MathOS Failure Atlas v0.1 (30 Collapse Patterns + Sensors + Truncate/Stitch/Retest)

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PAGE_START
PageID: EDUKATE::MATHOS::FAIL_ATLAS_01
Slug: /mathos-failure-atlas-v0-1/
Title: MathOS Failure Atlas v0.1 (30 Collapse Patterns + Sensors + Truncate/Stitch/Retest)
Version: v0.1 (LOCK)
Parent: /mathos-runtime-control-tower-v0-1/
Intent:

  • Provide CivOS-parity negative void completeness for MathOS
  • Enumerate failure patterns as runnable entries:
    Trigger -> FailureTrace -> Sensors -> Truncate -> Stitch -> Retest
  • Start with 12 canonical patterns (expand to 30 without renaming IDs)
    GrammarLock:
    Place×Lane×Zoom×Role×Type×ID
    Lane: MATH
    CivOSOverlaysAllowed:
  • ATLAS_ENTRIES
  • BOX_NEG_VOID_META
  • SENSOR_PANEL_ATLAS

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BLOCK_01_QUICK_ANSWER (AboveTheFold)
Answer:
This atlas lists the most common ways math competence collapses under load—at student, class, and system levels—and provides the exact repair loop for each. Every pattern has a trigger, a failure trace, the sensors that detect it early, and the truncation/stitching/retest actions that restore stability. Use it like a diagnostic manual: identify the pattern, apply the corridor, retest, then re-enter load.

Rule:
If you can name the pattern, you can repair it.
If you cannot name it, you will repeat it.

Pointers:

  • thresholds: /mathos-fenceos-threshold-table-v0-1/
  • corridors: /mathos-recovery-corridors-p0-to-p3/

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BOX_NEG_VOID_META (Atlas contract)
AtlasContract:

  • Each pattern entry is immutable once published
  • Upgrades add new patterns or append fields; never rename PatternID
  • Each entry contains:
    Trigger
    FailureTrace
    Sensors
    Truncate
    Stitch
    Retest
    Links

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ATLAS_ENTRIES

NOTE: v0.1 ships with 12 patterns (MATH_FAIL_001..012).

Future: extend to MATH_FAIL_030 (additive).

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_001
Name: Template Illusion (P1 Trap)
Trigger:

  • student succeeds on blocked repetition but fails on new skins
    FailureTrace:
    blocked practice -> autopilot -> TR stays low -> exam skin-change -> cannot start -> panic -> P0
    Sensors:
  • TR < 0.4
  • CHOICE low on mixed sets
    Truncate:
  • stop blocked-only worksheets
  • stop heavy timing
    Stitch:
  • daily 3-skin packs (same structure, different skin)
  • structure tag before solving
  • interleaving after TR improves
    Retest:
  • TR >= 0.7 on 2 packs
    Links:
  • /math-transfer-test-same-structure-different-skin/

PATTERN_END

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_002
Name: Solver-Copy Collapse (No Retrieval)
Trigger:

  • student uses solver as method, not feedback
    FailureTrace:
    solver-first copying -> no retrieval -> no error diagnosis -> P1 inflated -> exam collapse
    Sensors:
  • low FD detection
  • repeated same mistake type
    Truncate:
  • ban solver until after attempt
    Stitch:
  • protocol: attempt -> check -> mark first divergence -> reattempt
  • 1 skin-change variant after fix
    Retest:
  • reduced repeat errors over 2 sessions
    Links:
  • /math-solver-when-to-use-and-when-not-to/

PATTERN_END

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_003
Name: Meaning Drift Spiral (SML Failure)
Trigger:

  • symbols become decoration; units ignored
    FailureTrace:
    weak symbol binding -> wrong setup -> wrong steps -> answer mismatch -> panic -> avoidance
    Sensors:
  • SML low (cannot explain symbols/units/asked)
    Truncate:
  • stop timing; shrink width
    Stitch:
  • meaning line every question
  • 1 worked example + near copies
    Retest:
  • SML stable for 2 sessions
    Links:
  • /math-truncation-and-stitching-recovery-protocol/

PATTERN_END

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_004
Name: Parsing Drift (Order/Brackets)
Trigger:

  • precedence/bracket errors spike under stress
    FailureTrace:
    weak parsing grammar -> wrong evaluation -> compounding wrong steps
    Sensors:
  • E2 parsing errors dominate
    Truncate:
  • stop long expressions; re-train grammar
    Stitch:
  • parsing clinic + micro-drills
  • rewrite expression with explicit brackets
    Retest:
  • 0 parsing errors in 10-item drill
    Links:
  • /order-of-operations-why-people-get-it-wrong/

PATTERN_END

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_005
Name: Strategy Slip (Wrong Method Choice)
Trigger:

  • cannot label structure; chooses wrong method repeatedly
    FailureTrace:
    CHOICE collapse -> wrong first step -> time bleed -> panic cascade
    Sensors:
  • CHOICE low
  • E3 dominates
    Truncate:
  • force structure tag before solving
    Stitch:
  • method cards + interleaving
  • “choose-before-solve” drills
    Retest:
  • CHOICE >= 70% on 10 mixed items
    Links:
  • /math-worksheets/

PATTERN_END

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_006
Name: Verification Collapse (Oracle Off)
Trigger:

  • no sanity checks; cannot find first illegal step
    FailureTrace:
    unchecked steps -> silent errors -> repeated wrong answers -> confidence collapse
    Sensors:
  • ORA_present_rate low
  • FD_accuracy low
    Truncate:
  • stop; reinstate check discipline
    Stitch:
  • daily bug-hunt (first illegal step)
  • mandatory 1 check per question (units/sign/substitute)
    Retest:
  • FD_accuracy >= 70% on 5 bug-hunts
    Links:
  • /math-fenceos-stop-loss-for-exam-mistakes/

PATTERN_END

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_007
Name: Time Bleed Cascade (Chrono Failure)
Trigger:

  • stuck too long; no skip-return
    FailureTrace:
    time bleed -> rushing later -> more mistakes -> panic -> collapse
    Sensors:
  • TB_rate high
  • late-paper accuracy crash
    Truncate:
  • skip-return protocol
    Stitch:
  • time budgeting drills (marks vs minutes)
  • minimal-solve + one check
    Retest:
  • TB_rate drops over 2 timed sessions
    Links:
  • /math-fenceos-stop-loss-for-exam-mistakes/

PATTERN_END

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_008
Name: Load Premature Timing (LS Spike)
Trigger:

  • heavy timing applied before TR stabilizes
    FailureTrace:
    early timing -> LS spike -> meaning drift -> repeated phase slips -> avoidance
    Sensors:
  • LS_ratio < 0.75
  • TR < 0.7
    Truncate:
  • remove timer 48–72h
    Stitch:
  • rebuild TR with 3-skin packs
  • re-enter timing ladder
    Retest:
  • LS stable + TR>=0.7
    Links:
  • /math-phase-slip-why-students-panic/

PATTERN_END

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_009
Name: Word-to-Equation Translation Failure
Trigger:

  • cannot convert word problems into variables/relations
    FailureTrace:
    story-skin dominates -> no structure -> cannot start -> panic
    Sensors:
  • MF (model fit) low
  • CHOICE low
    Truncate:
  • stop solving; do representation drills
    Stitch:
  • 3 representations required: bar model/table/equation
  • label variables + units explicitly
    Retest:
  • 3 word problems solved with correct setup
    Links:
  • /math-as-simulation-language/

PATTERN_END

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_010
Name: Fraction/Decimal Switching Confusion
Trigger:

  • errors when switching forms; place value drift
    FailureTrace:
    unstable representation -> wrong conversions -> cascading errors
    Sensors:
  • E4 execution errors clustered around conversions
    Truncate:
  • enforce one representation per sub-step
    Stitch:
  • conversion drills + estimation sanity checks
    Retest:
  • 10 conversion items, >=90% accuracy
    Links:
  • /math-worksheets/

PATTERN_END

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_011
Name: Over-Choice / Sandbox Collapse (rho Spike)
Trigger:

  • too many new methods/corridors attempted at once
    FailureTrace:
    rho high -> confusion -> base skills degrade -> LS spikes -> phase slip
    Sensors:
  • rho high
  • LS spikes during exploration
    Truncate:
  • stop sandbox; return to exploit week
    Stitch:
  • cap to 1 corridor/day + Oracle audit
  • restore base TR/LS first
    Retest:
  • LS stable + TR stable before sandbox resumes
    Links:
  • /math-architect-training-pack-12-week/

PATTERN_END

PATTERN_START
PatternID: EDUKATE::MATHOS::FAIL::MATH_FAIL_012
Name: Error Shame Freeze (Avoidance Loop)
Trigger:

  • student hides errors; avoids correction
    FailureTrace:
    shame -> no feedback -> repeated errors -> identity collapse -> avoidance -> capability decay
    Sensors:
  • missing error logs
  • low feedback loop rate
    Truncate:
  • remove high-stakes timing; normalize error logging
    Stitch:
  • “first divergence” correction ritual (non-judgment)
  • 1 repair rule sentence + 1 variant
    Retest:
  • consistent error log for 2 weeks
    Links:
  • /math-truncation-and-stitching-recovery-protocol/

PATTERN_END

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SENSOR_PANEL_ATLAS (minimum mapping)
CoreSensors:

  • SML, EQ, TR, LS, CHOICE, ORA, FD, TB, MF, rho
    ActionRule:
  • Identify dominant failure pattern -> run its corridor -> retest -> re-enter

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NEXT_EXPANSION (additive; reserved PatternIDs)
ReserveIDs:
EDUKATE::MATHOS::FAIL::MATH_FAIL_013..MATH_FAIL_030
SuggestedNextPatterns:
013: Calculator Externalization Drift
014: Interleaving Absence (Discrimination Never Trained)
015: Proof-Gap Blindness (Assumption Leak)
016: Unit Drift (Physics/Word Problems)
017: Graph Misread (Axes/Scale Drift)
018: Over-Highlighting/Under-Doing (Note illusion)
019: Cramming Relapse (Spacing absent)
020: Notation Confusion (Similar symbols)
021: Negative Sign Drift
022: Algebraic Cancellation Illegal Move
023: Ratio Table Misuse
024: Percent Base Confusion
025: Geometry Diagram Assumption Trap
026: Probability Intuition Trap (base rate neglect)
027: Optimization Objective Drift
028: Bottleneck Misidentification (ProdOS)
029: Model Overfit (Stats misuse)
030: Confidence/Checking Tradeoff Collapse

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RELATED_PAGES
Links:

  • /mathos-runtime-control-tower-v0-1/
  • /mathos-sensors-pack-v0-1/
  • /mathos-fenceos-threshold-table-v0-1/
  • /mathos-recovery-corridors-p0-to-p3/ # next
  • /mathos-data-adapter-spec-v0-1/ # next
  • /math-transfer-test-same-structure-different-skin/
  • /math-fenceos-stop-loss-for-exam-mistakes/
  • /math-truncation-and-stitching-recovery-protocol/

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