Research-Stack/0-Core-Formalism/otom/docs/wiki/NotationNomenclatureRegistry.md

Research Notation and Nomenclature Registry

Status: HOLD / workbench projection Authority: internal wiki spine; not canonical until validator and Lean receipts exist Created: 2026-05-01

Purpose

This document is the internal wiki registry for names, symbols, types, authority levels, and projection rules across the research stack.

It exists to prevent the same idea from being rediscovered under incompatible names.

The registry is not a proof. It is a routing surface. Promotion requires receipts.

name -> type -> admissibility -> authority -> projection -> receipt

Source surfaces indexed in this pass

This first pass aligns the following surfaces:

• Lean-style modules and specs: SSMS, SSMS_nD, NBody, Semantics, FixedPoint, NBody dynamics, manifold networking, compression/invariant modules.
• Graph surfaces: GraphML, Mermaid, knowledge graph projections, concept maps.
• Wiki surfaces: GCL/MN-GCL, Semantic Mass, admissibility closure, Ring0 gates, Research Wiki Hub.
• JSON-LD ontology: NUVMAP / MetaProbe / AngrySphinx / Forest Map / Delta GCL / FAMM / BioKernel / Great Filter CCR.
• Conversation-derived conceptual surfaces: GeoCognition, behavioral manifold, Ricci-flow/turbulence, semantic mass, Mass-Number theory, SNPAR, SETI/steganographic signal verification.

Registry doctrine

No term promotes itself.
No symbol proves itself.
No projection is canonical by default.
No emotional force, visual centrality, or graph weight counts as proof.

Every term must declare:

type RegistryEntry = {
  id: string;
  preferred_name: string;
  aliases: string[];
  symbol?: string;
  type_class: TypeClass;
  definition: string;
  allowed_claim_states: ClaimState[];
  authority_scope: AuthorityScope;
  canonical_surface?: string;
  projection_surfaces: string[];
  receipt_requirements: ReceiptRequirement[];
  blocked_usages: string[];
};

Type classes

type TypeClass =
  | "Primitive"
  | "Operator"
  | "Metric"
  | "Gate"
  | "Manifold"
  | "Projection"
  | "Receipt"
  | "Protocol"
  | "Simulator"
  | "ClaimState"
  | "Policy"
  | "DangerBoundary";

Claim states

Use these names everywhere.

U_scope
  Unscoped or exploratory. May be useful, but not typed tightly enough.

HOLD
  Important, active, unresolved, not promoted.

V_scope
  Locally valid under an explicitly stated scope.

REVIEWED
  External or internal review exists and receipts are attached.

CANONICAL_LEAN
  Kernel-checked theorem/spec or machine-verifiable equivalent exists.

QUARANTINE
  Powerful, unsafe, overbroad, or likely to be misused without guardrails.

Never use true, proven, obvious, validated, or real as a claim state.

Authority scopes

workbench_projection
  Exploratory wiki/graph/language layer. Useful for orientation only.

simulation_only
  Implemented or visualized in code/sim, but not established as physical law.

receipt_backed
  Benchmarks, source audits, measurements, or reproducible traces exist.

canonical_lean
  Lean theorem/spec or typed formal artifact exists and builds without sorry.

external_source
  Imported from literature, standard math, public dataset, or external spec.

safety_policy
  Gate, refusal, ethics, privacy, or governance boundary.

Core primitive registry

ID	Preferred name	Aliases	Symbol	Type	Definition	Default state
gcl	Genetic Coding Language	GCL, deprecated alias: Grammar/Concept Language	GCL	Protocol	Genetic-code-inspired concept language for encoding research objects as typed, mutable, receipt-gated units with inheritance, mutation, recombination, repair, admissibility, projection, and formalization targets.	HOLD
mn_gcl	Mass-Number GCL	MN-GCL, MassNumber subset	MN-GCL	Protocol	Mass-Number subset/profile of Genetic Coding Language using typed expansion slots.	HOLD
mass_number	Mass Number	semantic mass number, mass index	M#	Primitive	Dimensionless semantic/accounting magnitude that may become route-cost evidence only after admissibility closure.	HOLD
semantic_mass	Semantic Mass	information mass, mass-like semantic pressure	m_s	Primitive	Dimensionless resistance/attraction/routing-cost feature; not SI physical mass.	HOLD
nan_mass	NaNMass	unresolved mass, infinite artifact	NaN_M	DangerBoundary	Typed unresolved mass state used when closure/accounting/admissibility fails.	HOLD
closed_mass	ClosedMass	admissible mass, receipt-backed mass	M_cl	Primitive	Finite mass value after closure receipt.	V_scope
admissibility_closure	Admissibility Closure	closure, closure gate	Cl_A	Operator	Turns raw mass-like pressure into pseudometric/quotient metric targets under constraints.	HOLD
compatibility_kernel	Compatibility Kernel	kernel K, admissibility kernel	K_R(x,y)	Metric	Regime-scoped compatibility between nodes under route/admissibility rules.	HOLD
phi	Phi potential	Φ, field potential, compression potential	Φ	Metric	Generic potential or invariant field; must be locally defined per module.	U_scope
torsion	Torsion	twist, mismatch, route torque	τ	Metric	Directional mismatch / twist / unresolved interface pressure.	HOLD
route_cost	Route Cost	traversal cost, adapter cost	C_R	Metric	Cost of moving a concept/state through a route or adapter chain.	HOLD
receipt	Receipt	evidence receipt, proof receipt	ρ	Receipt	Machine-readable evidence object tying a claim to source, theorem, benchmark, trace, or audit.	V_scope

Canonical non-identities

These are explicit category boundaries.

mass_number != distance
semantic_mass != physical_mass
projection != proof
graph_centrality != truth
simulator_success != theorem
infinity_like != MassValue
emotional_intensity != evidence
LLM_agreement != validation
genotype != phenotype
mutation != validation

GCL genetic-code doctrine

GCL borrows genetic-code architecture as an engineering pattern:

symbols/codons -> typed expressions -> traits/phenotypes -> regime expression -> gate pressure -> repair/mutation -> receipts

Allowed analogy:

codon-like slots
mutation/revision
recombination of concepts
repair pathways
expression under regimes
genotype/phenotype split
fitness under evidence gates

Forbidden overclaim:

GCL is literal DNA.
GCL proves biology.
GCL proves claims by evolutionary language alone.
GCL mutations are valid because they are generative.

MassValue type

Use this in GCL, MN-GCL, JSON, TypeScript, and future Lean mirrors.

type MassValue =
  | { tag: "FiniteMass"; value: number; unit: "dimensionless" }
  | { tag: "NaNMass"; reason: NaNMassReason; evidence: string[] }
  | { tag: "ClosedMass"; value: number; closure_receipt: string };

type NaNMassReason =
  | "division_by_unclosed_zero"
  | "unbounded_route_cost"
  | "missing_admissibility"
  | "regime_mismatch"
  | "infinite_projection_artifact"
  | "comparison_without_common_closure";

Universe-local infinity rule

Other universe:
  may permit completed infinity as a native object

This executable universe:
  requires finite thermodynamic accounting
  rejects infinity as MassValue
  routes infinity-like behavior to NaNMass

Use NaNMass, LimitBoundary, QuotientBoundary, or RenormalizationCandidate; do not use InfiniteMass.

Formal notation rules

Scalars

Symbol	Name	Scope
m_s	semantic mass	dimensionless semantic/routing feature
M#	mass number	nuclide-inspired semantic/accounting index
Φ	potential	must be module-local unless explicitly universalized
τ	torsion/turbulence	interface mismatch; must declare which layer
κ	curvature	geometry/route curvature; not free metaphor
ε	epsilon floor	nonzero numerical/log boundary
ρ	receipt	proof/evidence object
C_R	route cost	route-scoped cost
K_R	compatibility kernel	regime-scoped compatibility
d_θ	closed distance	admissibility-closed distance target

Operators

Symbol	Preferred name	Meaning
bind(x,opt,metric)	Bind	cognitive/load alignment operator
Cl_A(x)	Admissibility closure	closure under admissibility rules
Q(x)	Quotient	quotient by zero-distance/equivalence relation
Π_P(x)	Projection	projection to a rendering/surface, never proof
R_G(x)	RGFlow filter	scale-stability / attractor check
W_P(x)	WaveProbe	spectral/energy probe over a state
Gate_R(x)	Regime gate	safety/admissibility gate for regime R

Relations

Symbol	Preferred name	Meaning
x ~_A y	admissibly equivalent	equivalent under admissibility relation A
x ->_R y	route transition	transition through route R
x ⊢ ρ	receipt-backed	x has receipt ρ
x ⊣ Gate	gate-held	x is blocked/held by gate
x ⊘ R	refused in regime	rejected by regime R

Name casing rules

Lean namespaces/types: PascalCase
Lean functions/values: camelCase
Docs/wiki concepts: Title Case
Stable IDs: snake_case
Graph node IDs: kebab-case or snake_case, but do not mix in one graph
JSON-LD IDs: urn:<domain>:<type>:<name>:<version>
File paths: PascalCase for concept docs, snake_case for generated data

Examples:

Concept: Semantic Mass
Stable ID: semantic_mass
Lean type: SemanticMass
Lean function: semanticMassCost
Graph node: semantic-mass
JSON-LD: urn:otom:concept:semantic-mass:v0.1

Surface map

Surface	Canonical role	Allowed contents	Forbidden contents
Lean	formal kernel	types, theorems, executable checks	hype, metaphors as proof
GitHub docs	durable spec	registry, schemas, theorem targets	uncited promotion
Notion wiki	navigation/workbench	glossary, status, routing, backlinks	final authority unless receipts exist
GraphML/Neo4j	relationship projection	nodes, edges, typed relations	proof by centrality
Mermaid	lightweight diagram	flows and doctrine maps	canonical semantics
Three.js/WebGPU	visual projection	rendered state, dynamic symbols	truth claims from visuals
JSON-LD	machine ontology	IDs, types, links, policies	vague untyped terms
Linear	execution tracker	issues, acceptance criteria, sync receipts	scientific proof itself

Major framework names

Preferred name	Aliases	Definition	Notes
GeoCognition	geocognitive translation, geo-semantic translation	Meaning first represented as geometry, topology, route, pressure, flow, or manifold event before language.	Keep.
OTOM	Object Tracing on Manifolds, Object Model for Tracing Information	Publication-facing framing for tracing objects/information across manifolds.	Preferred over OMT for public docs.
OMT	Ontological Manifold Theory	Older conceptual name for manifold ontology.	Alias; avoid as public primary.
ENE	Endless Node Edges	Memory / topological storage substrate.	Define per repo/schema.
PTOS	Pipeline/Topological OS, traversal runtime	Runtime/ISA layer for traversal and routing.	Needs exact expansion lock.
GCL	Genetic Coding Language	Genetic-code-inspired concept language; deprecated alias: Grammar/Concept Language.	Canonical expansion corrected 2026-05-01.
MN-GCL	Mass-Number GCL	Mass-number subset/profile of Genetic Coding Language.	Keep.
SNPAR	Snapper	Snap/avalanche/reorganization model for entropy sorting/cognition.	HOLD pending formal type.
NUVMAP	Spectral pixel/state container	u/v spectral-albedo projection and wider JSON-LD approach.	Keep as container/ontology family.
WaveProbe	spectral probe	Energy/spectral probe and coarse-graining layer.	Keep.
RGFlow	lawfulness filter	Scale-stability / attractor / coarse-graining test.	Keep.
DIAT	Dual-Interval Algebraic Transform	Integers represented by distance to adjacent squares and related algebraic data.	Formalize separately.
AVMR	Algebraic Vector Mountain Range	Append-only hierarchical vector-state merge structure.	Formalize separately.
AMMR	Algebraic Merkle Mountain Range	Merkle-like algebraic commit/history structure.	Formalize separately.
AngrySphinx	refusal/containment layer	Allow-list-first, deny-by-default, receipt-writing gate layer.	Safety-critical.
FAMM	Failure/Attractor Memory Map	Stores scars/basins; repeated failures become routing constraints.	Needs acronym expansion lock.

Equation families

Every equation entry must declare:

type EquationEntry = {
  id: string;
  display: string;
  variables: VariableDecl[];
  domain: string;
  units: "dimensionless" | "SI" | "mixed" | "symbolic";
  source: "standard" | "derived" | "proposal" | "simulation";
  claim_state: ClaimState;
  receipt_refs: string[];
};

Reserved equation families

Family	ID prefix	Notes
Mass-number closure	eq_mn_	admissibility, compatibility, quotient closure
Compression	eq_comp_	CR, log-loss, arithmetic coding, Hutter targets
Geometry/topology	eq_geo_	manifolds, Ricci, curvature, geodesics
Dynamics	eq_dyn_	N-body, Hamiltonian, Verlet, flow
Signal	eq_sig_	WaveProbe, SETI, steganographic signal/noise
Governance/safety	eq_gate_	AngrySphinx, refusal, risk, thresholds
Biology/chemistry	eq_bio_	BioKernel, nitrogenase regression, OpenWorm
Cognition/load	eq_cog_	bind, routing load, dyscalculia route model, SNPAR

Projection discipline

A projection is a view of a formal object.

canonical object -> projection -> human-readable view

Allowed projections:

Lean -> theorem docs
JSON-LD -> ontology graph
GraphML -> Neo4j/topological map
Mermaid -> wiki diagram
Three.js/WebGPU -> dynamic symbol field
Notion -> navigation page
Linear -> issue/acceptance criteria

Blocked projection claims:

"The graph says it is true."
"The symbol looks heavy, so it is high mass."
"The simulation converged, so the theorem holds."
"The LLM agrees, so it is validated."

Receipt classes

type ReceiptRequirement =
  | "LeanTheorem"
  | "LakeBuild"
  | "Benchmark"
  | "Measurement"
  | "SourceAudit"
  | "DatasetRow"
  | "SimulationTrace"
  | "ExternalReview"
  | "SafetyGatePass"
  | "HumanApproval";

Gate registry

Gate	Symbol	Function
Ring0InternalAlarmGate	Gate_R0	Protects ring-0 cognition/trauma/load primitives from unsafe automatic expansion.
AngrySphinx	Gate_AS	Deny-by-default containment and refusal layer.
AdmissibilityGate	Gate_A	Blocks promotion until typed closure exists.
EvidenceGate	Gate_ρ	Blocks promotion until receipts exist.
ProjectionGate	Gate_Π	Blocks projection from being treated as proof.
SafetyScopeGate	Gate_S	Blocks unsafe or overbroad operationalization.

SETI/steganographic signal notation

Use this family for signal/noise work.

S          signal candidate
N          noise / unresolved question
R          receiver regime
C          code/channel hypothesis
K_R        receiver/regime compatibility kernel
ρ_S        signal receipt
H0         null/noise hypothesis
H1         structured/source hypothesis
Λ(S)       likelihood or evidence ratio
Π_C(S)     projection under code hypothesis C

Doctrine:

Noise is not garbage by default.
Noise is unresolved structure until the regime proves otherwise.

Cognitive/load notation

Use this family for routing-load and geo-semantic translation.

P          semantic packet
A_i        adapter/carrier
R          route
C_R(P)     route cost of packet P
τ_R(P)     turbulence on route R
bind       alignment operator
L_I        intrinsic load
L_G        germane load
L_R        routing load
L_E        extraneous load
L_M        memory load

Pipeline form:

P_final = A_math ∘ A_language ∘ A_metaphor ∘ A_motion ∘ A_spatial(P_initial)

Do not pathologize the route. Treat alternate routing as architecture, then measure cost and loss.

Lean naming target

Future Lean mirror should use:

namespace OTOM.Registry

inductive ClaimState
  | uScope
  | hold
  | vScope
  | reviewed
  | canonicalLean
  | quarantine

inductive AuthorityScope
  | workbenchProjection
  | simulationOnly
  | receiptBacked
  | canonicalLean
  | externalSource
  | safetyPolicy

inductive NaNMassReason
  | divisionByUnclosedZero
  | unboundedRouteCost
  | missingAdmissibility
  | regimeMismatch
  | infiniteProjectionArtifact
  | comparisonWithoutCommonClosure

inductive MassValue
  | finiteMass : Nat -> MassValue
  | nanMass : NaNMassReason -> MassValue
  | closedMass : Nat -> String -> MassValue

end OTOM.Registry

Actual numeric implementation should use fixed-point/integer representation, not Float, in hot paths.

Promotion checklist

An entry may move beyond HOLD only when all apply:

• It has a stable ID.
• It has one preferred name.
• Aliases are recorded.
• Type class is declared.
• Authority scope is declared.
• Claim state is declared.
• Projection/canonical boundary is explicit.
• Receipts are listed or explicitly missing.
• Blocked usages are listed.
• If executable, it avoids Float in hot paths unless legacy or explicitly scoped.

Immediate cleanup tasks

1. Create registry/terms.jsonld mirror from this table.
2. Create registry/symbols.yaml for custom symbol rendering.
3. Create Semantics/Registry.lean with claim-state and MassValue scaffolding.
4. Add validator rule: every wiki node must declare claim_state, authority_scope, and receipt_refs.
5. Create GraphML projection from this registry, but mark it projection_only.
6. Backfill existing docs: Semantic Mass, MN-GCL, SNPAR, NUVMAP, AngrySphinx, GeoCognition.

Operating sentence

The wiki is not a scrapbook. It is a typed routing surface from intuition to formal receipts.