Prove all-width input kernels for native full-frame histories (no new κ)

research/physical-zqy-scalar-span/ABI-CLOSURE.json

@@ -0,0 +1,32 @@
+{
+  "base_exact_non_Y_projection_rank_from_primary": 546,
+  "base_exact_rank_from_primary": 546,
+  "base_operator_count": 59,
+  "base_operator_set_sha256": "34ad3a3f37a53afd59e0d295d6dffa446819539b9ac46556ef51134eb888d831",
+  "base_rank_obligation": "The registered primary verify.py must pass; this command authenticates/replays the source and consumes its exact 546/546 certificate, rather than rerunning the large exact elimination.",
+  "coefficient_scope": "arbitrary complex scalar coefficients, allowed to depend on width",
+  "conclusion": "For every f>=59707 the declared finite left-image span has no nonzero pure-Y vector. Thus it cannot supply the nonzero eight-mode b=ZQY by an exact all-width identity within this fixed family.",
+  "distinct_left_maps": 1012,
+  "distinct_left_products": 59708,
+  "input_sha256": {
+    "normalizers": "ae8aad06aa5d1811d725895b3ab5a4f4daa9dcdd88294aa0d5f723e78bb1e0da",
+    "provider_interface": "676de7551d3364598f4a7e29ae97cae0e4364348786bbe70435b84294ba7dd65"
+  },
+  "left_map_set_sha256": "e83c2c7f31983321d0f1908d1c1aeb3a9ba1f63cc17106b6089e3cf833c33ccb",
+  "left_product_set_sha256": "ac702db8dfcf74b29c17686c0899ad1f2b805c50d23ef5e0cee013c57c65e24e",
+  "left_support_collision_count": 0,
+  "mode_normalizers": 8,
+  "new_kappa": false,
+  "physical_to_logical_left_transport": "F9^-1 T F9 = T, including absolute phase; all seeds centralize the full nine-axis Gaussian and so do their products.",
+  "port_normalizers": 112,
+  "product_exact_zero_anchor_checks": 59708,
+  "provider_full_frame_versions": 4891,
+  "raw_left_family_size": 1017,
+  "schema": "physical-zqy-fixed-abi-left-images/v1",
+  "scope": "Provider-backward whole history; independently chosen left images T in {I,Kp_i,Km_a,Km_a^-1 Kp_i}. No unrestricted products of these generators, no arbitrary monomial left closure, no changed producer or extra correlated data; no small-width nonmembership claim.",
+  "seed_exact_F9_signed_kernel_address_checks": 61440,
+  "seed_normalizer_inverse_additions": 0,
+  "status": "PASS_FIXED_Z_ABI_LEFT_IMAGES_EVENTUAL_WIDTH_NO_NEW_KAPPA",
+  "target_or_paid_profile_change": false,
+  "tensor_independence_degree_bound": 59707
+}

research/physical-zqy-scalar-span/FORMAL-KERNEL.json

@@ -0,0 +1,34 @@
+{
+  "actual_operator_identifications_used": false,
+  "cases": {
+    "provider_backward": {
+      "exact_formal_HK_zero": true,
+      "full_frame_histories": 4891,
+      "history_formal_terms": 119521,
+      "kernel_formula": "[I_112;I_112;0_408x112]",
+      "maximum_surviving_word_length": 1
+    },
+    "source_backward": {
+      "exact_formal_HK_zero": true,
+      "full_frame_histories": 5019,
+      "history_formal_terms": 80007,
+      "kernel_formula": "[I_112;I_112;0_408x112]",
+      "maximum_surviving_word_length": 1
+    },
+    "source_forward": {
+      "exact_formal_HK_zero": true,
+      "full_frame_histories": 4968,
+      "history_formal_terms": 94439,
+      "kernel_formula": "[0_112x112;I_112;0_408x112]",
+      "maximum_surviving_word_length": 1
+    }
+  },
+  "distinct_native_generator_names": 72,
+  "matrix_sum_relations_used": false,
+  "phase_or_group_normalization_used": false,
+  "reductions": "Only adjacent signed inverse cancellation on free words.",
+  "schema": "native-full-history-freeword-kernel/v1",
+  "scope": "Formal corroboration of the three frozen full-frame observation families, considered separately. Scalar identities over these formal words survive any consistent assignment of invertible operators, hence every tensor width. Ownership and legal native physical semantics remain inherited from the actual source.",
+  "source_native_sha256": "1bad1ffe747c3977d1a6bc1cfa9faa4127e38cbf49d7fcf4ae8060fbc7f67d4e",
+  "status": "PASS_FORMAL_FREEWORD_RIGHT_KERNEL_THREE_CASES"
+}

research/physical-zqy-scalar-span/INDEPENDENT-KERNEL-AUDIT.json

@@ -0,0 +1,83 @@
+{
+  "K_Y_identity_columns": 112,
+  "actual_group_annihilation_checks": 4891,
+  "actual_observation_operator_count": 59,
+  "actual_observation_operator_set_sha256": "34ad3a3f37a53afd59e0d295d6dffa446819539b9ac46556ef51134eb888d831",
+  "all_width_reason": "Each exact signed group identity lifts by operator composition to every tensor width. H_j K=0 retains scalar owner coefficients outside tensor powers and does not use physical width-one linear relations.",
+  "augmentation_nonY_rank": 474,
+  "controls": {
+    "Y_variation_without_nonY_compensation": {
+      "coefficient": "1/2",
+      "event": {
+        "event": 15380,
+        "frame": 1,
+        "role": [
+          "L",
+          299
+        ]
+      },
+      "first_nonzero_group_column": [
+        0,
+        17
+      ],
+      "history": 79,
+      "residual_terms": 4
+    },
+    "supplied_original_Y0_identity_observation": {
+      "identity_operator_coefficient": "1",
+      "non_annihilated_Y_column": 0
+    },
+    "wrong_Y_row": {
+      "coefficient": "1/2",
+      "event": {
+        "event": 15875,
+        "frame": 1,
+        "role": [
+          "L",
+          0
+        ]
+      },
+      "first_nonzero_group_column": [
+        0,
+        0
+      ],
+      "history": 269,
+      "residual_terms": 1
+    },
+    "wrong_nonY_compensation": {
+      "coefficient": "1/2",
+      "event": {
+        "event": 15875,
+        "frame": 1,
+        "role": [
+          "L",
+          0
+        ]
+      },
+      "first_nonzero_group_column": [
+        0,
+        0
+      ],
+      "history": 269,
+      "residual_terms": 1
+    }
+  },
+  "full_frame_histories": 4891,
+  "kernel_sha256": "250947ff109dcb1e72f9a379e40d82aed099f2925894537719bf719525a916ca",
+  "kernel_shape": "K=[I112;I112;0_408], and zero on all nine owned inputs",
+  "limits": "Only the unchanged frozen native full-frame snapshots. Separate reads of partial-frame/main Y, modified paid contacts/history or new supplied correlated observations are outside this theorem. Fixing helper or owned values alone does not evade this particular kernel, because it changes only X and Y. No paid lower bound, new caller or new kappa is asserted.",
+  "method": "Own Fraction elimination of augmentation proposes scalar K; decisive independent verification is H_j K=0 in every actual group coefficient of every original replay row. No decomposition certificate, search import, modular calculation or width-one matrix-sum relation is used. The candidate is derived without reading saved kernel rows, then compared with KERNEL.json.",
+  "nonzero_nonY_compensating_original_roles": 112,
+  "original_K_nonzero_entries": 224,
+  "original_history_group_terms": 119515,
+  "original_independent_roles": 632,
+  "owned_entry_roles": 9,
+  "paired_X_Y_group_terms_checked": 11262,
+  "physical_chart_guard": "Logical source variables are converted to physical independent inputs by their invertible birth frames. All snapshots share the one full inverse-transpose Gaussian Phi. Right birth factors and common Phi preserve annihilation and the hidden-Y fiber; owned chart/precision execution remains inherited.",
+  "seconds": 3.311939083971083,
+  "source_owned_compensation_is_zero": true,
+  "source_payload_sha256": "7679daa4ec6a40f56fc7f0202379a6f454310e94945aba4f48beaaaafb838d05",
+  "source_word_sha256": "7dc356001ed597ad6fc9fd3e0bc6ff7e3ec3a580a579a956827aa17fccfdd2dc",
+  "status": "PASS_INDEPENDENT_ORIGINAL_GROUP_HISTORY_HIDDEN_Y_KERNEL",
+  "theorem": "At every width, every original Y variation can be compensated by the same logical X variation, with all helpers and owned entries fixed, leaving every admitted full-frame history unchanged. Therefore no nonzero pure-Y linear observation lies in their module even under arbitrary address-End left coefficients; no deterministic postprocessing of only those snapshots can recover a nonconstant function of Y."
+}