nf.derivation.lsnf

Lawful Skeletal Filtration Normal Form (LSNF)

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

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1. Executive Summary & Metadata

Lawful Skeletal Filtration Normal Form (LSNF) enforces structural normalization and explicit defect routing in the derivation regime.

Property	Value
Canonical ID	nf.derivation.lsnf
Short Name	LSNF
Full Name	Lawful Skeletal Filtration 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	absent
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 (LSNF Candidate)	Anomaly risk: unrepresented ; attachment anomaly, retroactive ; index clamping, and inverted...
2. Normalization / Gate	LSNF Verification Gate	attachments use... (certified_implies_authorized: false)
3. After / Certified Output	Certified LSNF Output	Invariant: ['filtration_step', ; 'parent_policy', ; 'occurrence_token_store',...

Contract-Declared Worked Cases

- ref: https://github.com/dbccpage/19L57G1/blob/f1d56c010e6ba10a3b9418bd7cc5953c067250f2/lean4/Derivation/AttachmentLadder.lean
  section: lean4/Derivation/AttachmentLadder.lean
  note: lawful_to policy check and shell_guard

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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.lsnf
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	unrepresented attachment anomaly, retroactive index clamping, and inverted simplex boundary orientations
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: attachments use already-represented parents; cells retain all faces and a consistent signed boundary Protected Skeleton: ['filtration_step', 'parent_policy', 'occurrence_token_store', 'ascending_cell_boundary']
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 infinite complexes or transfinite induction
• does not derive manifold differential forms or smooth curvatures
• does not synthesize attachments without an explicit parent policy
• does not imply operational authority

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• filtration_depth
• parent_policy
• cell_dimension
• boundary_tuple
• face_incidence
• boundary_orientation_convention

5.2 Required Evidence

• lawfulness_certificate
• ascent_proof_receipt
• post_state_audit

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	for all k <= depth, parent(k+1) <= k
criterion	Check	for all simplicial cells, boundary vertices satisfy v_0 < v_1 < ... < v_k
criterion	Check	attachment occurs only to live unhalted passage states
criterion	Check	every nonempty face of every declared cell is present
criterion	Check	the declared signed boundary matrices compose to zero; ascending vertices alone are insufficient

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
AcceptLawfulAscent	Preserve
RefuseUnrepresentedParent	Refuse
RejectDescendingBoundary	Reject
RejectHaltedStateExtension	Refuse
Undetermined	Abstain

5.5 Declared Failure Modes

• symptom: child node k+1 specifies parent index exceeding k, diagnosis: attachment refers to an unrepresented future node, terminal: RefuseUnrepresentedParent
• symptom: cell boundary tuple is not strictly ascending, diagnosis: boundary vertices violate canonical ascending orientation, terminal: RejectDescendingBoundary

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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.lsnf (LSNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (AcceptLawfulAscent, RefuseUnrepresentedParent, RejectDescendingBoundary, RejectHaltedStateExtension) 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 unrepresented attachment anomaly, retroactive index clamping, and inverted simplex boundary orientations is either excluded under attachments use already-represented parents; cells retain all faces and a consistent signed boundary 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.lsnf.

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

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

# Draft declaration: no bound local contract evaluator is supplied; upstream mathematics and schema checks are separate evidence.
schema_version: smplx.nf.contract.v0
contract_kind: form_contract
identity:
  id: nf.derivation.lsnf
  name: Lawful Skeletal Filtration Normal Form
  short_name: LSNF
  version: v0
  status: draft
  family: derivation
  theory_status: established
  contract_status: draft
  verification_status: absent
classification:
  hierarchy_level: form
  subject_kind:
  - skeletal_filtration
  - attachment_ladder
  - simplicial_boundary
  data_posture: in_motion
  mathematical_posture: operational
purpose:
  excludes_anomaly: unrepresented attachment anomaly, retroactive index clamping, and inverted simplex
    boundary orientations
  preserves_invariant: attachments use already-represented parents; cells retain all faces and a consistent
    signed boundary
  protected_skeleton:
  - filtration_step
  - parent_policy
  - occurrence_token_store
  - ascending_cell_boundary
  erased_structure:
  - retroactive_clamping_heuristics
  non_claims:
  - does not claim infinite complexes or transfinite induction
  - does not derive manifold differential forms or smooth curvatures
  - does not synthesize attachments without an explicit parent policy
  - does not imply operational authority
quadrilateral:
  qualifies_as_true_normal_form: false
  qualification_gap: no_project_join_theorem
  anomaly_exclusion: future parent references, missing faces, repeated vertices, and inconsistent orientation
    signs
  lossless_join:
    status: filtration_replay_reconstruction
    statement: the complete skeletal complex is reconstructed losslessly by replaying the lawful UpFamily
      attachment blocks from genesis
  dependency_preservation:
    status: predecessor_dependency_preserved
    statement: parent availability is checked locally at step k without inspecting future extensions
  syntactic_decision:
    status: declaration_decidable
    statement: finite parent and vertex-index checks plus face closure and signed incidence verification
declarations_required:
- filtration_depth
- parent_policy
- cell_dimension
- boundary_tuple
- face_incidence
- boundary_orientation_convention
evidence_required:
- lawfulness_certificate
- ascent_proof_receipt
- post_state_audit
validation_criteria:
- for all k <= depth, parent(k+1) <= k
- for all simplicial cells, boundary vertices satisfy v_0 < v_1 < ... < v_k
- attachment occurs only to live unhalted passage states
- every nonempty face of every declared cell is present
- the declared signed boundary matrices compose to zero; ascending vertices alone are insufficient
terminal_routes:
- AcceptLawfulAscent
- RefuseUnrepresentedParent
- RejectDescendingBoundary
- RejectHaltedStateExtension
- Undetermined
terminal_route_map:
  AcceptLawfulAscent: Preserve
  RefuseUnrepresentedParent: Refuse
  RejectDescendingBoundary: Reject
  RejectHaltedStateExtension: Refuse
  Undetermined: Abstain
certification:
  certificate_required: true
  certificate_kind: skeletal_filtration_certificate
  obstruction_class_required: false
  loss_ledger_required: false
  verifier_required: true
authorization:
  authorized_by: null
  certified_implies_authorized: false
failure_modes:
- symptom: child node k+1 specifies parent index exceeding k
  diagnosis: attachment refers to an unrepresented future node
  terminal: RefuseUnrepresentedParent
- symptom: cell boundary tuple is not strictly ascending
  diagnosis: boundary vertices violate canonical ascending orientation
  terminal: RejectDescendingBoundary
examples:
- ref: https://github.com/dbccpage/19L57G1/blob/f1d56c010e6ba10a3b9418bd7cc5953c067250f2/lean4/Derivation/AttachmentLadder.lean
  section: lean4/Derivation/AttachmentLadder.lean
  note: lawful_to policy check and shell_guard
references:
- https://github.com/dbccpage/19L57G1/blob/f1d56c010e6ba10a3b9418bd7cc5953c067250f2/docs/GENESIS_CLOSEOUT.md
- ./README.md