nf.operational.schema totality

Declared SQL Key Projection and Candidate Totality Profile (SQL-TOTAL)

Contract ID: nf.operational.schema-totality | Family: evidence | Index Status: active | AuthorityEffect: None

⬅ Back to Wiki Home | View SVG Diagram

---

1. Executive Summary & Metadata

Declared SQL Key Projection and Candidate Totality Profile (SQL-TOTAL) enforces structural normalization and explicit defect routing in the evidence regime.

Property	Value
Canonical ID	nf.operational.schema-totality
Short Name	SQL-TOTAL
Full Name	Declared SQL Key Projection and Candidate Totality Profile
Family	evidence (Cryptographic Receipts, Dual Witnesses, Loss Ledgers, CDC Logs & Schema Totality)
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)

---

2. Visual Architecture & Normalization Diagram

---

3. Concrete Worked Example & Mechanism

Visual Transition Summary

Stage	Carrier / Operator	Concrete State / Invariant
1. Before / Candidate Input	Input Carrier (SQL-TOTAL Candidate)	Anomaly risk: Null identity, ; vacuous coverage, duplicate or ; foreign candidates, and unverif...
2. Normalization / Gate	SQL-TOTAL Verification Gate	Every source table has to... (certified_implies_authorized: false)
3. After / Certified Output	Certified SQL-TOTAL Output	Invariant: ['heading', ; 'total_keys', 'optional_domains', ; 'declared_fds', 'candidate_ids'...

---

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.operational.schema-totality
Pillar I: Excludes Anomaly	Name and eliminate a specific class of data or state defects.	Null identity, vacuous coverage, duplicate or foreign candidates, and unverified reconstruction.
Pillar II: Preserves Invariant	State the structural invariant and protected skeleton preserved across transitions.	Invariant: Every source table has total keys and lossless declared-key projections; coverage is exact in set and cardinality. Protected Skeleton: ['heading', 'total_keys', 'optional_domains', 'declared_fds', 'candidate_ids', 'input_digests']
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)

• SQL coverage does not support that an externally supplied verifier verdict is true.
• Storage scalars do not establish semantic atomicity of JSON or CSV payloads.
• No undeclared functional, multivalued, or join dependency is inferred.
• Key-plus-one-attribute projections do not certify unrestricted semantic 6NF.
• Educational REAL aggregate demos do not become exact mathematical solvers.
• Certification does not imply authorization or a Genesis scale extension.

---

5. Operational Verification & Terminal Routing

5.1 Required Declarations

• exhaustive SQL file and embedded-schema inventory
• total keys, optional domains, and closed key-FD scope
• nonempty candidate carrier with stable unique IDs and input digests

5.2 Required Evidence

• per-table projection and reconstruction SQL
• losslessness and dependency-preservation results
• null mutation and missing, duplicate, foreign, or input-mismatched candidate refusals

5.3 Validation Criteria

Criterion ID	Name	Condition
criterion	Check	Every declared schema source and table is inventoried.
criterion	Check	Protected facts reject SQL NULL on INSERT and UPDATE, including legacy text primary keys.
criterion	Check	Coverage uses set equality and cardinality, with input-bound foreign keys.
criterion	Check	Mathematical acceptance is separate from structural exhaustiveness.

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
PreserveDeclaredProfile	Preserve
RejectNullFact	Reject
RejectCarrierMismatch	Reject
RequireSemanticDependencies	Refuse

5.5 Declared Failure Modes

All defects route explicitly through the Terminal Route Map above.

---

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.operational.schema-totality (SQL-TOTAL) against its declared schema, boundary constraints, and witness obligations in this model.
   • Supports deterministic terminal routing (PreserveDeclaredProfile, RejectNullFact, RejectCarrierMismatch, RequireSemanticDependencies) 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 Null identity, vacuous coverage, duplicate or foreign candidates, and unverified reconstruction. is either excluded under Every source table has total keys and lossless declared-key projections; coverage is exact in set and cardinality. 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.operational.schema-totality.

---

7. Canonical YAML Contract (contracts/nf.operational.schema-totality.yaml)

Click to expand full canonical YAML contract (contracts/nf.operational.schema-totality.yaml)

schema_version: smplx.nf.contract.v0
schema_ref: ./normal_form_contract_schema.yaml
contract_kind: normal_form_contract
identity:
  id: nf.operational.schema-totality
  name: Declared SQL Key Projection and Candidate Totality Profile
  short_name: SQL-TOTAL
  version: v0
  status: active
  family: evidence
classification:
  hierarchy_level: normal_form
  subject_kind: [relvar, candidate_carrier, schema_inventory]
  data_posture: at_rest
  mathematical_posture: operational
purpose:
  excludes_anomaly: Null identity, vacuous coverage, duplicate or foreign candidates, and unverified reconstruction.
  preserves_invariant: Every source table has total keys and lossless declared-key projections; coverage is exact in set and cardinality.
  protected_skeleton: [heading, total_keys, optional_domains, declared_fds, candidate_ids, input_digests]
  erased_structure: []
  non_claims:
    - SQL coverage does not support that an externally supplied verifier verdict is true.
    - Storage scalars do not establish semantic atomicity of JSON or CSV payloads.
    - No undeclared functional, multivalued, or join dependency is inferred.
    - Key-plus-one-attribute projections do not certify unrestricted semantic 6NF.
    - Educational REAL aggregate demos do not become exact mathematical solvers.
    - Certification does not imply authorization or a Genesis scale extension.
definition:
  source: omega_engine_pfp/infrastructure/yaml/normal_forms/schema_pipeline.py
  formal_statement: >-
    For each declared table heading H and minimal total SQL keys K_i, use only
    K_i -> H as the FD theory. Choose a minimal key K and project onto K union {a}
    for each nonkey attribute a. Check heading coverage, chase losslessness, and
    dependency preservation separately. A candidate problem has a nonempty stable
    carrier; checks exhaust it only if IDs and cardinalities agree in both directions.
  quadrilateral:
    qualifies_as_true_normal_form: false
    qualification_gap: operational SQL profile; semantic domains and complete MVD/JD theories remain undeclared
    anomaly_exclusion: Null protected facts and incomplete or duplicate evidence cannot masquerade as total coverage.
    lossless_join:
      status: checked_under_declared_key_fds
      statement: Exact chase verifies reconstruction; optional payload values join through total keys.
    dependency_preservation:
      status: independently_checked
      statement: The projected FD theory must preserve original declared dependencies or expose a specific gap.
    syntactic_decision:
      status: finite_schema_decidable
      statement: SQLite metadata, finite key FD closure, and exact candidate set/cardinality determine this profile.
declarations_required:
  - exhaustive SQL file and embedded-schema inventory
  - total keys, optional domains, and closed key-FD scope
  - nonempty candidate carrier with stable unique IDs and input digests
evidence_required:
  - per-table projection and reconstruction SQL
  - losslessness and dependency-preservation results
  - null mutation and missing, duplicate, foreign, or input-mismatched candidate refusals
validation_criteria:
  - Every declared schema source and table is inventoried.
  - Protected facts reject SQL NULL on INSERT and UPDATE, including legacy text primary keys.
  - Coverage uses set equality and cardinality, with input-bound foreign keys.
  - Mathematical acceptance is separate from structural exhaustiveness.
terminal_routes: [PreserveDeclaredProfile, RejectNullFact, RejectCarrierMismatch, RequireSemanticDependencies]
terminal_route_map:
  PreserveDeclaredProfile: Preserve
  RejectNullFact: Reject
  RejectCarrierMismatch: Reject
  RequireSemanticDependencies: Refuse
certification:
  certificate_required: true
  certificate_kind: omega.nf.schema-inventory.v1
  obstruction_class_required: false
  loss_ledger_required: false
  loss_ledger_trigger_id: null
  verifier_required: true
authorization:
  authorized_by: null
  certified_implies_authorized: false
proof_obligations:
  - id: sql_totality.semantic_nf4_nf5_nf6
    status: open
    statement: Declare complete semantic domains, MVDs, and JDs before stronger normalization certification.
references:
  - ./normal_form_contract_schema.yaml
  - schema_pipeline.py