nf.physics.rpcnf

Relational Point Coincidence Normal Form (RPCNF)

Contract ID: nf.physics.rpcnf | Family: physics | Index Status: draft | AuthorityEffect: None

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1. Executive Summary & Metadata

Relational Point Coincidence Normal Form (RPCNF) enforces structural normalization and explicit defect routing in the physics regime.

Property	Value
Canonical ID	nf.physics.rpcnf
Short Name	RPCNF
Full Name	Relational Point Coincidence Normal Form
Family	physics (Discrete Differential Geometry, Regge Calculus, Gauge Theory, Lattice Fermions & Quantum Gravity)
Qualification	Extended Form Contract (Normal Form Contract)
Data / Math Posture	at_rest
Index Status	draft
Theory Status	experimental
Verification Status	executable
Contract Version	v0
Governance Fence	AuthorityEffect: None (certified_implies_authorized: false)

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2. Visual Architecture & Normalization Diagram

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3. Concrete Worked Example & Mechanism

Visual Transition Summary

Stage	Carrier / Operator	Concrete State / Invariant
1. Before / Candidate Input	Input Carrier (RPCNF Candidate)	Anomaly risk: coordinate-drift ; update anomalies, spurious event ; duplication across coordinate...
2. Normalization / Gate	RPCNF Verification Gate	physical point identity a... (certified_implies_authorized: false)
3. After / Certified Output	Certified RPCNF Output	Invariant: ; ['event_relation_schema', ; 'candidate_key_K',...

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4. The Four-Pillar Quadrilateral & Non-Claims

Every contract in simplex-normal-forms is evaluated against the Four-Pillar Quadrilateral defined in contracts/_golden_nfs/standard.yaml:

Pillar	Requirement	Contract Specification for nf.physics.rpcnf
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	coordinate-drift update anomalies, spurious event duplication across coordinate charts, missing intersection events caused by coordinate transformations, and substantivalist manifold point reification
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: physical point identity as an invariant relational candidate key dependency K -> U, and lossless reference sheet decomposition under Heath's theorem Protected Skeleton: ['event_relation_schema', 'candidate_key_K', 'invariant_field_attributes', 'functional_dependency_K_to_U', 'lossless_join_reconstruction']
Pillar III: Lossless Reconstruction	State the non-loss reconstruction operator (join, direct sum, pullback, or replay).	Lossless reconstruction under declared projection, direct sum, or pullback operators.
Pillar IV: Syntactic Decidability	State how conformance is decided from declared constraints without unbudgeted scans.	Decidable from declared schema and witness metadata within bounded evaluation budgets.

Explicit Non-Claims (certified_implies_authorized: false)

• does not support that four scalar fields remain non-degenerate everywhere without caustics
• does not derive continuous Einstein manifolds from discrete relational tuples
• does not solve quantum gravity
• does not ensure under declared assumptions observer agreement on instrument calibration

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• relation_schema: R(U, F) where U = K union A
• candidate_key: K = {phi0, phi1, phi2, phi3} with |K| = 4
• coordinate_ban: U intersect {x0, x1, x2, x3} = empty_set
• functional_dependency: K -> U in F^+

5.2 Required Evidence

• relation_attributes: list
• candidate_key: list
• functional_dependencies: list
• coordinate_free_verified: boolean
• candidate_key_verified: boolean
• heaths_lossless_join_verified: boolean

5.3 Validation Criteria

Criterion ID	Name	Condition
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5.4 Terminal Route Map

Every evaluation terminates in a declared local route mapped to a canonical terminal in standard.yaml:

Local Terminal Route	Canonical Terminal
RelationalPointCertified	Preserve
NonKeyCoincidenceViolation	Repair
BareCoordinateContamination	Refuse
LossyObserverDecomposition	Repair
CausticDegeneracyDetected	Escalate
Unsupported	Unsupported

5.5 Declared Failure Modes

All defects route explicitly through the Terminal Route Map above.

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6. Epistemic Claim Hygiene Quadrant

In accordance with the repository's epistemic claim discipline:

1. What it supports:
   • Supports syntactic and operational checking of nf.physics.rpcnf (RPCNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (RelationalPointCertified, NonKeyCoincidenceViolation, BareCoordinateContamination, LossyObserverDecomposition) when required declarations or invariants fail.
2. What it does not support:
   • Does not confer operational authority (AuthorityEffect: None, certified_implies_authorized: false).
   • Does not claim semantic truth of undeclared external processes or unverified upstream inputs beyond the declaredprotected skeleton.
3. The narrowest defensible claim:
   • Within the declared substrate at_rest, this contract enforces that coordinate-drift update anomalies, spurious event duplication across coordinate charts, missing intersection events caused by coordinate transformations, and substantivalist manifold point reification is either excluded under physical point identity as an invariant relational candidate key dependency K -> U, and lossless reference sheet decomposition under Heath's theorem or routed to an explicit refusal/recovery terminal.
4. The next test needed:
   • Property-based falsification and mutation testing across boundary edge cases and composed multi-step pipelines for nf.physics.rpcnf.

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7. Canonical YAML Contract (contracts/nf.physics.rpcnf.yaml)

Click to expand full canonical YAML contract (contracts/nf.physics.rpcnf.yaml)

schema_version: smplx.nf.contract.v0
contract_kind: normal_form_contract
identity:
  id: nf.physics.rpcnf
  name: Relational Point Coincidence Normal Form
  short_name: RPCNF
  version: v0
  theory_status: experimental
  contract_status: draft
  verification_status: executable
  family: physics
  status: draft
classification:
  hierarchy_level: normal_form
  subject_kind:
  - spacetime_events
  - relational_algebra
  - point_coincidences
  data_posture: at_rest
  mathematical_posture: formal_algebraic
purpose:
  excludes_anomaly: coordinate-drift update anomalies, spurious event duplication across
    coordinate charts, missing intersection events caused by coordinate transformations,
    and substantivalist manifold point reification
  preserves_invariant: physical point identity as an invariant relational candidate key
    dependency K -> U, and lossless reference sheet decomposition under Heath's theorem
  protected_skeleton:
  - event_relation_schema
  - candidate_key_K
  - invariant_field_attributes
  - functional_dependency_K_to_U
  - lossless_join_reconstruction
  erased_structure:
  - bare_manifold_coordinates_x_mu
  - chart_transition_functions
  - unobservable_gauge_labels
  non_claims:
  - does not support that four scalar fields remain non-degenerate everywhere without caustics
  - does not derive continuous Einstein manifolds from discrete relational tuples
  - does not solve quantum gravity
  - does not ensure under declared assumptions observer agreement on instrument calibration
declarations_required:
- relation_schema: R(U, F) where U = K union A
- candidate_key: K = {phi0, phi1, phi2, phi3} with |K| = 4
- coordinate_ban: U intersect {x0, x1, x2, x3} = empty_set
- functional_dependency: K -> U in F^+
validation_criteria:
- first_normal_form_check: all attribute domains consist of atomic rational or discrete scalars
- key_minimality_check: exactly four scalar fields form K, with no proper subset determining U
- coordinate_absence_check: no bare manifold coordinates appear in the schema attribute set
- coincidence_determinism_check: all non-trivial functional dependencies X -> Y have X as a superkey
- lossless_decomposition_check: Heath's theorem r = pi_{KA}(r) bowtie pi_{KB}(r) holds exactly
terminal_routes:
- RelationalPointCertified
- NonKeyCoincidenceViolation
- BareCoordinateContamination
- LossyObserverDecomposition
- CausticDegeneracyDetected
- Unsupported
terminal_route_map:
  RelationalPointCertified: Preserve
  NonKeyCoincidenceViolation: Repair
  BareCoordinateContamination: Refuse
  LossyObserverDecomposition: Repair
  CausticDegeneracyDetected: Escalate
  Unsupported: Unsupported
definition:
  source: omega_engine_atlas/coda_atlas/F004_papers/004_general_relativity/003_relational_point_coincidence_and_witnessed_difference
  formal_statement: A spacetime field relation schema R(U, F) is in Relational Point Coincidence
    Normal Form (RPCNF) iff U contains no bare manifold coordinates, there exists a minimal
    four-attribute candidate key K = {phi0, phi1, phi2, phi3} such that K -> U in F^+, and every
    decomposition across observer sheets overlapping on K is lossless under Heath's theorem.
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: a draft contract is not a true normal form
    anomaly_exclusion: coordinate-dependent update and insertion anomalies
    lossless_join:
      status: heath
      statement: For any decomposition R1 = pi_{K union A}(R), R2 = pi_{K union B}(R),
        the join R1 bowtie R2 = R is strictly lossless because K is a candidate key.
    dependency_preservation:
      status: preserved_on_key_projection
      statement: All non-trivial functional dependencies are determined by candidate key K.
    syntactic_decision:
      status: schema_decidable
      statement: Decidable by testing functional dependencies on schema F and attribute set U.
canonical_terminal_map:
  RelationalPointCertified: Preserve
  NonKeyCoincidenceViolation: Repair
  BareCoordinateContamination: Refuse
  LossyObserverDecomposition: Repair
  CausticDegeneracyDetected: Escalate
  Unsupported: Unsupported
authorization:
  authorized_by: null
  certified_implies_authorized: false
certification:
  certificate_required: true
  certificate_kind: nf.physics.rpcnf_certificate
  obstruction_class_required: false
  loss_ledger_required: false
  loss_ledger_trigger_id: null
  verifier_required: true
evidence_required:
- relation_attributes: list
- candidate_key: list
- functional_dependencies: list
- coordinate_free_verified: boolean
- candidate_key_verified: boolean
- heaths_lossless_join_verified: boolean
schema_ref: ./normal_form_contract_schema.yaml