{ "module_name": "IPD-12", "module_category": "framework", "module_version": "2026-1.1", "last_updated": "2026-07-10", "module_purpose": "Define the IPD-12 (Intransitive Prime-Numbered 12-Sided Engine) as a first-class framework artifact and agentic operator system within TriadicFrameworks, providing a physicalizable operator engine that encodes intransitive, prime-indexed cycles compatible with RTT, GU, FFT, and Pantheon structures, and specifying the agent classes, probe envelope, and output contract required to operate it.", "module_summary": "IPD-12 is a 12-faced, prime-indexed, intransitive operator engine that serves as the structural backbone of the TriadicFrameworks vST Micro-Agent. Each face corresponds to a prime-labeled operator state (P2–P37); directed intransitive relations between faces form four triad cycles, two hex-cycles, and one full paradox loop. The engine is operated by four agent classes (Envelope Interrogator, Structural Operator, Integration Coordinator, Coherence Guardian) against a 12-probe structural envelope. This module formalizes IPD-12 as a framework object, enabling RTT resonance-first interpretations, GU geometric embeddings, FFT field-theoretic cycle analysis, and Pantheon-tier mappings, and provides a complete 4×4×4 substrate cube (64 primitives) as its dimensional foundation.", "apex_operators": { "ipd_face_prime": "Represents a prime-indexed operator state on one of the 12 faces.", "ipd_intransitive_edge": "Directed relation between two faces forming non-transitive cycles.", "ipd_cycle": "Closed intransitive loop over a subset of faces (triad, hex, or full paradox loop).", "ipd_regime_transition": "Mapping of IPD cycles to RTT regime transitions.", "ipd_coherence_stabilizer": "Use of prime gaps and cycle structure as coherence stabilizers.", "ipd_envelope_interrogator": "Class A agent operator: resolves all 12 probe fields sequentially before any structural operator runs.", "ipd_structural_operator": "Class B agent operator: executes pattern, periodicity, local_symmetry, or transition_topology operators against a normalized stream guided by the filled envelope.", "ipd_integration_coordinator":"Class C agent operator: consolidates multi-operator results, enforces the output contract, and routes completed interpretations to storage.", "ipd_coherence_guardian": "Class D agent operator: monitors sessions for drift, invariant violations, and semantic inference contamination; issues WARN, HALT, or RESET signals." }, "structure_descriptors": { "faces": 12, "prime_sequence": [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37], "indexing_scheme": "Prime-numbered labels assigned to operator states; the first 12 primes map to 12 canonical positions.", "relation_type": "Directed, intransitive comparisons between faces.", "cycle_behavior": "Non-transitive cycles that model paradox and regime transitions; three nested levels: 4 triads, 2 hex-cycles, 1 full paradox loop.", "physicalizable": "Specified as a dodecahedral die with one prime face per side; see physical_layout.md.", "substrate_cube": "4×4×4 dimensional model: 4 substrate pairs × 4 observer modes × 4 regime shells = 64 substrate primitives.", "probe_envelope": "12 orthogonal probe fields (intent, regime, scale, transition, boundary, invariants, modifiers, substrate, lineage, failure_mode, time_regime, symmetry) that must all be resolved before any operator runs.", "hard_stop_fields": ["intent", "invariants", "substrate"] }, "resonance_descriptors": { "rtt_mapping": "IPD cycles interpreted as RTT paradox and regime operators over resonance fields.", "coherence_use": "Prime gaps and cycle stability used as coherence indicators; P11 and P31 are dedicated coherence-node operators.", "drift_interpretation":"Slow changes in cycle structure treated as drift; P5 and P29 are drift-anchor operators; drift is on-by-default and must be explicitly bounded.", "dimensional_hooks": "12-fold structure compatible with TriadicFrameworks canonical twelve-layer architectures; P23 activates +1D lift, P29 activates −1D collapse.", "session_anchor": "rtt=1 | coherence=declared | drift=bounded | paradox=structural" }, "observer_model": { "triadic_view": "Observer interacts with IPD-12 via choice (field / O1), cycle recognition (regime / O2), and stability assessment (coherence / O3).", "apex_view": "O4 (Apex) observer queries dimensional effects through P23, P29, and P37 at the +1D high-order level.", "pantheon_view":"Faces and cycles mapped to Celestial (P2–P7), Civilizational (P11–P19), and Chthonic (P23–P37) tiers.", "gu_view": "IPD cycles embedded as geometric states in GU-compatible interpretations: Connection (P2, P3), Curvature (P7, P11), Dilaton (P11, P31), Anomaly (P13, P37), Observerse (P17, P19, P23).", "fft_view": "Triad crossings = regime transitions; hex-cycle completions = boundary events; full paradox loop = dimensional gate; intransitive edges = closed flux loop topology." }, "paradox_and_cycles": { "paradox_summary": "Intransitive relations between faces generate paradox loops analogous to RTT paradox operators. Paradox is a structural condition, not an error; it is held open as a stable cycle rather than forced to collapse.", "cycle_summary": "Directed cycles over prime-indexed faces provide a combinatorial model of regime transitions and paradox resolution. Three nested levels: 4 triad cycles (3 nodes each), 2 hex-cycles (6 nodes each), 1 full paradox loop (12 nodes).", "triad_cycles": { "T1_Celestial": "P2 → P3 → P5 → P2", "T2_Coherence": "P7 → P11 → P13 → P7", "T3_Observerse": "P17 → P19 → P23 → P17", "T4_Apex": "P29 → P31 → P37 → P29" }, "hex_cycles": { "H1_Lower": "P2 → P3 → P5 → P7 → P11 → P13 → (back)", "H2_Upper": "P17 → P19 → P23 → P29 → P31 → P37 → (back)" }, "full_paradox_loop": "P2 → P3 → P5 → P7 → P11 → P13 → P17 → P19 → P23 → P29 → P31 → P37 → (back to P2)" }, "agent_model": { "summary": "Four agent classes govern all IPD-12 operations. No operator may run without a fully resolved envelope from Class A. Class D has unconditional interrupt authority over all other classes.", "class_a": "Envelope Interrogator — fills all 12 probe fields sequentially; no partial envelope may pass downstream.", "class_b": "Structural Operator — executes selected operators (pattern, periodicity, local_symmetry, transition_topology) against the normalized stream.", "class_c": "Integration Coordinator — consolidates multi-operator results, validates against schema, enforces output contract, routes to storage.", "class_d": "Coherence Guardian — monitors for drift, invariant violations, semantic inference contamination; issues WARN / HALT / RESET.", "output_contract_annotation": "Structural interpretation only; no semantic inference.", "full_spec": "./AGENTS.md" }, "documentation_inventory": { "about": { "file": "ABOUT.md", "role": "about", "description": "What, why, when, and where of the IPD-12 engine." }, "agents": { "file": "AGENTS.md", "role": "agents", "description": "Agent class manifest: permissions, prohibitions, task catalog, safety rules, collaboration models." }, "glossary": { "file": "GLOSSARY.md", "role": "glossary", "description": "Canonical single-source-of-truth definitions for all IPD-12 terms." }, "readme": { "file": "README.md", "role": "index", "description": "Front-door summary and module manifest." }, "module": { "file": "module.json", "role": "signature", "description": "Canonical agentic module schema." }, "operators": { "file": "operators.json", "role": "engine", "description": "Prime-indexed operator registry: all 12 states, edges, RTT/GU/Pantheon mappings." }, "regime_map": { "file": "regime_map.md", "role": "map", "description": "RTT regime shell mappings to IPD-12 cycles." }, "engine_block": { "file": "engine_block.md", "role": "engine", "description": "Engine block architecture: manifolds, rails, observer modes, output headers." }, "observer_model": { "file": "observer_model.md", "role": "engine", "description": "Triadic observer lattice: O1–O4 modes, prime subsets, dimensional levels." }, "observer_first": { "file": "observer_first_engine.md", "role": "engine", "description": "Observer-first execution model." }, "substrate_prims": { "file": "substrate_primitives.md", "role": "engine", "description": "4×4×4 substrate cube: 64 substrate primitive definitions." }, "substrate_json": { "file": "substrate_primitives.json", "role": "engine", "description": "Machine-readable 64-entry substrate primitive table." }, "substrate_schema":{ "file": "substrate.schema.json", "role": "engine", "description": "JSON schema for substrate engine validation." }, "dim_lift_map": { "file": "dimensional_lift_collapse_map.md", "role": "map", "description": "+1D / −1D transition diagrams." }, "prime_profiles": { "file": "prime_state_dimensional_profiles.md","role": "engine", "description": "Per-prime dimensional profiles." }, "cycle_diagrams": { "file": "cycle_diagrams.md", "role": "map", "description": "Visual cycle maps for triad, hex, and full paradox loop." }, "cycle_animation": { "file": "cycle_animation_ascii.md", "role": "map", "description": "ASCII cycle animation frames." }, "physical_layout": { "file": "physical_layout.md", "role": "extension", "description": "Physicalizable dodecahedral die specification." }, "output_headers": { "file": "output_headers.md", "role": "extension", "description": "H-RTT / H-GU / H-FFT / H-Pantheon / H-Meta output header definitions." }, "hpc_qc": { "file": "hpc_qc_substrate_engine.md", "role": "extension", "description": "HPC and quantum-computing substrate engine extensions." }, "compat_notes": { "file": "compatibility_notes.md", "role": "extension", "description": "RTT / GU / FFT / Pantheon interoperability constraints." }, "compat_tests": { "file": "compatibility_tests.md", "role": "diagnostic", "description": "Cross-framework compatibility test suite." }, "g_capture": { "file": "g_Capture.md", "role": "profile", "description": "Primary session capture and operator profile." }, "examples": { "file": "examples.md", "role": "example", "description": "Worked operator examples." } }, "capture_files": { "about": "./ABOUT.md", "agents": "./AGENTS.md", "glossary": "./GLOSSARY.md", "primary_capture": "./g_Capture.md", "operator_registry": "./operators.json", "regime_map": "./regime_map.md", "examples": "./examples.md" }, "roles": { "about": ["ABOUT.md"], "agents": ["AGENTS.md"], "glossary": ["GLOSSARY.md"], "engine": ["operators.json", "engine_block.md", "observer_model.md", "observer_first_engine.md", "substrate_primitives.md", "substrate_primitives.json", "substrate.schema.json", "prime_state_dimensional_profiles.md"], "profile": ["g_Capture.md"], "signature": ["module.json"], "diagnostic": ["compatibility_tests.md"], "map": ["regime_map.md", "dimensional_lift_collapse_map.md", "cycle_diagrams.md", "cycle_animation_ascii.md"], "example": ["examples.md"], "extension": ["compatibility_notes.md", "physical_layout.md", "output_headers.md", "hpc_qc_substrate_engine.md"], "index": ["README.md"], "template": ["module_template.md"] }, "analyzer_layers": { "operator": ["apex_operators", "structure_descriptors"], "regime": ["regime_map.md"], "coherence": ["resonance_descriptors"], "paradox": ["paradox_and_cycles"], "agent_model": ["AGENTS.md", "agent_model"], "cross-cutting":["compatibility_notes.md", "GLOSSARY.md"] }, "ai_metadata": { "ai.module": "IPD-12", "ai.version": "2026-1.1", "ai.last_updated":"2026-07-10", "ai.purpose": "Intransitive prime-numbered 12-sided operator engine with four agent classes, a 12-probe structural envelope, and a 4×4×4 substrate cube.", "ai.keywords": [ "IPD-12", "intransitive dice", "intransitive engine", "prime-indexed operators", "prime states", "12 probe fields", "structural envelope", "agent classes", "envelope interrogator", "structural operator", "integration coordinator", "coherence guardian", "vST Micro-Agent", "vST-SQL", "RTT", "Geometric Unity", "Framework Field Theory", "FFT", "pantheon", "framework artifact", "resonance fields", "paradox cycles", "regime transition", "dimensional lift", "dimensional collapse", "substrate cube", "substrate primitives", "drift", "coherence", "output contract", "structural operators", "GLOSSARY" ], "ai.audience": "Framework architects, RTT practitioners, combinatorial theorists, AI agent designers, substrate modelers, game and tool designers.", "ai.module.summary": "A physicalizable, prime-indexed, intransitive 12-sided operator engine with agent classes, structural probe envelope, and substrate cube.", "ai.module.category": "framework" } }