MathOS Registry — Error Taxonomy v0.1 (E1–E6 + Detection + Repair Mapping)Version: v0.1 (LOCK)

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PAGE_START
PageID: EDUKATE::MATHOS::REG_ERROR_TAX_01
Slug: /mathos-registry-error-taxonomy-v0-1/
Title: MathOS Registry — Error Taxonomy v0.1 (E1–E6 + Detection + Repair Mapping)
Version: v0.1 (LOCK)
Parent: /mathos-runtime-control-tower-v0-1/
Intent:

  • Provide a stable registry of error types (named primitives)
  • Map each error to sensors, common signatures, and default recovery corridors
  • Used by: sensors pack, failure atlas, data adapter, tutor/parent protocols
    GrammarLock:
    Place×Lane×Zoom×Role×Type×ID
    Lane: MATH

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BLOCK_01_DEFINITION_LOCK
ErrorType :=
a classified failure mode in a solution process that predicts the correct repair action.
Rule:
If you cannot name the error type, you cannot select the correct corridor.

RegistryContract:

  • IDs E1..E6 never change
  • New subtypes are appended as E1a, E1b… (no rename)
  • Every subtype maps to:
    detection signatures
    dominant sensors
    default corridors

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REGISTRY::ERROR_TYPES

E1_MEANING_DRIFT
ID: E1
Name: Meaning Drift (SML failure)
Definition:
symbols/units/what’s asked are not bound; symbols become decoration
DetectionSignatures:
– cannot say what x means
– units absent or inconsistent
– wrong setup even if computation is fine
DominantSensors:
– SML low
– MF low (often co-occurs)
DefaultCorridors:
– RC_002 Meaning-Lock Rebuild
– RC_010 Translation Repair (if word problems)
LinkedFailurePatterns:
– MATH_FAIL_003
– MATH_FAIL_009

E2_PARSING_DRIFT
ID: E2
Name: Parsing Drift (grammar/precedence)
Definition:
expression parsing errors (brackets, order of operations, notation confusion)
DetectionSignatures:
– wrong evaluation order
– missing brackets
– index/negative sign misread
DominantSensors:
– ErrorTypeDistribution shows E2 dominance
DefaultCorridors:
– RC_005 Parsing Grammar Clinic
LinkedFailurePatterns:
– MATH_FAIL_004

E3_STRATEGY_SLIP
ID: E3
Name: Strategy Slip (CHOICE failure)
Definition:
wrong method selected; cannot label structure; template grabbing
DetectionSignatures:
– cannot start even though topic “known”
– picks familiar method regardless of structure
DominantSensors:
– CHOICE low
– TR low (often)
DefaultCorridors:
– RC_006 Strategy Choice Rebuild
– RC_004 Transfer Repair (if TR low)
LinkedFailurePatterns:
– MATH_FAIL_005
– MATH_FAIL_001

E4_EXECUTION_SLIP
ID: E4
Name: Execution Slip (calculation/algebra mechanics)
Definition:
arithmetic or algebraic manipulation errors despite correct plan
DetectionSignatures:
– wrong sign in expansion
– copying errors
– fraction/decimal conversion mistakes
DominantSensors:
– repeated wrong final answers with correct setup
DefaultCorridors:
– RC_003 Equivalence Discipline (if illegal move)
– RC_011 Representation Stabilization (fractions/decimals)
– micro-drills + verification (ORA)
LinkedFailurePatterns:
– MATH_FAIL_010

E5_VERIFICATION_COLLAPSE
ID: E5
Name: Verification Collapse (Oracle off)
Definition:
lack of checks and inability to detect first illegal step; silent errors persist
DetectionSignatures:
– no sanity check
– cannot locate first divergence after feedback
– repeated same wrong pattern
DominantSensors:
– ORA_present_rate low
– FD_accuracy low
DefaultCorridors:
– RC_007 Oracle Recovery
LinkedFailurePatterns:
– MATH_FAIL_006
– MATH_FAIL_002

E6_TIME_BLEED
ID: E6
Name: Time Bleed (Chrono failure)
Definition:
time spent exceeds budget with low progress; leads to rushing and cascades
DetectionSignatures:
– stuck too long on one question
– late-paper collapse
DominantSensors:
– TB_rate high
DefaultCorridors:
– RC_008 Time Bleed Triage
– RC_009 Timed Re-entry (if panic triggered)
LinkedFailurePatterns:
– MATH_FAIL_007
– MATH_FAIL_008

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BLOCK_02_SUBTYPE_RESERVES (for expansion; additive)
ReserveSubtypes:
E1a: Unit Drift
E1b: Variable Definition Missing
E2a: Negative Sign Drift
E2b: Index/Exponent Misread
E3a: Method Overgeneralization
E3b: Structure Mislabel
E4a: Place Value Drift
E4b: Illegal Cancellation
E5a: Counterexample Blindness
E6a: Skip-Return Failure

Rule:
Add subtypes only when you have:
– detection signatures
– distinct repair corridor mapping

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BLOCK_03_QUICK MAP (ErrorType -> Default repair)
Map:
E1 -> RC_002 (Meaning) + RC_010 (Translation)
E2 -> RC_005 (Parsing clinic)
E3 -> RC_006 (Choice) + RC_004 (Transfer)
E4 -> RC_011 (Representation) + RC_007 (Verification)
E5 -> RC_007 (Oracle recovery)
E6 -> RC_008 (Time triage) + RC_009 (Timed ladder)

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BLOCK_04_USAGE (how to apply in sessions)
SessionProtocol:

  • after checking:
    mark first divergence step (FD)
    label error type E1..E6
    run default corridor mini-step (5 minutes)
    do 1 skin-change variant

SeeAlso:

  • /mathos-recovery-corridors-p0-to-p3/
  • /mathos-failure-atlas-v0-1/

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RELATED_PAGES
Links:

  • /mathos-runtime-control-tower-v0-1/
  • /mathos-sensors-pack-v0-1/
  • /mathos-data-adapter-spec-v0-1/
  • /mathos-failure-atlas-v0-1/
  • /mathos-recovery-corridors-p0-to-p3/
  • /math-fenceos-stop-loss-for-exam-mistakes/

NEXT_OUTPUT (if you say “Next”)
PageID: EDUKATE::MATHOS::REG_SKILL_NODES_01
slug: /mathos-registry-skill-nodes-v0-1/

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