters": 240,
+  "recipe_sha256": "5bfabfdf50aff6d3387d7eb702dbba740b4ca64e7a449ec4924cc9d9f34b6d09",
+  "all_child_equalities_include_global_phase": true,
+  "small_full_column_controls": [
+    {
+      "h": 1,
+      "circuits": 32,
+      "all_address_columns": 64,
+      "wrong_global_phase_rejected": 32
+    },
+    {
+      "h": 2,
+      "circuits": 32,
+      "all_address_columns": 128,
+      "wrong_global_phase_rejected": 32
+    },
+    {
+      "h": 3,
+      "circuits": 32,
+      "all_address_columns": 256,
+      "wrong_global_phase_rejected": 32
+    },
+    {
+      "h": 4,
+      "circuits": 32,
+      "all_address_columns": 512,
+      "wrong_global_phase_rejected": 32
+    }
+  ],
+  "seconds": 135.1804957499262,
+  "scope": "Fixed E8 local frames, every used nested transition, copied-center directions and old/new endpoint adapters. Does not by itself admit nine-stage global cover, routing or all-size theorem."
+}

research/nine-stage-complex-e8-validation/GLOBAL-REVIEW.json

@@ -0,0 +1,70 @@
+{
+  "status": "PASS_NINE_STAGE_SOURCE_BOUND_TEMPLATE_OWNERS_PROFILE_AND_FINITE_INVOICE",
+  "m": 73,
+  "live": 14727,
+  "physical": 15520,
+  "invocations": 72,
+  "local_source_events": 1242936,
+  "paid_calls": 310455,
+  "rank_mass": 1072575,
+  "deficit": 2496,
+  "profile": {
+    "1": 157599,
+    "2": 43488,
+    "3": 37296,
+    "4": 10080,
+    "5": 15480,
+    "6": 23832,
+    "7": 3096,
+    "8": 7488,
+    "9": 576,
+    "16": 3840,
+    "32": 3840,
+    "48": 3840
+  },
+  "whole_residual_assignments": 56376,
+  "bank_padding_calls": 7047,
+  "bridge_additions": 17280,
+  "terminal_shift_calls": 3840,
+  "terminal_complete_stream_movements": 7680,
+  "work_lifetimes_freshly_revalidated": true,
+  "owner_injections": true,
+  "cover_route_bijections": "Explicit invertible right factors; roles sharing a bank have different disjoint block images, hence different right factors.",
+  "template_sha256": "fb51fe86a8299b4c5f3d03d90e8766e321d534f29fe4ab9d093fdfb8b9826a13",
+  "finite_invoice": {
+    "local_primitive_bound": 7040446135448,
+    "local_adapters": 271472,
+    "compiler": 25934336,
+    "scalar_primitives_all_invocations": 5057712,
+    "outside_adapter_bound": 1988400,
+    "pervertex": 558479956303543,
+    "group_bits": 2628,
+    "live_stock_bits": 2642,
+    "physical_stock_bits": 2642,
+    "logical_groups_bits": 2677,
+    "router_bits": 7984,
+    "literal_bits": 35284,
+    "required_C0_bits": 200012,
+    "G_exponent": 30000,
+    "E_exponent": 100000,
+    "C0_exponent": 210000,
+    "halving_degree": 2,
+    "halving_integer_inequality": [
+      5329,
+      4608
+    ],
+    "induction_gap_multiple_B": 49,
+    "physical_row_coefficient": 15445,
+    "retained_row_coefficient": 20161
+  },
+  "source_hashes": {
+    "/Users/chenzhihao/Documents/Codex/2026-10-11/integer-mult-joint-breakthrough/work/complex-nine-pr-audit/work/native358/vendor/complex-reserve/upstream/pr352/code/complex/code/complex_splice.py": "aaf46c8e5c68875b8315892e924e082b2f219f8d042dd14937e7cd2f72456dce",
+    "work/complex-nine-native/local-admission/UPSTREAM-GUARD.json": "9cc4b3819eda28a1fd1fa5e9913c36fd3041ec69608474a3be8b812945d69944",
+    "work/complex-nine-native/local-admission/INDEPENDENT-AUDIT.json": "2912f82f8cad02fd166f7c328e96a51451e8c960178b226173ace3338cf6a60c",
+    "work/complex-nine-native/CLIFFORD-REVIEW.json": "da4eb36041e4793a83500a5e3e40c15ded2dba0a1fcb1296ca977e5e6bc6063a",
+    "work/complex-nine-native/DATA-PHASES.json": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a"
+  },
+  "seconds": 22.21225808293093,
+  "scope": "Finite source-bound global recipe, exact owner factors, paid histogram and conservative scalar/tape/precision/row invoice. Requires explicit mathematical integration of the compressed window lift and arbitrary-bank dirty composition; this is not a Lean proof or final multiplication exponent certificate.",
+  "cover_correction_calls": 14727
+}

research/nine-stage-complex-e8-validation/INDEPENDENT-TEMPLATE-AUDIT.json

@@ -0,0 +1,32 @@
+{
+  "status": "PASS_INDEPENDENT_EMITTED_TEMPLATE_AUDIT_AND_TWO_MOMENTS",
+  "template_sha256": "fb51fe86a8299b4c5f3d03d90e8766e321d534f29fe4ab9d093fdfb8b9826a13",
+  "coarse_complex": "999240641319551/1000000000000000000",
+  "next_grid_rejected": true,
+  "all_eight_signed_data_columns": true,
+  "bridge_omission_controls": 9,
+  "structural_controls_rejected": [
+    "missing_cover_phase",
+    "aliased_helper_route",
+    "missing_padding",
+    "wrong_reverse_local",
+    "omitted_terminal_exchange"
+  ],
+  "paid_profile": {
+    "1": 157599,
+    "2": 43488,
+    "3": 37296,
+    "4": 10080,
+    "5": 15480,
+    "6": 23832,
+    "7": 3096,
+    "8": 7488,
+    "9": 576,
+    "16": 3840,
+    "32": 3840,
+    "48": 3840
+  },
+  "fixed_baseline_kappa": "804849251275843/1000000000000000000",
+  "final_kappa_improvement_claim": false,
+  "scope": "Finite complex component with explicit PROOF.txt retaining the analytic interfaces. No Lean rebuild and no improved bit-side or multiplication certificate."
+}

research/nine-stage-complex-e8-validation/OUTER-FIXED-BIT.json

@@ -0,0 +1,57 @@
+{
+  "status": "PASS_NUMERICAL_OUTER_CHECK_WITH_FIXED_BIT_NO_KAPPA_IMPROVEMENT",
+  "bit_coarse": "12585899309117/15625000000000000",
+  "complex_coarse": "999240641319551/1000000000000000000",
+  "kappa": "804849251275843/1000000000000000000",
+  "strict_constraints": {
+    "bit_positive": "48011395656026162941798323251605247229077813982484814646630779/59604644775390625000000000000000000000000000000000000000000000000",
+    "complex_above_bit": "11547987814959190051213151357769752770922186017515185353369221/59604644775390625000000000000000000000000000000000000000000000000",
+    "complex_below_one_over32": "30250759358680449/1000000000000000000",
+    "beta_positive": "1/1000000000",
+    "beta_below_one": "999999999/1000000000",
+    "leaf_saving_above_bit": "11547987755399806580227798364758278161547186017515185353369221/59604644775390625000000000000000000000000000000000000000000000000",
+    "q_positive": "24005697827965070075243135462860825291287301744013329509332904685353369221/29802322387695312500000000000000000000000000000000000000000000000000000000000",
+    "q_below_internal": "48011395656026162941798323251605247229077813982484814646630779/29802322387695312500000000000000000000000000000000000000000000000000000000000",
+    "q_below_leaf": "5773993877747914685769925345320937404025198255986670490667095314646630779/29802322387695312500000000000000000000000000000000000000000000000000000000000",
+    "c_positive": "24005697835415650672166963587860825291287301744013329509332904685353369221/29802322387695312500000000000000000000000000000000000000000000000000000000000",
+    "c_below_one": "29778316689859896849327833036412139174708712698255986670490667095314646630779/29802322387695312500000000000000000000000000000000000000000000000000000000000",
+    "q_below_reservations": "1/4000000000000",
+    "lambda_above_tau": "48011395656026162941798323251605247229077813982484814646630779/59604644775390625000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_sigma": "11547987815007201446869177520711551094173791264744263167351705814646630779/59604644775390625000000000000000000000000000000000000000000000000000000000000",
+    "lambda_above_internal": "48011395656026162941798323251605247229077813982484814646630779/59604644775390625000000000000000000000000000000000000000000000000000000000000",
+    "lambda_prime_above_lambda": "48011395656026162941798323251605247229077813982484814646630779/59604644775390625000000000000000000000000000000000000000000000000000000000000",
+    "compact_leaf": "5773993877747914685769925345320937404025198255986670490667095314646630779/29802322387695312500000000000000000000000000000000000000000000000000000000000",
+    "compact_reservations": "1/4000000000000",
+    "lambda_prime_below_one": "24005697827965070075243135462860825291287301744013329509332904685353369221/29802322387695312500000000000000000000000000000000000000000000000000000000000",
+    "epsilon_positive": "29802322387665510177612304687500000000000000000000000000000000000000000000000/29826328085523277570075243135462860825291287301744013329509332904685353369221",
+    "epsilon_below_one": "24005697857767392462938447962860825291287301744013329509332904685353369221/29826328085523277570075243135462860825291287301744013329509332904685353369221",
+    "guard_width": "24005697857767392462938447962860825291287301744013329509332904685353369221/29826328085523277570075243135462860825291287301744013329509332904685353369221",
+    "K_geometry": "22375747488606900025672166963587860825291287301744013329509332904685353369221/29826328085523277570075243135462860825291287301744013329509332904685353369221000000000000",
+    "K_dominates_log": "24005697835391644974331547937188658327699440918722042207588891355844036316314646630779/29826328085523277570075243135462860825291287301744013329509332904685353369221000000000000",
+    "record_suffix": "24005697857767392462938447962860825291287301744013329509332904685353369221/29826328085523277570075243135462860825291287301744013329509332904685353369221",
+    "phase_local": "192045582832312811617984306132811359194835553126815348772919224153317620863314646630779/238610624684186220560601945083702886602330298413952106636074663237482826953768000000000000",
+    "phase_boundary": "38409116542601499855178239170502077330596821965130039913188634167056057848914646630779/47722124936837244112120389016740577320466059682790421327214932647496565390753600000000000",
+    "gamma_sublinear": "1/2000000000000",
+    "cell_above_band": "59604644775301194027139086097429924756864537139174708712698255986670490667095314646630779/119305312342093110280300972541851443301165149206976053318037331618741413476884000000000000",
+    "prime_interval_packing": "24005697857767392462938447962860825291287301744013329509332904685353369221/29826328085523277570075243135462860825291287301744013329509332904685353369221",
+    "alpha_positive": "48011395685708456840353618355646407447111742662735371716921796041197405537314646630779/59652656171046555140150486270925721650582574603488026659018665809370706738442000000000000",
+    "alpha_below_one": "59604644775360846683310132652570075243135462860825291287301744013329509332904685353369221/59652656171046555140150486270925721650582574603488026659018665809370706738442000000000000",
+    "alpha_below_one_fourth": "14865152647075930328197267949375784005198531908209271293037744656301479279073185353369221/59652656171046555140150486270925721650582574603488026659018665809370706738442000000000000",
+    "delta_positive": "1/8000000000000",
+    "delta_below_one_eighth": "999999999999/8000000000000",
+    "short_record_fallback": "1774924835759793604408709866477081711561913004451520898927784557202451722506207813029076166919246613425481572846488799048916609691076350146841/1777787690491871688966467567411831666546540695532799561590512568037829003883659839630126953125000000000000000000000000000000000000000000000000",
+    "small_field_exposure": "1/1000000000000",
+    "artificial_boundary": "1670466418372255162048173693002333318548048775894092726950502537939851143628858056060107663/238610624684186220560601945083702886602330298413952106636074663237482826953768000000000000",
+    "literal_scalar_guard": "1",
+    "row_product_gap": "23971789/25",
+    "balanced_prefix_above_kappa": "29826334749503291056878384925518885383748024824168328030655865254685029767102971697/29826328085523277570075243135462860825291287301744013329509332904685353369221000000000000000000",
+    "coordinate_movement_above_kappa": "38641935990431149348372079730247229077813982484814646630779/59604644775390625000000000000000000000000000000000000000000000000",
+    "compact_phase_layer_above_kappa": "6663980013486803141790056024558456737522424314701146532349999676397881971697/29826328085523277570075243135462860825291287301744013329509332904685353369221000000000000000000",
+    "bulk_exposure_above_kappa": "38641935990431149348372079730247229077813982484814646630779/59604644775390625000000000000000000000000000000000000000000000000",
+    "Gaussian_arithmetic_above_kappa": "11184879696051242575581357965854597367940970260578319699712532189256683911339846697/29826328085523277570075243135462860825291287301744013329509332904685353369221000000000000000000",
+    "scalar_work_above_kappa": "26098043738812881360618979533586027780586613911450326364467198641599360595950346697/29826328085523277570075243135462860825291287301744013329509332904685353369221000000000000000000",
+    "dimension_above_kappa": "29778316689837569119898869530594017559634231583639734695314835423345302496033685029767102971697/29826328085523277570075243135462860825291287301744013329509332904685353369221000000000000000000"
+  },
+  "next_grid_rejected": true,
+  "scope": "Numerical assembly only. The complex proof retains analytic interfaces; no new bit supplier or final combined theorem claimed."
+}

research/nine-stage-complex-e8-validation/README.md

@@ -0,0 +1 @@
+These are fresh contributor validation receipts for the source manifest named in VERIFICATION.json. Reproduce them with `make complex-nine-verify`. They record finite component checks and conditional pricing, not an independent human review or a formal proof of the full multiplication theorem. Large generated template and phase ledgers are rebuilt by the verifier rather than treated as trusted inputs.

research/nine-stage-complex-e8-validation/VERIFICATION.json

@@ -0,0 +1,73 @@
+{
+  "status": "PASS_PORTABLE_NINE_STAGE_COMPLEX_FINITE_COMPONENT",
+  "source_manifest_sha256": "3743f954b5a652e51fa9ae5101318345d79f4c897ff9a29d5c54387b92118458",
+  "fresh_stages": [
+    {
+      "stage": "frozen-source-integrity",
+      "returncode": 0,
+      "seconds": 0.06710633309558034,
+      "log_sha256": "8275b348307e4aa5a846ed5c81c863c09091acebfbb5bc035f1174bd2d0f2d8f"
+    },
+    {
+      "stage": "fresh-local-admission",
+      "returncode": 0,
+      "seconds": 2.3953759169671685,
+      "log_sha256": "ea59968fc1becce7944aa07c4bf857098ad890905a318fc48ffc8413570c7735"
+    },
+    {
+      "stage": "finite-data-banks-profile",
+      "returncode": 0,
+      "seconds": 2.401814791955985,
+      "log_sha256": "5710852ec4a262070040312fddad15dda0eedc4b1e32fe1edfaf5639ac6a2110"
+    },
+    {
+      "stage": "exact-clifford-recipes",
+      "returncode": 0,
+      "seconds": 135.24364987493027,
+      "log_sha256": "66308d1e9d27f60a5a11aac4ef9a424aa4ac3d819d27465122b0ab59900cfcb6"
+    },
+    {
+      "stage": "exact-data-and-cover-phases",
+      "returncode": 0,
+      "seconds": 11.506640959065408,
+      "log_sha256": "0abaa1d2933b0aff9fc78f5ab6f28217d5e8fa4068c37805f42b3af8464f4b31"
+    },
+    {
+      "stage": "global-template-and-invoice",
+      "returncode": 0,
+      "seconds": 22.304862333112396,
+      "log_sha256": "454ce86863118a2ade54208b33329438edee2613b6d936ef8e760ceb0ca86cd7"
+    },
+    {
+      "stage": "independent-template-two-moments",
+      "returncode": 0,
+      "seconds": 2.634225584100932,
+      "log_sha256": "c7008e701d628c9385265feb811f57f76c06ffc75d70ce35080080b296737491"
+    },
+    {
+      "stage": "fixed-bit-outer-check",
+      "returncode": 0,
+      "seconds": 0.03739691595546901,
+      "log_sha256": "72b2e4e23347fd983b3eaf8185ce0e17b756bfb2afafbf22ab26411848011cba"
+    }
+  ],
+  "complex_coarse": "999240641319551/1000000000000000000",
+  "fixed_bit_kappa": "804849251275843/1000000000000000000",
+  "new_final_kappa_claim": false,
+  "final_kappa_one_percent_milestone_reached": false,
+  "proof": "work/complex-nine-native/PROOF.txt",
+  "receipt_sha256": {
+    "INDEPENDENT-TEMPLATE-AUDIT.json": "34b80dc65161caaf5bcf348eb7307e92df6265dcb4a5f61993ac07410d06978c",
+    "CLIFFORD-REVIEW.json": "da4eb36041e4793a83500a5e3e40c15ded2dba0a1fcb1296ca977e5e6bc6063a",
+    "DATA-PHASES.json": "f621f6d4296cb215f334830356c5f79fe10d6d04d15b3ccda76ba0885ab67d0a",
+    "CLIFFORD-RECIPES.json": "5bfabfdf50aff6d3387d7eb702dbba740b4ca64e7a449ec4924cc9d9f34b6d09",
+    "GLOBAL-TEMPLATE.json.gz": "1b84904a31a733aab9bfdda3f528c06719f590d2133a43687a8bded955dc991e",
+    "OUTER-FIXED-BIT.json": "c157055c115b9c0706e672bc73873db93580d2abf46043e6511399e79bd6502d",
+    "GLOBAL-REVIEW.json": "5ab0d754c01500879dd6c2a70322d08016e2917b3f5f84655923d383729411ad",
+    "PROOF.txt": "ea0edb8cfb6b2f2c1adb2de12cc0aa5fb7c57e649033528565af3e52087beda7",
+    "local-admission/UPSTREAM-GUARD.json": "9cc4b3819eda28a1fd1fa5e9913c36fd3041ec69608474a3be8b812945d69944",
+    "local-admission/INDEPENDENT-AUDIT.json": "2912f82f8cad02fd166f7c328e96a51451e8c960178b226173ace3338cf6a60c"
+  },
+  "seconds": 176.59799158398528,
+  "scope": "The explicit proof retains local E8, Clifford/compiler, common-grid and row/analytic interfaces. No Lean kernel build, astronomical cover enumeration, certificate-producer regeneration or improved bit-side theorem is claimed."
+}