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Jeremy H. Carroll edited this page Nov 3, 2026 · 5 revisions

Simplex Normal Forms: Boundary-Certified Data Architecture & Cochain Catalog

AuthorityEffect: None (certified_implies_authorized: false)
Total Canonical Normal Form Contracts: 112 (each with its own dedicated Wiki treatise and visual SVG diagram)

Current project status and evidence levels: Studio is live at smplxnf.anomalon.com; HTTPS/API checks passed on 2026-11-02. Full live browser acceptance remains incomplete. Contract pages describe declarations and intended behavior. Their diagrams and “Certified Output” labels are not execution receipts; see the status guide before interpreting those claims.

Simplex Normal Forms Architecture

1. Overview & Architectural Regimes

Simplex Normal Forms unifies classical relational database normalization (Codd, Boyce, Fagin, Date, Darwen) with post-Codd operational regimes: data in motion (Boundary-Quotient Normal Form / BQNF), data in representation (GNF, CODA_MUR representation transport, CpNF compilation), data under observation (Epistemic & Observer-Relative Normal Forms), and simplicial, cochain, and physical substrates (TSNF, DHNF, ZFNF, Regge calculus, and Fermion Sign Problem normal forms).

Nomenclature Note (CODA_MUR): Legacy references to CODA_MUR have been retired across the estate. Representation transport is governed by CODA_MUR (nf.coda.mur.transport), where updates commute with representation changes up to a sealed Loss Ledger (coda_mur.unmapped_field_drop).

Regime Core Question Canonical Normal Forms
1. Data at Rest Does the stored schema eliminate redundancy and reconstruct losslessly? nf.classical.0nf, nf.classical.1nf, nf.classical.2nf, nf.classical.3nf, nf.classical.eknf, nf.classical.bcnf, nf.classical.4nf, nf.classical.etnf, nf.classical.rfnf, nf.classical.sknf, nf.classical.5nf, nf.classical.6nf, nf.classical.dknf, nf.classical.nf2
2. Data in Motion Does a streaming write event (INSERT/UPDATE/DELETE) admit an exact $O(1)$ local coboundary repair $\omega = d^0\alpha$? nf.change.bqnf, nf.coda.gbqnf, nf.change.bqnf.fermion_sign, nf.change.rational_quotient, nf.change.sign_switching, nf.evidence.cdc
3. Data in Representation Do updates commute with representation translation $F: \text{Rep}_A \to \text{Rep}_B$ up to declared loss? nf.coda.mur.transport (CODA_MUR), nf.representation.gnf, nf.compilation.cpnf, nf.representation.tbnf, nf.representation.dbcnf, nf.fsp.bssnf, nf.fsp.micnf
4. Data under Observation Is a claim fresh, provenance-chained, and distinguishable relative to the reading observer $O_i$? nf.epistemic.authority, nf.epistemic.freshness, nf.epistemic.observer, nf.coda.eqnf, nf.epistemic.odnf, nf.epistemic.nar_nf, nf.ddc.terminal_partition
5. Cochain, Topological & Physics Substrate Does the discrete complex satisfy $\partial^2 = 0$, orthogonal Hodge decomposition, exact rational duality ($\text{gap} = 0$), and Bianchi/Regge closure? nf.coda.tsnf, nf.cochain.dhnf, nf.ddc.hodge_canonical, nf.runtime.zfnf, nf.ddc.dual_witness, nf.physics.bianchi_regge, nf.physics.schlafli_regge, nf.physics.lorentzian_cdt, nf.physics.wdw, nf.physics.page_wootters

2. Foundational Wiki Guides

  1. Theory and Cochain Substrate — The Four-Pillar Quadrilateral, Heath/Fagin/Rissanen theorems, BQNF homological sequence $Q^1 = C^1/\operatorname{im}(d^0)$, priority-queue extrema cochains, $\epsilon$-BQNF quantile sketches, and CODA_MUR descent compatibility.
  2. Observer-Relative Ontology — The Table–Relation–Relvar–Boundary-Relvar triad, observer poset monotonicity, EQNF, ODNF, and the strict governance wall (certified_implies_authorized: false).
  3. Concrete Worked Examples — Step-by-step SQL, JSON, Python, and Simplex-NF Studio (web/app.py / smplxnf.anomalon.com) execution walkthroughs (NormalFormsEvaluator, BqnfValidator, 0NF$\to$1NF, 3NF Bernstein synthesis, 5NF consulting witness, BQNF CDC repair, CODA_MUR transport, 4-layer NF-IR compiler, and IMPORT_GUIDE.md blueprints).
  4. Relational Geometrodynamics and Physics Substrate — Discrete Regge calculus, Cayley-Menger metric positivity, Schläfli identity, Lorentzian CDT foliation, Wheeler-DeWitt, Page-Wootters relational time, and Fermion Sign Problem normal forms.

3. Master Architectural Diagrams

Boundary-Quotient Normal Form (BQNF) Observer-Relative Ontology
BQNF Diagram Observer Ontology Diagram
Four-Pillar Standard (standard.yaml) Catalog Overview (index.yaml)
Standard Diagram Catalog Index Diagram

4. Complete Directory of All 112 Normal Forms (One Page Per Normal Form)

Every Normal Form below links to its dedicated Wiki page containing prose explanations, its custom SVG visual diagram, worked examples, Four-Pillar Quadrilateral specification, terminal routing table, and canonical YAML contract.

shape — Relational, Algebraic & Cochain Shape Normal Forms (Data at Rest & Structural Decompositions) (17 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.classical.0nf (SVG) 0NF Raw / Unnormalized Form draft Extended Form
nf.classical.1nf (SVG) 1NF Atomic Domain First Normal Form active Extended Form
nf.classical.2nf (SVG) 2NF Full Functional Dependency Second Normal Form active Extended Form
nf.classical.3nf (SVG) 3NF Third Normal Form active Extended Form
nf.classical.4nf (SVG) 4NF Multivalued Dependency Fourth Normal Form active Extended Form
nf.classical.5nf (SVG) 5NF Project-Join Normal Form / Fifth Normal Form active Extended Form
nf.classical.6nf (SVG) 6NF Sixth Normal Form active Extended Form
nf.classical.bcnf (SVG) BCNF Boyce-Codd Normal Form active Extended Form
nf.classical.dknf (SVG) DKNF Domain-Key Normal Form active Extended Form
nf.classical.eknf (SVG) EKNF Elementary Key Normal Form active Extended Form
nf.classical.etnf (SVG) ETNF Essential Tuple Normal Form active Extended Form
nf.classical.nf2 (SVG) NF2 Non-First Normal Form Nested Relation Form draft Extended Form
nf.classical.rfnf (SVG) RFNF Redundancy-Free Normal Form / Key-Component Normal Form active Extended Form
nf.classical.sknf (SVG) SKNF Superkey Normal Form / Fifth Normal Form Restricted active Extended Form
nf.cochain.dhnf (SVG) DHNF Discrete Hodge Normal Form draft Extended Form
nf.ddc.hodge_canonical (SVG) HCNF Hodge Canonical Normal Form active Extended Form
nf.mssn (SVG) MSSNF Minimal Symbol System Normal Form draft Extended Form

change — Data in Motion & Boundary-Quotient Incremental Maintenance Contracts (BQNF & Cochain Repair) (6 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.change.bqnf (SVG) BQNF Boundary-Quotient Normal Form draft Extended Form
nf.change.bqnf.fermion_sign (SVG) BQNF-FSIGN Boundary-Quotient Normal Form Instance for the Fermion Sign Problem active Extended Form
nf.change.rational_quotient (SVG) RATIONAL_QUOTIENT Rational cochain quotient section active Extended Form
nf.change.sign_switching (SVG) SIGN_SWITCHING Binary graph sign switching section active Extended Form
nf.coda.gbqnf (SVG) GBQNF Generalized Boundary-Quotient Normal Form draft Extended Form
nf.mssn.bqnf (SVG) MSSN-BQNF MSS-N Boundary-Quotient Normal Form draft Extended Form

coda — CODA Foundational Quotient, Representation Transport (CODA_MUR) & Proof-Fact Contracts (2 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.coda.mur.transport (SVG) coda_mur CODA-MUR Representation Transport Contract draft Extended Form
nf.pfp.pfnf (SVG) PFNF Proposal Fidelity Normal Form draft Extended Form

representation — Data in Representation, Canonical Wire Grammars, Orbit Representatives & Gauge Fixing (5 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.fsp.bssnf (SVG) BSS-NF Binary Sign-Switching Normal Form draft Extended Form
nf.fsp.micnf (SVG) MIC-NF Meron Involutive Cancellation Normal Form draft Extended Form
nf.physics.bqnf_fsign (SVG) BQNF-FSIGN Fermion Sign Problem Boundary-Quotient Normal Form draft Extended Form
nf.representation.dbcnf (SVG) DBCNF De Bruijn Cyclic Normal Form draft Extended Form
nf.representation.tbnf (SVG) TBNF Token-Bounded Normal Form draft Extended Form

transport — Scale Ascent/Descent & Representation Transport Ledgers (LNLF, LLNF, GNF) (3 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.ddc.lift_ledger (SVG) LNLF Lift Ledger Normal Form active Extended Form
nf.ddc.loss_ledger (SVG) LLNF Loss Ledger Normal Form active Extended Form
nf.representation.gnf (SVG) GNF Gauge Normal Form draft Extended Form

compilation — Compilation & Query Lowering Preservation Contracts (CpNF) (1 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.compilation.cpnf (SVG) CpNF Compilation Normal Form draft Extended Form

epistemic — Observer-Relative Epistemic, Freshness, Context, Provenance & Distinguishability Contracts (15 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.coda.eqnf (SVG) EQNF Epistemic Quotient Normal Form draft Extended Form
nf.epistemic.authority (SVG) ANF Authority Normal Form draft Extended Form
nf.epistemic.cnf (SVG) CNF Context Normal Form draft Extended Form
nf.epistemic.efnf (SVG) EFNF Endogenous Fidelity Normal Form draft Extended Form
nf.epistemic.enf (SVG) ENF Epistemic Normal Form draft Extended Form
nf.epistemic.freshness (SVG) FNF Freshness Normal Form draft Extended Form
nf.epistemic.location (SVG) LNF Location Normal Form draft Extended Form
nf.epistemic.nar_nf (SVG) NAR-NF Non-Authoritative Realization Normal Form draft Extended Form
nf.epistemic.observer (SVG) ObsNF Observer Normal Form draft Extended Form
nf.epistemic.odnf (SVG) ODNF Observer Distinguishability Normal Form draft Extended Form
nf.epistemic.onf (SVG) ONF Orchestration Normal Form draft Extended Form
nf.epistemic.pvnf (SVG) PvNF Provenance Normal Form draft Extended Form
nf.epistemic.replica (SVG) RNF Replica Normal Form draft Extended Form
nf.epistemic.snnf (SVG) SnNF Stripe Normal Form draft Extended Form
nf.epistemic.state (SVG) StNF State Normal Form draft Extended Form

authority — Terminal Partition & Authority Boundary Contracts (TPNF) (1 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.ddc.terminal_partition (SVG) TPNF Terminal Partition Normal Form active Extended Form

evidence — Cryptographic Receipts, Dual Witnesses, Loss Ledgers, CDC Logs & Schema Totality (8 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.ddc.dual_witness (SVG) DWNF Dual Witness Normal Form active Extended Form
nf.ddc.refusal_receipt (SVG) RRNF Refusal Receipt Normal Form active Extended Form
nf.evidence.cdc (SVG) CDCEF CDC Evidence Form draft Extended Form
nf.evidence.certificate (SVG) CertF Certificate Form draft Extended Form
nf.evidence.ddanf (SVG) DDANF Deterministic Data-Flow Architecture Normal Form draft Extended Form
nf.evidence.loss_ledger (SVG) LLF Loss Ledger Form draft Extended Form
nf.evidence.provenance (SVG) ProvF Provenance Form draft Extended Form
nf.operational.schema-totality (SVG) SQL-TOTAL Declared SQL Key Projection and Candidate Totality Profile active Extended Form

derivation — MSS-N Tower Algebraic Derivation, Split Extension-Retraction & Obstruction Contracts (12 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.derivation.aonf (SVG) AONF Active Obstruction Normal Form draft Extended Form
nf.derivation.apnf (SVG) APNF Constructive Apartness Normal Form draft Extended Form
nf.derivation.ignf (SVG) IGNF Isomorphism Gauge Normal Form draft Extended Form
nf.derivation.irnf (SVG) IRNF Integer Ray Normal Form draft Extended Form
nf.derivation.lsnf (SVG) LSNF Lawful Skeletal Filtration Normal Form draft Extended Form
nf.derivation.obnf (SVG) OBNF Obstruction Relativization Normal Form draft Extended Form
nf.derivation.pdnf (SVG) PDNF Primitive Difference Normal Form draft Extended Form
nf.derivation.rpnf (SVG) RPNF Replay Provenance Normal Form draft Extended Form
nf.derivation.scnf (SVG) SCNF Separation Cost Normal Form draft Extended Form
nf.derivation.sernf (SVG) SERNF Split Extension-Retraction Normal Form draft Extended Form
nf.ontology.ainf (SVG) AINF Adjoint-Invariant Normal Form draft Extended Form
nf.wdp.wdnf (SVG) WDNF Witnessed Difference Normal Form draft Extended Form

topology — Simplicial Complexes, Boundary Nilpotency & Context Boundary Purity (TSNF, CBNF) (2 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.coda.tsnf (SVG) TSNF Topological Simplex Normal Form draft Extended Form
nf.ddc.context_boundary (SVG) CBNF Context Boundary Normal Form active Extended Form

physics — Discrete Differential Geometry, Regge Calculus, Gauge Theory, Lattice Fermions & Quantum Gravity (20 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.physics.bianchi_regge (SVG) RBNF Regge-Bianchi Normal Form (arXiv:1904.01966 Recovery) draft Extended Form
nf.physics.bqnf_regge (SVG) BQNF-REGGE Boundary-Quotient Normal Form for Regge Geometrodynamics draft Extended Form
nf.physics.cdt_fermion_sign (SVG) CDT-FSIGN-NF 4D CDT Fermionic Grassmann Path Integrals & BQNF Sign Normal Form draft Extended Form
nf.physics.cdt_kd_doubling (SVG) CDT-KD-DOUBLING-NF 4D CDT Kähler-Dirac Fermion Doubling Resolution & Topological Spin Normal Form draft Extended Form
nf.physics.cdt_matter_coupling (SVG) CDT-MATTER-NF CDT Dynamical Matter Field & Lattice Gauge Coupling Normal Form draft Extended Form
nf.physics.cdt_overlap_fermions (SVG) CDT-OVERLAP-NF 4D CDT Ginsparg-Wilson & Overlap Dirac Operator Normal Form draft Extended Form
nf.physics.cdt_spectral_dimension (SVG) CDT-SPEC-NF CDT Spectral Dimension & Dynamical Dimensional Reduction Normal Form draft Extended Form
nf.physics.cdt_susy_witten (SVG) CDT-SUSY-WITTEN-NF 4D CDT Supersymmetric Topological Witten Index, Nicolai Map & Super-WDW Normal Form draft Extended Form
nf.physics.cdt_topological_charge (SVG) CDT-TOPO-CHARGE-NF 4D CDT Topological Charge Fluctuations & Instanton Susceptibility Normal Form draft Extended Form
nf.physics.cdt_wick_mc (SVG) CDT-WMC-NF Wick-Rotated Lorentzian CDT Monte Carlo Statistical Weight Sampler Contract draft Extended Form
nf.physics.cdt_zolotarev_overlap (SVG) CDT-ZOLOTAREV-NF 4D CDT Rational Zolotarev & Deflated Overlap Dirac Operator Contract draft Extended Form
nf.physics.dfnf (SVG) DFNF Dressing Field Normal Form draft Extended Form
nf.physics.l1_constraint_closure (SVG) L1CCNF L1 Constraint Closure and Duality Normal Form draft Extended Form
nf.physics.lorentzian_cdt (SVG) LCNF 4D Lorentzian Regge Causal Triangulation Normal Form draft Extended Form
nf.physics.pachner_lp_scaling (SVG) L1PSNF 4D Pachner Moves and Joint LP Scaling Normal Form draft Extended Form
nf.physics.pwnf (SVG) PWNF Page-Wootters Relational Clock Normal Form draft Extended Form
nf.physics.rcnf (SVG) RCNF Regge Calculus Normal Form draft Extended Form
nf.physics.rpcnf (SVG) RPCNF Relational Point Coincidence Normal Form draft Extended Form
nf.physics.schlafli_nf (SVG) SIDNF Schläfli Differential Identity Normal Form draft Extended Form
nf.physics.wdwnf (SVG) WDWNF Wheeler-DeWitt Constraint and Kernel Normal Form draft Extended Form

relativistic — Causal Lightcone Structure & Relativistic Clock Synchronization Contracts (2 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.relativistic.lightcone (SVG) LCNF Light-Cone Causality Normal Form draft Extended Form
nf.relativistic.time_sync (SVG) CSNF Clock-Synchronization Normal Form draft Extended Form

motion — Flow Control, Horizon Emission & Lieb-Robinson Locality Bounds (3 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.motion.flow_control (SVG) FCNF Flow Control Normal Form draft Extended Form
nf.motion.horizon_emission (SVG) HENF Horizon Emission Normal Form draft Extended Form
nf.motion.locality_lrb (SVG) LRBNF Lieb-Robinson Locality Normal Form draft Extended Form

runtime — Exact Rational Zero-Duality-Gap Certifiers & Merkle Trace Execution Contracts (3 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.ddc.trace_merkle (SVG) TMNF Trace Merkle Normal Form active Extended Form
nf.runtime.mtnf (SVG) MTNF Mazurkiewicz Trace Normal Form draft Extended Form
nf.runtime.zfnf (SVG) ZFNF Zero-Float Rational Normal Form draft Extended Form

experimental — Bounded Quantum-Classical, Contextuality, Quantifier Alternation & Agent-State Contracts (8 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.ai.ascnf (SVG) ASCNF Agent-State Cohomology Normal Form draft Extended Form
nf.cohomology.acnf (SVG) ACNF Autopoietic Cohomology Normal Form deprecated Extended Form
nf.experimental.7nf (SVG) 7NF Observer-Separable Fact Normal Form draft Extended Form
nf.experimental.bell_contextuality (SVG) BellCNF Bell Contextuality Observer Contract draft Extended Form
nf.experimental.gauge (SVG) XGauge Gauge Experimental Extension draft Extended Form
nf.experimental.qm_classical (SVG) QCNF Quantum-Classical Experiment Normal Form active Extended Form
nf.experimental.quantum_observer_ontology (SVG) QONF Quantum Observer-Ontology Contract draft Extended Form
nf.logic.qanf (SVG) QANF Quantifier Alternation Normal Form draft Extended Form

bridge — Cross-Substrate Bridge Contracts (WIR to Relational Variable Lowering) (1 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.bridge.wir_relvar (SVG) WIR-Relvar Bridge WIR to Relvar Bridge Contract draft Extended Form

query — Relational & Cochain Query Evaluation Normal Forms (1 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.query.spja (SVG) SPJA Selection Projection Join Aggregate Form draft Extended Form

recursion — Autopoietic Self-Reference Refusal & Caller-Verifier Separation (ASRF) (1 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.recursion.asrf (SVG) ASRF Autopoietic Self-Reference Refusal Form draft Extended Form

security — Endogenous Fidelity & Security Boundary Normal Forms (1 contracts)

Wiki Page & Diagram Short Name Full Name Status Qualification
nf.security.efnf (SVG) EFNF Epistemic-Fibration Normal Form draft Extended Form

5. Epistemic Claim Hygiene Quadrant

  1. What it supports:
    • Supports machine-checkable schema validation, cochain defect classification, and explicit terminal routing across all 112 normal-form contracts in this repository.
  2. What it does not support:
    • Does not grant operational authority (AuthorityEffect: None) or certify unmodeled external environments.
  3. The narrowest defensible claim:
    • Every contract in contracts/ conforms to standard.yaml, maps its local routes to canonical terminals, and enforces certified_implies_authorized: false.
  4. The next test needed:
    • Automated cross-contract composition testing across multi-stage relational-to-cochain pipelines.

Simplex Normal Forms • 112 Canonical Contracts & SVG Diagrams • CODA_MUR Transport • certified_implies_authorized: false • AuthorityEffect: None

🏛️ Simplex Normal Forms

📚 112 Normal Forms by Family

shape (17)
change (6)
coda (2)
representation (5)
transport (3)
compilation (1)
epistemic (15)
authority (1)
evidence (8)
derivation (12)
topology (2)
physics (20)
relativistic (2)
motion (3)
runtime (3)
experimental (8)
bridge (1)
query (1)
recursion (1)
security (1)

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