MathOS Registry — Concept Nodes v0.1 (Core Territories + Canonical IDs)

“`yaml id=”r1p8vz”
PAGE_START
PageID: EDUKATE::MATHOS::REG_CONCEPT_NODES_01
Slug: /mathos-registry-concept-nodes-v0-1/
Title: MathOS Registry — Concept Nodes v0.1 (Core Territories + Canonical IDs)
Version: v0.1 (LOCK)
Parent: /mathos-runtime-control-tower-v0-1/
Intent:

  • Provide stable ConceptNode IDs for MathOS runtime (CivOS parity)
  • Enumerate core math territories as nodes (Z0–Z6)
  • Each node includes: scope, prerequisites (binds), typical failure modes, linked method corridors
    GrammarLock:
    Place×Lane×Zoom×Role×Type×ID
    Lane: MATH

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BLOCK_01_DEFINITION_LOCK
ConceptNode :=
a named territory of mathematics with:
– Scope (what it includes/excludes)
– Zoom band (Z0..Z6 primary)
– Prereq binds (incoming edges)
– Typical confusions (links to ErrorTaxonomy)
– Canonical method corridors (links to Method registry)
Rule:
ConceptNode IDs are immutable.
Expansions append new nodes or fields; never rename.

============================================================

REGISTRY::CONCEPT_NODES (CORE SET v0.1)

# Z0–Z1 (quantity + operations)

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::NUM_QUANTITY_01
Name: Number Sense / Quantity / Magnitude
ZPrimary: Z0
Scope:

  • magnitude, estimation, units intuition
    PrereqBinds:
  • none (base)
    CommonFailures:
  • E1 Meaning drift (units)
  • E4 execution (place value)
    LinkedMethods:
  • estimation corridor
    LinkedSkills:
  • SML_01

NODE_END

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::ARITHMETIC_OPS_01
Name: Arithmetic Operations (integers/fractions/decimals/percent)
ZPrimary: Z1
Scope:

  • operations + conversions + simplification
    PrereqBinds:
  • NUM_QUANTITY_01
    CommonFailures:
  • E2 parsing (order)
  • E4 execution (conversion)
    LinkedMethods:
  • fraction common denominator corridor
  • percent-of corridor
    LinkedSkills:
  • EQ_01, ORA_01

NODE_END

# Z2 (equivalence + algebra grammar)

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::EQUIVALENCE_REWRITE_01
Name: Equivalence & Rewrite Grammar (the algebra engine)
ZPrimary: Z2
Scope:

  • transformations that preserve meaning
    PrereqBinds:
  • ARITHMETIC_OPS_01
    CommonFailures:
  • E2 parsing drift
  • E4 illegal cancellation
    LinkedMethods:
  • simplify/factor/expand corridors
    LinkedSkills:
  • EQ_01, ORA_01

NODE_END

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::EQUATIONS_LINEAR_01
Name: Linear Equations (family solving)
ZPrimary: Z2
Scope:

  • ax+b=c, simultaneous linear systems (later)
    PrereqBinds:
  • EQUIVALENCE_REWRITE_01
    CommonFailures:
  • E3 strategy slip (wrong method)
  • E1 meaning drift (word setup)
    LinkedMethods:
  • isolate variable corridor
  • substitution/elimination corridors (future node)
    LinkedSkills:
  • TR_01, CHOICE_01

NODE_END

# Z3 (functions/change/graphs)

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::FUNCTIONS_01
Name: Functions (input-output; representations)
ZPrimary: Z3
Scope:

  • function notation, evaluation, domain/range intuition
    PrereqBinds:
  • EQUATIONS_LINEAR_01
    CommonFailures:
  • E1 meaning drift (what is f(x)?)
  • E2 parsing drift (notation)
    LinkedMethods:
  • table/graph/equation representation corridor
    LinkedSkills:
  • MF_01, CHOICE_01

NODE_END

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::GRAPHS_MODELS_01
Name: Graphs & Linear Models (y=mx+c as a production model)
ZPrimary: Z3
Scope:

  • slope/intercept, model fitting, interpretation
    PrereqBinds:
  • FUNCTIONS_01
    CommonFailures:
  • E1 meaning drift (axes/units)
  • E3 strategy slip (model choice)
    LinkedMethods:
  • linearization corridor (future)
    LinkedSkills:
  • MF_01, ORA_01

NODE_END

# Z4 (proof + structure)

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::PROOF_PATTERNS_01
Name: Proof Patterns (induction/contradiction/contrapositive/invariants)
ZPrimary: Z4
Scope:

  • validity discipline inside mathematics
    PrereqBinds:
  • EQUIVALENCE_REWRITE_01
    CommonFailures:
  • E5 verification collapse (proof gaps)
    LinkedMethods:
  • proof skeleton corridors
    LinkedSkills:
  • ORA_01, CHOICE_01

NODE_END

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::STRUCTURE_ABSTRACTION_01
Name: Structure & Abstraction (definitions as compression)
ZPrimary: Z4
Scope:

  • abstraction, generalization, lemma building
    PrereqBinds:
  • PROOF_PATTERNS_01
    CommonFailures:
  • rho spike (too many abstractions at once)
    LinkedMethods:
  • generalize-then-specialize corridor
    LinkedSkills:
  • ARCH_VALID_01, ARCH_REUSE_01, rho_01

NODE_END

# Z5 (systems, optimization, uncertainty)

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::PROBABILITY_EXPECTATION_01
Name: Probability & Expectation (uncertainty objects)
ZPrimary: Z5
Scope:

  • randomness, expectation, simple inference intuition
    PrereqBinds:
  • ARITHMETIC_OPS_01
  • FUNCTIONS_01 (often)
    CommonFailures:
  • E1 meaning drift (what does probability mean?)
  • E3 strategy slip (wrong model)
    LinkedMethods:
  • expected value corridor
    LinkedSkills:
  • MF_01, ORA_01

NODE_END

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::OPTIMIZATION_CONSTRAINTS_01
Name: Optimization Under Constraints (ProductionOS math)
ZPrimary: Z5
Scope:

  • objective/constraints, tradeoffs, best decision under limits
    PrereqBinds:
  • FUNCTIONS_01
    CommonFailures:
  • E3 strategy slip (objective drift)
  • E6 time bleed (over-solving)
    LinkedMethods:
  • constraint write-down corridor (future)
    LinkedSkills:
  • CHOICE_01, TB_01

NODE_END

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::QUEUES_BOTTLENECKS_01
Name: Queues & Bottlenecks (rate dominance)
ZPrimary: Z5
Scope:

  • backlog, throughput, variability effects (conceptual)
    PrereqBinds:
  • OPTIMIZATION_CONSTRAINTS_01 (optional)
    CommonFailures:
  • E1 meaning drift (rates/units)
    LinkedMethods:
  • bottleneck hunt corridor (future)
    LinkedSkills:
  • MF_01, ORA_01

NODE_END

# Z6 (frameworks + simulation language)

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::SIMULATION_STATE_TRANSITION_01
Name: Simulation Language (state/transition/policy/uncertainty)
ZPrimary: Z6
Scope:

  • system state, transitions, policies, stress tests
    PrereqBinds:
  • OPTIMIZATION_CONSTRAINTS_01
  • PROBABILITY_EXPECTATION_01 (optional)
    CommonFailures:
  • E1 meaning drift (state variables unclear)
  • E3 strategy slip (wrong model class)
    LinkedMethods:
  • simulation template corridor
    LinkedSkills:
  • MF_01, ORA_01

NODE_END

NODE_START
NodeID: EDUKATE::MATHOS::CONCEPT::FRAMEWORKS_METHOD_NAMES_01
Name: Frameworks & Method Names (truth depends on definitions)
ZPrimary: Z6
Scope:

  • statements true in one framework, false in another; method naming discipline
    PrereqBinds:
  • PROOF_PATTERNS_01
    CommonFailures:
  • category error; definition drift
    LinkedMethods:
  • “label the framework” corridor (future)
    LinkedSkills:
  • SML_01, ORA_01

NODE_END

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BLOCK_02_BIND RESERVES (future additive nodes)
ReserveConceptNodes (append later):

  • GEOMETRY_INVARIANTS_01
  • TRIGONOMETRY_01
  • COMPLEX_NUMBERS_01
  • SERIES_LIMITS_01
  • CALCULUS_DERIVATIVE_01
  • CALCULUS_INTEGRAL_01
  • LINEAR_ALGEBRA_01
  • GRAPH_THEORY_01
  • STATISTICS_INFERENCE_01

Rule:
Add when:
– scope + prereq binds are clear
– at least one method corridor exists
– typical confusions mapped to E1–E6

============================================================

BLOCK_03_USAGE (how registries power the runtime)
UsedBy:

  • /mathos-registry-binds-v0-1/ (graph edges)
  • /mathos-registry-method-corridors-v0-1/ (canonical routes)
  • /mathos-registry-transfer-packs-v0-1/ (3-skin packs per node)
  • /mathos-data-adapter-spec-v0-1/ (topic_tag -> concept node)
  • /mathos-sensors-pack-v0-1/ (Z-band sensor mapping)

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RELATED_PAGES
Links:

  • /mathos-runtime-control-tower-v0-1/
  • /mathos-registry-skill-nodes-v0-1/
  • /mathos-registry-error-taxonomy-v0-1/
  • /mathos-data-adapter-spec-v0-1/
  • /mathos-sensors-pack-v0-1/
  • /how-mathematics-works/
  • /what-is-mathematics/

NEXT_OUTPUT (if you say “Next”)
PageID: EDUKATE::MATHOS::REG_BINDS_01
slug: /mathos-registry-binds-v0-1/
(prereq edges + confusion edges + method edges)

PAGE_END
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