nf.physics.dfnf

Dressing Field Normal Form (DFNF)

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

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1. Executive Summary & Metadata

Dressing Field Normal Form (DFNF) enforces structural normalization and explicit defect routing in the physics regime.

Property	Value
Canonical ID	nf.physics.dfnf
Short Name	DFNF
Full Name	Dressing Field 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	in_motion
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 (DFNF Candidate)	Anomaly risk: Gribov ambiguity ; anomalies from non-injective ; gauge-fixing slices, spurious...
2. Normalization / Gate	DFNF Verification Gate	gauge-basic physical degr... (certified_implies_authorized: false)
3. After / Certified Output	Certified DFNF Output	Invariant: ['raw_field_carrier', ; 'gauge_group_action', ; 'dressing_field_operator',...

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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.dfnf
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	Gribov ambiguity anomalies from non-injective gauge-fixing slices, spurious boundary edge-mode charges induced by cutting gauge orbits, Faddeev-Popov ghost proliferation, and gauge-dependent state vector corruption
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: gauge-basic physical degrees of freedom extracted via an equivariant dressing field u without gauge-fixing cuts, with idempotent retraction Pi^2 = Pi Protected Skeleton: ['raw_field_carrier', 'gauge_group_action', 'dressing_field_operator', 'basic_invariant_submanifold', 'dressing_retraction_idempotence']
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 an equivariant dressing field exists globally for all topology classes
• does not solve the non-abelian Gribov problem for full continuous QCD without chart covers
• does not replace BRST cohomology where boundary modes are physical observables
• does not ensure under declared assumptions unweighted convergence of discrete lattice dressing to continuum limits

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• field_configuration: phi in FieldSpace
• gauge_group_action: rho(g, phi) mapping G x FieldSpace to FieldSpace
• dressing_operator: u mapping FieldSpace to G
• dressing_equivariance: u(rho(g, phi)) = g^{-1} u(phi) for all g in G

5.2 Required Evidence

• field_state: string
• dressing_operator_ref: string
• equivariance_verified: boolean
• idempotence_verified: boolean
• gauge_invariance_verified: boolean
• ghost_free_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
DressingFieldCertified	Preserve
EquivarianceViolation	Refuse
NonIdempotentRetraction	Repair
GaugeLeakageDetected	Repair
GlobalObstructionGribov	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.dfnf (DFNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (DressingFieldCertified, EquivarianceViolation, NonIdempotentRetraction, GaugeLeakageDetected) 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_motion, this contract enforces that Gribov ambiguity anomalies from non-injective gauge-fixing slices, spurious boundary edge-mode charges induced by cutting gauge orbits, Faddeev-Popov ghost proliferation, and gauge-dependent state vector corruption is either excluded under gauge-basic physical degrees of freedom extracted via an equivariant dressing field u without gauge-fixing cuts, with idempotent retraction Pi^2 = Pi 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.dfnf.

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

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

schema_version: smplx.nf.contract.v0
contract_kind: normal_form_contract
identity:
  id: nf.physics.dfnf
  name: Dressing Field Normal Form
  short_name: DFNF
  version: v0
  theory_status: experimental
  contract_status: draft
  verification_status: executable
  family: physics
  status: draft
classification:
  hierarchy_level: normal_form
  subject_kind:
  - gauge_field_theory
  - dressing_field_method
  - relational_invariants
  data_posture: in_motion
  mathematical_posture: formal_algebraic
purpose:
  excludes_anomaly: Gribov ambiguity anomalies from non-injective gauge-fixing slices,
    spurious boundary edge-mode charges induced by cutting gauge orbits, Faddeev-Popov
    ghost proliferation, and gauge-dependent state vector corruption
  preserves_invariant: "gauge-basic physical degrees of freedom extracted via an equivariant dressing field u without gauge-fixing cuts, with idempotent retraction Pi^2 = Pi"
  protected_skeleton:
  - raw_field_carrier
  - gauge_group_action
  - dressing_field_operator
  - basic_invariant_submanifold
  - dressing_retraction_idempotence
  erased_structure:
  - longitudinal_gauge_redundancies
  - faddeev_popov_ghost_fields
  - artificial_boundary_edge_modes
  non_claims:
  - does not support that an equivariant dressing field exists globally for all topology classes
  - does not solve the non-abelian Gribov problem for full continuous QCD without chart covers
  - does not replace BRST cohomology where boundary modes are physical observables
  - does not ensure under declared assumptions unweighted convergence of discrete lattice dressing to continuum limits
declarations_required:
- field_configuration: phi in FieldSpace
- gauge_group_action: "rho(g, phi) mapping G x FieldSpace to FieldSpace"
- dressing_operator: "u mapping FieldSpace to G"
- dressing_equivariance: "u(rho(g, phi)) = g^{-1} u(phi) for all g in G"
validation_criteria:
- dressing_equivariance_check: "verify u(rho(g, phi)) == g^{-1} * u(phi) across declared test instances"
- retraction_idempotence_check: "verify Pi(Pi(phi)) == Pi(phi) where Pi(phi) = rho(u(phi), phi)"
- gauge_invariance_check: "verify Pi(rho(g, phi)) == Pi(phi) for all test group elements g"
- basic_presentation_check: "stored state vector satisfies phi_stored == Pi(phi) with zero ghost components"
- zero_gauge_residual_check: "gauge coboundary defect delta_gauge(phi_stored) == 0"
terminal_routes:
- DressingFieldCertified
- EquivarianceViolation
- NonIdempotentRetraction
- GaugeLeakageDetected
- GlobalObstructionGribov
- Unsupported
terminal_route_map:
  DressingFieldCertified: Preserve
  EquivarianceViolation: Refuse
  NonIdempotentRetraction: Repair
  GaugeLeakageDetected: Repair
  GlobalObstructionGribov: 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 field theory configuration is in Dressing Field Normal Form (DFNF) iff all local gauge degrees of freedom are factorized by an equivariant dressing field into basic gauge invariants phi_basic = rho(u(phi), phi), satisfying retraction idempotence Pi^2 = Pi and zero boundary edge-mode artifacts."
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: transformation_and_projection_rather_than_relational_project_join
    anomaly_exclusion: Gribov ambiguities, spurious boundary charges, and ghost-field pollution
    lossless_join:
      status: declared_reconstruction
      statement: Field decomposition into basic invariant degrees of freedom plus gauge group
        element is invertible on each local bundle trivialization.
    dependency_preservation:
      status: gauge_orbit_preservation
      statement: Preserves physical observable algebra invariant under gauge action.
    syntactic_decision:
      status: operator_decidable
      statement: Verified by checking operator equivariance and idempotence on test inputs.
canonical_terminal_map:
  DressingFieldCertified: Preserve
  EquivarianceViolation: Refuse
  NonIdempotentRetraction: Repair
  GaugeLeakageDetected: Repair
  GlobalObstructionGribov: Escalate
  Unsupported: Unsupported
authorization:
  authorized_by: null
  certified_implies_authorized: false
certification:
  certificate_required: true
  certificate_kind: nf.physics.dfnf_certificate
  obstruction_class_required: false
  loss_ledger_required: false
  loss_ledger_trigger_id: null
  verifier_required: true
evidence_required:
- field_state: string
- dressing_operator_ref: string
- equivariance_verified: boolean
- idempotence_verified: boolean
- gauge_invariance_verified: boolean
- ghost_free_verified: boolean
schema_ref: ./normal_form_contract_schema.yaml