MathOS Registry — Method Corridors v0.1 (Canonical Routes + Conditions + Checks)Version: v0.1 (LOCK)

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PAGE_START
PageID: EDUKATE::MATHOS::REG_METHODS_01
Slug: /mathos-registry-method-corridors-v0-1/
Title: MathOS Registry — Method Corridors v0.1 (Canonical Routes + Conditions + Checks)
Version: v0.1 (LOCK)
Parent: /mathos-runtime-control-tower-v0-1/
Intent:

  • Publish canonical method corridors as stable records (machine-runnable)
  • Each method includes: when to use, steps, conditions, common illegal moves, fast checks
  • Methods are referenced by binds + transfer pack registry
    GrammarLock:
    Place×Lane×Zoom×Role×Type×ID
    Lane: MATH

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BLOCK_01_DEFINITION_LOCK
MethodCorridor :=
a named, reusable solution route for a family of problems, with explicit conditions and verification checks.

MethodContract:

  • MethodIDs never renamed
  • Steps must be minimal and stable
  • Every method includes:
    Trigger (when to use)
    Conditions (domain / exclusions)
    Steps (canonical)
    IllegalMoves (common failure)
    FastChecks (Oracle)
    LinkedTransferPacks (optional)

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REGISTRY::METHOD_CORRIDORS (CORE SET v0.1)

METHOD_START
MethodID: EDUKATE::MATHOS::METHOD::LINEAR_ISOLATE_01
Name: Linear Isolate Variable (ax + b = c)
Z: Z2
Trigger:

  • equation in form ax + b = c
    Conditions:
  • a ≠ 0
    Steps:
    1) subtract b from both sides (equivalence)
    2) divide both sides by a (equivalence)
    3) state x = (c – b)/a
    IllegalMoves:
  • divide by a when a=0 (unstated)
  • “move term” without equivalence operation
    FastChecks:
  • substitute x back into ax+b to confirm equals c
    LinkedConcept:
  • CONCEPT::EQUATIONS_LINEAR_01
    DefaultErrors:
  • E2/E4 illegal cancellation
  • E1 meaning drift (word setup)

METHOD_END

METHOD_START
MethodID: EDUKATE::MATHOS::METHOD::LINEAR_DISTRIBUTE_01
Name: Expand/Distribute Then Isolate (a(x+b)=c)
Z: Z2
Trigger:

  • variable inside bracket with multiplier
    Conditions:
  • a ≠ 0
    Steps:
    1) expand a(x+b)=ax+ab
    2) reduce to ax + (ab) = c
    3) apply LINEAR_ISOLATE_01
    IllegalMoves:
  • distribute incorrectly (sign errors)
  • divide by bracket term incorrectly
    FastChecks:
  • back-substitute

METHOD_END

METHOD_START
MethodID: EDUKATE::MATHOS::METHOD::FACTOR_ZERO_01
Name: Factor Then Zero-Product
Z: Z2
Trigger:

  • expression equals 0 and can be factored
    Conditions:
  • equation in form (px+q)(rx+s)=0
    Steps:
    1) factor expression
    2) set each factor =0
    3) solve resulting linear equations
    IllegalMoves:
  • cancel x across sum terms
  • set px+q=rx+s (wrong)
    FastChecks:
  • substitute solutions back into original polynomial

METHOD_END

METHOD_START
MethodID: EDUKATE::MATHOS::METHOD::RATIO_TABLE_01
Name: Ratio Table / Unit Rate Corridor
Z: Z1–Z2
Trigger:

  • proportional relationships (constant ratio)
    Conditions:
  • assumption: proportionality holds
    Steps:
    1) write known pair (a ↔ b)
    2) compute unit rate (b/a) OR scale factor (new_a/a)
    3) compute unknown via multiplication
    IllegalMoves:
  • mixing additive and multiplicative reasoning
  • wrong base quantity
    FastChecks:
  • sanity: does result scale correctly (bigger input -> bigger output)?

METHOD_END

METHOD_START
MethodID: EDUKATE::MATHOS::METHOD::PERCENT_OF_01
Name: Percent-of Corridor
Z: Z1
Trigger:

  • “p% of N”
    Conditions:
  • p interpreted as p/100
    Steps:
    1) convert p% -> p/100
    2) multiply (p/100)*N
    IllegalMoves:
  • divide instead of multiply
  • wrong base (percent of what?)
    FastChecks:
  • estimate: 10% of N then scale

METHOD_END

METHOD_START
MethodID: EDUKATE::MATHOS::METHOD::MODEL_Y_MX_C_01
Name: Linear Model Mapping (fixed fee + rate×quantity)
Z: Z3
Trigger:

  • “fixed + rate per unit × units”
    Conditions:
  • linear assumption valid
    Steps:
    1) define variables with units
    2) write y = mx + c
    3) identify m (rate), c (fixed)
    4) interpret slope and intercept in context
    IllegalMoves:
  • swapping axes (units mismatch)
  • using rate as intercept
    FastChecks:
  • plug in x=0; does y match fixed fee?

METHOD_END

METHOD_START
MethodID: EDUKATE::MATHOS::METHOD::GRAPH_READ_SLOPE_01
Name: Read Slope/Intercept from Graph
Z: Z3
Trigger:

  • straight line graph
    Conditions:
  • consistent axis scales
    Steps:
    1) pick two clear points
    2) slope m = Δy/Δx
    3) intercept c = y when x=0
    IllegalMoves:
  • using unequal scales incorrectly
  • picking points not on line
    FastChecks:
  • verify with third point

METHOD_END

METHOD_START
MethodID: EDUKATE::MATHOS::METHOD::EV_EXPECTED_VALUE_01
Name: Expected Value (simple discrete)
Z: Z5
Trigger:

  • outcomes with probabilities and payoffs
    Conditions:
  • probabilities sum to 1
    Steps:
    1) list outcomes i with p_i and value v_i
    2) compute EV = Σ p_i v_i
    IllegalMoves:
  • probabilities not normalized
  • mixing percent and probability
    FastChecks:
  • EV must lie within min/max payoff bounds (if all v_i bounded)

METHOD_END

METHOD_START
MethodID: EDUKATE::MATHOS::METHOD::SIM_TEMPLATE_01
Name: Simulation Template (state/transition/objective/constraints/noise)
Z: Z6
Trigger:

  • system over time with decisions under uncertainty
    Conditions:
  • state variables defined; transitions explicit
    Steps:
    1) define state S(t)
    2) define transition T + noise ε
    3) define constraints C
    4) define objective J
    5) run baseline + 3 stress cases
    IllegalMoves:
  • undefined variables (meaning drift)
  • no units/scale; no invariants
    FastChecks:
  • sanity checks + invariants + sensitivity tests

METHOD_END

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

BLOCK_02_METHOD PROMOTION RULES (stability + transfer)
MethodPromotion:
A method is “installed” only when:
– TR>=0.7 on 3-skin pack for that method family
– ORA checks are present
– illegal move rate low

If not:

  • method is “seen” but not installed (still fragile)

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BLOCK_03_LINKS TO TRANSFER PACKS (next registry)
Need:

  • /mathos-registry-transfer-packs-v0-1/
    Purpose:
  • each MethodCorridor gets at least one 3-skin transfer pack

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RELATED_PAGES
Links:

  • /mathos-registry-binds-v0-1/
  • /mathos-registry-concept-nodes-v0-1/
  • /mathos-registry-skill-nodes-v0-1/
  • /mathos-fenceos-threshold-table-v0-1/
  • /math-transfer-test-same-structure-different-skin/

NEXT_OUTPUT (if you say “Next”)
PageID: EDUKATE::MATHOS::REG_TRANSFER_PACKS_01
slug: /mathos-registry-transfer-packs-v0-1/
(canonical 3-skin packs keyed by MethodID + ConceptNode)

PAGE_END
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