MathOS FenceOS Threshold Table: Understanding Sensor Actions

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PAGE_START
PageID: EDUKATE::MATHOS::FENCE_TABLE_01
Slug: /mathos-fenceos-threshold-table-v0-1/
Title: MathOS FenceOS Threshold Table v0.1 (Sensors → Thresholds → Truncate/Stitch/Retest)
Version: v0.1 (LOCK)
Parent: /mathos-runtime-control-tower-v0-1/
Intent:

Provide the unified threshold table that makes MathOS runnable (CivOS parity)
Map sensors to actions at Z0 (student) and Z1 (cohort)
Include society-level threshold (ProjectionUnlock) for CivOS symmetry A
GrammarLock:
Place×Lane×Zoom×Role×Type×ID
Lane: MATH
CivOSOverlaysAllowed:
TABLE_Z0_CORE
TABLE_Z1_COHORT
TABLE_SOCIAL
BOX_NEG_VOID

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BLOCK_01_QUICK_ANSWER (AboveTheFold; PAA-ready)
Answer_70_110w:
This is the MathOS stop-loss table: it converts sensor readings into immediate actions so mistakes don’t cascade. At student level (Z0), the main triggers are meaning-lock failure (SML↓), transfer collapse (TR↓), load shear (LS↑), strategy-choice collapse (CHOICE↓), verification collapse (ORA↓), and time bleed (TB↑). Each trigger forces truncation (stop the bleed), stitching (repair the missing bind), and retest (prove recovery). At system level, the same control physics becomes a social threshold: when f_math(P2), education pipeline strength, verification norms, and unit standardization are high, society unlocks stable high-Z coordination.
Bullets:

Sensors are useless without thresholds + actions
Truncate early, stitch correctly, retest before re-entering load
Same control physics scales from student exams to civilisation scaling
SeeAlso:
/mathos-sensors-pack-v0-1/
/mathos-failure-atlas-v0-1/
/mathos-recovery-corridors-p0-to-p3/

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BLOCK_02_DEFINITION_LOCK (No drift)
FenceOS :=
threshold guard that prevents irreversible degradation by triggering:
Sensors -> Thresholds -> Truncate -> Stitch -> Retest -> Re-Enter

KeyRule:

Never increase load when a below-threshold signal is present.
“Felt confidence” is not a pass. Retest is the pass.

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TABLE_Z0_CORE (Student thresholds; minimal viable runtime)

Z0_THRESHOLDS:

T0_MEANING_LOCK (SML):
Trigger:
SML low OR cannot explain symbols/units/asked in 10s
Truncate:
– stop timing immediately
– write 1 meaning line before any further work
– reduce width: 1 structure only
Stitch:
– do 1 worked example + 2 near copies + 2 independent
– add 1 explanation sentence per step (why legal)
Retest:
– 3 questions untimed with meaning line
ReEnter:
– only after SML stable for 2 sessions
CorridorLink:
– /math-truncation-and-stitching-recovery-protocol/

T1_EQUIVALENCE (EQ):
Trigger:
illegal transformations detected; rewrite changes meaning
Truncate:
– switch to “legal moves only” mode
– stop multi-step algebra expansions
Stitch:
– equivalence drills + bug-hunt (first illegal step)
– rewrite 3 equivalent forms for 3 expressions
Retest:
– 5 rewrite questions, 0 illegal steps
CorridorLink:
– /math-fenceos-stop-loss-for-exam-mistakes/

T2_TRANSFER (TR):
Trigger:
TR < 0.4 on 3-skin pack Truncate: – stop doing 30 identical questions (blocked repetition) – stop mixed timed papers Stitch: – 3-skin packs daily (same structure, different skin) – add structure tag before solving – interleaving only after single-family TR improves Retest: – TR >= 0.7 on 2 separate packs
ReEnter:
– begin timed ladder Level1 only after TR>=0.7
CorridorLink:
– /math-transfer-test-same-structure-different-skin/

T3_LOAD_SHEAR (LS):
Trigger:
LS_ratio (timed/untimed) < 0.75 OR error spike when timer starts Truncate: – remove timer 48–72h – narrow width; restore SML and ORA checks Stitch: – timed re-entry ladder Level0->Level2
– short timed sets (6Q) + mandatory sanity check
Retest:
– LS stable across 2 sessions
CorridorLink:
– /math-phase-slip-why-students-panic/

T4_STRATEGY_CHOICE (CHOICE):
Trigger:
cannot label structure in 5s; wrong method choice on mixed sets
Truncate:
– pause solving; force structure tag first
Stitch:
– method cards (choose-before-solve)
– interleaving sets (ABCABC) with justification line
Retest:
– CHOICE accuracy >= 70% BEFORE solving 10 mixed questions
CorridorLink:
– /math-worksheets/

T5_VERIFICATION (ORA):
Trigger:
no sanity check for last 2 questions OR FD detection low
Truncate:
– stop; re-enable check discipline
Stitch:
– bug-hunt drills daily (find first illegal step)
– 1 sanity check per question (units/sign/substitute back)
Retest:
– FD accuracy >= 70% on 5 bug-hunt items
CorridorLink:
– /math-fenceos-stop-loss-for-exam-mistakes/

T6_TIME_BLEED (TB):
Trigger:
time spent > budget AND progress stalled
Truncate:
– skip-return protocol (park and move)
Stitch:
– triage practice: mark value vs time budget
– reduce perfectionism; enforce minimal-solve + check
Retest:
– TB_rate decreases over 2 timed sessions
CorridorLink:
– /math-fenceos-stop-loss-for-exam-mistakes/

T7_SANDBOX_RHO (Architect safety):
Trigger:
rho high OR LS spikes during exploration
Truncate:
– stop Architect tasks immediately
Stitch:
– return to exploit week (Operator/Oracle/Visionary)
– cap corridor attempts (max 1/day)
Retest:
– LS stable + TR stable before sandbox resumes
CorridorLink:
– /math-architect-training-pack-12-week/

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TABLE_Z1_COHORT (Class-level thresholds; distributions)

Z1_THRESHOLDS:

C1_TR_DISTRIBUTION:
Trigger:
majority TR < 0.4 OR long tail of collapse
Truncate:
– stop “blocked-only homework”
– stop “single-topic tests only”
Stitch:
– deploy standard 3-skin packs across cohort
– raise interleave ratio gradually
Retest:
– TR_distribution shifts upward in 2 weeks

C2_LS_DISTRIBUTION:
Trigger:
timed collapse widespread (LS low)
Truncate:
– reduce strict timing; rebuild SML/EQ first
Stitch:
– timed ladder across cohort after TR stabilizes
Retest:
– LS distribution stabilizes; panic signatures drop

C3_ERROR_DOMINANCE (E1–E6):
Trigger:
one error type dominates (e.g., parsing drift E2)
Truncate:
– stop adding new topics
Stitch:
– run clinic module targeting that error type
Retest:
– error distribution flattens; performance rises

C4_REMEDIATION_LATENCY:
Trigger:
failures persist > 2 weeks without repair corridor
Truncate:
– freeze pacing
Stitch:
– enforce corridor directory usage + weekly retests
Retest:
– latency falls; recovery rate rises

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TABLE_SOCIAL (CivOS symmetry A threshold; society scaling)

SOCIAL_THRESHOLD::PROJECTION_UNLOCK:

Variables:
f_math(P2): fraction of population transfer-stable under load
EDU_PIPE: education pipeline strength (quality-weighted)
ORA_NORM: verification culture prevalence (audit norms)
UNIT_STD: unit/notation standardization

Condition:
if (f_math(P2) high) AND (EDU_PIPE strong) AND (ORA_NORM strong) AND (UNIT_STD high)
-> stable high-Z coordination unlock (“energy projection”)

Failure:
if L(t) rising while these remain weak
-> error_rate exceeds verification capacity
-> brittle failure cascades

SeeAlso:
– /math-threshold-why-societies-suddenly-scale/
– /symmetry-of-mathematics-genesis-selfie/

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BOX_NEG_VOID (Google-style)
NegativeVoid:

sensors are measured but no thresholds exist
timing is increased while meaning is weak
transfer collapse is ignored (blocked repetition continues)
Outcome:
predictable exam collapse + repeated phase slips
system-level: scaling attempts fracture under rising load
FailureTrace:
missing thresholds -> late detection -> wrong intervention -> cascade -> loss of trust -> avoidance/pipeline decay

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RELATED_PAGES (internal sitelinks)
Links:

/mathos-runtime-control-tower-v0-1/
/mathos-sensors-pack-v0-1/
/mathos-failure-atlas-v0-1/ # next
/mathos-recovery-corridors-p0-to-p3/ # next
/mathos-data-adapter-spec-v0-1/ # next
/math-transfer-test-same-structure-different-skin/
/math-phase-slip-why-students-panic/
/math-fenceos-stop-loss-for-exam-mistakes/
/math-truncation-and-stitching-recovery-protocol/

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MathOS FenceOS Threshold Table v0.1 (Sensors → Thresholds → Truncate/Stitch/Retest)

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