nf.derivation.aonf

Active Obstruction Normal Form (AONF)

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

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1. Executive Summary & Metadata

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

Property	Value
Canonical ID	nf.derivation.aonf
Short Name	AONF
Full Name	Active Obstruction 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 (AONF Candidate)	Anomaly risk: acting at an ; obstruction that was never shown ; to be active, or selecting one ...
2. Normalization / Gate	AONF Verification Gate	at an active obstruction ... (certified_implies_authorized: false)
3. After / Certified Output	Certified AONF Output	Invariant: ['activity_predicate', ; 'repair_family', ; 'exhaustion_certificate',...

Contract-Declared Worked Cases

- ref: 19L57G1
  section: paper/primitive_difference_map.md
  note: the two-rule stated at the first active obstruction, under declared hypotheses

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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.aonf
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	acting at an obstruction that was never shown to be active, or selecting one arm of a tie without declaring the selection
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: at an active obstruction the menu is exactly two arms, remove the obstruction or construct structure, and a tie between them stays a tie Protected Skeleton: ['activity_predicate', 'repair_family', 'exhaustion_certificate', 'extension_family', 'selection_record']
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 treat a proposal as an execution; proposing an extension is gated separately from performing one
• does not select between tied arms; a tie is recorded as a tie and the selection stays absent
• does not treat a refusal as a terminal; a refusal is inert and a terminal absorbs
• does not act when any activity conjunct is unverified; the menu is then silent
• does not imply authorization

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• activity_predicate
• repair_family
• exhaustion_certificate
• extension_family
• selection_policy
• cost_measure

5.2 Required Evidence

• activity_conjunct_status
• repair_family_membership
• exhaustion_status_at_the_same_level
• extension_proposal_membership
• selection_record

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	the obstruction is shown active before any arm is read, and a missing conjunct makes the menu silent
criterion	Check	the same-level repair family is nonempty, or same-level exhaustion is certified and the extension proposal family is nonempty
criterion	Check	a proposal is recorded as a proposal and is not executed by the same act
criterion	Check	when both arms are constructible and no declared invariant separates them, the selection is recorded as absent
criterion	Check	a selection, when made, names the further declaration that made it
criterion	Check	a refusal is recorded as inert and does not absorb the run

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
Repair	Preserve
Extend	Preserve
Tie	Preserve
Silent	Preserve
Refuse	Refuse
Terminal	Preserve
Escalate	Preserve

5.5 Declared Failure Modes

• symptom: an arm is taken although one activity conjunct was never checked, diagnosis: the obstruction was not shown active, so the menu was silent, terminal: Silent
• symptom: one of two equally admissible arms is taken with no reason recorded, diagnosis: a tie was broken by position rather than by a declaration, terminal: Tie
• symptom: an extension is performed by the act that proposed it, diagnosis: proposal and execution were not separately gated, terminal: Refuse
• symptom: a refusal ends the run, diagnosis: refusal treated as absorbing, which is the behaviour of a terminal, terminal: Terminal

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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.aonf (AONF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (Repair, Extend, Tie, Silent) 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 acting at an obstruction that was never shown to be active, or selecting one arm of a tie without declaring the selection is either excluded under at an active obstruction the menu is exactly two arms, remove the obstruction or construct structure, and a tie between them stays a tie 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.aonf.

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

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

schema_version: smplx.nf.contract.v0
contract_kind: form_contract
identity:
  id: nf.derivation.aonf
  name: Active Obstruction Normal Form
  short_name: AONF
  version: v0
  status: draft
  family: derivation
  theory_status: established
  contract_status: draft
  verification_status: executable
classification:
  hierarchy_level: form
  subject_kind:
  - obstruction_claim
  - repair_family
  - extension_family
  data_posture: in_motion
  mathematical_posture: operational
purpose:
  excludes_anomaly: acting at an obstruction that was never shown to be active, or selecting
    one arm of a tie without declaring the selection
  preserves_invariant: at an active obstruction the menu is exactly two arms, remove the obstruction
    or construct structure, and a tie between them stays a tie
  protected_skeleton:
  - activity_predicate
  - repair_family
  - exhaustion_certificate
  - extension_family
  - selection_record
  erased_structure: []
  non_claims:
  - does not treat a proposal as an execution; proposing an extension is gated separately
    from performing one
  - does not select between tied arms; a tie is recorded as a tie and the selection stays
    absent
  - does not treat a refusal as a terminal; a refusal is inert and a terminal absorbs
  - does not act when any activity conjunct is unverified; the menu is then silent
  - does not imply authorization
quadrilateral:
  qualifies_as_true_normal_form: false
  qualification_gap: no_project_join_theorem
  anomaly_exclusion: an arm taken before the obstruction is shown active, or a tie broken
    with no recorded declaration
  lossless_join:
    status: not_a_relational_decomposition
    statement: no project-join theorem is claimed
  dependency_preservation:
    status: menu_and_gate_preserved
    statement: the two-arm menu and the separation of proposal from execution stay intact
  syntactic_decision:
    status: declaration_decidable
    statement: the menu is read from the recorded conjuncts and the declared families
activity_predicate:
  conjuncts:
  - retained
  - observer_zero
  - guarded
  rule: all three conjuncts hold, and each is recorded separately
  independence: no conjunct is implied by the other two
declarations_required:
- activity_predicate
- repair_family
- exhaustion_certificate
- extension_family
- selection_policy
- cost_measure
evidence_required:
- activity_conjunct_status
- repair_family_membership
- exhaustion_status_at_the_same_level
- extension_proposal_membership
- selection_record
validation_criteria:
- the obstruction is shown active before any arm is read, and a missing conjunct makes the
  menu silent
- the same-level repair family is nonempty, or same-level exhaustion is certified and the
  extension proposal family is nonempty
- a proposal is recorded as a proposal and is not executed by the same act
- when both arms are constructible and no declared invariant separates them, the selection
  is recorded as absent
- a selection, when made, names the further declaration that made it
- a refusal is recorded as inert and does not absorb the run
proof_obligations:
- id: aonf.two_rule_at_an_active_obstruction
  status: upstream_theorem
  ref: 19L57G1
  section: lean4/Derivation/PrimitivePassage.lean
- id: aonf.proposal_is_not_execution
  status: upstream_theorem
  ref: 19L57G1
  section: lean4/Derivation/PrimitivePassage.lean
- id: aonf.extension_resolves
  status: upstream_theorem
  ref: 19L57G1
  section: lean4/Derivation/PrimitivePassage.lean
- id: aonf.refusal_inert_terminal_absorbing
  status: upstream_theorem
  ref: 19L57G1
  section: lean4/Derivation/PrimitivePassage.lean
- id: aonf.station_order_is_supplied_not_derived
  status: declared_upstream
  ref: 19L57G1
  section: paper/primitive_difference_passage.md
terminal_routes:
- Repair
- Extend
- Tie
- Silent
- Refuse
- Terminal
- Escalate
certification:
  certificate_required: true
  certificate_kind: passage_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: an arm is taken although one activity conjunct was never checked
  diagnosis: the obstruction was not shown active, so the menu was silent
  terminal: Silent
- symptom: one of two equally admissible arms is taken with no reason recorded
  diagnosis: a tie was broken by position rather than by a declaration
  terminal: Tie
- symptom: an extension is performed by the act that proposed it
  diagnosis: proposal and execution were not separately gated
  terminal: Refuse
- symptom: a refusal ends the run
  diagnosis: refusal treated as absorbing, which is the behaviour of a terminal
  terminal: Terminal
examples:
- ref: 19L57G1
  section: paper/primitive_difference_map.md
  note: the two-rule stated at the first active obstruction, under declared hypotheses
references:
- 19L/PIN.md
- ./nf.derivation.obnf.yaml
- ./README.md
schema_ref: ./normal_form_contract_schema.yaml
terminal_route_map:
  Repair: Preserve
  Extend: Preserve
  Tie: Preserve
  Silent: Preserve
  Refuse: Refuse
  Terminal: Preserve
  Escalate: Preserve