REGISTRY.MathOS.v2.0
Compatibility:
  Unified-CivOS v2.0
  CivOS-HD vNext+HD
Roles:
  AVOO (Architect, Visionary, Oracle, Operator)
Core Law:
  Stability ↔ (G>D) AND (Ω_real>Ω_crit)
WarOS Lens:
  DeadlineLock := TTC<=TTC_min
  ConflictTrigger := DeadlineLock AND dΩ/dt<0 AND (d²S spike OR R>1 OR FloorStability collapse)
Fence:
  Truncate() then Stitch() then Promote()

MODULE v2.0
ID: CIVOS×MATH×Z6×PILLAR×MathOS_Lattice_Pillar×v2.0
Type: Pillar
Zoom: Z6
Definition: Civilisation-grade MathOS lattice spec (Node×Bind×Weight, AVOO, WarOS clocks, Fence).
BindsTo:
  CIVOS×MATH×CORE×Lattice×v2.0
  CIVOS×MATH×CORE×Fence×v2.0
  CIVOS×MATH×CORE×Sensors×v2.0
  CIVOS×MATH×CORE×Protocols×v2.0

CORE v2.0
ID: CIVOS×MATH×CORE×Lattice×v2.0
Type: Core
Definition: Node×Bind×Weight with TR under load + FloorStability; Promotion + Fence rules.

MODULE v2.0
ID: CIVOS×MATH×Z0×MODULE×MathOS_PRIMARY×v2.0
Type: RuntimeModule
Zoom: Z0→Z2
Definition: Primary foundations + representation + transfer; detects paper-spam masking.
MODULE v2.0
ID: CIVOS×MATH×Z2×MODULE×MathOS_PSLE×v2.0
Type: RuntimeModule
Zoom: Z2
Definition: PSLE deadline-lock runtime; floor+model stability; conflict corridor protection.
MODULE v2.0
ID: CIVOS×MATH×Z0×MODULE×MathOS_SEC_EMATH×v2.0
Type: RuntimeModule
Zoom: Z0→Z2
Definition: Secondary E-Math transfer under interference; binds ExamClockOS.SEC.
MODULE v2.0
ID: CIVOS×MATH×Z0×MODULE×MathOS_AMATH×v2.0
Type: RuntimeModule
Zoom: Z0→Z2
Definition: Additional Math multi-step chain lattice; StepStability; binds ExamClockOS.SEC.

DEPENDENCY v1.0
ID: CIVOS×EXAM×SEC×Z2×MODULE×ExamClockOS_SEC×v1.0
Type: Dependency
Definition: WA/EOY/Prelim/N/O as deadline locks; TTC computation; conflict trigger inputs.
DEPENDENCY v2.0
ID: CIVOS×EXAM×PSLE×Z2×MODULE×PSLEMathExamOS×v2.0
Type: Dependency
Definition: PSLE clock runtime; TTC_PSLE; conflict corridor protection.

SENSOR v2.0
ID: CIVOS×MATH×O×Sensor×TR_UnderLoad×v2.0
Role: Oracle
Definition: Transfer reliability under time + mixed topics + novel context.
Outputs: PromotionEligibility, ConflictContribution
SENSOR v2.0
ID: CIVOS×MATH×O×Sensor×FloorStability×v2.0
Role: Oracle
Definition: Minimum stable floor (fluency floor for primary/PSLE; step stability for A-Math).
Outputs: RiskOfOptionDeath, ConflictContribution
SENSOR v2.0
ID: CIVOS×MATH×O×Sensor×Shear_S×v2.0
Role: Oracle
Definition: mismatch distance between claims/grades and TR reality.
Outputs: dS, d²S regime detection
SENSOR v2.0
ID: CIVOS×MATH×O×Sensor×TTC_ExamClock×v2.0
Role: Oracle
Definition: time-to-deadline lock (WA/EOY/Prelim/N/O/PSLE).
Outputs: DeadlineLock, ConflictContribution
SENSOR v2.0
ID: CIVOS×MATH×O×Sensor×ErrorSignature×v2.0
Role: Oracle
Definition: ranked error causes {concept, method, careless, language, time, algebra-slip}.
Outputs: FocusSet selection, protocol routing
SENSOR v2.0
ID: CIVOS×MATH×O×Sensor×CoverageGap×v2.0
Role: Oracle
Definition: topics not stable at TR target; drives corridor width decision.
Outputs: CorridorPlan input

PROTOCOL v2.0
ID: CIVOS×MATH×A×Protocol×CorridorPlanGenerator×v2.0
Role: Architect
Definition: converts diagnostics + TTC into TopicOrder×DrillMix×ReviewTopology×TimeBudget×BufferPlan.
Outputs: CorridorPlan v2.0
PROTOCOL v2.0
ID: CIVOS×MATH×Op×Protocol×Fence_Truncate×v2.0
Role: Operator
Definition: freezes expansion, narrows to Top-3 bind chains, shortens feedback latency.
Outputs: stabilized floor, stopped d²S escalation
PROTOCOL v2.0
ID: CIVOS×MATH×Op×Protocol×Fence_Stitch×v2.0
Role: Operator
Definition: bind repair + spaced retrieval + transfer training + timed stability.
Outputs: TR stability across contexts
PROTOCOL v2.0
ID: CIVOS×MATH×Op×Protocol×PromoteRule×v2.0
Role: Operator
Definition: promotes only when TR>=target across 3 contexts + Day1/3/7 retrieval stable.
Outputs: promotion decision

EXEC_PACK v1.0
ID: CIVOS×MATH×Op×ExecPack×Primary_SessionPack×v1.0
Definition: 35–45 min primary sessions: fluency + bind repair + word transfer + representation.
EXEC_PACK v1.0
ID: CIVOS×MATH×Op×ExecPack×PSLE_SessionPack×v1.0
Definition: 45–60 min PSLE sessions: floor + model mastery + mixed transfer + error elimination.
EXEC_PACK v1.0
ID: CIVOS×MATH×Op×ExecPack×Sec_EMath_SessionPack×v1.0
Definition: 50–65 min secondary sessions: micro-repair + mixed sets + long problem + retrieval.
EXEC_PACK v1.0
ID: CIVOS×MATH×Op×ExecPack×Sec_AMath_SessionPack×v1.0
Definition: 60–75 min A-Math sessions: slip audit + bind chain + timed long Q + retrieval.
EXEC_PACK v1.0
ID: CIVOS×MATH×Op×ExecPack×Conflict_48to72h×v1.0
Definition: conflict mode daily loop: score floor + timed micro-sets + immediate correction; feedback<24h.

RUNNER v2.0
ID: CIVOS×MATH×RUNNER×Pillar_Level×v2.0
Definition: returns Z0→Z6 impact + conflict status + plan outputs (A/O/Op).
RUNNER v2.0
ID: CIVOS×MATH×RUNNER×Primary×v2.0
Definition: outputs diagnostics + corridor plan + sessions + promotion.
RUNNER v2.0
ID: CIVOS×MATH×RUNNER×PSLE×v2.0
Definition: outputs 12–16 week plan + clock-based conflict loop.
RUNNER v2.0
ID: CIVOS×MATH×RUNNER×Sec_EMath×v2.0
Definition: outputs mixed diagnostic + plan + exam-clock integration.
RUNNER v2.0
ID: CIVOS×MATH×RUNNER×AMath×v2.0
Definition: outputs mixed+long diagnostic + StepStability + plan + conflict loop.

PLACE_IMPLEMENTATION v2.0
ID: SGP×BUKIT_TIMAH×MATH×Z4×Implementation×MathOS×v2.0
Type: PlaceBinding
Definition: Bukit Timah implementation of MathOS modules + TuitionOS routing + execution packs.
Implements:
  CIVOS×MATH×Z0×MODULE×MathOS_PRIMARY×v2.0
  CIVOS×MATH×Z2×MODULE×MathOS_PSLE×v2.0
  CIVOS×MATH×Z0×MODULE×MathOS_SEC_EMATH×v2.0
  CIVOS×MATH×Z0×MODULE×MathOS_AMATH×v2.0
DependsOn:
  CIVOS×EXAM×SEC×Z2×MODULE×ExamClockOS_SEC×v1.0
  CIVOS×EXAM×PSLE×Z2×MODULE×PSLEMathExamOS×v2.0
  CIVOS×MATH×A×Protocol×CorridorPlanGenerator×v2.0
  CIVOS×MATH×Op×Protocol×Fence_Truncate×v2.0
  CIVOS×MATH×Op×Protocol×Fence_Stitch×v2.0
  CIVOS×MATH×Op×Protocol×PromoteRule×v2.0

START_HERE.MathOS.v2.0
1) Run TR_UnderLoad diagnostic + ErrorSignature.
2) Compute TTC (next exam clock).
3) If ConflictTrigger true: run Conflict_48to72h pack.
4) Else: run CorridorPlanGenerator.
5) Execute SessionPack + Day1/3/7 retrieval.
6) Promote only when TR stable across 3 contexts.

CivOS-HD.v2.0 (Math Instantiation)
State:
  P ∈ {P0,P1,P2,P3}
  Z ∈ {Z0..Z6}
  G(t), D(t), R = D/G
  Ω_real(t), S(NL↔SL), TTC
  Derivatives: dG/dt, dD/dt, dΩ/dt, dS/dt, d²S/dt², ΔCoupling/Δt
  NIT := (Ω_real < Ω_crit) AND (IrreversibleCost=true)
Roles (AVOO):
  Architect(A): corridor permutation generator (routing)
  Visionary(V): safe Ω expansion
  Oracle(O): sensors + thresholds + derivative detection
  Operator(Op): execution + repair (Fence: truncate/stitch)
WarOS Conflict (Education form):
  DeadlineLock := assessment clocks compress TTC
  ConflictTrigger :=
     DeadlineLock AND dΩ/dt<0 AND (d²S spike OR R>1 OR FloorStability collapses)

LATTICE.Math.v2.0
Node := concept-capability unit (e.g., place value, algebra manipulation, function mapping)
Bind := prerequisite edge (Node_i -> Node_j)
Weight := bind thickness (transfer reliability contribution)
Context := {time_limit, mixed_topics, novel_context, stress}
TR(Node) := P(correct | Context)
FloorStability := minimum stable performance for core nodes
Promotion:
  Promote(Node) only when:
    TR(Node) >= target across 3 contexts AND Retrieval(Day1/3/7) stable

SPEC.MathOS.PRIMARY.v2.0
Zoom:
  Z0 student, Z0 family routines; contributes to Z1 class and Z2 school
Core Nodes:
  N0_NumberSense
  N1_PlaceValue
  N2_OperationsFluency
  N3_FractionsDecimalsMeaning
  N4_RatioUnitary (upper pri)
  N5_WordProblemParsing (language bind)
  N6_BarModelRepresentation
  N7_MultiStepPlanning
  N8_SpeedAccuracyLowStress
Key Binds:
  N0->N2
  N1->N3->N4
  N5->N6->N7
  N2->N6
Primary Sensors:
  FluencyFloor := stable speed×accuracy on N0–N2
  TR_primary := transfer success on novel word problems
  ErrorSignature := {careless, concept, method, language, time}
  FeedbackLatency
  Shear S := distance(parent/grade-claims, TR_primary)
Failure Mask:
  PaperSpam := hours↑ but bind weights unchanged
Fence:
  if R>1 for τ OR d²S spike -> Truncate() then Stitch()

SPEC.MathOS.PSLE.v2.0
Clock:
  TTC_PSLE
  DeadlineLock := (TTC_PSLE <= TTC_min)
PSLE Nodes emphasis:
  FluencyFloor (N0–N2)
  Parsing+Model mapping (N5–N6)
  Multi-step planning under time (N7)
PSLE Sensors:
  TR_PSLE (timed, mixed, novel)
  ModelStability := P(correct mapping: text->bar model->steps)
  FluencyFloor stability
  d²S spike, dΩ/dt
ConflictTrigger:
  DeadlineLock AND dΩ/dt<0 AND (d²S spike OR R>1 OR FluencyFloor unstable)
Conflict Protocol:
  Freeze type spread; protect score floor; 48–72h repair loops; feedback<24h

SPEC.MathOS.SEC_EMATH.v2.0
Core Nodes:
  S0_FractionsRatioRate
  S1_AlgebraManipulation
  S2_EquationsInequalities
  S3_GeometryAnglesSimilarity
  S4_Mensuration
  S5_StatsProbability
  S6_CoordinateGeometry
  S7_FunctionsGraphs (where applicable)
  S8_Modeling (cross-cutting)
Key Binds:
  S0->S1->S2
  S1->S7
  S3->(many geometry chains)
  S8->ALL
Sensors:
  TR_underLoad := timed mixed-topic transfer
  FeedbackLatency
  Shear S := distance(reported grade, TR_underLoad)
  CoverageGap := nodes not stable
  d²S spike, dΩ/dt
Fence:
  if TTC_exam short OR R>1 -> Truncate(); Stitch()

SPEC.MathOS.AMATH.v2.0
Core Nodes:
  A0_AlgebraCore (indices, surds, factorisation, log laws)
  A1_FunctionsGraphs (transformations, inverse)
  A2_Trigonometry (identities->equations)
  A3_CoordinateGeometry
  A4_Calculus (differentiation + applications)
  A5_ExponentialLog
  A6_LongQuestionReasoning (proof/show-that chains)
  A7_Modeling (cross-cutting)
Key Sensors:
  StepStability := probability(no slip across multi-step chain)
  TR_amath := timed mixed-topic + long question transfer
  ErrorSignature := {concept, algebra-slip, method-choice, careless, time}
  d²S spike, dΩ/dt, TTC_exam
ConflictTrigger:
  DeadlineLock AND dΩ/dt<0 AND (d²S spike OR R>1 OR StepStability collapse)
Fence:
  Truncate syllabus expansion; repair top bind chains; rebuild StepStability; then stitch transfer

FENCE.Math.v2.0
Trigger:
  if TTC short OR R>1 for τ OR d²S spike OR (FloorStability collapse):
      Truncate()
      Stitch()
Truncate():
  - freeze expansion width
  - narrow to Top-3 bind chains (highest yield)
  - shorten feedback latency (<24–72h)
  - restore buffers (sleep/time)
Stitch():
  - BindRepair (prereqs)
  - SpacedRetrieval (Day1/3/7)
  - TransferTraining (mixed topics, novel contexts)
  - StressStability (timed sets)
Promote():
  - promote only when TR stable across 3 contexts + retrieval stable

CIVILISATION_GRADE_IMPORTANCE.Math.v2.0
Let:
  HRL := Human Regenerative Lattice
  G := capability regeneration rate
  D := capability decay rate
  Ω_real := real option space
MathOS impacts:
  OperatorQuality ↑  => execution reliability ↑ => D ↓
  OracleQuality ↑    => measurement fidelity ↑ => prevents truth drift => D ↓
  ArchitectCapacity ↑=> better routing + redundancy => Ω_real ↑
  VisionarySafety ↑  => Ω expansion without brittleness => avoids collapse
Failure (systemic Math collapse):
  TR_underLoad low across cohorts
  -> engineering + finance + governance measurement fails
  -> repair latency increases
  -> coupling failures synchronize across lanes
  -> d²S spike at Z5
  -> Ω_real crosses Ω_crit
  -> NIT (irreversible decline corridor)
Therefore:
  Math Lattice Upgrade is a civilisation-level stabilizer: it increases G, decreases D, preserves Ω.

RECORD v2.0
ID: SGP×BUKIT_TIMAH×MATH×Z0×O×Sensor×TR_UnderLoad×v2.0
Type: Sensor
Definition: Measures transfer reliability under time + mixed topics + novel context.
Thresholds: TR_target, TR_floor, d²S_spike
Outputs: PS_fast, ConflictTrigger, PromotionEligibility
RECORD v2.0
ID: SGP×BUKIT_TIMAH×MATH×Z0×O×Sensor×FloorStability×v2.0
Type: Sensor
Definition: Minimum stable performance on core nodes (fluency floor / step stability).
Outputs: RiskOfOptionDeath, TTC contribution
RECORD v2.0
ID: SGP×BUKIT_TIMAH×MATH×Z0×A×Protocol×CorridorPlanGenerator×v2.0
Type: Protocol
Role: Architect
Definition: Generates TopicOrder×DrillMix×ReviewTopology×TimeBudget from diagnostics+TTC.
Outputs: CorridorPlan v2.0
RECORD v2.0
ID: SGP×BUKIT_TIMAH×MATH×Z0×Op×Protocol×Fence_TruncateStitch×v2.0
Type: Protocol
Role: Operator
Definition: Executes truncation then stitching until TR stable across contexts.
Evidence: TR improves + shear decreases + retrieval stable

LATTICE.Math.v2.0 (Unified)
Node := concept-capability unit
Bind := prerequisite edge (Node_i -> Node_j)
Weight := bind thickness
TR(Node) := P(correct | time_limit, mixed_topics, novel_context, stress)
FloorStability := minimum stable performance on core nodes
Promotion:
  Promote(Node) only when:
    TR >= target across 3 contexts AND Retrieval(Day1/3/7) stable
Fence:
  if TTC short OR R>1 for τ OR d²S spike OR FloorStability collapses:
      Truncate()
      Stitch()

CIV_GRADE_WHY.Math.v2.0
MathOS manufactures:
  Operators (execution reliability under load)
  Oracles (measurement + calibration fidelity)
  Architects (corridor design + abstraction routing)
Systemic Math collapse =>
  measurement drift + engineering throughput loss + coordination failures
  -> repair latency rises
  -> multi-lane coupling synchronizes failures
  -> Ω_real shrinks below Ω_crit
  -> NIT (irreversible decline corridor)
Therefore Math Lattice Upgrade =>
  increases G, decreases D, preserves Ω_real (civilisation stabilizer)

SPEC.MathOS.PRIMARY.v2.0
Zoom:
  Z0 student + Z0 family routines; impacts Z1 class and Z2 school
Core Nodes:
  N0_NumberSense
  N1_PlaceValue
  N2_OperationsFluency
  N3_FractionsDecimalsMeaning
  N4_RatioUnitary (upper pri)
  N5_WordProblemParsing (language bind)
  N6_BarModelRepresentation
  N7_MultiStepPlanning
  N8_SpeedAccuracyLowStress
Key Binds:
  N0->N2
  N1->N3->N4
  N5->N6->N7
  N2->N6
Sensors:
  FluencyFloor, TR_primary, ErrorSignature, FeedbackLatency, Shear S, TTC_assessment
Derivatives:
  dTR/dt, dFluency/dt, dS/dt, d²S/dt², dΩ/dt
Failure Mask:
  PaperSpam := hours↑ but FluencyFloor/TR unchanged across 2 weeks

PROTOCOL.Truncate.PRIMARY.v2.0 (48–72h)
Stop: paper spam, premature shortcuts, widening topic spread during leaks
Do: Top-2 binds/day repair + daily fluency sprint + feedback <72h (or <24h if close)
PROTOCOL.Stitch.PRIMARY.v2.0 (2–8 weeks)
BindRepair + Day1/3/7 retrieval + TransferSets (novel contexts) + LowStressTiming
Promote: FluencyFloor stable + TR_primary >= target across 3 contexts

RECORD v2.0
ID: SGP×BUKIT_TIMAH×PRI_MATH×Z0×O×Sensor×FluencyFloor×v2.0
Type: Sensor
Definition: Minimum stable fundamentals performance required for transfer.
Outputs: Risk + ConflictContribution
RECORD v2.0
ID: SGP×BUKIT_TIMAH×PRI_MATH×Z0×Op×Protocol×Fence_TruncateStitch×v2.0
Type: Protocol
Definition: Primary truncation+stitching loop.
Evidence: FluencyFloor↑ and TR_primary↑ across contexts

RUNNER.PRI_MATH.v2.0
Input: P level, recent work, next assessment date, time/week.
Output: diagnostics + CorridorPlan + daily sessions + promotion rule.

SPEC.MathOS.PSLE.v2.0
Clock:
  TTC_PSLE
  DeadlineLock := (TTC_PSLE <= TTC_min)
Emphasis Nodes:
  FluencyFloor (N0–N2)
  Parsing+Model mapping (N5–N6)
  Multi-step planning under time (N7)
Sensors:
  FluencyFloor, TR_PSLE, ModelStability, ErrorSignature, FeedbackLatency, Shear S, d²S, dΩ/dt

CONFLICTTRIGGER.PSLE.v2.0
ConflictTrigger :=
  DeadlineLock AND dΩ/dt<0 AND (d²S spike OR R>1 OR FluencyFloor unstable)
PROTOCOL.Conflict.PSLE.v2.0 (48–72h)
Freeze: question-type spread expansion
Focus: FluencyFloor + top model types + error elimination
Feedback: <24h
Exit: TR stabilizes + dΩ/dt stops shrinking

PROTOCOL.Stitch.PSLE.v2.0
1) FoundationBindRepair
2) ModelTypeMastery
3) TransferSets (novel contexts)
4) LowStressTiming
5) Full-paper sims only after stability
Promote: TR_PSLE>=target across 3 contexts + FluencyFloor stable

RECORD v2.0
ID: SGP×PSLE_MATH×Z2×O×Sensor×ModelStability×v2.0
Type: Sensor
Definition: Success mapping text->model->steps under time.
Outputs: ConflictContribution + PromotionEligibility
RECORD v2.0
ID: SGP×PSLE_MATH×Z2×Op×Protocol×PSLE_Fence_TruncateStitch×v2.0
Type: Protocol
Definition: PSLE truncation+stitching corridor protection.
Evidence: FluencyFloor stable + TR_PSLE improves across contexts

RUNNER.PSLE_MATH.v2.0
Input: P5/P6 work, TTC_PSLE, time/week.
Output: 12–16 week corridor + weekly sensors + emergency 72h loop if triggered.

SPEC.MathOS.SEC_EMATH.v2.0
Nodes:
  S0_FractionsRatioRate
  S1_AlgebraManipulation
  S2_EquationsInequalities
  S3_GeometryAnglesSimilarity
  S4_Mensuration
  S5_StatsProbability
  S6_CoordinateGeometry
  S7_FunctionsGraphs
  S8_Modeling (cross-cutting)
Binds:
  S0->S1->S2
  S1->S7
  S3->(geometry chains)
  S8->ALL
Sensors:
  TR_underLoad, CoverageGap, ErrorSignature, FeedbackLatency, Shear S, TTC_exam, d²S, dΩ/dt

BIND.ExamClock.SEC.v2.0
DeadlineLock := (TTC_exam <= TTC_min) OR (prelim/O/N phase)
ConflictTrigger := DeadlineLock AND dΩ/dt<0 AND (d²S spike OR R>1)

PROTOCOL.Truncate.SEC_EMATH.v2.0
Freeze: syllabus width expansion
Focus: Top-3 choke bind chains
Feedback: <24–72h
Goal: stop d²S escalation; stabilize TR_floor
PROTOCOL.Stitch.SEC_EMATH.v2.0
BindRepair + Day1/3/7 + MixedTopicTransfer + StressStability (timed)
Promote: TR_underLoad>=target across 3 contexts + stable ErrorSignature

RECORD v2.0
ID: SGP×SEC_MATH×Z0×O×Sensor×CoverageGap×v2.0
Type: Sensor
Definition: topics not stable at TR target; drives routing.
Outputs: CorridorPlan inputs + ConflictContribution
RECORD v2.0
ID: SGP×SEC_MATH×Z0×Op×Protocol×Fence_TruncateStitch×v2.0
Type: Protocol
Definition: Secondary fence loop.
Evidence: TR under load rises across contexts; gap shrinks

RUNNER.SEC_EMATH.v2.0
Input: level, scripts, TTC_exam, time/week.
Output: diagnostic + CorridorPlan + weekly sensors + conflict plan if needed.

SPEC.MathOS.AMATH.v2.0
Nodes:
  A0_AlgebraCore (indices, surds, factorisation, log laws)
  A1_EquationsIneq
  A2_FunctionsGraphs (transformations, inverse)
  A3_Trigonometry (identities->equations->graphs)
  A4_CoordinateGeometry
  A5_Calculus (diff + applications)
  A6_ExponentialLog
  A7_LongQuestionReasoning
  A8_Modeling (cross-cutting)
Binds:
  A0->A1->A2->A5
  A0->A6
  A3->A5
  A0->A4
  A8->ALL
Sensors:
  StepStability, TR_amath, ErrorSignature(algebra-slip), Shear S, TTC_exam, d²S, dΩ/dt

CONFLICTTRIGGER.AMATH.v2.0
ConflictTrigger :=
  DeadlineLock AND dΩ/dt<0 AND (d²S spike OR R>1 OR StepStability collapses)

PROTOCOL.Truncate.AMATH.v2.0
Freeze: syllabus expansion
Focus: Top-3 bind chains + slip elimination
Feedback: <24h
Goal: restore StepStability in long questions
PROTOCOL.Stitch.AMATH.v2.0
BindRepair + Day1/3/7 + MixedTransfer + TimedLongQuestionTraining
Promote: StepStability stable + TR_amath>=target across 3 contexts

RECORD v2.0
ID: SGP×AMATH×Z0×O×Sensor×StepStability×v2.0
Type: Sensor
Definition: probability of algebraic correctness across multi-step chain.
Outputs: ConflictContribution + PromotionEligibility
RECORD v2.0
ID: SGP×AMATH×Z0×Op×Protocol×AMATH_Fence_TruncateStitch×v2.0
Type: Protocol
Definition: A-Math fence loop.
Evidence: long-question stability improves; slip rate decreases

RUNNER.AMATH.v2.0
Input: Sec3/4 scripts, TTC_exam, time/week.
Output: mixed+long diagnostic, StepStability, CorridorPlan, conflict plan if triggered.

CivOS-HD.Math.v2.0
State:
  P ∈ {P0,P1,P2,P3}
  Z ∈ {Z0..Z6}
  G(t), D(t), R=D/G
  Ω_real(t), S(NL↔SL), TTC
  Derivatives: dΩ/dt, dS/dt, d²S/dt², dG/dt, dD/dt, ΔCoupling/Δt
  NIT := (Ω_real<Ω_crit) AND (IrreversibleCost=true)
Roles (AVOO):
  Architect(A): corridor permutation generator (routing under constraints)
  Visionary(V): safe Ω expansion (only when buffers stable)
  Oracle(O): sensors + thresholds + derivative detection (truth stability)
  Operator(Op): execution + repair (Fence: truncate/stitch)
WarOS (education form):
  DeadlineLock := TTC <= TTC_min
  ConflictTrigger :=
     DeadlineLock AND dΩ/dt<0 AND (d²S spike OR R>1 OR FloorStability collapse)

LATTICE.Math.v2.0
Node := concept-capability unit
Bind := prerequisite edge (Node_i -> Node_j)
Weight := bind thickness (contributes to transfer reliability)
Context := {time_limit, mixed_topics, novel_context, stress}
TR(Node) := P(correct | Context)
FloorStability := minimum stable performance on core nodes (fluency/step-stability)
Promotion Rule:
  Promote(Node) iff:
    TR(Node) >= target across 3 contexts AND Retrieval(Day1/3/7) stable
Fence Rule:
  if TTC short OR R>1 for τ OR d²S spike OR FloorStability collapses:
      Truncate()
      Stitch()

LAW.MathOS.v2.0
If capability regeneration rate G(t) falls below decay D(t) for long enough:
  R=D/G > 1  => lattice thins
  -> error accumulation + truth drift increase
  -> repair latency exceeds stress cycle length
  -> coupling failures synchronize across lanes
  -> Ω_real shrinks below Ω_crit
  -> NIT crossing (irreversible decline corridor)

ROLE_OUTPUT.MathOS.v2.0
OperatorQuality↑ => execution reliability↑ => D↓
OracleQuality↑   => measurement fidelity↑ => prevents truth drift => D↓
ArchitectCapacity↑ => routing + redundancy↑ => Ω_real↑
VisionarySafety↑ => controlled expansion avoids brittleness => avoids collapse

ZMAP.MathOS.v2.0
Z0 (Individual):
  - TR under load determines exam stability and self-efficacy
  - prevents P3→P0 trap under variation
Z1 (Family/Peer):
  - schedule stability + feedback latency; family buffers prevent panic drift
Z2 (School):
  - assessment clocks create DeadlineLocks; curriculum routing defines bind thickness
Z3 (Industry):
  - engineering/finance/ops demand Operators + Oracles; weak math raises systemic error rates
Z4 (District/City node):
  - education gravity + tutor routing quality influences local cohort stability (e.g., Bukit Timah)
Z5 (Nation):
  - national capability regeneration: STEM pipeline, productivity, governance measurement
Z6 (World):
  - global coordination + innovation throughput; weak math increases fragility in global systems

WAROS.MathOS.v2.0
Conflict in education := DeadlineLock + option death risk
DeadlineLock := TTC <= TTC_min
OptionDeathMechanisms:
  - repair window closes
  - stress increases load; interference rises
  - feedback latency becomes fatal
  - streaming/combi consequences become irreversible
Therefore:
  ConflictTrigger => switch to ConflictMode:
    freeze expansion, protect floor, 48–72h repair cycles, feedback <24h

MODULES.MathOS.v2.0
M1: MathOS.PRIMARY.v2.0
M2: MathOS.PSLE.v2.0
M3: MathOS.SEC_EMATH.v2.0  (binds ExamClockOS.SEC)
M4: MathOS.AMATH.v2.0      (binds ExamClockOS.SEC)

FENCE.Math.v2.0
Truncate():
  - freeze syllabus width expansion
  - narrow to Top-3 highest-yield bind chains
  - shorten feedback latency (<24–72h)
  - restore buffers (sleep/time)
Stitch():
  - BindRepair (prereqs)
  - SpacedRetrieval (Day1/3/7)
  - TransferTraining (mixed + novel)
  - StressStability (timed sets)
Promote():
  - TR >= target across 3 contexts + retrieval stable

RECORD v2.0
ID: CIVOS×MATH×O×Sensor×TR_UnderLoad×v2.0
Type: Sensor
Definition: transfer reliability under time + mixed topics + novel context.
Outputs: ConflictTrigger contribution + PromotionEligibility
RECORD v2.0
ID: CIVOS×MATH×O×Sensor×FloorStability×v2.0
Type: Sensor
Definition: minimum stable performance floor (fluency / step-stability).
Outputs: RiskOfOptionDeath + TTC contribution
RECORD v2.0
ID: CIVOS×MATH×A×Protocol×CorridorPlanGenerator×v2.0
Type: Protocol
Definition: generates TopicOrder×DrillMix×ReviewTopology from diagnostics + TTC.
RECORD v2.0
ID: CIVOS×MATH×Op×Protocol×Fence_TruncateStitch×v2.0
Type: Protocol
Definition: executes truncation+stitching until TR stable across contexts.

BIND.PlaceImplementation.v2.0
Place: SGP×BUKIT_TIMAH
Implements:
  - MathOS.PRIMARY.v2.0
  - MathOS.PSLE.v2.0
  - MathOS.SEC_EMATH.v2.0
  - MathOS.AMATH.v2.0
With:
  - TuitionOS routing + Operator Daily Execution Pack
  - ExamClockOS.SEC v1.0 + PSLEMathExamOS v2.0

RUNNER.CIV_GRADE_MATHOS.v2.0
Input: Level, TTC, time/week, diagnostics.
Output:
  - Z-level impact statement (Z0→Z6)
  - ConflictTrigger status
  - CorridorPlan (A) + ThresholdPack (O) + SessionPack (Op)
  - Promotion rules + next-week targets