nf.change.sign_switching

Binary graph sign switching section (SIGN_SWITCHING)

Contract ID: nf.change.sign_switching | Family: change | Index Status: active | AuthorityEffect: None

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1. Executive Summary & Metadata

Binary graph sign switching section (SIGN_SWITCHING) enforces structural normalization and explicit defect routing in the change regime.

Property	Value
Canonical ID	nf.change.sign_switching
Short Name	SIGN_SWITCHING
Full Name	Binary graph sign switching section
Family	change (Data in Motion & Boundary-Quotient Incremental Maintenance Contracts (BQNF & Cochain Repair))
Qualification	Extended Form Contract (Normal Form Contract)
Data / Math Posture	in_transformation
Index Status	active
Theory Status	proposed
Verification Status	executable
Contract Version	v1
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 (SIGN_SWITCHING Candidate)	Anomaly risk: Different ; representatives of a declared ; equivalence class appearing as...
2. Normalization / Gate	SIGN_SWITCHING Verification Gate	The declared equivalence... (certified_implies_authorized: false)
3. After / Certified Output	Certified SIGN_SWITCHING Output	Invariant: ; ['fixed_ordered_ambient_carrier', ; 'declared_gauge_action']

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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.change.sign_switching
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	Different representatives of a declared equivalence class appearing as distinct normal representatives
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: The declared equivalence class Protected Skeleton: ['fixed_ordered_ambient_carrier', 'declared_gauge_action']
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)

• No polynomial algorithm for arbitrary succinct fermionic Hamiltonians
• No normalization across changes of labels, bases, carrier size, or equivalence relation

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• ordered finite carrier
• exact input
• declared gauge action

5.2 Required Evidence

• exact_gauge_witness: binary_vector

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	replay the returned gauge witness exactly
criterion	Check	check the representative condition

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
Normalized	Preserve
Refused	Refuse

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.change.sign_switching (SIGN_SWITCHING) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (Normalized, Refused) 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 in_transformation, this contract enforces that Different representatives of a declared equivalence class appearing as distinct normal representatives is either excluded under The declared equivalence class 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.change.sign_switching.

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7. Canonical YAML Contract (contracts/nf.change.sign_switching.yaml)

Click to expand full canonical YAML contract (contracts/nf.change.sign_switching.yaml)

schema_version: smplx.nf.contract.v1
contract_kind: normal_form_contract
identity:
  version: v1
  status: active
  theory_status: proposed
  contract_status: active
  verification_status: executable
  family: change
  id: nf.change.sign_switching
  name: Binary graph sign switching section
  short_name: SIGN_SWITCHING
classification:
  hierarchy_level: normal_form
  subject_kind:
  - finite_quotient
  data_posture: in_transformation
  mathematical_posture: formal_algebraic
purpose:
  excludes_anomaly: Different representatives of a declared equivalence class appearing
    as distinct normal representatives
  preserves_invariant: The declared equivalence class
  protected_skeleton:
  - fixed_ordered_ambient_carrier
  - declared_gauge_action
  erased_structure:
  - declared_gauge_redundancy
  non_claims:
  - No polynomial algorithm for arbitrary succinct fermionic Hamiltonians
  - No normalization across changes of labels, bases, carrier size, or equivalence
    relation
declarations_required:
- ordered finite carrier
- exact input
- declared gauge action
evidence_required:
- exact_gauge_witness: binary_vector
validation_criteria:
- replay the returned gauge witness exactly
- check the representative condition
terminal_routes:
- Normalized
- Refused
terminal_route_map:
  Normalized: Preserve
  Refused: Refuse
certification:
  certificate_required: true
  certificate_kind: explicit_gauge_witness
  obstruction_class_required: true
  loss_ledger_required: false
  loss_ledger_trigger_id: null
  verifier_required: true
authorization:
  authorized_by: null
  certified_implies_authorized: false
extensions:
  normalization:
    kind: canonicalizer
    claim_scope: A normal form for diagonal +/-1 basis gauges on an explicitly supplied
      sign graph; no claim for arbitrary unitary basis changes or succinct graph construction.
    domain: F2^E for a fixed ordered labelled finite undirected multigraph, including
      loops
    equivalence: s ~ s_prime iff s_prime(uv) = s(uv) + a(u) + a(v) mod 2
    normalizer: code/bqnf_sign_evaluator.py:normalize_sign_cochain
    representative_condition: All edges in the edge-order spanning forest have parity
      zero
    laws:
      soundness: N(s)(uv) = s(uv) xor returned_gauge(u) xor returned_gauge(v)
      idempotence: N(N(s)) = N(s)
      completeness: N(s) = N(s_prime) iff s and s_prime differ by vertex switching
      determinism: Edge order fixes the forest; least-vertex roots fix its gauge
    evidence:
    - ../docs/normal_form_audit.md
    - ../code/tests/test_normal_form_laws.py
quadrilateral:
  qualifies_as_true_normal_form: false