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Certified normal forms, obstruction contracts, and authority boundaries for moving, transformed, and observer-relative data.

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Simplex Normal Forms

Boundary-Certified Data Architecture, Relational Normalization, Cochain Retraction & Representation Transport (CODA_MUR)
Epistemic Standard: Landau Rigor / Claim Discipline Compliant (AuthorityEffect: None, certified_implies_authorized: false)

Deployment status Deployment: Render Adoption Guide: IMPORT_GUIDE.md Architecture Spec: MVP_SELECTION.md Wiki: 112 Normal Forms Contracts: 112 Validated SVGs: 112 Visual Diagrams

Simplex Normal Forms Architecture


🌟 Interactive Web MVP: Simplex-NF Studio

Experience the core theoretical and engineering capabilities of simplex-normal-forms in real time:

Live URL: smplxnf.anomalon.com. On 2026-11-02, HTTPS and all 15 API smoke checks passed on the separate smplxnf-live Render service. Full live browser acceptance remains incomplete. See project status and the Render deployment and smoke-test runbook.

Four Flagship Engineering Workbenches

  1. Relational Synthesis & Tableau Chase Studio (Flagship Landing View): Interactive attribute closure, candidate key derivation, prime/non-prime attribute partitioning, minimal canonical cover, Bernstein (1976) dependency-preserving 3NF synthesis, Tsou-Fischer BCNF decomposition trees, and step-by-step Tableau Chase verification with spurious tuple counterexample witnesses.
  2. Streaming BQNF Delta Repair Simulator: Incremental Change Data Capture (CDC) boundary maintenance, signed coboundary delta calculation, priority-queue extremum cochain tracking in $O(\log K)$ without base table scans, and dynamic dyadic-bucket $\epsilon$-quantile sketch rebalancing under skewed streams.
  3. NF-IR Compiler Explorer: Functional-dependency lowering into SQLite triggers (BEFORE INSERT/UPDATE), Python guards, and counterexample fixtures, with a constructed subsumption comparison. The four-layer library architecture includes operadic wiring; this endpoint does not execute arbitrary wiring DAGs or compile the full contract catalog.
  4. AI Agent LossLedger Gateway: Context projection and token budget truncation for RAG and Model Context Protocol (MCP) tool pipelines with cryptographic SHA-256 Merkle LossLedger generation, exact additive token conservation ($\text{retained} + \text{truncated} == \text{source}$), and strict authority firewall gating (certified_implies_authorized: false).

📖 Read the Full Architectural Specification: docs/MVP_SELECTION.md
🚀 Step-by-Step Developer Integration Guide: IMPORT_GUIDE.md


1. What Is Simplex Normal Forms?

Classical database theory (Codd 1970–1974, Fagin 1977–1981, Date & Darwen 2002–2012) defines normal forms (1NF through 6NF, BCNF, EKNF, ETNF, DKNF) for data at rest: a single relational schema evaluated against functional, multivalued, and join dependencies.

Modern software and scientific computing architectures operate across four additional regimes where classical at-rest normalization is silent:

  1. Data at Rest (shape): Eliminating update/insertion/deletion anomalies with lossless join reconstruction (1NF–6NF, BCNF, EKNF, ETNF, RFNF, SKNF).
  2. Data in Motion (change / BQNF): Incremental view and cache maintenance under Change Data Capture (INSERT/UPDATE/DELETE) streams via the homological quotient $Q^1 = C^1 / \operatorname{im}(d^0)$, priority-queue extrema cochains, and $\epsilon$-BQNF quantile sketches.
  3. Data in Representation (coda / CODA_MUR, representation, transport, compilation): Certified representation transport (nf.coda.mur.transport, replacing legacy CODA_MUR), enforcing that updates commute with representation changes up to an explicit Loss Ledger (coda_mur.unmapped_field_drop).
  4. Data under Observation (epistemic, authority, evidence): Observer-relative freshness posets, epistemic quotient kernels (EQNF), observer distinguishability pseudometrics (ODNF), cryptographic Merkle trace receipts (TMNF), and strict separation of certification from authorization (certified_implies_authorized: false).
  5. Simplicial, Cochain & Physical Substrates (topology, physics, runtime, derivation): Simplicial boundary nilpotency ($\partial^2 = 0$), discrete Hodge decomposition ($C^1 = \operatorname{im} d_0 \oplus H^1 \oplus \operatorname{im} d_1^*$), exact rational zero-duality-gap witnesses (ZFNF), discrete Regge calculus, Lorentzian CDT foliation, and Fermion Sign Problem normal forms (BSS-NF, MIC-NF, BQNF-FSIGN).

2. Visual Overview

Boundary-Quotient Normal Form (BQNF) Observer-Relative Ontology
BQNF Diagram Observer Ontology Diagram

3. Repository Structure

simplex-normal-forms/
├── contracts/                  # 112 canonical YAML normal-form contracts (smplx.nf.contract.v1 / v0)
│   ├── _golden_nfs/            # Meta-schemas (standard.yaml, normal_form_definitions.yaml, SQLite schema)
│   ├── bqnf/                   # BQNF & Fermion Sign contracts and boundary quotient SVGs
│   ├── data/                   # JSON fixtures for CDC events, observers, orders, and certificates
│   └── nf.<family>.<name>.yaml # Individual machine-checkable normal form contracts
├── normal_forms/               # Standalone Python verifier, SQLite cochain evaluator & NF-IR compiler
│   ├── catalog.py              # CLI & library validator checking all 112 contracts against standard.yaml
│   ├── evaluator.py            # SQLite session evaluator (0NF->1NF, 5NF witness, BQNF CDC repair, S_N)
│   ├── ai.py                   # @coda_mur_projection & @observer_freshness_gate RAG/MCP decorator pipeline
│   ├── ir_kernel.py            # NF-IR Layer 1: Primitive WDP/OBNF witness micro-kernel (NFKernelSpec)
│   ├── ir_subsumption.py       # NF-IR Layer 2: Poset subsumption (NF_A <= NF_B) & dead-check elimination
│   ├── ir_wiring.py            # NF-IR Layer 3: Operadic DAG wiring (seq, par, guard) & Merkle loss chains
│   ├── ir_lowering.py          # NF-IR Layer 4: Python @nf_kernel_guard, SQLite triggers & counterexample fuzzer
│   ├── domain/                 # Pure-Python relational (2NF/3NF/BCNF/4NF), BQNF, ASRF, Hodge & ZFNF verifiers
│   └── *_example.py            # Executable demos for BQNF, Observer Freshness, Certificates & Reconciliation
├── web/                        # Simplex-NF Studio presentation layer (FastAPI backend & Tailwind SPA)
│   ├── app.py                  # REST API endpoints and static asset serving
│   ├── static/                 # Stylesheets, diagrams, and frontend JavaScript
│   ├── templates/              # High-contrast interactive workbench dashboard
│   └── requirements.txt        # Web tier dependencies (fastapi, uvicorn, pyyaml)
├── docs/                       # Architectural dossiers and technical research
│   ├── MVP_SELECTION.md        # Single MVP specification, trade-off matrix, and Render deployment design
│   ├── plans/                  # Master Plan of Plans (plan_of_plans.md) & Plans 1-4 NF-IR specifications
│   └── research_forum/         # 6-document Research Forum & Commercial Strategy Dossier (SimpleCache vs IVM)
├── images/                     # 112 per-contract visual SVG diagrams + architectural overview SVGs
├── wiki/                       # Complete mirror of the GitHub Wiki (one markdown page per normal form)
├── tests/                      # Unit, replay, scalar-equivalence, and API verification
├── pyproject.toml              # Standard PEP 517/518 build definition for zero-friction pip install
├── render.yaml                 # Infrastructure-as-code blueprint for smplxnf.anomalon.com
├── IMPORT_GUIDE.md             # Developer adoption guide with 4 runnable integration blueprints
└── README.md                   # Repository documentation and entry point

4. Quickstart: Installation, Tests & Local Workbench

Install in development mode and run the full test suite in under thirty seconds:

# 1. Clone the repository
git clone https://github.com/dbccpage/simplex-normal-forms.git
cd simplex-normal-forms

# 2. Create and activate a clean virtual environment
python -m venv .venv
source .venv/bin/activate  # On Windows: .venv\Scripts\activate

# 3. Install in editable development mode with development and web dependencies
pip install -e ".[dev,web]"

# 4. Run the automated test suite (all tests pass)
pytest tests/ -v

# 5. Launch the interactive Simplex-NF Studio workbench locally
uvicorn web.app:app --reload --host 127.0.0.1 --port 8000

Verify the health check endpoint:

curl http://127.0.0.1:8000/healthz
# Output: {"status":"ok","service":"smplxnf-studio","version":"0.1.0"}

Then navigate to http://127.0.0.1:8000 to interactively run relational synthesis, simulate CDC stream repairs, inspect lowered SQLite triggers, or test AI LossLedger context projections.

Legacy CLI Demos

You can also run standalone command-line verification scripts directly:

# Validate all 112 normal-form contracts against standard.yaml
python -m normal_forms.catalog

# Run BQNF CDC stream evaluation demo
python -m normal_forms.paid_revenue_example

# Run unverified certificate refusal gate demo (certified != authorized)
python -m normal_forms.unverified_certificate_example

# Run observer-relative freshness SLA poset monotonicity demo
python -m normal_forms.observer_freshness_example

# Run cross-domain reconciliation & LossLedger verification demo
python -m normal_forms.reconciliation_example

5. Wiki & Architectural Documentation

Explore the GitHub Wiki (also mirrored locally in wiki/):


6. Complete Normal Form Contract Register (112 Contracts)

112 contract files. The index lists 25 active and 87 draft entries, with nf.cohomology.acnf also listed as deprecated. These lifecycle labels are distinct from executable verification: contract metadata currently labels 35 executable, 75 verification-absent, and two unspecified. Catalog validation checks document structure. Every contract includes a dedicated Wiki page and visual SVG diagram.

Contract YAML Short Name Full Name Family Status Theory Verification Wiki & SVG Diagram
nf.change.bqnf.fermion_sign BQNF-FSIGN Boundary-Quotient Normal Form Instance for the Fermion Sign Problem change active proposed executable Wiki • SVG
nf.change.rational_quotient RATIONAL_QUOTIENT Rational cochain quotient section change active proposed executable Wiki • SVG
nf.change.sign_switching SIGN_SWITCHING Binary graph sign switching section change active proposed executable Wiki • SVG
nf.classical.1nf 1NF Atomic Domain First Normal Form shape active established absent Wiki • SVG
nf.classical.2nf 2NF Full Functional Dependency Second Normal Form shape active established absent Wiki • SVG
nf.classical.3nf 3NF Third Normal Form shape active established executable Wiki • SVG
nf.classical.4nf 4NF Multivalued Dependency Fourth Normal Form shape active established absent Wiki • SVG
nf.classical.5nf 5NF Project-Join Normal Form / Fifth Normal Form shape active established absent Wiki • SVG
nf.classical.6nf 6NF Sixth Normal Form shape active established executable Wiki • SVG
nf.classical.bcnf BCNF Boyce-Codd Normal Form shape active established absent Wiki • SVG
nf.classical.dknf DKNF Domain-Key Normal Form shape active established absent Wiki • SVG
nf.classical.eknf EKNF Elementary Key Normal Form shape active established absent Wiki • SVG
nf.classical.etnf ETNF Essential Tuple Normal Form shape active established absent Wiki • SVG
nf.classical.rfnf RFNF Redundancy-Free Normal Form / Key-Component Normal Form shape active established absent Wiki • SVG
nf.classical.sknf SKNF Superkey Normal Form / Fifth Normal Form Restricted shape active established absent Wiki • SVG
nf.ddc.context_boundary CBNF Context Boundary Normal Form topology active established executable Wiki • SVG
nf.ddc.dual_witness DWNF Dual Witness Normal Form evidence active established executable Wiki • SVG
nf.ddc.hodge_canonical HCNF Hodge Canonical Normal Form shape active established executable Wiki • SVG
nf.ddc.lift_ledger LNLF Lift Ledger Normal Form transport active established executable Wiki • SVG
nf.ddc.loss_ledger LLNF Loss Ledger Normal Form transport active established executable Wiki • SVG
nf.ddc.refusal_receipt RRNF Refusal Receipt Normal Form evidence active established executable Wiki • SVG
nf.ddc.terminal_partition TPNF Terminal Partition Normal Form authority active established executable Wiki • SVG
nf.ddc.trace_merkle TMNF Trace Merkle Normal Form runtime active established executable Wiki • SVG
nf.experimental.qm_classical QCNF Quantum-Classical Experiment Normal Form experimental active experimental executable Wiki • SVG
nf.operational.schema-totality SQL-TOTAL Declared SQL Key Projection and Candidate Totality Profile evidence active Wiki • SVG
nf.ai.ascnf ASCNF Agent-State Cohomology Normal Form experimental draft proposed absent Wiki • SVG
nf.bridge.wir_relvar WIR-Relvar Bridge WIR to Relvar Bridge Contract bridge draft proposed absent Wiki • SVG
nf.change.bqnf BQNF Boundary-Quotient Normal Form change draft proposed absent Wiki • SVG
nf.classical.0nf 0NF Raw / Unnormalized Form shape draft established executable Wiki • SVG
nf.classical.nf2 NF2 Non-First Normal Form Nested Relation Form shape draft proposed absent Wiki • SVG
nf.cochain.dhnf DHNF Discrete Hodge Normal Form shape draft established absent Wiki • SVG
nf.coda.eqnf EQNF Epistemic Quotient Normal Form epistemic draft established executable Wiki • SVG
nf.coda.gbqnf GBQNF Generalized Boundary-Quotient Normal Form change draft established executable Wiki • SVG
nf.coda.mur.transport coda_mur CODA-MUR Representation Transport Contract coda draft proposed absent Wiki • SVG
nf.coda.tsnf TSNF Topological Simplex Normal Form topology draft established executable Wiki • SVG
nf.cohomology.acnf ACNF Autopoietic Cohomology Normal Form experimental deprecated proposed absent Wiki • SVG
nf.compilation.cpnf CpNF Compilation Normal Form compilation draft Wiki • SVG
nf.derivation.aonf AONF Active Obstruction Normal Form derivation draft established executable Wiki • SVG
nf.derivation.apnf APNF Constructive Apartness Normal Form derivation draft established absent Wiki • SVG
nf.derivation.ignf IGNF Isomorphism Gauge Normal Form derivation draft established absent Wiki • SVG
nf.derivation.irnf IRNF Integer Ray Normal Form derivation draft established absent Wiki • SVG
nf.derivation.lsnf LSNF Lawful Skeletal Filtration Normal Form derivation draft established absent Wiki • SVG
nf.derivation.obnf OBNF Obstruction Relativization Normal Form derivation draft established executable Wiki • SVG
nf.derivation.pdnf PDNF Primitive Difference Normal Form derivation draft established executable Wiki • SVG
nf.derivation.rpnf RPNF Replay Provenance Normal Form derivation draft established executable Wiki • SVG
nf.derivation.scnf SCNF Separation Cost Normal Form derivation draft established executable Wiki • SVG
nf.derivation.sernf SERNF Split Extension-Retraction Normal Form derivation draft established executable Wiki • SVG
nf.epistemic.authority ANF Authority Normal Form epistemic draft proposed absent Wiki • SVG
nf.epistemic.cnf CNF Context Normal Form epistemic draft proposed absent Wiki • SVG
nf.epistemic.efnf EFNF Endogenous Fidelity Normal Form epistemic draft established absent Wiki • SVG
nf.epistemic.enf ENF Epistemic Normal Form epistemic draft proposed absent Wiki • SVG
nf.epistemic.freshness FNF Freshness Normal Form epistemic draft proposed absent Wiki • SVG
nf.epistemic.location LNF Location Normal Form epistemic draft proposed absent Wiki • SVG
nf.epistemic.nar_nf NAR-NF Non-Authoritative Realization Normal Form epistemic draft established executable Wiki • SVG
nf.epistemic.observer ObsNF Observer Normal Form epistemic draft proposed absent Wiki • SVG
nf.epistemic.odnf ODNF Observer Distinguishability Normal Form epistemic draft proposed absent Wiki • SVG
nf.epistemic.onf ONF Orchestration Normal Form epistemic draft proposed absent Wiki • SVG
nf.epistemic.pvnf PvNF Provenance Normal Form epistemic draft proposed absent Wiki • SVG
nf.epistemic.replica RNF Replica Normal Form epistemic draft proposed absent Wiki • SVG
nf.epistemic.snnf SnNF Stripe Normal Form epistemic draft proposed absent Wiki • SVG
nf.epistemic.state StNF State Normal Form epistemic draft proposed absent Wiki • SVG
nf.evidence.cdc CDCEF CDC Evidence Form evidence draft proposed absent Wiki • SVG
nf.evidence.certificate CertF Certificate Form evidence draft proposed absent Wiki • SVG
nf.evidence.ddanf DDANF Deterministic Data-Flow Architecture Normal Form evidence draft proposed absent Wiki • SVG
nf.evidence.loss_ledger LLF Loss Ledger Form evidence draft proposed absent Wiki • SVG
nf.evidence.provenance ProvF Provenance Form evidence draft proposed absent Wiki • SVG
nf.experimental.7nf 7NF Observer-Separable Fact Normal Form experimental draft experimental absent Wiki • SVG
nf.experimental.bell_contextuality BellCNF Bell Contextuality Observer Contract experimental draft experimental absent Wiki • SVG
nf.experimental.gauge XGauge Gauge Experimental Extension experimental draft experimental absent Wiki • SVG
nf.experimental.quantum_observer_ontology QONF Quantum Observer-Ontology Contract experimental draft experimental absent Wiki • SVG
nf.fsp.bssnf BSS-NF Binary Sign-Switching Normal Form representation draft proposed absent Wiki • SVG
nf.fsp.micnf MIC-NF Meron Involutive Cancellation Normal Form representation draft proposed absent Wiki • SVG
nf.logic.qanf QANF Quantifier Alternation Normal Form experimental draft proposed absent Wiki • SVG
nf.motion.flow_control FCNF Flow Control Normal Form motion draft proposed absent Wiki • SVG
nf.motion.horizon_emission HENF Horizon Emission Normal Form motion draft proposed absent Wiki • SVG
nf.motion.locality_lrb LRBNF Lieb-Robinson Locality Normal Form motion draft proposed absent Wiki • SVG
nf.mssn MSSNF Minimal Symbol System Normal Form shape draft proposed executable Wiki • SVG
nf.mssn.bqnf MSSN-BQNF MSS-N Boundary-Quotient Normal Form change draft proposed executable Wiki • SVG
nf.ontology.ainf AINF Adjoint-Invariant Normal Form derivation draft proposed absent Wiki • SVG
nf.pfp.pfnf PFNF Proposal Fidelity Normal Form coda draft established executable Wiki • SVG
nf.physics.bianchi_regge RBNF Regge-Bianchi Normal Form (arXiv:1904.01966 Recovery) physics draft admitted absent Wiki • SVG
nf.physics.bqnf_fsign BQNF-FSIGN Fermion Sign Problem Boundary-Quotient Normal Form representation draft experimental executable Wiki • SVG
nf.physics.bqnf_regge BQNF-REGGE Boundary-Quotient Normal Form for Regge Geometrodynamics physics draft admitted absent Wiki • SVG
nf.physics.cdt_fermion_sign CDT-FSIGN-NF 4D CDT Fermionic Grassmann Path Integrals & BQNF Sign Normal Form physics draft admitted absent Wiki • SVG
nf.physics.cdt_kd_doubling CDT-KD-DOUBLING-NF 4D CDT Kähler-Dirac Fermion Doubling Resolution & Topological Spin Normal Form physics draft admitted absent Wiki • SVG
nf.physics.cdt_matter_coupling CDT-MATTER-NF CDT Dynamical Matter Field & Lattice Gauge Coupling Normal Form physics draft admitted absent Wiki • SVG
nf.physics.cdt_overlap_fermions CDT-OVERLAP-NF 4D CDT Ginsparg-Wilson & Overlap Dirac Operator Normal Form physics draft admitted absent Wiki • SVG
nf.physics.cdt_spectral_dimension CDT-SPEC-NF CDT Spectral Dimension & Dynamical Dimensional Reduction Normal Form physics draft admitted absent Wiki • SVG
nf.physics.cdt_susy_witten CDT-SUSY-WITTEN-NF 4D CDT Supersymmetric Topological Witten Index, Nicolai Map & Super-WDW Normal Form physics draft admitted absent Wiki • SVG
nf.physics.cdt_topological_charge CDT-TOPO-CHARGE-NF 4D CDT Topological Charge Fluctuations & Instanton Susceptibility Normal Form physics draft admitted absent Wiki • SVG
nf.physics.cdt_wick_mc CDT-WMC-NF Wick-Rotated Lorentzian CDT Monte Carlo Statistical Weight Sampler Contract physics draft experimental absent Wiki • SVG
nf.physics.cdt_zolotarev_overlap CDT-ZOLOTAREV-NF 4D CDT Rational Zolotarev & Deflated Overlap Dirac Operator Contract physics draft established absent Wiki • SVG
nf.physics.dfnf DFNF Dressing Field Normal Form physics draft experimental executable Wiki • SVG
nf.physics.l1_constraint_closure L1CCNF L1 Constraint Closure and Duality Normal Form physics draft experimental absent Wiki • SVG
nf.physics.lorentzian_cdt LCNF 4D Lorentzian Regge Causal Triangulation Normal Form physics draft established absent Wiki • SVG
nf.physics.pachner_lp_scaling L1PSNF 4D Pachner Moves and Joint LP Scaling Normal Form physics draft experimental absent Wiki • SVG
nf.physics.pwnf PWNF Page-Wootters Relational Clock Normal Form physics draft established absent Wiki • SVG
nf.physics.rcnf RCNF Regge Calculus Normal Form physics draft established absent Wiki • SVG
nf.physics.rpcnf RPCNF Relational Point Coincidence Normal Form physics draft experimental executable Wiki • SVG
nf.physics.schlafli_nf SIDNF Schläfli Differential Identity Normal Form physics draft established absent Wiki • SVG
nf.physics.wdwnf WDWNF Wheeler-DeWitt Constraint and Kernel Normal Form physics draft established absent Wiki • SVG
nf.query.spja SPJA Selection Projection Join Aggregate Form query draft proposed executable Wiki • SVG
nf.recursion.asrf ASRF Autopoietic Self-Reference Refusal Form recursion draft proposed absent Wiki • SVG
nf.relativistic.lightcone LCNF Light-Cone Causality Normal Form relativistic draft proposed absent Wiki • SVG
nf.relativistic.time_sync CSNF Clock-Synchronization Normal Form relativistic draft proposed absent Wiki • SVG
nf.representation.dbcnf DBCNF De Bruijn Cyclic Normal Form representation draft established absent Wiki • SVG
nf.representation.gnf GNF Gauge Normal Form transport draft proposed absent Wiki • SVG
nf.representation.tbnf TBNF Token-Bounded Normal Form representation draft proposed absent Wiki • SVG
nf.runtime.mtnf MTNF Mazurkiewicz Trace Normal Form runtime draft established absent Wiki • SVG
nf.runtime.zfnf ZFNF Zero-Float Rational Normal Form runtime draft established executable Wiki • SVG
nf.security.efnf EFNF Epistemic-Fibration Normal Form security draft proposed executable Wiki • SVG
nf.wdp.wdnf WDNF Witnessed Difference Normal Form derivation draft established executable Wiki • SVG

7. Epistemic Claim Hygiene Quadrant

  1. What it supports:
    • Supports machine validation of 112 declarative normal-form contracts against standard.yaml, executable SQLite/Python evaluation of relational decompositions (0NF–6NF, BCNF), BQNF incremental CDC repair, CODA_MUR representation transport with loss ledgers, observer-relative freshness posets, and discrete Hodge/rational duality witnesses in this repository's model.
  2. What it does not support:
    • Does not confer operational authority (AuthorityEffect: None, certified_implies_authorized: false).
    • Does not claim that mathematical toy models or finite simplicial complexes constitute empirical physical evidence or replace production distributed consensus.
  3. The narrowest defensible claim:
    • Every contract in contracts/ satisfies the syntactic structure checked by python -m normal_forms.catalog, maps its local outcomes to canonical terminals, and is documented with an explicit Four-Pillar Quadrilateral and visual SVG diagram.
  4. The next test needed:
    • Multi-node distributed benchmark replaying production PostgreSQL/MySQL logical replication WAL streams across concurrent observer poset tenants and diamond CODA_MUR representation DAGs.

License

Released under the MIT License.

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Certified normal forms, obstruction contracts, and authority boundaries for moving, transformed, and observer-relative data.

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