nf.mssn

Minimal Symbol System Normal Form (MSSNF)

Contract ID: nf.mssn | Family: shape | Index Status: draft | AuthorityEffect: None

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1. Executive Summary & Metadata

Minimal Symbol System Normal Form (MSSNF) enforces structural normalization and explicit defect routing in the shape regime.

Property	Value
Canonical ID	nf.mssn
Short Name	MSSNF
Full Name	Minimal Symbol System Normal Form
Family	shape (Relational, Algebraic & Cochain Shape Normal Forms (Data at Rest & Structural Decompositions))
Qualification	Extended Form Contract (Normal Form Contract)
Data / Math Posture	in_motion
Index Status	draft
Theory Status	proposed
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 (MSSNF Candidate)	Anomaly risk: smuggled ambient ; container, untyped alphabet ; expansion, unverified level lif...
2. Normalization / Gate	MSSNF Verification Gate	admitted inscriptions... (certified_implies_authorized: false)
3. After / Certified Output	Certified MSSNF Output	Invariant: ['level_index_n', ; 'active_alphabet_a_n', ; 'declared_start_profile',...

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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.mssn
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	smuggled ambient container, untyped alphabet expansion, unverified level lift, unwitnessed diagonal self-loop under Rent Rule, and unearned semantic truth attribution
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: admitted inscriptions strictly use declared initial segment A_N without an ambient container; level lifts satisfy retraction r_N o ell_N = id; and relation additions satisfy diagonal avoidance witnessed by distinct endpoints Protected Skeleton: ['level_index_n', 'active_alphabet_a_n', 'declared_start_profile', 'rent_rule_witness', 'syntactic_firewall_receipt', 'retraction_image']
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 assert empirical truth, physical measurement, or semantic validity of parsed expressions (e.g. 1 > 2 parses syntactically; truth evaluation belongs to downstream model checkers)
• does not authorize downstream bytecode execution or automated policy actions
• does not assume general context-free grammar equivalence is decidable
• does not claim an infinite universe without explicit inductive constructor derivation
• does not imply a single blanket monolithic parser or default union grammar over all starts

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5. Operational Verification & Terminal Routing

5.1 Required Declarations

• level_index_n: integer between -1 and 38
• active_alphabet: list of terminals in A_N
• declared_start_profile: one of the 22 public starts in mssn.ebnf or 6 retained profiles
• rent_policy: unconstrained or diagonal_avoidance_irreflexive
• firewall_status: syntax_only
• resource_limits: {'max_bytes': 65536, 'max_nodes': 4096, 'max_depth': 32}

5.2 Required Evidence

• submitted_wire_bytes
• parsed_ast_or_token_stream
• restriction_image_under_prior_level
• rent_rule_witness_pair: required when N in [2, 28, 37, 38] and rent policy is active

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	input contains only terminals declared in active_alphabet A_N
criterion	Check	if level is -1, input is absent; no string derivation or container exists
criterion	Check	input is fully consumed by declared start profile without trailing characters or whitespace
criterion	Check	AST node count, byte length, and recursion depth remain within declared resource limits
criterion	Check	under diagonal_avoidance_irreflexive, relational endpoints must be distinct (a != b in a < b)
criterion	Check	restriction r_N maps lifted word back to identical prior word (r_N o ell_N = id)
criterion	Check	parser acceptance emits UNVERIFIED semantic status across external evaluator interfaces

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
AcceptMSSN	Preserve
RejectSmuggledContainer	Refuse
RejectUndeclaredTerminal	Reject
RejectParseFailure	Reject
RejectBudgetOverflow	BudgetUnknown
RejectDiagonalSelfLoop	Reject
RejectUncertifiedLift	Refuse
EscalateToSemanticEvaluator	Escalate

5.5 Declared Failure Modes

• symptom: empty string epsilon submitted at Level -1 where void is required, diagnosis: smuggled container trap, terminal: RejectSmuggledContainer
• symptom: terminal character outside active initial segment A_N encountered, diagnosis: undeclared terminal expansion, terminal: RejectUndeclaredTerminal
• symptom: adjacent glyphs submitted to glyph_path (e.g. a0), diagnosis: profile tokenization violation, terminal: RejectParseFailure
• symptom: self-loop relational claim submitted (e.g. a < a or a > a), diagnosis: diagonal violation under irreflexive rent rule, terminal: RejectDiagonalSelfLoop
• symptom: lifted expression restricted to prior level does not equal original, diagnosis: split extension failure, terminal: RejectUncertifiedLift
• symptom: syntactically valid expression assumed empirically true without evaluation, diagnosis: syntactic firewall violation, terminal: EscalateToSemanticEvaluator

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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.mssn (MSSNF) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (AcceptMSSN, RejectSmuggledContainer, RejectUndeclaredTerminal, RejectParseFailure) 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 smuggled ambient container, untyped alphabet expansion, unverified level lift, unwitnessed diagonal self-loop under Rent Rule, and unearned semantic truth attribution is either excluded under admitted inscriptions strictly use declared initial segment A_N without an ambient container; level lifts satisfy retraction r_N o ell_N = id; and relation additions satisfy diagonal avoidance witnessed by distinct endpoints 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.mssn.

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7. Canonical YAML Contract (contracts/nf.mssn.yaml)

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

schema_version: smplx.nf.contract.v0
schema_ref: ./normal_form_contract_schema.yaml
contract_kind: normal_form_contract
identity:
  id: nf.mssn
  name: Minimal Symbol System Normal Form
  short_name: MSSNF
  version: v0
  theory_status: proposed
  contract_status: draft
  verification_status: executable
  family: shape
  status: draft
classification:
  hierarchy_level: normal_form
  subject_kind:
  - glyph_inscription
  - mssn_ladder_state
  - level_presentation
  - level_lift_transition
  data_posture: in_motion
  mathematical_posture: operational
purpose:
  excludes_anomaly: smuggled ambient container, untyped alphabet expansion, unverified
    level lift, unwitnessed diagonal self-loop under Rent Rule, and unearned semantic
    truth attribution
  preserves_invariant: admitted inscriptions strictly use declared initial segment
    A_N without an ambient container; level lifts satisfy retraction r_N o ell_N =
    id; and relation additions satisfy diagonal avoidance witnessed by distinct endpoints
  protected_skeleton:
  - level_index_n
  - active_alphabet_a_n
  - declared_start_profile
  - rent_rule_witness
  - syntactic_firewall_receipt
  - retraction_image
  erased_structure:
  - formatting_whitespace
  - cosmetic_label_permutations
  non_claims:
  - does not assert empirical truth, physical measurement, or semantic validity of
    parsed expressions (e.g. 1 > 2 parses syntactically; truth evaluation belongs
    to downstream model checkers)
  - does not authorize downstream bytecode execution or automated policy actions
  - does not assume general context-free grammar equivalence is decidable
  - does not claim an infinite universe without explicit inductive constructor derivation
  - does not imply a single blanket monolithic parser or default union grammar over
    all starts
definition:
  source: omega_engine_atlas/coda_atlas/F004_papers/001_finite_obstruction_calculus/000_pre_genesis_to_mssn/paper.md
  formal_statement: 'An inscription or level state is in Minimal Symbol System Normal
    Form (MSSNF) when: (1) It is defined over an explicitly declared stage N in [-1,
    38] whose terminal inventory A_N is the initial segment of the fixed lexical order
    (a..z, 0..9, <, >), where Level -1 enforces the radical void (absence of grammar
    and derivation; no empty string epsilon admitted). (2) It is consumed byte-for-byte
    under an explicitly selected public start profile from the 22 canonical MSS-N
    starts (or 6 retained runtime profiles) without trimming, guessing, or implicit
    outer enclosures. (3) The Syntactic Firewall is respected: syntax acceptance verifies
    character formation against grammar productions and does not attest to semantic
    truth. (4) Any level lift ell_N splits via restriction r_N(L) = L cap A_N* with
    (r_N o ell_N)(w) = w, and under the Rent Rule, every newly admitted key x_{N+1}
    must occur in a witnessed sentence connecting two non-identical items (avoiding
    the diagonal Delta).'
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: reconstruction_is_split_extension_and_parser_retraction_not_relational_project_join
    anomaly_exclusion: Smuggled ambient containers, untyped profile guessing, uncertified
      diagonal self-loops, and unearned semantic truth attribution.
    lossless_join:
      status: retraction_agreement
      statement: (r_N o ell_N)(w) = w on all words of Language N; restriction discards
        only new terminals and recovers the exact prior syntax tree without loss.
    dependency_preservation:
      status: profile_and_level_bound
      statement: Level N alphabet A_N, declared start symbol, and rent rules are bound
        before intake; input cannot enlarge its active terminal set during parsing.
    syntactic_decision:
      status: declaration_plus_grammar_decidable
      statement: Decidable by standard CFG recognition over A_N and budget bounds
        (65536 bytes, 4096 nodes, depth 32).
declarations_required:
- level_index_n: integer between -1 and 38
- active_alphabet: list of terminals in A_N
- declared_start_profile: one of the 22 public starts in mssn.ebnf or 6 retained profiles
- rent_policy: unconstrained or diagonal_avoidance_irreflexive
- firewall_status: syntax_only
- resource_limits:
    max_bytes: 65536
    max_nodes: 4096
    max_depth: 32
evidence_required:
- submitted_wire_bytes
- parsed_ast_or_token_stream
- restriction_image_under_prior_level
- rent_rule_witness_pair: required when N in [2, 28, 37, 38] and rent policy is active
validation_criteria:
- input contains only terminals declared in active_alphabet A_N
- if level is -1, input is absent; no string derivation or container exists
- input is fully consumed by declared start profile without trailing characters or
  whitespace
- AST node count, byte length, and recursion depth remain within declared resource
  limits
- under diagonal_avoidance_irreflexive, relational endpoints must be distinct (a !=
  b in a < b)
- restriction r_N maps lifted word back to identical prior word (r_N o ell_N = id)
- parser acceptance emits UNVERIFIED semantic status across external evaluator interfaces
proof_obligations:
- id: mssn.split_extension_retraction
  status: theorem_shaped
  ref: omega_engine_atlas/coda_atlas/F004_papers/001_finite_obstruction_calculus/000_pre_genesis_to_mssn/paper.md
  section: 13.1 (chain-retraction obstruction)
- id: mssn.rent_rule_diagonal_avoidance
  status: theorem_shaped
  ref: omega_engine_atlas/coda_atlas/F004_papers/001_finite_obstruction_calculus/000_pre_genesis_to_mssn/paper.md
  section: 15 (repair obligations; no general diagonal-avoidance theorem claimed)
- id: mssn.syntactic_firewall_soundness
  status: theorem_shaped
  ref: omega_engine_atlas/coda_atlas/F004_papers/001_finite_obstruction_calculus/000_pre_genesis_to_mssn/paper.md
  section: 14 (grammar recognition and its semantic limits)
- id: mssn.radical_void_container_refusal
  status: theorem_shaped
  ref: omega_engine_atlas/coda_atlas/F004_papers/001_finite_obstruction_calculus/000_pre_genesis_to_mssn/paper.md
  section: 1 (input distinctions; no object-level void-generation theorem)
terminal_routes:
- AcceptMSSN
- RejectSmuggledContainer
- RejectUndeclaredTerminal
- RejectParseFailure
- RejectBudgetOverflow
- RejectDiagonalSelfLoop
- RejectUncertifiedLift
- EscalateToSemanticEvaluator
terminal_route_map:
  AcceptMSSN: Preserve
  RejectSmuggledContainer: Refuse
  RejectUndeclaredTerminal: Reject
  RejectParseFailure: Reject
  RejectBudgetOverflow: BudgetUnknown
  RejectDiagonalSelfLoop: Reject
  RejectUncertifiedLift: Refuse
  EscalateToSemanticEvaluator: Escalate
certification:
  certificate_required: true
  certificate_kind: mssn_conformance_certificate
  obstruction_class_required: true
  loss_ledger_required: false
  verifier_required: true
  loss_ledger_trigger_id: null
authorization:
  authorized_by: null
  certified_implies_authorized: false
failure_modes:
- symptom: empty string epsilon submitted at Level -1 where void is required
  diagnosis: smuggled container trap
  terminal: RejectSmuggledContainer
- symptom: terminal character outside active initial segment A_N encountered
  diagnosis: undeclared terminal expansion
  terminal: RejectUndeclaredTerminal
- symptom: adjacent glyphs submitted to glyph_path (e.g. a0)
  diagnosis: profile tokenization violation
  terminal: RejectParseFailure
- symptom: self-loop relational claim submitted (e.g. a < a or a > a)
  diagnosis: diagonal violation under irreflexive rent rule
  terminal: RejectDiagonalSelfLoop
- symptom: lifted expression restricted to prior level does not equal original
  diagnosis: split extension failure
  terminal: RejectUncertifiedLift
- symptom: syntactically valid expression assumed empirically true without evaluation
  diagnosis: syntactic firewall violation
  terminal: EscalateToSemanticEvaluator
references:
- ../../../../omega_engine_atlas/coda_atlas/F004_papers/001_finite_obstruction_calculus/000_pre_genesis_to_mssn/paper.md
- ../grammar/mssn.ebnf
- ../../../ow/omega_engine_pfp_v0.2/grammar/README.md
- ./normal_form_contract_schema.yaml