{ "schema": "nexah.a0.jarp-cross-lens-extension/1.0.0", "extension_id": "A0:JARP:X1", "extends_protocol": "A0:JARP:V1", "date": "2026-10-13", "status": "INTERNAL_SOURCE_BOUND_ENGINEERING_EXTENSION_NOT_SCIENCE_RUN", "publication_authorized": false, "frozen_core_unchanged": true, "result_vocabulary": [ "PASS_EXACT_RETURN", "PASS_EXACT_PROFILE", "PASS_NEGATIVE_CONTROL", "HOLD_MISSING_WITNESS", "HOLD_UNRESOLVED_ALIAS", "REJECT_IDENTITY_COLLAPSE" ], "cases": [ { "id": "APP-11", "title": "Q4 placement and complement return", "class": "representation-return", "input": { "addresses": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], "one_based_magic_square": [16, 2, 3, 13, 5, 11, 10, 8, 9, 7, 6, 12, 4, 14, 15, 1] }, "operator": "v=x-1, four-bit complement c(v)=15-v, declared 4x4 placement", "expected": { "address_count": 16, "complement_involution": true, "complement_pair_sum_zero_based": 15, "magic_line_sum_one_based": 34, "result": "PASS_EXACT_RETURN" }, "required_witness": ["placement operator", "label convention"], "application": "return between Q4 addresses, decimal labels and one declared magic-square placement", "source_roles": ["ART:A0:MATHEMATICAL_JOINTS", "MOD:NUMBER_VIEW_SUITE"] }, { "id": "APP-12", "title": "Boundary graph and Pascal mirror", "class": "typed-joint", "input": {"a": 47, "b": 74}, "operator": "n=a+b with Pascal comparator C(n,a)=C(n,b)", "expected": { "n": 121, "mirror_index": 74, "grid_side": 11, "grid_area": 121, "result": "PASS_EXACT_PROFILE" }, "required_witness": ["ordered rectangle sides", "declared n=a+b bridge"], "application": "typed bridge between boundary inputs and Pascal mirror symmetry without carrier identity", "source_roles": ["ART:A0:MATHEMATICAL_JOINTS", "ART:NUMBER:PRIMEGRID_BLOCK02A_PASCAL"] }, { "id": "APP-13", "title": "Pascal to quaternion four-channel return", "class": "exact-connector", "input": {"pascal_triple": [3, 4, 5]}, "operator": "Phi(a,b,c)=(a+b+c)1+ai+bj+ck", "expected": { "quaternion_channels": [12, 3, 4, 5], "inverse_coordinates": [3, 4, 5], "injective_on_declared_carrier": true, "c3_equivariant": true, "result": "PASS_EXACT_RETURN" }, "required_witness": ["channel order", "declared carrier"], "application": "lossless four-channel serializer with an exact inverse on the declared Pascal carrier", "source_roles": ["A0OE:PASCAL_QUATERNION_TEST", "ART:A0:MATHEMATICAL_JOINTS"] }, { "id": "APP-14", "title": "Q106 fold and interface residual", "class": "residual-return", "input": {"dimension": 3, "folded_coordinates": 2, "interface_branch_bits": 1}, "operator": "coordinate fold plus declared interface assembly", "expected": { "fiber_size": 8, "pointwise_minimal_witness_bits": 3, "uniform_coordinate_witness_bits": 3, "result": "PASS_EXACT_RETURN" }, "required_witness": ["two fold bits", "one interface branch bit"], "application": "minimal residual budget for branch-aware Return after a lossy fold and interface gluing", "source_roles": ["NN:MRB_ACR_NCS_Q106_RETURN_CROSSWALK", "A0OE:PASCAL_PENTAGON_D5_TEST"] }, { "id": "APP-15", "title": "GAME 4 LIFE +1 synchronized view return", "class": "multi-view-identifiability", "input": { "carrier": "LIFE08-BOUNDARY-CYLINDER", "view_keys": ["field", "event-register", "q-control", "parallel-3d", "residual"] }, "operator": "project one deterministic transition record into five typed synchronized views", "expected": { "view_count": 5, "shared_carrier": true, "new_life_rule": false, "result": "PASS_EXACT_RETURN" }, "required_witness": ["persistent cell/event addresses", "transition index", "view type"], "application": "cross-view synchronization and exact source return without cross-domain mechanism transfer", "source_roles": ["NEXAH_LIFE_BOUNDARY_CYLINDER_LIFE08_2026_10_11", "ART:A0:MATHEMATICAL_JOINTS"] }, { "id": "APP-16", "title": "LIFE08 and E8 coordinate non-identity control", "class": "matched-control", "input": { "holdout_half_residuals": 33, "spinor_half_selections": 97, "holdout_records": 150, "permutation_reproduces_rate": true }, "operator": "compare observed coordinate/root residuals with random-axis, rotated-E8 and permuted-channel controls", "expected": { "half_residual_explained_by_coordinate_root_family": true, "semantic_channel_order_specific": false, "e8_specificity_established": false, "life_e8_identity": false, "result": "PASS_NEGATIVE_CONTROL" }, "required_witness": ["coordinate convention", "root family", "matched control class"], "application": "retain the useful residual explanation while rejecting an E8-specific LIFE mechanism", "source_roles": ["LIFE04B1", "LIFE08-BOUNDARY-CYLINDER"] }, { "id": "APP-17", "title": "ROOT7 and epsilon7 alias gate", "class": "alias-and-namespace-control", "input": {"vector": [2, 1, 1, 1], "candidate_alias": "epsilon7"}, "operator": "compute norm and search the bound ROOT7 source contract for the candidate alias", "expected": { "norm_squared": 7, "norm": "sqrt(7)", "root7_axis_identifiable": false, "epsilon7_source_definition_found": false, "result": "HOLD_UNRESOLVED_ALIAS" }, "required_witness": ["dated epsilon7 source definition", "typed map to ROOT7", "operator and return rule"], "application": "keep exact ROOT7 arithmetic while preventing an unsupported epsilon7 identity", "source_roles": ["NEXAH:NAVIGATOR:ROOT7:LOOK:2026-10-08", "MOD:TESSAREC", "MOD:NUMBER_VIEW_SUITE"] }, { "id": "APP-18", "title": "ILAU typed residual completeness gate", "class": "residual-schema", "input": { "required_fields": ["point", "direction", "curvature", "history"], "provided_fields": ["point", "direction"] }, "operator": "typed Return/Residual completeness audit", "expected": { "missing_fields": ["curvature", "history"], "complete": false, "result": "HOLD_MISSING_WITNESS" }, "required_witness": ["curvature residual", "history/provenance address"], "application": "fail-closed handoff between visual orientation instruments and machine-readable Return records", "source_roles": ["ILAU:RETURN_RESIDUAL_LOCK", "ILAU:FROM_GAP_TO_RETURN"] } ], "identity_reuse": [ "NN:A0_JOINT_APPLICATION_RETURN_PROTOCOL", "ART:A0:MATHEMATICAL_JOINTS", "MOD:TESSAREC", "MOD:NUMBER_VIEW_SUITE", "NN:MRB_ACR_NCS_Q106_RETURN_CROSSWALK", "NEXAH:NAVIGATOR:ROOT7:LOOK:2026-10-08", "NEXAH_LIFE_BOUNDARY_CYLINDER_LIFE08_2026_10_11", "A0OE:PASCAL_QUATERNION_TEST" ], "claim_ceiling": "Exact finite representation, Return, residual and matched-control engineering only. LIFE, E8, ROOT7, epsilon7, Q4, Pascal and ILAU remain non-identical source domains; no new Study, E8/LIFE mechanism, epsilon7 identity, physical law, canonical count change or publication authority." }