nf.wdp.wdnf

Witnessed Difference Normal Form (WDNF)

Contract ID: nf.wdp.wdnf | Family: derivation | Index Status: draft | AuthorityEffect: None

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1. Executive Summary & Metadata

Witnessed Difference Normal Form (WDNF) enforces structural normalization and explicit defect routing in the derivation regime.

Property	Value
Canonical ID	nf.wdp.wdnf
Short Name	WDNF
Full Name	Witnessed Difference Normal Form
Family	derivation (MSS-N Tower Algebraic Derivation, Split Extension-Retraction & Obstruction 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 (WDNF Candidate)	Anomaly risk: ghost distinctions ; asserted without an explicit ; witness pair or on carriers of...
2. Normalization / Gate	WDNF Verification Gate	every admitted difference... (certified_implies_authorized: false)
3. After / Certified Output	Certified WDNF Output	Invariant: ['carrier', ; 'distinction_relation', ; 'witness_map']

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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.wdp.wdnf
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	ghost distinctions asserted without an explicit witness pair or on carriers of size less than two
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: every admitted difference is irreflexive and witnessed by an explicit pair with support size >= 2 Protected Skeleton: ['carrier', 'distinction_relation', 'witness_map']
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 claim infinite continuous separations
• does not grant execution authority

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• carrier
• distinction_relation
• witness_map

5.2 Required Evidence

• carrier_size
• witness_pair_presence

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	carrier size satisfies
criterion	Check	distinction relation is strictly irreflexive (no element differs from itself)
criterion	Check	every asserted distinction carries at least one verified witness pair

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
AcceptWitnessedDifference	Preserve
RejectGhostDistinction	Reject
RejectSelfDifference	Reject
RequireSupportDeclaration	Refuse

5.5 Declared Failure Modes

• symptom: distinction claimed on a singleton carrier, diagnosis: subsingleton distinction violation, terminal: RequireSupportDeclaration
• symptom: distinction claimed without an empirical or formal witness pair, diagnosis: ghost distinction, terminal: RejectGhostDistinction
• symptom: term claimed distinct from itself, diagnosis: irreflexivity violation, terminal: RejectSelfDifference

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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.wdp.wdnf (WDNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (AcceptWitnessedDifference, RejectGhostDistinction, RejectSelfDifference, RequireSupportDeclaration) 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 ghost distinctions asserted without an explicit witness pair or on carriers of size less than two is either excluded under every admitted difference is irreflexive and witnessed by an explicit pair with support size >= 2 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.wdp.wdnf.

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7. Canonical YAML Contract (contracts/nf.wdp.wdnf.yaml)

Click to expand full canonical YAML contract (contracts/nf.wdp.wdnf.yaml)

schema_version: smplx.nf.contract.v0
contract_kind: form_contract
identity:
  id: nf.wdp.wdnf
  name: Witnessed Difference Normal Form
  short_name: WDNF
  version: v0
  status: draft
  family: derivation
  theory_status: established
  contract_status: draft
  verification_status: executable
classification:
  hierarchy_level: form
  subject_kind:
  - difference_claim
  - witness_pair
  - support_carrier
  data_posture: at_rest
  mathematical_posture: formal_algebraic
purpose:
  excludes_anomaly: ghost distinctions asserted without an explicit witness pair or on carriers of size less than two
  preserves_invariant: every admitted difference is irreflexive and witnessed by an explicit pair with support size >= 2
  protected_skeleton:
  - carrier
  - distinction_relation
  - witness_map
  erased_structure:
  - observation_path_transients
  non_claims:
  - does not claim infinite continuous separations
  - does not grant execution authority
declarations_required:
- carrier
- distinction_relation
- witness_map
evidence_required:
- carrier_size
- witness_pair_presence
validation_criteria:
- carrier size satisfies |carrier| >= 2
- distinction relation is strictly irreflexive (no element differs from itself)
- every asserted distinction carries at least one verified witness pair
proof_obligations:
- id: wdnf.support_size_floor
  status: upstream_theorem
  ref: 070_witnessed_difference_programme_wdp
  section: levels/level_00_admitted_cut.md
terminal_routes:
- AcceptWitnessedDifference
- RejectGhostDistinction
- RejectSelfDifference
- RequireSupportDeclaration
terminal_route_map:
  AcceptWitnessedDifference: Preserve
  RejectGhostDistinction: Reject
  RejectSelfDifference: Reject
  RequireSupportDeclaration: Refuse
certification:
  certificate_required: true
  certificate_kind: witnessed_difference_certificate
  obstruction_class_required: false
  loss_ledger_required: false
  loss_ledger_trigger_id: null
  verifier_required: true
authorization:
  authorized_by: null
  certified_implies_authorized: false
failure_modes:
- symptom: distinction claimed on a singleton carrier
  diagnosis: subsingleton distinction violation
  terminal: RequireSupportDeclaration
- symptom: distinction claimed without an empirical or formal witness pair
  diagnosis: ghost distinction
  terminal: RejectGhostDistinction
- symptom: term claimed distinct from itself
  diagnosis: irreflexivity violation
  terminal: RejectSelfDifference
definition:
  formal_statement: a difference claim is in Witnessed Difference Normal Form iff it is defined on a carrier with support size at least 2, is irreflexive, and every distinction is witnessed by an explicit non-identical pair
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: ontological_boundary_not_relational_project_join
    anomaly_exclusion: ghost distinctions, subsingleton claims, and self-difference
    lossless_join:
      status: quotient_reconstruction
      statement: quotient carrier is reconstructed modulo the indistinguishability relation
    dependency_preservation:
      status: irreflexivity_preserved
      statement: irreflexivity and witness presence are preserved locally on carrier pairs
    syntactic_decision:
      status: witness_decidable
      statement: decidable from the finite incidence matrix of witness pairs
schema_ref: ./normal_form_contract_schema.yaml