OZ-RT-BZ-T3-010-C: exact shared-coefficient extraction gate

campaigns/odd_zeta/OZ_RT_BZ_T3_010/.t3_011_b_branch_marker

@@ -0,0 +1,3 @@
+issue=486
+operation=OZ-RT-BZ-T3-011-B
+predecessor_merge=862f7680e1bf09f66f475c1f371f3c4a377f4cad

campaigns/odd_zeta/OZ_RT_BZ_T3_010/.t3_011_c_branch_marker

@@ -0,0 +1,4 @@
+issue=494
+operation=OZ-RT-BZ-T3-011-C
+predecessor_reviewed_head=7876a44286f3c958bf03ce120117c2cd689b2379
+predecessor_merge=f8dc03a4e546a47b7a2b6d77a96d689f47e4d9a3

campaigns/odd_zeta/OZ_RT_BZ_T3_010/README_011_B.md

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+# OZ-RT-BZ-T3-011-B
+
+This bounded successor tests exactly the 311 channel-linear lifts of T3-010-C unknowns whose complete global degree-zero response column is nonzero: 67 candidates in each of `n1`, `n2`, and `n3`, and 110 candidates in `k1`; `l1` remains mirror-derived.
+
+For each candidate, the producer reconstructs the exact normalized cokernel witness, computes the exact obstruction pairing `lambda_c v_G`, rejects zero-pairing candidates without rank promotion, and runs exact Q rank/solution extraction only when the pairing is nonzero. The independent verifier reconstructs the C systems through the reverse path and treats exact rank and substitution as authoritative.
+
+The operation does not admit pairs, arbitrary linear combinations, mixing with the exhausted zero-response bank, new harmonic support, a generic degree-one envelope, rational prefactors, adaptive basis growth, raw-jet reopening, or recurrence search.
+
+Claim firewall remains:
+
+- `residual_sum_zero_proved = false`
+- `proof_effect = NONE`
+- `promotion_effect = NONE`
+- `t3_status = OPEN_WITH_CHARACTERIZED_BLOCKER`

campaigns/odd_zeta/OZ_RT_BZ_T3_010/README_011_C.md

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+# OZ-RT-BZ-T3-011-C
+
+This operation audits the response-generator semantics used by the completed T3-011-B bounded search. It freezes the exact 311 independent nonzero-response single-channel lifts from T3-011-B and the 110 mirror-derived `l1` checks.
+
+For each frozen candidate, a third response path reconstructs the raw finite difference of `x_c G` directly from the protected primitive harmonic shift semantics:
+
+`Delta_c(x_c G) = (x_c + Delta_c x_c) S_c(G) - x_c G`.
+
+The same path independently expands the discrete product rule
+
+`Delta_c(x_c G) = x_c Delta_c(G) + (Delta_c x_c) S_c(G)`,
+
+then requires exact equality with the existing T3-011-B producer response and the separately implemented T3-011-B verifier response.
+
+The direct path is source-audited so it cannot call either predecessor lifted response generator, or the producer/verifier shift-specialization-response helper chain that would collapse the comparison into shared authority.
+
+A successful audit terminates only as `T3_011_B_LIFTED_RESPONSE_GENERATOR_SEMANTICS_CERTIFIED`. A disagreement terminates fail-closed as `T3_011_B_LIFTED_RESPONSE_GENERATOR_SEMANTICS_MISMATCH`.
+
+No candidate widening, pair search, generic degree-one envelope, support or harmonic enlargement, rational prefactor, raw-jet reopening, correction-layer recombination, recurrence search, or theorem promotion is authorized.

campaigns/odd_zeta/OZ_RT_BZ_T3_010/README_011_D.md

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+# OZ-RT-BZ-T3-011-D
+
+Question: **does polynomial degree, by itself, break the cokernel obstruction while everything else remains frozen?**
+
+The only admitted widening from the certified T3-011-B/C class is the multiplier `x_c -> x_c^2`. The producer scans the frozen 311 independent nonzero-response candidates in predecessor order and stops at the first exact nonzero pairing with the normalized base cokernel witness. If the independent bank remains invisible, the 110 `l1` mirror images of the frozen `k1` bank are checked before a negative terminal is allowed.
+
+Producer response: `(x_c+h_c)^2 S_c(G)-x_c^2 G`.
+
+Independent verifier response: `x_c^2 Delta_c(G)+(2 h_c x_c+h_c^2)S_c(G)`, compared under the exact T3-011-C semantic normal form over `Q[n,k,l]`.
+
+Positive terminal: `MINIMAL_SINGLE_CHANNEL_QUADRATIC_COKERNEL_BREAKING_DIRECTION_FOUND`.
+
+Negative terminal: `SINGLE_CHANNEL_QUADRATIC_RESPONSE_CLASS_COKERNEL_INVISIBLE`.
+
+No pair search, mixed-channel monomial, arbitrary polynomial envelope, degree above two, support/harmonic enlargement, rational prefactor, adaptive growth, raw-jet reopening, recurrence search, recombination, proof, or promotion is authorized.

campaigns/odd_zeta/OZ_RT_BZ_T3_010/README_011_E.md

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+# OZ-RT-BZ-T3-011-E
+
+T3-011-E asks whether the certified degree-0/1/2 cokernel annihilation closes the entire frozen single-channel polynomial-multiplier axis.
+
+It does **not** scan degree 3, 4, and so on. Instead it derives finite raw moment ledgers for each frozen candidate:
+
+- `<w, x^j S(G)>`;
+- `<w, x^j G>`;
+- `<w, (x+h)^j S(G)>`.
+
+The semantic identity
+
+`<w,(x+h)^d S(G)-x^d G> = sum_j binom(d,j) h^(d-j) <w,x^j S(G)> - <w,x^d G>`
+
+then determines the all-degree sequence exactly.
+
+A closure terminal requires the coordinate-shift relation to be representation-independent for all `d` and every remaining finite original moment to vanish. If the semantic relation itself fails, E stops at `POLYNOMIAL_CLOSURE_NOT_CERTIFIED__SEMANTIC_FUNCTIONAL_AMBIGUITY`. If the relation is sound but only finitely many higher original moments remain, E returns `POLYNOMIAL_CLOSURE_REDUCES_TO_FINITE_HIGHER_DEGREE_SET`.
+
+No direct higher-degree response pairing is authorized.

campaigns/odd_zeta/OZ_RT_BZ_T3_010/T3_010_C_CONTRACT.json

@@ -0,0 +1,77 @@
+{
+  "schema_version": "1.0.0",
+  "issue": 403,
+  "operation": "SYMMETRY_REDUCED_CHANNEL_HARMONIC_BLOCK_WITH_SHELL_STRATA_001",
+  "stage": "T3_010_C_BOUNDED_EXACT_SHARED_COEFFICIENT_SOLUTION_EXTRACTION_GATE",
+  "t3_010_b_checkpoint": {
+    "validated_head": "3a6cfba4d8fc5f44d0b9f17e9521e9df43e83fc8",
+    "producer_blob": "11ce437f2a26d73d3362df3e923f6cf9c4cf91f9",
+    "contract_blob": "d6eae2adbd34d4d3d61e985d42d6e3d01ffcefd0",
+    "verifier_blob": "89e4100e7750ccc8b86c8ddb2e28b97a8e15b7cd",
+    "required_status": "EXACT_CORRECTION_FLUX_COEFFICIENT_MATRIX_RANK_CONSISTENCY_GATE_COMPLETE"
+  },
+  "bounded_correction_class": {
+    "id": "SUPPORT_LOCKED_ORIENTED_ONE_BODY_DEGREE0_WEIGHT_CORRECTION_001",
+    "coefficient_degree": 0,
+    "new_harmonic_monomials": false,
+    "adaptive_basis_growth": false,
+    "rational_prefactor_search": false,
+    "generic_198_raw_jet_reopened": false
+  },
+  "shared_coefficient_system": {
+    "field": "Q",
+    "unknown_identity": "scalar-family x support-locked oriented primitive correction weight",
+    "sharing_rule": "The same exact rational unknown is used in every structurally active shell stratum and every overlapping harmonic-block projection belonging to its independent shift channel.",
+    "independent_channels": [
+      "n1",
+      "n2",
+      "n3",
+      "k1"
+    ],
+    "mirror_derived_channel": "l1",
+    "row_namespace": "local cell id x exact coefficient coordinate",
+    "row_namespace_reason": "Retaining the local cell id forbids cancellation between logically separate shell/block equations when constructing the global compatibility system.",
+    "global_consistency": "rank_Q([A_global|b_global]) = rank_Q(A_global)",
+    "global_inconsistency": "rank_Q([A_global|b_global]) > rank_Q(A_global)"
+  },
+  "solution_extraction": {
+    "admitted_only_for_globally_consistent_channel": true,
+    "exact_field": "Q",
+    "canonical_policy": "deterministic sparse elimination in declared unknown order with nonpivot/free coefficients set to zero",
+    "required_check": "direct exact substitution into every active local B equation",
+    "affine_solution_is_certificate": false,
+    "channelwise_solution_is_full_flux_certificate": false
+  },
+  "mirror_policy": {
+    "l1_independent_search": false,
+    "required_check": "Reconstruct the complete l1 global system independently, mirror the extracted k1 coefficient map exactly, and require exact substitution into all active l1 shell/block equations."
+  },
+  "negative_boundary": {
+    "meaning": "A globally inconsistent independent-channel system exactly excludes a complete shared-coefficient realization only for the declared support-locked degree-zero correction class.",
+    "higher_degree_excluded": false,
+    "expanded_support_excluded": false,
+    "other_correction_architectures_excluded": false,
+    "t3_refuted": false
+  },
+  "positive_boundary": {
+    "meaning": "Global channelwise compatibility plus exact coefficient extraction authorizes full correction-layer recombination as the next gate only.",
+    "full_correction_layer_recombined": false,
+    "full_symbolic_flux_identity_substituted": false,
+    "finite_boundary_assembly_completed": false,
+    "candidate_certificate": false,
+    "final_n_holonomic_search": false
+  },
+  "required_outputs": {
+    "global_exact_rank_and_augmented_rank_per_independent_channel": true,
+    "exact_solution_for_each_globally_consistent_channel": true,
+    "exact_local_substitution_replay": true,
+    "exact_k1_l1_solution_mirror": true,
+    "independent_verifier": true,
+    "mutation_tests": true
+  },
+  "finite_sampling_used_as_sum_proof": false,
+  "residual_sum_zero_proved": false,
+  "proof_effect": "NONE",
+  "promotion_effect": "NONE",
+  "t3_status": "OPEN_WITH_CHARACTERIZED_BLOCKER"
+}

campaigns/odd_zeta/OZ_RT_BZ_T3_010/T3_011_A_CONTRACT.json

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+{
+  "schema_version": "1.0.0",
+  "issue": 444,
+  "operation": "OZ-RT-BZ-T3-011-A",
+  "stage": "T3_011_A_EXACT_COKERNEL_GUIDED_SINGLE_CHANNEL_LINEAR_ZERO_RESPONSE_LIFT_VIABILITY_GATE",
+  "t3_010_c_checkpoint": {
+    "validated_head": "ca02bb6dad2970c169eb9b8745c871d4332447fb",
+    "producer_blob": "c6359f01c12011a22194bfe7ff960aa3e30452d3",
+    "contract_blob": "4f547f29d8bcb734f5e76816c5838d2b095a51b9",
+    "verifier_blob": "e7defaf7fb6fa05128923ecdb1023f07882d3d36",
+    "required_terminal": "BOUNDED_SUPPORT_LOCKED_DEGREE0_CORRECTION_CLASS_GLOBALLY_INCOMPATIBLE"
+  },
+  "bounded_correction_class": {
+    "id": "SUPPORT_LOCKED_SINGLE_CHANNEL_LINEAR_ZERO_RESPONSE_LIFT_001",
+    "base_class": "SUPPORT_LOCKED_ORIENTED_ONE_BODY_DEGREE0_WEIGHT_CORRECTION_001",
+    "independent_channels": ["n1", "n2", "n3", "k1"],
+    "mirror_derived_channel": "l1",
+    "channel_coordinate": {"n1": "n", "n2": "n", "n3": "n", "k1": "k", "l1": "l"},
+    "channel_coordinate_increment": {"n1": 1, "n2": 2, "n3": 3, "k1": 1, "l1": 1},
+    "candidate_bank": "exactly the complete-global-response-zero T3-010-C unknowns",
+    "expected_candidate_counts": {"n1": 49, "n2": 49, "n3": 49, "k1": 48},
+    "expected_independent_trials": 195,
+    "lifts_per_trial": 1,
+    "pairs_admitted": false,
+    "arbitrary_linear_combinations_admitted": false,
+    "new_harmonic_monomials": false,
+    "full_degree1_envelope": false,
+    "rational_prefactor_search": false,
+    "adaptive_basis_growth": false,
+    "generic_198_raw_jet_reopened": false
+  },
+  "lift_response": {
+    "equation": "Delta_c(x_c G)=x_c Delta_c(G)+(Delta_c x_c) S_c(G)",
+    "exact_field": "Q",
+    "coefficient_ring": "existing affine-Laurent Q ring from protected T3-009 residual canonicalization",
+    "shell_semantics": "preserve exact protected pinv specialization before coefficient-coordinate assembly"
+  },
+  "cokernel_gate": {
+    "witness": "deterministic finitely-supported exact row functional lambda_c",
+    "requirements": ["lambda_c A_c = 0", "lambda_c b_c = 1"],
+    "candidate_pairing": "lambda_c v_G",
+    "zero_pairing_rejection": true,
+    "nonzero_pairing_requires_exact_rank_test": true,
+    "rank_method": "exact Q incremental quotient/echelon reduction, with exact full-solver substitution for every rank-consistent candidate"
+  },
+  "canonical_selection": {
+    "candidate_order": "existing C unknown order restricted to zero global response columns",
+    "policy": "first exact-rank-consistent candidate in canonical order",
+    "selected_candidate_requires_exact_solution": true,
+    "selected_k1_requires_exact_l1_mirror_substitution": true
+  },
+  "positive_boundary": {
+    "meaning": "All four independent channels have a canonical single-lift exact solution and the selected k1 lift mirrors exactly to l1.",
+    "full_correction_layer_recombined": false,
+    "finite_boundary_assembly_completed": false,
+    "final_n_holonomic_search": false,
+    "next_gate": "separately governed full correction-layer reconstruction and exact recombination for the selected T3-011-A lift class"
+  },
+  "negative_boundary": {
+    "terminal": "BOUNDED_SINGLE_CHANNEL_LINEAR_ZERO_RESPONSE_LIFT_CLASS_EXHAUSTED",
+    "two_lift_class_authorized": false,
+    "full_degree1_authorized": false,
+    "expanded_support_authorized": false,
+    "rational_prefactor_search_authorized": false,
+    "generic_198_raw_jet_reopened": false
+  },
+  "required_outputs": {
+    "exact_cokernel_witness_per_independent_channel": true,
+    "exact_candidate_pairing_per_trial": true,
+    "exact_rank_classification_per_nonzero_pairing_trial": true,
+    "canonical_survivor_per_channel": true,
+    "exact_solution_and_substitution_for_rank_consistent_candidates": true,
+    "exact_k1_l1_mirror_for_selected_candidate": true,
+    "independent_verifier": true,
+    "mutation_tests": true
+  },
+  "residual_sum_zero_proved": false,
+  "proof_effect": "NONE",
+  "promotion_effect": "NONE",
+  "t3_status": "OPEN_WITH_CHARACTERIZED_BLOCKER"
+}

campaigns/odd_zeta/OZ_RT_BZ_T3_010/T3_011_B_AUTHORITY.md

@@ -0,0 +1,5 @@
+# Authority
+
+Issue #486 is the sole authority for this bounded successor. It descends from reviewed T3-011-A head `c7bdd6c76f7abd76ea39430dc6758418ea557a19` and merge commit `862f7680e1bf09f66f475c1f371f3c4a377f4cad`.
+
+The authorized class is `SUPPORT_LOCKED_SINGLE_CHANNEL_LINEAR_NONZERO_RESPONSE_LIFT_001`; exactly 311 one-column trials before `l1` mirror reduction. All broader classes remain closed.

campaigns/odd_zeta/OZ_RT_BZ_T3_010/T3_011_B_CONTRACT.json

@@ -0,0 +1,87 @@
+{
+  "schema_version": "1.0.0",
+  "issue": 486,
+  "operation": "OZ-RT-BZ-T3-011-B",
+  "stage": "T3_011_B_EXACT_COKERNEL_ACTIVE_SINGLE_CHANNEL_LINEAR_NONZERO_RESPONSE_LIFT_VIABILITY_GATE",
+  "t3_011_a_checkpoint": {
+    "reviewed_head": "c7bdd6c76f7abd76ea39430dc6758418ea557a19",
+    "merge_commit": "862f7680e1bf09f66f475c1f371f3c4a377f4cad",
+    "producer_blob": "af3fc961e768b08c059ee40b2058b735df20a1fc",
+    "contract_blob": "395ba53261d5480d5e6912948624e092d5d0048b",
+    "verifier_blob": "84d765ddce83e8a5af9b5b8f2362423e7eeed90c",
+    "required_terminal": "BOUNDED_SINGLE_CHANNEL_LINEAR_ZERO_RESPONSE_LIFT_CLASS_EXHAUSTED"
+  },
+  "bounded_correction_class": {
+    "id": "SUPPORT_LOCKED_SINGLE_CHANNEL_LINEAR_NONZERO_RESPONSE_LIFT_001",
+    "base_class": "SUPPORT_LOCKED_ORIENTED_ONE_BODY_DEGREE0_WEIGHT_CORRECTION_001",
+    "independent_channels": ["n1", "n2", "n3", "k1"],
+    "mirror_derived_channel": "l1",
+    "channel_coordinate": {"n1": "n", "n2": "n", "n3": "n", "k1": "k", "l1": "l"},
+    "channel_coordinate_increment": {"n1": 1, "n2": 2, "n3": 3, "k1": 1, "l1": 1},
+    "candidate_bank": "exactly the complete-global-response-nonzero T3-010-C unknowns",
+    "expected_candidate_counts": {"n1": 67, "n2": 67, "n3": 67, "k1": 110},
+    "expected_independent_trials": 311,
+    "lifts_per_trial": 1,
+    "pairs_admitted": false,
+    "arbitrary_linear_combinations_admitted": false,
+    "mix_with_zero_response_bank": false,
+    "new_harmonic_monomials": false,
+    "full_degree1_envelope": false,
+    "rational_prefactor_search": false,
+    "adaptive_basis_growth": false,
+    "generic_198_raw_jet_reopened": false,
+    "recurrence_search": false
+  },
+  "lift_response": {
+    "equation": "Delta_c(x_c G)=x_c Delta_c(G)+(Delta_c x_c) S_c(G)",
+    "exact_field": "Q",
+    "coefficient_ring": "existing affine-Laurent Q ring from protected T3-009 residual canonicalization",
+    "shell_semantics": "preserve exact protected pinv specialization before coefficient-coordinate assembly"
+  },
+  "cokernel_gate": {
+    "witness": "deterministic finitely-supported exact row functional lambda_c",
+    "requirements": ["lambda_c A_c = 0", "lambda_c b_c = 1"],
+    "candidate_pairing": "lambda_c v_G",
+    "zero_pairing_rejection": true,
+    "nonzero_pairing_requires_exact_rank_test": true,
+    "rank_method": "exact Q incremental quotient/echelon reduction, with exact full-solver substitution for every rank-consistent candidate"
+  },
+  "canonical_selection": {
+    "candidate_order": "existing T3-010-C unknown order restricted to nonzero global response columns",
+    "policy": "first exact-rank-consistent candidate in canonical order",
+    "selected_candidate_requires_exact_solution": true,
+    "selected_k1_requires_exact_l1_mirror_substitution": true
+  },
+  "positive_boundary": {
+    "meaning": "All four independent channels have a canonical single-lift exact solution and the selected k1 lift mirrors exactly to l1.",
+    "full_correction_layer_recombined": false,
+    "finite_boundary_assembly_completed": false,
+    "final_n_holonomic_search": false,
+    "next_gate": "separately governed exact correction-layer reconstruction and recombination for the selected T3-011-B lift class"
+  },
+  "negative_boundary": {
+    "terminal": "BOUNDED_SINGLE_CHANNEL_LINEAR_NONZERO_RESPONSE_LIFT_CLASS_EXHAUSTED",
+    "cokernel_active_subset_may_be_retained_for_separate_successor": true,
+    "two_lift_class_authorized": false,
+    "full_degree1_authorized": false,
+    "expanded_support_authorized": false,
+    "rational_prefactor_search_authorized": false,
+    "generic_198_raw_jet_reopened": false,
+    "recurrence_search_authorized": false
+  },
+  "required_outputs": {
+    "exact_cokernel_witness_per_independent_channel": true,
+    "exact_candidate_pairing_per_trial": true,
+    "exact_pairing_distribution_per_channel": true,
+    "exact_rank_classification_per_nonzero_pairing_trial": true,
+    "canonical_survivor_per_channel": true,
+    "exact_solution_and_substitution_for_rank_consistent_candidates": true,
+    "exact_k1_l1_mirror_for_selected_candidate": true,
+    "independent_verifier": true,
+    "mutation_tests": true
+  },
+  "residual_sum_zero_proved": false,
+  "proof_effect": "NONE",
+  "promotion_effect": "NONE",
+  "t3_status": "OPEN_WITH_CHARACTERIZED_BLOCKER"
+}

campaigns/odd_zeta/OZ_RT_BZ_T3_010/T3_011_B_RESULT_SCHEMA_NOTE.md

@@ -0,0 +1,11 @@
+# T3-011-B result ledger semantics
+
+The producer emits one exact JSON object. Each independent channel record contains the complete candidate ledger in canonical T3-010-C unknown order restricted to nonzero global response columns. Every trial records the exact cokernel pairing, whether an exact rank test was run, the resulting coefficient/augmented ranks when applicable, consistency classification, and any exact selected-solution digest.
+
+Canonical channel dispositions are:
+
+- `CANONICAL_SINGLE_LIFT_SURVIVOR`;
+- `COKERNEL_ACTIVE_SINGLE_LIFTS_EXACTLY_INCONSISTENT`;
+- `ALL_NONZERO_RESPONSE_SINGLE_LIFTS_COKERNEL_INVISIBLE`.
+
+The aggregate terminal is positive only if all four independent channels have a canonical survivor and the selected `k1` solution mirrors exactly to `l1`; otherwise the bounded class terminates as `BOUNDED_SINGLE_CHANNEL_LINEAR_NONZERO_RESPONSE_LIFT_CLASS_EXHAUSTED`.

campaigns/odd_zeta/OZ_RT_BZ_T3_010/T3_011_B_RUNBOOK.md

@@ -0,0 +1,11 @@
+# T3-011-B replay
+
+Governed replay entrypoints:
+
+```text
+python3 campaigns/odd_zeta/OZ_RT_BZ_T3_010/t3_011_b.py
+python3 campaigns/odd_zeta/OZ_RT_BZ_T3_010/verify_t3_011_b.py
+python3 tests/test_oz_rt_bz_t3_011_b.py
+```
+
+The producer output is the authoritative 311-trial candidate ledger only after independent verifier agreement. No successor class is inferred until the canonical per-channel geometry is read from that exact output.

campaigns/odd_zeta/OZ_RT_BZ_T3_010/T3_011_C_AUTHORITY.md

@@ -0,0 +1,12 @@
+# Authority
+
+Issue #494 is the sole authority for `OZ-RT-BZ-T3-011-C`.
+
+The audit is pinned to:
+
+- T3-011-B exact reviewed head `7876a44286f3c958bf03ce120117c2cd689b2379`;
+- protected merge commit `f8dc03a4e546a47b7a2b6d77a96d689f47e4d9a3`;
+- T3-011-B terminal `BOUNDED_SINGLE_CHANNEL_LINEAR_NONZERO_RESPONSE_LIFT_CLASS_EXHAUSTED`;
+- exactly 311 independent frozen candidates (`n1=67`, `n2=67`, `n3=67`, `k1=110`) and 110 mirror-derived `l1` checks.
+
+This authority is an implementation-semantics audit only. It creates no mathematical search authority beyond the frozen T3-011-B response bank.