MathOS Registry — Skill Nodes v0.1 (SML/EQ/TR/LS/CHOICE/ORA… + Contracts)Version: v0.1 (LOCK)

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PAGE_START
PageID: EDUKATE::MATHOS::REG_SKILL_NODES_01
Slug: /mathos-registry-skill-nodes-v0-1/
Title: MathOS Registry — Skill Nodes v0.1 (SML/EQ/TR/LS/CHOICE/ORA… + Contracts)
Version: v0.1 (LOCK)
Parent: /mathos-runtime-control-tower-v0-1/
Intent:

  • Provide stable SkillNode IDs for the MathOS graph (Node×Bind)
  • Each skill node has: contract, observable outputs, sensors, thresholds, default corridors
  • Used by: sensors pack, fence table, data adapter, training packs
    GrammarLock:
    Place×Lane×Zoom×Role×Type×ID
    Lane: MATH

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BLOCK_01_DEFINITION_LOCK
SkillNode :=
a named capability primitive with:
– Contract (what it is)
– Output (what it produces)
– Sensor (how we measure it)
– Threshold (when it is “stable”)
– Repair corridor (how to rebuild it)

RegistryContract:

  • SkillNodeIDs never renamed
  • New nodes are appended, not substituted
  • SkillNodes can be versioned forward with additive fields

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REGISTRY::SKILL_NODES (Core set v0.1)

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::SML_01
Name: Symbol-Meaning Lock (SML)
Contract:

  • For any problem, learner can state:
    what each symbol represents
    units (if applicable)
    what is asked
    ObservableOutput:
  • “Meaning line” written before solving
    Sensors:
  • SML_present_rate
    Thresholds:
  • stable if SML_present_rate >= 0.9 across 1 week
    DefaultCorridors:
  • RC_002 Meaning-Lock Rebuild
    Links:
  • /mathos-recovery-corridors-p0-to-p3/
    SKILL_NODE_END

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::EQ_01
Name: Equivalence Discipline (EQ)
Contract:

  • Rewrites preserve meaning; all moves are legal under the system
    ObservableOutput:
  • step justification; no illegal cancellations; correct transformations
    Sensors:
  • illegal_move_rate
    Thresholds:
  • stable if illegal_move_rate = 0 for 2 sessions
    DefaultCorridors:
  • RC_003 Equivalence Discipline
    Links:
  • /mathos-recovery-corridors-p0-to-p3/
    SKILL_NODE_END

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::TR_01
Name: Transfer (TR) — Same Structure, Different Skin
Contract:

  • Recognizes structure across different surface forms; can apply method correctly
    ObservableOutput:
  • solves 3-skin variants without coaching
    Sensors:
  • TR_score = correct/3 on 3-skin pack
    Thresholds:
  • stable if TR_score >= 0.7 on 2 packs
    DefaultCorridors:
  • RC_004 Transfer Repair
    Links:
  • /math-transfer-test-same-structure-different-skin/
    SKILL_NODE_END

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::LS_01
Name: Load Stability (LS)
Contract:

  • Performance remains stable when time pressure increases (no phase slip)
    ObservableOutput:
  • timed sets solved with checks; minimal panic signature
    Sensors:
  • LS_ratio = timed_accuracy / untimed_accuracy
    Thresholds:
  • stable if LS_ratio >= 0.75 across 2 sessions
    DefaultCorridors:
  • RC_009 Timed Re-entry Ladder
    Links:
  • /math-phase-slip-why-students-panic/
    SKILL_NODE_END

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::CHOICE_01
Name: Strategy Selection (CHOICE)
Contract:

  • Labels structure + chooses method BEFORE solving
    ObservableOutput:
  • “structure tag” and 1-line plan written first
    Sensors:
  • CHOICE_accuracy (pre-solve method/structure)
    Thresholds:
  • stable if CHOICE_accuracy >= 0.7 (P2) and >=0.8 (P3/Visionary track)
    DefaultCorridors:
  • RC_006 Strategy Choice Rebuild
    Links:
  • /math-worksheets/
    SKILL_NODE_END

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::ORA_01
Name: Oracle Habit (ORA) — Verification Control
Contract:

  • Detects first illegal step; uses sanity checks consistently
    ObservableOutput:
  • 1 sanity check per question; bug-hunt success
    Sensors:
  • ORA_present_rate
  • FD_accuracy
    Thresholds:
  • stable if ORA_present_rate >= 0.8 AND FD_accuracy >= 0.7
    DefaultCorridors:
  • RC_007 Oracle Recovery
    Links:
  • /math-fenceos-stop-loss-for-exam-mistakes/
    SKILL_NODE_END

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::TB_01
Name: Time Triage (TB control)
Contract:

  • Prevents time bleed using skip-return and value-based pacing
    ObservableOutput:
  • skips and returns; avoids getting stuck
    Sensors:
  • TB_rate
    Thresholds:
  • stable if TB_rate decreases over 2 timed sessions
    DefaultCorridors:
  • RC_008 Time Bleed Triage
    Links:
  • /math-fenceos-stop-loss-for-exam-mistakes/
    SKILL_NODE_END

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::MF_01
Name: Model Fit (MF) — Word→Math Translation
Contract:

  • Converts story to variables/relations/constraints with correct units
    ObservableOutput:
  • correct setup before computation
    Sensors:
  • MF_score (setup correct rate)
    Thresholds:
  • stable if MF_score >= 0.75 on 10 word problems
    DefaultCorridors:
  • RC_010 Translation Repair
    Links:
  • /math-as-simulation-language/
    SKILL_NODE_END

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REGISTRY::SKILL_NODES (Architect track v0.1; sandbox only)

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::RHO_01
Name: Symmetry Budget Control (rho)
Contract:

  • Keeps exploration choice intensity below capacity to avoid collapse
    ObservableOutput:
  • sandbox ratio respected; corridor attempts capped
    Sensors:
  • rho (choice injected / capacity proxy)
    Thresholds:
  • stable if rho in safe band for 2 weeks AND LS stable
    DefaultCorridors:
  • RC_012 Sandbox Safety Reset
    Links:
  • /math-architect-training-pack-12-week/
    SKILL_NODE_END

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::ARCH_VALID_01
Name: Architect Validity (Audit Pass)
Contract:

  • Any new corridor passes Oracle audit and states conditions
    ObservableOutput:
  • corridor record includes conditions + audit checklist
    Sensors:
  • ValidityRate
    Thresholds:
  • stable if ValidityRate high over 2 weeks
    DefaultCorridors:
  • Oracle drills + corridor cap
    Links:
  • /math-architect-corridors-representation-invariant-reduction/
    SKILL_NODE_END

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::ARCH_REUSE_01
Name: Architect Reuse (3-Variant Pass)
Contract:

  • corridor works across 3 skin-changed variants
    ObservableOutput:
  • ReuseScore=3
    Sensors:
  • ReuseScore
    Thresholds:
  • stable if ReuseScore=3 for 3 corridors
    DefaultCorridors:
  • reduce corridor count; increase audit and variant tests
    Links:
  • /math-architect-corridors-representation-invariant-reduction/
    SKILL_NODE_END

SKILL_NODE_START
SkillNodeID: EDUKATE::MATHOS::SKILL::ARCH_COMP_01
Name: Compression Gain
Contract:

  • corridor reduces steps/cases without losing validity
    ObservableOutput:
  • shorter solution trace with stated conditions
    Sensors:
  • CompressionGain
    Thresholds:
  • stable if CompressionGain positive on 3 corridors
    DefaultCorridors:
  • reduction drills + representation invention
    Links:
  • /math-architect-corridors-representation-invariant-reduction/
    SKILL_NODE_END

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BLOCK_02_NODE_GROUPS (for graph convenience)
Groups:
CORE_STABILITY:
– SML_01, EQ_01, TR_01, LS_01
CONTROL:
– CHOICE_01, ORA_01, TB_01, MF_01
ARCH_SANDBOX:
– RHO_01, ARCH_VALID_01, ARCH_REUSE_01, ARCH_COMP_01

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RELATED_PAGES
Links:

  • /mathos-runtime-control-tower-v0-1/
  • /mathos-registry-error-taxonomy-v0-1/
  • /mathos-sensors-pack-v0-1/
  • /mathos-fenceos-threshold-table-v0-1/
  • /mathos-recovery-corridors-p0-to-p3/
  • /avoo-mathematics-role-lattice/

NEXT_OUTPUT (if you say “Next”)
PageID: EDUKATE::MATHOS::REG_CONCEPT_NODES_01
slug: /mathos-registry-concept-nodes-v0-1/

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