SG-MATH Master Graph v0.1 (Primary → Secondary → JC) — Executable Syllabus Lattice

TITLE: SG-MATH Master Graph v0.1 (Primary → Secondary → JC) — Executable Syllabus Lattice
VERSION: CivOS Unified Spec v1.x
MODE: Almost-Code / LLM-first / WordPress paste-ready
OWNER: eduKateSG Fence Learning Systems
SCOPE: Singapore Math Syllabus (core topics) + CivOS-HD sensors + FenceOS + CH/ai scheduler hooks
GOAL: Turn “syllabus” into a computable capability graph: Detect → Predict → Repair → Upgrade under load
CANONICAL CLAIM:
- Math failure is almost never “IQ”. It is (a) prerequisite debt + (b) late fencing + (c) weak transfer under load.
- This graph makes prerequisite debt visible, uses FenceOS to stop irreversible drift, and routes repair using CH/ai.
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0) GLOBAL PRIMITIVES (LOCKED)
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Phase (Reliability Under Load):
- P0 collapse, P1 scaffolded, P2 reliable normal load, P3 stable high load + variation
Zoom (Coordination Scale):
- Z0 learner, Z1 family/tutor, Z2 school, Z3 city, Z4 nation, Z5 civilisation, Z6 supranational
FenceOS Ratios:
- R = Ḋ/Ġ (loss/decay rate over repair/regeneration rate)  ; stable if R < 1
- Θ = T_fence / T_repair                               ; must be < 1
- Λ = T_enforce / T_fence                              ; preferred < 1
Core Sensors (generic):
- ErrorRepeatCycle (ERC)
- SpeedInstabilityIndex (SII)
- TransferReliability% (TR)
- VariationFailureRate (VFR)
- AvoidanceSlope d(Avoid)/dt
- BacklogNodes (BN)
- TTC (weeks to exam / checkpoint)
Fence Actions:
- Truncation: reduce scope + stop-loss on accelerating failure
- Stitching: targeted repair loop + buffer rebuild + rejoin safe trajectory (APRC)
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1) GRAPH FORMALISM (HOW TO READ THIS)
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Node := capability unit (not “chapter title”)
Edge := prerequisite dependency or cross-topic transfer dependency
NodeRecord := {
  ID, LevelBand, Domain, Prereq[], Outputs[],
  LoadProfile, PhaseTargetByStage,
  TransferTests[], Sensors[], FailureModes[], RepairLoops[],
  FenceRules (stop-loss/downgrade/off-ramps)
}
ID Grammar (LOCK):
Place×Lane×Zoom×Role×Type×ID
Place: SG
Lane: MATH
Zoom: Z0 (core; extendable Z1–Z6)
Role: Learner / Tutor / Teacher / Operator
Type: Node / Edge / SensorPack / Protocol / Test / Panel
ID: stable slug
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2) MASTER DOMAINS (TOP-LEVEL CLUSTERS)
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Primary Core Domains:
- NUM: Number & Operations
- FRAC: Fractions/Decimals/Percent
- RPP: Ratio/Proportion/Percentage
- ALG0: Algebraic precursors (patterns, unknowns)
- GEO: Geometry & Measurement
- WP: Word Problem Engine (model method; multi-step reasoning)
- DATA0: Basic data/statistics (intro)
Secondary Core Domains:
- ALG1: Algebra (manipulation, equations, functions)
- GRAPH: Graphs & Coordinate plane
- QUAD: Quadratics
- TRIG: Trigonometry
- STAT: Statistics & Probability
- AMATH: Advanced Math lane (logs, calculus intro, coord geom deeper)
JC Domains:
- CALC: Differentiation/Integration + applications
- VEC: Vectors
- CNUM: Complex numbers
- PDIS: Probability distributions & inference
- DEQ: Differential equations (H2)
- SERIES: sequences/series (depending track)
- PROOF: structured reasoning (implicit across nodes)
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3) PRIMARY (P1–P6) — NODE SET v0.1
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3.1 NUM SPINE (Whole-number operations)
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Node: SG×MATH×Z0×Learner×Node×NUM-PLACEVALUE
Prereq: []
Outputs: NUM-4OPS
LoadProfile: low→medium (accuracy + attention)
PhaseTarget: {P2 by P2, P3 by P4}
TransferTests: {TT0: read/write numbers; TT1: timed accuracy}
Sensors: {ERC, SII}
FailureModes: {CarelessSlipCluster}
RepairLoops: {micro-drills + error tagging}
FenceRules:
- If ERC>=3 on same slip type → Truncate: isolate slip class → Stitch: targeted drill
Node: SG×MATH×Z0×Learner×Node×NUM-4OPS
Prereq: [NUM-PLACEVALUE]
Outputs: NUM-MULTDIV-FLUENCY
LoadProfile: medium (speed + carry/borrow logic)
PhaseTarget: {P2 by P3, P3 by P5}
TransferTests: {TT1 timed mixed ops; TT-V variation problems}
Sensors: {SII, TR}
FailureModes: {ProcedureWithoutMeaning, SpeedCollapse}
RepairLoops: {concept+drill split; spaced retrieval}
FenceRules:
- If SII high under timing → Truncate timing → Stitch speed ladder
Node: SG×MATH×Z0×Learner×Node×NUM-MULTDIV-FLUENCY
Prereq: [NUM-4OPS]
Outputs: FRAC-EQUIV, WP-ARITH
LoadProfile: high (multiplicative reasoning)
PhaseTarget: {P2 by P4, P3 by P6}
TransferTests: {mixed sets; 2-step word problems}
Sensors: {TR, VFR}
FailureModes: {AdditiveBias (uses + where × needed)}
RepairLoops: {multiplicative cues training + mixed practice}
FenceRules:
- If AdditiveBias detected → Truncate word problems → Stitch multiplicative cue drill
----------------------------------------
3.2 FRAC / DEC / PERCENT SPINE
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Node: SG×MATH×Z0×Learner×Node×FRAC-CONCEPT
Prereq: [NUM-MULTDIV-FLUENCY]
Outputs: FRAC-EQUIV, FRAC-4OPS
LoadProfile: high (concept + representation)
PhaseTarget: {P1 by P4, P2 by P5, P3 by P6 (top band)}
TransferTests: {representations; compare/order; explain}
Sensors: {NIT-math (reason chain), ERC}
FailureModes: {LabelOnly, PartWholeConfusion}
RepairLoops: {CPA: concrete→pictorial→abstract}
FenceRules:
- If cannot explain with picture → Truncate procedure → Stitch concept via CPA
Node: SG×MATH×Z0×Learner×Node×FRAC-EQUIV
Prereq: [FRAC-CONCEPT]
Outputs: FRAC-4OPS, RPP-RATIO
LoadProfile: medium→high (pattern + simplification)
PhaseTarget: {P2 by P5, P3 by P6}
TransferTests: {equivalence + simplification timed}
Sensors: {ERC, SII}
FailureModes: {RandomSimplify}
RepairLoops: {GCF method + practice sets}
FenceRules:
- If RandomSimplify persists → Truncate → Stitch: single-rule lock + drills
Node: SG×MATH×Z0×Learner×Node×FRAC-4OPS
Prereq: [FRAC-EQUIV]
Outputs: DEC-CONVERT, PERCENT-CONVERT, WP-FRAC
LoadProfile: high (multi-step + accuracy)
PhaseTarget: {P2 by P6, P3 top band}
TransferTests: {mixed fraction ops; word problems}
Sensors: {TR, VFR, SII}
FailureModes: {CommonDenominatorFailure, TimeCollapse}
RepairLoops: {denominator strategy + spaced mixed practice}
FenceRules:
- If TTC short + low TR → Truncate mixed set → Stitch weakest op first
Node: SG×MATH×Z0×Learner×Node×DEC-CONVERT
Prereq: [FRAC-EQUIV]
Outputs: PERCENT-CONVERT, WP-RPP
LoadProfile: medium
PhaseTarget: {P2 by P6}
TransferTests: {fraction↔decimal conversions}
Sensors: {ERC}
FailureModes: {PlaceValueDrift}
RepairLoops: {place-value chart + drills}
FenceRules: standard ERC rule
Node: SG×MATH×Z0×Learner×Node×PERCENT-CONVERT
Prereq: [DEC-CONVERT]
Outputs: RPP-PERCENT, WP-RPP
LoadProfile: high (multiplicative reasoning + word problems)
PhaseTarget: {P2 by P6, P3 top band}
TransferTests: {percentage of quantity; reverse %}
Sensors: {TR, VFR}
FailureModes: {AdditiveBias, Reverse%Failure}
RepairLoops: {unitary method + bar model bridge}
FenceRules:
- If reverse% fails twice → Truncate reverse problems → Stitch unitary method
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3.3 RATIO / PROPORTION (Primary bridge to Secondary)
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Node: SG×MATH×Z0×Learner×Node×RPP-RATIO
Prereq: [FRAC-EQUIV, NUM-MULTDIV-FLUENCY]
Outputs: RPP-PROPORTION, WP-RPP
LoadProfile: high (structure)
PhaseTarget: {P2 by P6}
TransferTests: {equivalent ratios; part:part; part:whole}
Sensors: {NIT-math, TR}
FailureModes: {PartWholeSwap}
RepairLoops: {ratio table + bar model}
FenceRules: concept-first
Node: SG×MATH×Z0×Learner×Node×RPP-PROPORTION
Prereq: [RPP-RATIO]
Outputs: SEC-ALG1 (rates), WP-RPP
LoadProfile: high
PhaseTarget: {P2 by P6}
TransferTests: {rate problems; unitary method}
Sensors: {TR}
FailureModes: {WrongUnit, InverseProportionConfusion}
RepairLoops: {unit tracking + unitary method}
FenceRules:
- WrongUnit repeated → Truncate: unit tagging → Stitch: unit drills
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3.4 WP ENGINE (Model Method & multi-step)
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Node: SG×MATH×Z0×Learner×Node×WP-BAR-MODEL
Prereq: [NUM-4OPS]
Outputs: WP-ARITH, WP-RPP, SEC-ALG1 (structure readiness)
LoadProfile: high (translation language→math)
PhaseTarget: {P2 by P5, P3 by P6 top band}
TransferTests: {unseen PSLE-style questions}
Sensors: {TR, VFR, LanguageCouplingScore}
FailureModes: {Misread, WrongStructure, PanicSkip}
RepairLoops: {3-pass read; bar sketch; checkpoint questions}
FenceRules:
- If VFR spikes under timing → Truncate: untimed structure → Stitch: timed ramps
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3.5 GEO & MEASUREMENT (Primary)
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Node: SG×MATH×Z0×Learner×Node×GEO-AREA-VOL
Prereq: [NUM-MULTDIV-FLUENCY]
Outputs: SEC-GEOM, TRIG readiness (later)
LoadProfile: medium
PhaseTarget: {P2 by P6}
TransferTests: {mixed area/volume}
Sensors: {ERC}
FailureModes: {FormulaSwap}
RepairLoops: {formula family grouping + drills}
FenceRules: ERC rule
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4) SECONDARY (Sec1–Sec4/5) — NODE SET v0.1
========================================================
Secondary splits into:
- Core E-Math nodes (everyone)
- A-Math nodes (advanced lane; heavy algebra)
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4.1 ALG1 CORE (E-Math backbone)
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Node: SG×MATH×Z0×Learner×Node×ALG-EXPRESSIONS
Prereq: [WP-BAR-MODEL, RPP-PROPORTION]
Outputs: ALG-EQ-LINEAR, GRAPH-LINEAR
LoadProfile: high (symbol manipulation)
PhaseTarget: {P2 by Sec2, P3 by Sec4 top band}
TransferTests: {simplify; factor basic; evaluate}
Sensors: {ERC, SII}
FailureModes: {SignErrorCluster, LikeTermsConfusion}
RepairLoops: {algebra hygiene checklist + spaced drills}
FenceRules:
- If SignErrorCluster persists → Truncate: sign-only drills → Stitch: reintroduce complexity
Node: SG×MATH×Z0×Learner×Node×ALG-EQ-LINEAR
Prereq: [ALG-EXPRESSIONS]
Outputs: ALG-SIMULT, GRAPH-LINEAR
LoadProfile: high
PhaseTarget: {P2 by Sec2}
TransferTests: {word→equation; solve; verify}
Sensors: {TR, VFR}
FailureModes: {EquationSetupFailure}
RepairLoops: {sentence parsing + structure templates}
FenceRules:
- If setup fails 2+ → Truncate word problems → Stitch WP templates
Node: SG×MATH×Z0×Learner×Node×GRAPH-LINEAR
Prereq: [ALG-EQ-LINEAR]
Outputs: GRAPH-INTERPRET, STAT
LoadProfile: medium
PhaseTarget: {P2 by Sec3}
TransferTests: {plot + interpret gradient/intercept}
Sensors: {ERC}
FailureModes: {AxisConfusion}
RepairLoops: {graph muscle memory drills}
FenceRules: ERC rule
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4.2 QUADRATICS (E-Math + A-Math bridge)
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Node: SG×MATH×Z0×Learner×Node×QUAD-FOUNDATION
Prereq: [ALG-EXPRESSIONS]
Outputs: QUAD-SOLVE, GRAPH-QUAD
LoadProfile: high
PhaseTarget: {P2 by Sec3}
TransferTests: {expand/factor; recognize forms}
Sensors: {ERC, SII}
FailureModes: {FactorBlindness}
RepairLoops: {factor pattern bank + drills}
FenceRules: If FactorBlindness → Truncate to patterns → Stitch to mixed forms
Node: SG×MATH×Z0×Learner×Node×QUAD-SOLVE
Prereq: [QUAD-FOUNDATION]
Outputs: AM-CALC-PRE, GRAPH-QUAD
LoadProfile: high
PhaseTarget: {P2 by Sec4}
TransferTests: {solve; check; word problem}
Sensors: {TR}
FailureModes: {ChooseWrongMethod}
RepairLoops: {method selector rubric}
FenceRules: method selector before timed sets
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4.3 TRIG (E-Math)
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Node: SG×MATH×Z0×Learner×Node×TRIG-RATIOS
Prereq: [GEO-AREA-VOL]
Outputs: TRIG-APPLICATIONS
LoadProfile: medium
PhaseTarget: {P2 by Sec4}
TransferTests: {SOHCAHTOA; right triangle}
Sensors: {ERC}
FailureModes: {RatioSwap}
RepairLoops: {triangle labeling protocol}
FenceRules: ERC rule
Node: SG×MATH×Z0×Learner×Node×TRIG-APPLICATIONS
Prereq: [TRIG-RATIOS]
Outputs: JC-VEC bridge (spatial)
LoadProfile: high
PhaseTarget: {P2 by Sec4}
TransferTests: {bearing/height-distance}
Sensors: {TR, VFR}
FailureModes: {DiagramFailure}
RepairLoops: {diagram-first habit}
FenceRules: Truncate wordy questions → Stitch diagram protocol
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4.4 STAT/PROB (E-Math)
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Node: SG×MATH×Z0×Learner×Node×STAT-DATA
Prereq: [GRAPH-LINEAR]
Outputs: PROB-BASICS, JC-PDIS
LoadProfile: medium
PhaseTarget: {P2 by Sec4}
TransferTests: {mean/median; charts; interpretation}
Sensors: {ERC}
FailureModes: {InterpretationDrift}
RepairLoops: {sentence frames for interpretation}
FenceRules: NIT-lite for explanation correctness
Node: SG×MATH×Z0×Learner×Node×PROB-BASICS
Prereq: [STAT-DATA]
Outputs: JC-PDIS
LoadProfile: high
PhaseTarget: {P2 by Sec4}
TransferTests: {combined events; tree diagrams}
Sensors: {TR, VFR}
FailureModes: {Overcounting}
RepairLoops: {sample-space listing + tree discipline}
FenceRules: if Overcounting repeated → Truncate to sample space
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4.5 A-MATH LANE (critical for STEM pipeline)
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Node: SG×MATH×Z0×Learner×Node×AM-ALGEBRA-FLUENCY
Prereq: [ALG-EXPRESSIONS, QUAD-FOUNDATION]
Outputs: AM-LOGS, AM-TRIG, AM-CALC-PRE
LoadProfile: very high (speed + accuracy)
PhaseTarget: {P2 by Sec3, P3 by Sec4 top band}
TransferTests: {timed mixed algebra; identity manip}
Sensors: {SII, ERC, TR}
FailureModes: {BrittleAlgebra (small slip → total collapse)}
RepairLoops: {algebra hygiene + speed ladder + mixed sets}
FenceRules:
- If SII high and TTC short → Truncate scope to core forms → Stitch speed ladder
- If ERC on same slip class → isolate slip class immediately
Node: SG×MATH×Z0×Learner×Node×AM-LOGS
Prereq: [AM-ALGEBRA-FLUENCY]
Outputs: JC-CALC readiness
LoadProfile: high
PhaseTarget: {P2 by Sec4}
TransferTests: {laws + solve equations}
Sensors: {ERC}
FailureModes: {LawSwap}
RepairLoops: {law card + drills}
FenceRules: ERC rule
Node: SG×MATH×Z0×Learner×Node×AM-CALC-PRE
Prereq: [AM-ALGEBRA-FLUENCY]
Outputs: JC-CALC
LoadProfile: high
PhaseTarget: {P2 by Sec4}
TransferTests: {rate of change intuition; function handling}
Sensors: {TR}
FailureModes: {FunctionBlindness}
RepairLoops: {function concept pack + graph links}
FenceRules: concept-first before procedures
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5) JC (H1/H2) — NODE SET v0.1
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5.1 CALCULUS (core)
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Node: SG×MATH×Z0×Learner×Node×JC-CALC-DIFF
Prereq: [AM-CALC-PRE, AM-ALGEBRA-FLUENCY]
Outputs: JC-CALC-APPS, JC-DEQ (H2)
LoadProfile: very high (pace + abstraction)
PhaseTarget: {P2 by JC1 mid, P3 by A-level top band}
TransferTests: {timed differentiation + mixed applications}
Sensors: {SII, TR, BN}
FailureModes: {PaceOverload, HiddenPrereqDebt}
RepairLoops: {weekly mixed sets + prereq patching}
FenceRules:
- If BN>3 nodes + TTC short → Truncate: core techniques only → Stitch: apps after stability
- If HiddenPrereqDebt detected → immediate prereq patch (algebra)
Node: SG×MATH×Z0×Learner×Node×JC-CALC-INTEG
Prereq: [JC-CALC-DIFF]
Outputs: JC-CALC-APPS, JC-DEQ (H2)
LoadProfile: very high
PhaseTarget: {P2 by JC2 early}
TransferTests: {method selection + timed}
Sensors: {TR, VFR}
FailureModes: {ChooseWrongMethod, SetupFailure}
RepairLoops: {method selector tree + drills}
FenceRules: selector enforced before timed sets (Λ control)
Node: SG×MATH×Z0×Learner×Node×JC-CALC-APPS
Prereq: [JC-CALC-DIFF, JC-CALC-INTEG]
Outputs: A-level transfer
LoadProfile: extreme (multi-topic integration)
PhaseTarget: {P2 majority, P3 top band}
TransferTests: {full-paper sections}
Sensors: {TR, VFR, SII}
FailureModes: {IntegrationCollapseUnderTime}
RepairLoops: {paper simulation + weakest-node repair}
FenceRules: paper sims only after node stability
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5.2 VECTORS / COMPLEX / PDIS
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Node: SG×MATH×Z0×Learner×Node×JC-VEC
Prereq: [GRAPH-LINEAR, TRIG-APPLICATIONS]
Outputs: mechanics/physics coupling
LoadProfile: high (spatial abstraction)
PhaseTarget: {P2 by JC1}
TransferTests: {vector geometry problems}
Sensors: {TR}
FailureModes: {DiagramFailure}
RepairLoops: {diagram protocol}
FenceRules: diagram-first enforced
Node: SG×MATH×Z0×Learner×Node×JC-CNUM
Prereq: [AM-ALGEBRA-FLUENCY]
Outputs: advanced algebra reasoning
LoadProfile: high
PhaseTarget: {P2 by JC1}
TransferTests: {arg/mod; operations}
Sensors: {ERC}
FailureModes: {RepresentationConfusion}
RepairLoops: {form conversion drills}
FenceRules: ERC rule
Node: SG×MATH×Z0×Learner×Node×JC-PDIS
Prereq: [PROB-BASICS, STAT-DATA]
Outputs: inference readiness
LoadProfile: high
PhaseTarget: {P2 by JC2}
TransferTests: {distribution selection + calculation}
Sensors: {TR, VFR}
FailureModes: {WrongDistributionChoice}
RepairLoops: {distribution selector rubric}
FenceRules: enforce selector before timed
Node: SG×MATH×Z0×Learner×Node×JC-DEQ (H2)
Prereq: [JC-CALC-DIFF, JC-CALC-INTEG]
Outputs: model systems
LoadProfile: high
PhaseTarget: {P2 by JC2}
TransferTests: {separable DE; modeling}
Sensors: {TR}
FailureModes: {SetupFailure}
RepairLoops: {template bank + drills}
FenceRules: template enforcement
========================================================
6) CORE EDGES (PREREQUISITE + TRANSFER) — v0.1
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Edge: SG×MATH×Z0×Operator×Edge×E-FRAC→RPP
From: FRAC-EQUIV
To: RPP-RATIO
Weight: very high
TypicalFailure: PartWholeSwap
RepairBridge: bar model + ratio table
Edge: SG×MATH×Z0×Operator×Edge×E-RPP→ALG
From: RPP-PROPORTION
To: ALG-EXPRESSIONS
Weight: high
TypicalFailure: wrong unit / wrong variable mapping
RepairBridge: unit tagging + equation templates
Edge: SG×MATH×Z0×Operator×Edge×E-WP→ALG
From: WP-BAR-MODEL
To: ALG-EQ-LINEAR
Weight: high
TypicalFailure: setup failure
RepairBridge: sentence parsing protocol
Edge: SG×MATH×Z0×Operator×Edge×E-ALG→AM
From: ALG-EXPRESSIONS
To: AM-ALGEBRA-FLUENCY
Weight: very high
TypicalFailure: brittle algebra
RepairBridge: algebra hygiene + speed ladder
Edge: SG×MATH×Z0×Operator×Edge×E-AM→JC-CALC
From: AM-CALC-PRE
To: JC-CALC-DIFF
Weight: very high
TypicalFailure: hidden prereq debt
RepairBridge: algebra patch + function concept pack
========================================================
7) CIVOS-HD SENSOR PACK (MATH EDITION) — v0.1
========================================================
SensorPack: SG×MATH×Z0×Tutor×SensorPack×SENS-MATH-HD
Inputs:
- ERC, SII, TR, VFR, BN, TTC
Derived:
- DriftVelocity: d(TR)/dt, d(SII)/dt
- Fence Timing: Θ, Λ (qualitative if no precise times)
Triggers:
- TR < 70% on mixed sets → Stitch weakest prerequisite chain
- VFR spikes on variation → increase variation exposure + reduce scaffolding
- SII high under timing → speed ladder + timed ramp
- BN > 3 with TTC < 8w → truncate scope to core nodes + stitch essentials
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8) FENCE RULES (GLOBAL STOP-LOSS) — v0.1
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FenceRules.Global:
- If (TTC short) AND (BN high) → TRUNCATE scope immediately
- If ERC>=3 on same error type → isolate error class before continuing
- If SII deteriorates week-on-week → reduce load + rebuild buffer
- If TR fails across 2+ formats (TT0, TT1, TT-V) → treat as meaning-layer break (NIT-math) and repair concept
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9) CH/ai SCHEDULER HOOK (OUTPUT SPEC) — v0.1
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CH/ai.Inputs:
- TTC (weeks)
- AvailableHoursPerWeek (buffer)
- NodePhaseScores (per node)
- BN (backlog nodes)
- EdgeWeights (prereq criticality)
- VolatilityIndex (school events)
CH/ai.Outputs:
- WeeklyRoutePlan: [RepairNodes] + [StabilityDrills] + [LoadSims]
- DowngradeLogic: what to drop first when TTC tight
- StitchPlan: order of prerequisite repair (highest edge weight first)
- ReTestSchedule: when to run TT0/TT1/TT-V/TT-M
DowngradeLogic (default):
1) Drop low-weight enrichment nodes
2) Keep prereq-critical nodes + WP structure
3) Delay full-paper sims until node stability achieved
4) Run micro-sims weekly once P2 stable across core nodes
========================================================
10) REQUIRED SHORT FAILURE MODE TRACE (CANONICAL)
========================================================
Trace:
FRAC drift → RPP instability → ALG brittleness → AMATH rejection → JC pace overload → P2→P0 exam shock
Fence Repair:
Detect TR fall + ERC loops early → Truncate → Stitch FRAC/RPP/ALG chain → rebuild buffer → timed transfer ramps → maintain P2/P3
========================================================
END: SG-MATH Master Graph v0.1
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WORDPRESS PASTE-READY PAGE STRUCTURE
H1: Singapore Mathematics Syllabus (Primary→JC) as a Lattice — SG-MATH Master Graph v0.1
H2: Why a “Graph” beats a syllabus list (Detect→Predict→Repair)
H2: Phase (P0–P3) and Zoom (Z0–Z6) in Singapore Math
H2: Primary Master Nodes (NUM/FRAC/RPP/WP/GEO)
H2: Secondary Nodes (E-Math + A-Math) and the Algebra Bottleneck
H2: JC Nodes (Calculus, Vectors, Complex, Distributions)
H2: Core Edges (Prerequisite Dependencies)
H2: CivOS-HD Sensor Pack + Fence Rules (Stop-loss + Stitching)
H2: CH/ai Scheduler Hook (how to generate weekly route plans)
H2: Failure Mode Trace (short) + Repair Trace (short)