MathOS Sensors Pack v0.1 (Z0–Z6) — What to Measure, How to Read Drift, What to Do Next

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PageID: EDUKATE::MATHOS::SENSORS_PACK_01
Slug: /mathos-sensors-pack-v0-1/
Title: MathOS Sensors Pack v0.1 (Z0–Z6) — What to Measure, How to Read Drift, What to Do Next
Version: v0.1 (LOCK)
Parent: /mathos-runtime-control-tower-v0-1/
Intent:

  • Provide the CivOS-parity sensor layer for MathOS
  • Define sensors at every Z (student->class->school->city->nation->global)
  • Provide: sensor definitions + collection methods + interpretation + action links
    GrammarLock:
    Place×Lane×Zoom×Role×Type×ID
    Lane: MATH
    CivOSOverlaysAllowed:
  • BOX_SENSOR_TO_ACTION
  • BOX_NEG_VOID
  • SENSOR_TABLES_ALL_Z

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BLOCK_01_QUICK_ANSWER (AboveTheFold; PAA-ready)
Answer_70_110w:
A MathOS “sensor” is a measurable signal that predicts whether math capability is stable or drifting under load. At student level (Z0) the core sensors are meaning-lock (SML), equivalence (EQ), transfer (TR), load shear (LS), strategy choice (CHOICE), and verification habit (ORA). At higher levels (class/school/city/nation) sensors become distributions and pipeline measures: transfer distributions, top error types, interleaving ratio, education quality, numeracy proxies, and verification culture. This pack defines what to measure, what thresholds mean, and which repair corridor to run next.
Bullets:

  • Z0: measure the loops that make math work (SML/EQ/TR/LS/CHOICE/ORA)
  • Z1–Z2: measure distributions + pipeline health (not single scores)
  • Z3–Z6: measure system capability (education throughput + verification culture + numeracy proxies)
    SeeAlso:
  • /mathos-fenceos-threshold-table-v0-1/
  • /mathos-failure-atlas-v0-1/
  • /mathos-recovery-corridors-p0-to-p3/

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BLOCK_02_DEFINITION_LOCK (No drift)
Sensor :=
a measurable signal that updates state of MathOS capability under load.

SensorRules:
R1: Sensors update state; they do not overwrite structure.
R2: Every sensor maps to an action via thresholds (FenceOS tables).
R3: Prefer distributions over single scores at Z1+.
R4: A sensor without a repair corridor is not a sensor; it is trivia.

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BOX_SENSOR_TO_ACTION (control loop)
ControlLoop:
Sensors -> Thresholds -> Truncate -> Stitch -> Retest -> Re-Enter
Pointers:
Threshold tables: /mathos-fenceos-threshold-table-v0-1/
Recovery corridors: /mathos-recovery-corridors-p0-to-p3/
Failure patterns: /mathos-failure-atlas-v0-1/

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SENSOR_TABLES_ALL_Z

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Z0::STUDENT SENSORS (core; minimal viable set)

Z0_CORE_SENSORS:
SML (Symbol-Meaning Lock):
definition:
can explain symbols/units/what’s asked in 10 seconds
capture:
teacher/tutor checklist; student writes “meaning line”
output:
SML_score ∈ {0,1} per question; aggregate per session

EQ (Equivalence Stability):
definition:
rewrites preserve meaning (legal transforms only)
capture:
bug-hunt, step justification, rewrite drills
output:
EQ_error_rate

TR (Transfer Rate):
definition:
3-skin pack correct/3 (same structure, different skin)
capture:
weekly 3-skin pack per topic family
output:
TR ∈ {0..1}

LS (Load Shear):
definition:
accuracy drop when timed vs untimed
capture:
untimed set then mild timed set
output:
LS_ratio = timed_accuracy / untimed_accuracy

CHOICE (Strategy Selection):
definition:
can label structure + choose method BEFORE solving
capture:
“structure tag” prompt on mixed set
output:
CHOICE_accuracy

ORA (Oracle Habit):
definition:
uses sanity checks + finds first illegal step
capture:
require 1 check per question; run bug-hunt drills
output:
ORA_present_rate, FD_accuracy

TB (Time Bleed):
definition:
time spent beyond value without progress
capture:
time per question vs mark weight
output:
TB_rate (per paper)

Z0_OPTIONAL_SAND_BOX (Architect track):
NoveltyRate:
corridors attempted per week
ValidityRate:
% corridor attempts passing Oracle audit
ReuseScore:
corridor works on 3 variants (0..3)
CompressionGain:
steps saved vs baseline
rho:
choice injected / capacity estimate

Z0_OUTPUT_STATE (canonical):
StudentState :=
{P_level_estimate, SML, EQ, TR, LS, CHOICE, ORA, TB, TopErrorTypes(E1..E6), sandbox_metrics(optional)}

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Z1::CLASS / COHORT SENSORS (distributions > averages)

Z1_SENSORS:
TR_distribution:
– histogram of TR scores across students
LS_distribution:
– histogram of LS_ratio across students
ErrorTypeDistribution:
– E1..E6 frequency distribution across cohort
PromotionRates:
– % at P1, P2, P3 by topic family
InterleaveRatio:
– % of homework/classwork that is mixed vs blocked
FeedbackLoopRate:
– % of sessions using retrieval->feedback->FD diagnosis
TimeBleedRate:
– fraction of students with TB above threshold

Z1_ACTION_MAP:

  • if TR_distribution low -> restructure practice: 3-skin packs + interleaving
  • if LS_distribution collapses -> remove timing; rebuild SML/EQ; timed ladder later
  • if ErrorType E2 parsing dominates -> parsing clinics (OOO)
  • if ErrorType E3 choice dominates -> structure tagging + method cards

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Z2::SCHOOL / PROGRAM SENSORS (pipeline health)

Z2_SENSORS:
EDU_PIPE_strength:
– curriculum coherence + practice design + feedback routines
TeacherCapabilityDensity:
– Oracle culture proxy: prevalence of error diagnosis + proof-like checking
AssessmentMix:
– proportion of mixed items vs single-topic tests
TransferOutcomeIndex:
– school-level TR stability across grades
RemediationLatency:
– time-to-repair after failure signals (days/weeks)
EquityGap_TR:
– TR distribution gap between groups/classes (not identity labels; purely performance)

Z2_ACTION_MAP:

  • if EDU_PIPE weak -> implement standard loops:
    worked example -> retrieval -> feedback -> variant -> interleaving
  • if remediation latency high -> enforce FenceOS triggers + corridor directory usage
  • if assessment mix too blocked -> add mixed papers earlier (but gated by TR)

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Z3::CITY / REGION SENSORS (ecosystem)

Z3_SENSORS:
CurriculumLoadProfile:
– pacing + topic density + exam pressure pattern
SupportEcosystemDensity:
– availability of tutoring/after-school supports (neutral metric)
NumeracyProxyAvailability:
– available city/regional measures (where public)
VerificationCultureSignals:
– norms of checking, standards adherence, error correction climate

Z3_ACTION_MAP:

  • if load spikes without pipeline upgrades -> drift risk
  • if verification culture weak -> promote audit/check habits in curricula and supports

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Z5::NATION SENSORS (civilisation capacity proxy)

Z5_SENSORS:
NumeracyProxy:
– e.g., historical numeracy estimation via age heaping (where studied)
EDU_PIPE:
– school enrollment × quality × persistence
STEM_Throughput:
– number of learners reaching advanced math stability (P2/P3 proxies)
VerificationCulture:
– standards, audits, professional norms in critical industries
ProjectionUnlockReadiness:
– composite: f_math(P2) + EDU_PIPE + ORA_NORM + UNIT_STD

Anchor references (conceptual):

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Z6::GLOBAL SENSORS (frontier + coordination language)

Z6_SENSORS:
FrontierAttentionMap:
– density of activity around major open problems / key fields (high-level)
ProofCultureSignals:
– norms of verification, reproducibility, peer review strength (proxy)
ToolchainEvolution:
– growth of simulation/optimization/ML+math integration
GlobalProjectionCapacity:
– ability to coordinate massive systems safely (risk modeling, supply chains, climate, etc.)

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BLOCK_03_ERROR TAXONOMY (required for sensor completeness)
REG_ERROR_TAXONOMY_01 (preview):
E1 Meaning Drift (SML failure)
E2 Parsing Drift (grammar/precedence)
E3 Strategy Slip (CHOICE failure)
E4 Execution Slip (calculation/algebra)
E5 Verification Collapse (Oracle off)
E6 Time Bleed (Chrono failure)
Pointers:

  • recovery: /math-truncation-and-stitching-recovery-protocol/
  • stop-loss: /math-fenceos-stop-loss-for-exam-mistakes/

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BLOCK_04_COLLECTION PROTOCOLS (minimum viable; no fancy tools)

COLLECT_Z0 (per session):

  • 6 questions + 1 transfer variant
  • record:
    accuracy
    time per Q (rough)
    SML yes/no
    ORA check yes/no
    error type E1..E6 (if wrong)

COLLECT_Z1 (weekly):

  • TR packs per topic family (3 skins)
  • LS test (mild timed)
  • cohort distributions chart (even manual)

COLLECT_Z2 (monthly):

  • assessment mix audit (blocked vs mixed)
  • remediation latency log
  • teacher Oracle habit sampling (bug-hunt exercise)

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BOX_NEG_VOID (Google-style)
NegativeVoid:

  • measuring only grades hides drift
  • no TR/LS sensors -> collapse surprises
  • no error taxonomy -> wrong repairs repeated
    Outcome:
  • P1 illusion persists
  • exam skin-change causes P2->P0 slips
    FailureTrace:
    missing sensors -> late detection -> high-cost remediation -> avoidance -> pipeline decay

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FAQ_PACK (PAA-ready)

Q1: What should I measure to improve math fast?
A_45_85w:
Measure transfer and load stability, not just marks. Use a weekly 3-skin transfer pack (same structure, different skin) to get TR, and compare timed vs untimed accuracy to get LS. Add meaning-lock (SML) checks and a simple error taxonomy (meaning/parsing/choice/execution/verification/time). Then apply threshold actions: truncate timing when meaning collapses, stitch the missing bind, and retest.
Bullets:

  • TR: transfer
  • LS: timed stability
  • SML/ORA: meaning + verification
  • Error taxonomy: correct repair
    SeeAlso:
  • /mathos-fenceos-threshold-table-v0-1/
  • /math-truncation-and-stitching-recovery-protocol/

Q2: Why are grades not enough as a metric?
A_40_75w:
Grades mix many factors and can hide fragile template performance. A student can score well on blocked practice and still collapse when the exam changes the skin. Transfer (TR) and load shear (LS) predict that collapse earlier. Measuring distributions (class-level) also reveals system issues like weak interleaving or slow remediation that average grades conceal.
Bullets:

  • Grades hide fragility
  • TR/LS reveal real stability
  • Distributions reveal pipeline health
    SeeAlso: /math-transfer-test-same-structure-different-skin/

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RELATED_PAGES (internal sitelinks)
Links:

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

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