nf.ddc.context_boundary

Context Boundary Normal Form (CBNF)

Contract ID: nf.ddc.context_boundary | Family: topology | Index Status: active | AuthorityEffect: None

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1. Executive Summary & Metadata

Context Boundary Normal Form (CBNF) enforces structural normalization and explicit defect routing in the topology regime.

Property	Value
Canonical ID	nf.ddc.context_boundary
Short Name	CBNF
Full Name	Context Boundary Normal Form
Family	topology (Simplicial Complexes, Boundary Nilpotency & Context Boundary Purity (TSNF, CBNF))
Qualification	Extended Form Contract (Normal Form Contract)
Data / Math Posture	at_rest
Index Status	active
Theory Status	established
Verification Status	executable
Contract Version	v0
Governance Fence	AuthorityEffect: None (certified_implies_authorized: false)

Foundational Treatise Specification

• Family: topology
• Runes: ['C']
• Target Runtime Law: Law 8 (Context Boundary Purity)
• Domain: Dynamic carrier subcomplexes K \subset K' and observation windows.
• Anomaly Excluded: Scope laundering, discarding inconvenient defects by re-scoping without lease contracts.
• Preserved Invariant: Disjoint partition E(K') = E_int \sqcup E_bnd with non-decreasing defect mass.
• Reconstruction Theorem: Re-embedding internal and boundary subcomplexes recovers global carrier losslessly.

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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 (CBNF Candidate)	Anomaly risk: scope laundering and ; unmonitored carrier expansion ; where boundary dependencies are...
2. Normalization / Gate	CBNF Verification Gate	disjoint carrier edge... (certified_implies_authorized: false)
3. After / Certified Output	Certified CBNF Output	Invariant: ; ['subcomplex_carrier_K', ; 'ambient_carrier_K_prime',...

Contract-Declared Worked Cases

- ref: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/00_discrete_deformation_calculus_foundations.md
  section: '2.1'

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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.ddc.context_boundary
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	scope laundering and unmonitored carrier expansion where boundary dependencies are disguised as resolved defects
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: disjoint carrier edge partition E(K') = E_int ⊔ E_bnd with monotonic non-decreasing defect mass Φ₁ and Γ₂ Protected Skeleton: ['subcomplex_carrier_K', 'ambient_carrier_K_prime', 'internal_edges', 'boundary_edges', 'defect_evaluations']
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 context exposure reduces residual defect; Law 8 mandates that declaring boundaries is not repair
• does not claim exposed boundary edges are gauge-repairable without further licensed carrier inclusion
• does not confer operational authority; authority_effect is unconditionally None

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• base_carrier
• extended_carrier
• internal_edge_count
• boundary_edge_count
• defect_monotonicity_witness

5.2 Required Evidence

None declared.

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	interior and boundary edge sets are strictly disjoint
criterion	Check	all vertices incident to interior edges belong to base carrier K
criterion	Check	Φ₁ and Γ₂ on extended carrier K' are greater than or equal to their values on K

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
AdmitExposedContext	Preserve
RejectScopeLaundering	Refuse
RejectBoundaryNonDisjoint	Reject

5.5 Declared Failure Modes

• symptom: defect mass decreases across context exposure without explicit repair rune, diagnosis: scope laundering attempted; violates Law 8, terminal: RejectScopeLaundering
• symptom: intersection of interior and boundary edges is non-empty, diagnosis: carrier partition is not disjoint, terminal: RejectBoundaryNonDisjoint

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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.ddc.context_boundary (CBNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (AdmitExposedContext, RejectScopeLaundering, RejectBoundaryNonDisjoint) 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 scope laundering and unmonitored carrier expansion where boundary dependencies are disguised as resolved defects is either excluded under disjoint carrier edge partition E(K') = E_int ⊔ E_bnd with monotonic non-decreasing defect mass Φ₁ and Γ₂ 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.ddc.context_boundary.

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7. Canonical YAML Contract (contracts/nf.ddc.context_boundary.yaml)

Click to expand full canonical YAML contract (contracts/nf.ddc.context_boundary.yaml)

schema_version: smplx.nf.contract.v0
schema_ref: ./normal_form_contract_schema.yaml
contract_kind: normal_form_contract
identity:
  id: nf.ddc.context_boundary
  name: Context Boundary Normal Form
  short_name: CBNF
  version: v0
  theory_status: established
  contract_status: active
  status: active
  verification_status: executable
  family: topology
classification:
  hierarchy_level: normal_form
  subject_kind:
    - carrier_complex
    - observation_window
    - boundary_subcomplex
  data_posture: at_rest
  mathematical_posture: operational
purpose:
  excludes_anomaly: scope laundering and unmonitored carrier expansion where boundary dependencies are disguised as resolved defects
  preserves_invariant: disjoint carrier edge partition E(K') = E_int ⊔ E_bnd with monotonic non-decreasing defect mass Φ₁ and Γ₂
  protected_skeleton:
    - subcomplex_carrier_K
    - ambient_carrier_K_prime
    - internal_edges
    - boundary_edges
    - defect_evaluations
  erased_structure:
    - external_complex_topology_beyond_boundary
  non_claims:
    - does not claim context exposure reduces residual defect; Law 8 mandates that declaring boundaries is not repair
    - does not claim exposed boundary edges are gauge-repairable without further licensed carrier inclusion
    - does not confer operational authority; authority_effect is unconditionally None
definition:
  source: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/normal_forms/README.md
  section: '2.0'
  formal_statement: >
    On a discrete simplicial or cell complex carrier K exposed to an ambient window K',
    Context Boundary Normal Form (CBNF) losslessly partitions edges into disjoint interior
    and boundary sets E(K') = E_int ⊔ E_bnd. Context exposure rune C declares this partition
    and verifies that residual mass Φ₁ and curvature defect Γ₂ are monotonic non-decreasing,
    forbidding false defect relief through unmonitored carrier expansion.
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: topological_sheaf_partition_not_relational_project_join
    anomaly_exclusion: scope laundering (attempting to decrease Φ₁ or Γ₂ by expanding the carrier boundary)
    lossless_join:
      status: disjoint_sum_reconstruction
      statement: E(K') is losslessly partitioned into E_int ⊔ E_bnd with explicit indicator functions
    dependency_preservation:
      status: subcomplex_embedding_preserved
      statement: internal cochain relations are preserved identically on E_int
    syntactic_decision:
      status: combinatorial_subgraph_decidable
      statement: membership is decidable by checking vertex incident inclusion and edge partition counts
declarations_required:
  - base_carrier
  - extended_carrier
  - internal_edge_count
  - boundary_edge_count
  - defect_monotonicity_witness
evidence_required: []
validation_criteria:
  - interior and boundary edge sets are strictly disjoint
  - all vertices incident to interior edges belong to base carrier K
  - Φ₁ and Γ₂ on extended carrier K' are greater than or equal to their values on K
terminal_routes:
  - AdmitExposedContext
  - RejectScopeLaundering
  - RejectBoundaryNonDisjoint
terminal_route_map:
  AdmitExposedContext: Preserve
  RejectScopeLaundering: Refuse
  RejectBoundaryNonDisjoint: Reject
certification:
  certificate_required: false
  certificate_kind: null
  obstruction_class_required: false
  loss_ledger_required: false
  verifier_required: true
  loss_ledger_trigger_id: null
authorization:
  authorized_by: null
  certified_implies_authorized: false
failure_modes:
  - symptom: defect mass decreases across context exposure without explicit repair rune
    diagnosis: scope laundering attempted; violates Law 8
    terminal: RejectScopeLaundering
  - symptom: intersection of interior and boundary edges is non-empty
    diagnosis: carrier partition is not disjoint
    terminal: RejectBoundaryNonDisjoint
examples:
  - ref: omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/00_discrete_deformation_calculus_foundations.md
    section: '2.1'
references:
  - omega_engine_education/documentation/14_discrete_deformation_calculus_ddc/00_discrete_deformation_calculus_foundations.md
  - omega_engine_governance/contracts/contracts_omega_engine_crates/mathematics/discrete_deformation_algebra/context_embedding_operator.contract.yaml