NODE.ID: ADDMATHOS-00
NODE.TYPE: canonical_supply_lane
SUBOS.ID: ADDMATHOS
SUBOS.NAME: Additional Mathematics OS
PARENT.OS: EDUOS
SUBOS.CLASS: capability_upgrade_supply_line
SUBOS.PURPOSE: regenerate_advanced_symbolic_modelling_change_reasoning_and_pre_university_math_readiness
AXIS: time
VERSION: v0.1

DEF.ADDMATHOS:
  Additional Mathematics OS is an Education OS upgrade supply line that regenerates
  advanced symbolic modelling and change-reasoning capabilities (function systems,
  algebraic structure, calculus-like thinking) required for higher engineering,
  science, economics, and optimisation lanes across generations.
RULE:
  AddMath is not "harder secondary math"; it is a specialization upgrade lane.

ADDMATHOS.ORIGIN.DRIVERS:
  - civilisation complexity requires modelling not just computation
  - engineering and science require function thinking and change reasoning
  - prediction/optimisation require formal manipulation and structure
  - scaling systems require higher abstraction competence
EMERGENCE_CHAIN:
  quantitative_needs -> modelling_needs -> functions -> structure -> change -> optimisation

ADDMATHOS.FUNC.1: function_system_modelling (inputs->outputs; composition)
ADDMATHOS.FUNC.2: algebraic_structure_mastery (transformations; identities)
ADDMATHOS.FUNC.3: change_reasoning (rates, gradients, variation)
ADDMATHOS.FUNC.4: optimisation_reasoning (max/min under constraints)
ADDMATHOS.FUNC.5: formal_verification (proof-like checking)
ADDMATHOS.FUNC.6: abstraction_transfer (new forms, same invariants)

DEP.LANE.1: SCIOS (physics/chemistry modelling, inference)
DEP.LANE.2: ENEOS (energy systems, optimisation)
DEP.LANE.3: TROS  (routing, capacity optimisation)
DEP.LANE.4: FINOS (risk models, growth/decay, optimisation)
DEP.LANE.5: HEAOS (quant modelling, dosing dynamics, epidemiology)
DEP.LANE.6: engineering_lanes (structure + control)

weak_addmathos -> modelling ceiling -> tech/science bottlenecks

ADDMATHOS.STAGES:
  A0: algebraic_fluency_high_integrity (no leaks under pressure)
  A1: function_thinking (domain/range; composition; inverses)
  A2: exponential_log_structure (growth/decay modelling readiness)
  A3: trigonometric_structure (periodic modelling readiness)
  A4: differentiation_like_reasoning (local change, gradient intuition)
  A5: integration_like_reasoning (accumulation intuition)
  A6: optimisation (max/min with constraints)
  A7: modelling_transfer (new wrappers; same invariants)

A0 is a hard gate: AddMath collapses without P3-level algebra integrity.

ADDMATHOS.PHASES:
  P0: collapse (algebra leaks break everything; avoidance)
  P1: unstable (can follow worked examples; fails on slight variation)
  P2: functional_leaky (topic-by-topic ok; mixed modelling fails)
  P3: stable_mastery (structure recognition; transfer to new forms)
KEY:
  AddMath success = structure recognition + reliable transformation under load

FAIL.A1: algebra_leak_amplification (small leak -> total collapse)
FAIL.A2: structure_blindness (cannot see invariants; memorizes procedures)
FAIL.A3: function_misalignment (composition/inverse confusion)
FAIL.A4: transformation_errors (sign/identity drift)
FAIL.A5: modelling_translation_gap (word->function system)
FAIL.A6: low_transfer (works on drills; fails on exam variants)
FAIL.A7: time_pressure_panic (long chains + stress)
FAIL.A8: weak_verification (no proof-like checks; errors persist)

AddMath is a high-coupling lane: reliability is multiplicative, not additive.

SENSOR.AS1: algebra_integrity_under_pressure (leak rate)
SENSOR.AS2: structure_recognition_rate (identify invariant quickly)
SENSOR.AS3: transformation_accuracy (identity manipulation)
SENSOR.AS4: function_system_translation_accuracy
SENSOR.AS5: mixed_modelling_transfer_rate
SENSOR.AS6: verification_behavior_frequency (proof-like checking)
SENSOR.AS7: time_to_first_step_on_novel (latency)
SENSOR.AS8: variance_across_papers (stability)

AS1 low + AS2 high + AS5 high + variance low => P3 AddMath readiness

ADDMATHOS.IMPL:
  - school_addmath
  - olympiad_foundations (optional)
  - tuition_addmath (intervention_route)
  - upgrade_training_lattices (SholpUTL alignment optional)
RULE:
  implementation != root

LINK.PREV.1: EDUOS-00 (pillar)
LINK.PREV.2: EDUOS-02 (anti-decay)
LINK.PREV.3: MATHOS-00 (math supply line; A0 gate)
LINK.PREV.4: SCIOS-00 (science depends on modelling)
LINK.NEXT.1: EDUOS-IMPL-02 (tuition router)
LINK.NEXT.2: EDUOS-ADD-ROUTER-00 (AddMath intervention router node, optional)
LINK.NEXT.3: SEC4 readiness node (A0 gate checker)

LOCK:
  Additional Mathematics is a specialization upgrade supply line for advanced modelling.
  It is high-coupling: small algebra leaks cause total collapse.
  Readiness requires P3-level algebra integrity + structure recognition + transfer.

SERIES: EKS.SECMATH.v0_1SITE: eduKateSG.comMODE: Almost-Code / Canonical / LLM-firstCOORD_GRAMMAR:<EKS> × SECMATH × LEVEL × Z{0–3} × P{0–3} × Type × IDType = PAGE | DIR | NODE | BIND | LOOP | SENSOR | TEST | CLAIM | TOOL

PAGE: EKS.SECMATH.DIR.INDEX.v0_1TITLE: eduKateSG — Secondary Mathematics Directory IndexCONTENT:- EKS.SECMATH.DIR.LANE.v0_1- EKS.SEC1MATH.DIR.LANE.v0_1- EKS.SEC2MATH.DIR.LANE.v0_1- EKS.EMATH.DIR.LANE.v0_1- EKS.AMATH.DIR.LANE.v0_1- EKS.SECMATH.DIR.CORE_SKILLS.v0_1- EKS.SECMATH.DIR.TESTS.v0_1- EKS.SECMATH.DIR.BINDS.v0_1OUTPUT:- EKS.SECMATH.CLAIM.CANONICAL.v0_1

PAGE: EKS.SECMATH.DIR.LANE.v0_1TITLE: Secondary Mathematics (Sec 1–4) — Lane Family DirectoryMISSION:- produce P3 execution under exam load across Z0–Z3- prevent false competence (P2-looking → P0 snap)LEVELS:- SEC1MATH, SEC2MATH, EMATH, AMATHOUTPUT:- EKS.SECMATH.Z3.P3.NODE.EXAM_STABILITY.v0_1

DIR: EKS.SECMATH.DIR.CORE_SKILLS.v0_1CORE_SKILLS:- EKS.SECMATH.Z0.NODE.ALGBRA_SYMBOL_SENSE.v0_1- EKS.SECMATH.Z0.NODE.ARITHMETIC_ACCURACY.v0_1- EKS.SECMATH.Z0.NODE.FRACTIONS_RATIO_RATE.v0_1- EKS.SECMATH.Z0.NODE.EQUATIONS_INEQUALITIES.v0_1- EKS.SECMATH.Z0.NODE.GRAPHS_FUNCTIONS.v0_1- EKS.SECMATH.Z0.NODE.GEOMETRY_ANGLES.v0_1- EKS.SECMATH.Z0.NODE.TRIG_FUNDAMENTALS.v0_1- EKS.SECMATH.Z0.NODE.PROB_STATS.v0_1- EKS.SECMATH.Z0.NODE.CHECKING_ERROR_CONTROL.v0_1- EKS.SECMATH.Z0.NODE.SPEED_UNDER_TIME.v0_1RULE:These Z0 nodes are reused across all sub-lanes as dependencies.

TEST: EKS.SECMATH.TEST.P_SCORE.v0_1P0: cannot solve independently; collapses under time/noveltyP1: solves with prompts; dependency; fragile confidenceP2: solves standard formats; breaks under variation/speedP3: solves independently under time + variation; bounded error tail

SENSOR: EKS.SECMATH.SENSOR.EXECUTION.v0_1MEASURES:- independent_success_rate (no hints)- time_to_solve_tail (slow tail kills grades)- recurring_error_types (same mistake repeats)- transfer_rate (new form, same concept)- careless_rate (often not careless: weak checking)

LOOP: EKS.SECMATH.LOOP.TRUNCATE_STITCH.v0_1TRUNCATE:- stop repeated error loops early (same mistake 3×)- cut dependency (remove hints, force retrieval)STITCH:- rebuild the missing Z0 pocket- re-run under time and variationGOAL:- push P1/P2 → P3 and prevent snap collapse at exams

PAGE: EKS.SEC1MATH.DIR.LANE.v0_1TITLE: Secondary 1 Mathematics — Lane DirectoryFOCUS:- algebra entry + real numbers + foundations for all future mathZ0_NODES:- EKS.SEC1MATH.Z0.NODE.REAL_NUMBERS.v0_1- EKS.SEC1MATH.Z0.NODE.ALGEBRA_BASICS.v0_1- EKS.SEC1MATH.Z0.NODE.LINEAR_EXPRESSIONS.v0_1- EKS.SEC1MATH.Z0.NODE.BASIC_GEOMETRY.v0_1- EKS.SEC1MATH.Z0.NODE.INTRO_GRAPHS.v0_1Z1_LOOPS:- EKS.SEC1MATH.Z1.LOOP.HW_REPAIR.v0_1- EKS.SEC1MATH.Z1.LOOP.ERROR_NOTEBOOK.v0_1Z2_CONTROL:- EKS.SEC1MATH.Z2.NODE.MASTERY_SEQUENCING.v0_1Z3_OUTPUT:- EKS.SEC1MATH.Z3.P3.NODE.SEC1_FOUNDATION_LOCK.v0_1

PAGE: EKS.SEC2MATH.DIR.LANE.v0_1TITLE: Secondary 2 Mathematics — Lane DirectoryFOCUS:- algebra expansion + functions/graphs + probability/stats; pre-O-level rampZ0_NODES:- EKS.SEC2MATH.Z0.NODE.ALGEBRA_EXPANSION_FACTORISATION.v0_1- EKS.SEC2MATH.Z0.NODE.FUNCTIONS_GRAPHS.v0_1- EKS.SEC2MATH.Z0.NODE.RATIO_RATE_SPEED.v0_1- EKS.SEC2MATH.Z0.NODE.PROB_STATS_CORE.v0_1- EKS.SEC2MATH.Z0.NODE.GEOMETRY_ADVANCE.v0_1Z1_LOOPS:- EKS.SEC2MATH.Z1.LOOP.TOPICAL_VARIATION.v0_1- EKS.SEC2MATH.Z1.LOOP.SPEED_BUILD.v0_1Z2_CONTROL:- EKS.SEC2MATH.Z2.NODE.EXAM_FORMAT_TRANSFER.v0_1Z3_OUTPUT:- EKS.SEC2MATH.Z3.P3.NODE.SEC2_STABILITY_LOCK.v0_1

PAGE: EKS.EMATH.DIR.LANE.v0_1TITLE: E-Mathematics — O-Level Lane DirectoryFOCUS:- full-syllabus execution + exam strategy + speed + checkingZ0_NODES:- EKS.EMATH.Z0.NODE.ALGEBRA_SYSTEMS.v0_1- EKS.EMATH.Z0.NODE.GRAPHS_FUNCTIONS.v0_1- EKS.EMATH.Z0.NODE.GEOMETRY_TRIG.v0_1- EKS.EMATH.Z0.NODE.MENSURATION.v0_1- EKS.EMATH.Z0.NODE.PROB_STATS.v0_1- EKS.EMATH.Z0.NODE.MODELLING_WORD_PROBLEMS.v0_1Z1_LOOPS:- EKS.EMATH.Z1.LOOP.TEN_YEAR_SERIES.v0_1- EKS.EMATH.Z1.LOOP.CARELESSNESS_ZEROING.v0_1Z2_CONTROL:- EKS.EMATH.Z2.NODE.PAPER_ROUTING.v0_1  (Paper 1 vs Paper 2 tactics)Z3_OUTPUT:- EKS.EMATH.Z3.P3.NODE.OLEVEL_A1_STABILITY.v0_1

PAGE: EKS.AMATH.DIR.LANE.v0_1TITLE: A-Mathematics — O-Level Lane DirectoryFOCUS:- algebraic power + calculus + trig identities; high-precision executionZ0_NODES:- EKS.AMATH.Z0.NODE.ALGEBRA_TECHNIQUE.v0_1- EKS.AMATH.Z0.NODE.TRIG_IDENTITIES_EQUATIONS.v0_1- EKS.AMATH.Z0.NODE.LOGS_EXPONENTIALS.v0_1- EKS.AMATH.Z0.NODE.CALCULUS_DIFF.v0_1- EKS.AMATH.Z0.NODE.CALCULUS_INTEGRATION.v0_1- EKS.AMATH.Z0.NODE.PROOF_CHAINING.v0_1Z1_LOOPS:- EKS.AMATH.Z1.LOOP.SKILL_DRILLS_TO_VARIATION.v0_1- EKS.AMATH.Z1.LOOP.EXAM_SPEED_PRECISION.v0_1Z2_CONTROL:- EKS.AMATH.Z2.NODE.TOPIC_DEPENDENCY_ROUTER.v0_1Z3_OUTPUT:- EKS.AMATH.Z3.P3.NODE.OLEVEL_AMATH_A1_STABILITY.v0_1

DIR: EKS.SECMATH.DIR.TESTS.v0_1TESTS:- EKS.SECMATH.TEST.P_SCORE.v0_1- EKS.SECMATH.TEST.INDEPENDENCE.v0_1- EKS.SECMATH.TEST.SPEED_TAIL.v0_1- EKS.SECMATH.TEST.TRANSFER.v0_1- EKS.SECMATH.TEST.ERROR_REPEAT.v0_1

TEST: EKS.SECMATH.TEST.INDEPENDENCE.v0_1PASS: ≥80% correct with zero hints on mixed setFAIL: needs prompts/rescues or only works on “same-format” questions

TEST: EKS.SECMATH.TEST.SPEED_TAIL.v0_1PASS: tail time bounded (no time sink questions)FAIL: a few questions consume most time → paper collapses

DIR: EKS.SECMATH.DIR.BINDS.v0_1BINDS:- EKS.SECMATH.BIND.EDU_CORE.v0_1      TO: EDU.Z3.P3.NODE.CAPABILITY_STABILITY.v0_1- EKS.SECMATH.BIND.FAM_LOAD.v0_1      TO: FAM.Z0.NODE.HOMEWORK_SUPPORT.v0_1- EKS.SECMATH.BIND.HLT_STRESS.v0_1    TO: HLT.Z0.NODE.PATIENT_MONITORING.v0_1CLAIM:Secondary Maths stability reduces household load and prevents P0 education collapse.

CLAIM: EKS.SECMATH.CLAIM.CANONICAL.v0_1Secondary Mathematics works when Z0 execution becomes P3 under time + variation,and repair loops prevent false competence from snapping into exam collapse.