nf.derivation.obnf

Obstruction Relativization Normal Form (OBNF)

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

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1. Executive Summary & Metadata

Obstruction Relativization Normal Form (OBNF) enforces structural normalization and explicit defect routing in the derivation regime.

Property	Value
Canonical ID	nf.derivation.obnf
Short Name	OBNF
Full Name	Obstruction Relativization Normal Form
Family	derivation (MSS-N Tower Algebraic Derivation, Split Extension-Retraction & Obstruction Contracts)
Qualification	Extended Form Contract (Normal Form Contract)
Data / Math Posture	in_motion
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 (OBNF Candidate)	Anomaly risk: an obstruction ; asserted without naming the law it ; obstructs
2. Normalization / Gate	OBNF Verification Gate	a collision is a positive... (certified_implies_authorized: false)
3. After / Certified Output	Certified OBNF Output	Invariant: ['source_relation', ; 'collapse_map', ; 'collision_witness',...

Contract-Declared Worked Cases

- ref: 19L57G1
  section: paper/primitive_difference.md S3
  note: collision defined prior to any law; obstruction defined relative to one

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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.derivation.obnf
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	an obstruction asserted without naming the law it obstructs
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: a collision is a positive fact about a collapse, and becomes an obstruction only relative to a declared protected law that its pushforward violates Protected Skeleton: ['source_relation', 'collapse_map', 'collision_witness', 'protected_law']
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 make every collision an obstruction; a bare collapse can stay admissible
• does not fix which law is protected; that is a declaration, and a different declaration gives a different verdict on the same collapse
• does not derive the collapse map from the relation it collapses
• does not imply authorization

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• source_relation
• collapse_map
• protected_law
• admissibility_policy

5.2 Required Evidence

• colliding_pair
• pushforward_of_the_law
• law_status_before_and_after

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	a collision is recorded as an existence claim with the colliding pair as its witness
criterion	Check	an obstruction claim names the protected law it is relative to
criterion	Check	the pushforward of the protected law along the collapse is evaluated, not assumed
criterion	Check	a collapse whose protected law survives is recorded as an admissible collision, not an obstruction
criterion	Check	identification of two terms is recorded as always colliding, which is a fact about the map and not yet a defect

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
AcceptAdmissibleCollision	Preserve
PromoteToObstruction	Preserve
RejectUnrelativizedObstruction	Reject
RequireProtectedLawDeclaration	Refuse

5.5 Declared Failure Modes

• symptom: a merge is reported as an obstruction with no law named, diagnosis: obstruction asserted absolutely rather than relative to a protected property, terminal: RejectUnrelativizedObstruction
• symptom: a collapse is refused although every declared law survives it, diagnosis: collision treated as defect, terminal: AcceptAdmissibleCollision
• symptom: the same collapse is an obstruction in one report and not in another, diagnosis: two different protected laws were in force and only one was recorded, terminal: RequireProtectedLawDeclaration

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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.derivation.obnf (OBNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (AcceptAdmissibleCollision, PromoteToObstruction, RejectUnrelativizedObstruction, RequireProtectedLawDeclaration) 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 an obstruction asserted without naming the law it obstructs is either excluded under a collision is a positive fact about a collapse, and becomes an obstruction only relative to a declared protected law that its pushforward violates 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.derivation.obnf.

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7. Canonical YAML Contract (contracts/nf.derivation.obnf.yaml)

Click to expand full canonical YAML contract (contracts/nf.derivation.obnf.yaml)

schema_version: smplx.nf.contract.v0
contract_kind: form_contract
identity:
  id: nf.derivation.obnf
  name: Obstruction Relativization Normal Form
  short_name: OBNF
  version: v0
  status: draft
  family: derivation
  theory_status: established
  contract_status: draft
  verification_status: executable
classification:
  hierarchy_level: form
  subject_kind:
  - collapse_map
  - protected_law
  - obstruction_claim
  data_posture: in_motion
  mathematical_posture: operational
purpose:
  excludes_anomaly: an obstruction asserted without naming the law it obstructs
  preserves_invariant: a collision is a positive fact about a collapse, and becomes an obstruction
    only relative to a declared protected law that its pushforward violates
  protected_skeleton:
  - source_relation
  - collapse_map
  - collision_witness
  - protected_law
  erased_structure: []
  non_claims:
  - does not make every collision an obstruction; a bare collapse can stay admissible
  - does not fix which law is protected; that is a declaration, and a different declaration
    gives a different verdict on the same collapse
  - does not derive the collapse map from the relation it collapses
  - does not imply authorization
quadrilateral:
  qualifies_as_true_normal_form: false
  qualification_gap: no_project_join_theorem
  anomaly_exclusion: an obstruction named without the law it is claimed to obstruct
  lossless_join:
    status: not_a_relational_decomposition
    statement: the collapse map is recorded; it is not reconstructed by a natural join
  dependency_preservation:
    status: law_stays_attached_to_the_verdict
    statement: a change of protected law is a different declaration and a different verdict
  syntactic_decision:
    status: declaration_decidable
    statement: the verdict is computed from the collapse, the colliding pair, and the named
      law
declarations_required:
- source_relation
- collapse_map
- protected_law
- admissibility_policy
evidence_required:
- colliding_pair
- pushforward_of_the_law
- law_status_before_and_after
validation_criteria:
- a collision is recorded as an existence claim with the colliding pair as its witness
- an obstruction claim names the protected law it is relative to
- the pushforward of the protected law along the collapse is evaluated, not assumed
- a collapse whose protected law survives is recorded as an admissible collision, not an obstruction
- identification of two terms is recorded as always colliding, which is a fact about the map
  and not yet a defect
proof_obligations:
- id: obnf.identification_always_collides
  status: upstream_theorem
  ref: 19L57G1
  section: paper/primitive_difference.md S3
- id: obnf.collision_becomes_obstruction_under_irreflexivity
  status: upstream_theorem
  ref: 19L57G1
  section: paper/primitive_difference.md S3
terminal_routes:
- AcceptAdmissibleCollision
- PromoteToObstruction
- RejectUnrelativizedObstruction
- RequireProtectedLawDeclaration
certification:
  certificate_required: true
  certificate_kind: collision_certificate
  obstruction_class_required: true
  loss_ledger_required: true
  verifier_required: true
  loss_ledger_trigger_id: null
authorization:
  authorized_by: null
  certified_implies_authorized: false
failure_modes:
- symptom: a merge is reported as an obstruction with no law named
  diagnosis: obstruction asserted absolutely rather than relative to a protected property
  terminal: RejectUnrelativizedObstruction
- symptom: a collapse is refused although every declared law survives it
  diagnosis: collision treated as defect
  terminal: AcceptAdmissibleCollision
- symptom: the same collapse is an obstruction in one report and not in another
  diagnosis: two different protected laws were in force and only one was recorded
  terminal: RequireProtectedLawDeclaration
examples:
- ref: 19L57G1
  section: paper/primitive_difference.md S3
  note: collision defined prior to any law; obstruction defined relative to one
references:
- 19L/PIN.md
- ./nf.derivation.pdnf.yaml
- ./README.md
schema_ref: ./normal_form_contract_schema.yaml
terminal_route_map:
  AcceptAdmissibleCollision: Preserve
  PromoteToObstruction: Preserve
  RejectUnrelativizedObstruction: Reject
  RequireProtectedLawDeclaration: Refuse