nf.epistemic.nar_nf

Non-Authoritative Realization Normal Form (NAR-NF)

Contract ID: nf.epistemic.nar_nf | Family: epistemic | Index Status: draft | AuthorityEffect: None

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1. Executive Summary & Metadata

Non-Authoritative Realization Normal Form (NAR-NF) enforces structural normalization and explicit defect routing in the epistemic regime.

Property	Value
Canonical ID	nf.epistemic.nar_nf
Short Name	NAR-NF
Full Name	Non-Authoritative Realization Normal Form
Family	epistemic (Observer-Relative Epistemic, Freshness, Context, Provenance & Distinguishability Contracts)
Qualification	Extended Form Contract (Normal Form Contract)
Data / Math Posture	at_rest
Index Status	draft
Theory Status	established
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 (NAR-NF Candidate)	Anomaly risk: shadow-authority ; leakage where downstream ; mathematical realizations R(S(n...
2. Normalization / Gate	NAR-NF Verification Gate	one-way representation ar... (certified_implies_authorized: false)
3. After / Certified Output	Certified NAR-NF Output	Invariant: ['genesis_state', ; 'representation_arrow', ; 'realization_target']

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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.epistemic.nar_nf
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	shadow-authority leakage where downstream mathematical realizations R(S(n)) inject unforced structure into Genesis
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: one-way representation arrow S(n) -> R(S(n)) with zero reverse generative authority Protected Skeleton: ['genesis_state', 'representation_arrow', 'realization_target']
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 deny the mathematical validity of R(S(n)) within its external framework
• does not grant execution authority

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• genesis_state
• representation_arrow
• external_realization

5.2 Required Evidence

• provenance_trace
• extension_forcing_witness

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	no extension rule in S(n+1) cites an external realization R(S(n)) as its generating authority
criterion	Check	representation arrows are strictly covariant and non-generative in reverse
criterion	Check	discovery of continuous or algebraic symmetries in R(S(n)) does not force new discrete symbols into S(n)

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
AcceptEndogenousGenesis	Preserve
RejectShadowAuthorityLeakage	Reject
RejectReverseGenerativeArrow	Refuse
QuarantineRealizationProposal	Quarantine

5.5 Declared Failure Modes

• symptom: an extension S(n) -> S(n+1) is justified by properties of continuous manifolds or Hilbert spaces, diagnosis: shadow-authority leakage violating Boxed Law 2, terminal: RejectShadowAuthorityLeakage
• symptom: realization mapping R contains an arrow R(S(n)) -> S(n+1), diagnosis: illegal reverse generative arrow, terminal: RejectReverseGenerativeArrow

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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.epistemic.nar_nf (NAR-NF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (AcceptEndogenousGenesis, RejectShadowAuthorityLeakage, RejectReverseGenerativeArrow, QuarantineRealizationProposal) 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 shadow-authority leakage where downstream mathematical realizations R(S(n)) inject unforced structure into Genesis is either excluded under one-way representation arrow S(n) -> R(S(n)) with zero reverse generative authority 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.epistemic.nar_nf.

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7. Canonical YAML Contract (contracts/nf.epistemic.nar_nf.yaml)

Click to expand full canonical YAML contract (contracts/nf.epistemic.nar_nf.yaml)

schema_version: smplx.nf.contract.v0
contract_kind: form_contract
identity:
  id: nf.epistemic.nar_nf
  name: Non-Authoritative Realization Normal Form
  short_name: NAR-NF
  version: v0
  status: draft
  family: epistemic
  theory_status: established
  contract_status: draft
  verification_status: executable
classification:
  hierarchy_level: form
  subject_kind:
  - mathematical_realization
  - representation_arrow
  - genesis_state
  data_posture: at_rest
  mathematical_posture: formal_algebraic
purpose:
  excludes_anomaly: shadow-authority leakage where downstream mathematical realizations R(S(n)) inject unforced structure into Genesis
  preserves_invariant: one-way representation arrow S(n) -> R(S(n)) with zero reverse generative authority
  protected_skeleton:
  - genesis_state
  - representation_arrow
  - realization_target
  erased_structure:
  - realization_specific_auxiliaries
  non_claims:
  - does not deny the mathematical validity of R(S(n)) within its external framework
  - does not grant execution authority
declarations_required:
- genesis_state
- representation_arrow
- external_realization
evidence_required:
- provenance_trace
- extension_forcing_witness
validation_criteria:
- no extension rule in S(n+1) cites an external realization R(S(n)) as its generating authority
- representation arrows are strictly covariant and non-generative in reverse
- discovery of continuous or algebraic symmetries in R(S(n)) does not force new discrete symbols into S(n)
proof_obligations:
- id: narnf.boxed_law_two
  status: upstream_theorem
  ref: 002_s_n
  section: sn.md
terminal_routes:
- AcceptEndogenousGenesis
- RejectShadowAuthorityLeakage
- RejectReverseGenerativeArrow
- QuarantineRealizationProposal
terminal_route_map:
  AcceptEndogenousGenesis: Preserve
  RejectShadowAuthorityLeakage: Reject
  RejectReverseGenerativeArrow: Refuse
  QuarantineRealizationProposal: Quarantine
certification:
  certificate_required: true
  certificate_kind: realization_boundary_certificate
  obstruction_class_required: false
  loss_ledger_required: false
  verifier_required: true
authorization:
  authorized_by: null
  certified_implies_authorized: false
failure_modes:
- symptom: an extension S(n) -> S(n+1) is justified by properties of continuous manifolds or Hilbert spaces
  diagnosis: shadow-authority leakage violating Boxed Law 2
  terminal: RejectShadowAuthorityLeakage
- symptom: realization mapping R contains an arrow R(S(n)) -> S(n+1)
  diagnosis: illegal reverse generative arrow
  terminal: RejectReverseGenerativeArrow
definition:
  formal_statement: a derivation step is in Non-Authoritative Realization Normal Form iff all generative morphisms are strictly endogenous to S(n) and every external mathematical realization R(S(n)) has zero authority to extend S(n)
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: epistemic_boundary_not_relational_project_join
    anomaly_exclusion: shadow-authority leakage and reverse generative arrows
    lossless_join:
      status: one_way_representation
      statement: realization is uniquely determined by representation arrow rho and Genesis state
    dependency_preservation:
      status: endogenous_preservation
      statement: endogenous Genesis invariants are preserved without external axioms
    syntactic_decision:
      status: provenance_decidable
      statement: decidable by checking whether generating authorities in the provenance graph belong to Genesis
schema_ref: ./normal_form_contract_schema.yaml