SERIES: EKS.SECMATH.v0_1
SITE: eduKateSG.com
MODE: Almost-Code / Canonical / LLM-first
COORD_GRAMMAR:
<EKS> × SECMATH × LEVEL × Z{0–3} × P{0–3} × Type × ID
Type = PAGE | DIR | NODE | BIND | LOOP | SENSOR | TEST | CLAIM | TOOL

PAGE: EKS.SECMATH.DIR.INDEX.v0_1
TITLE: eduKateSG — Secondary Mathematics Directory Index
CONTENT:
- 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_1
OUTPUT:
- EKS.SECMATH.CLAIM.CANONICAL.v0_1

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

DIR: EKS.SECMATH.DIR.CORE_SKILLS.v0_1
CORE_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_1
RULE:
These Z0 nodes are reused across all sub-lanes as dependencies.

TEST: EKS.SECMATH.TEST.P_SCORE.v0_1
P0: cannot solve independently; collapses under time/novelty
P1: solves with prompts; dependency; fragile confidence
P2: solves standard formats; breaks under variation/speed
P3: solves independently under time + variation; bounded error tail

SENSOR: EKS.SECMATH.SENSOR.EXECUTION.v0_1
MEASURES:
- 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_1
TRUNCATE:
- 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 variation
GOAL:
- push P1/P2 → P3 and prevent snap collapse at exams

PAGE: EKS.SEC1MATH.DIR.LANE.v0_1
TITLE: Secondary 1 Mathematics — Lane Directory
FOCUS:
- algebra entry + real numbers + foundations for all future math
Z0_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_1
Z1_LOOPS:
- EKS.SEC1MATH.Z1.LOOP.HW_REPAIR.v0_1
- EKS.SEC1MATH.Z1.LOOP.ERROR_NOTEBOOK.v0_1
Z2_CONTROL:
- EKS.SEC1MATH.Z2.NODE.MASTERY_SEQUENCING.v0_1
Z3_OUTPUT:
- EKS.SEC1MATH.Z3.P3.NODE.SEC1_FOUNDATION_LOCK.v0_1

PAGE: EKS.SEC2MATH.DIR.LANE.v0_1
TITLE: Secondary 2 Mathematics — Lane Directory
FOCUS:
- algebra expansion + functions/graphs + probability/stats; pre-O-level ramp
Z0_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_1
Z1_LOOPS:
- EKS.SEC2MATH.Z1.LOOP.TOPICAL_VARIATION.v0_1
- EKS.SEC2MATH.Z1.LOOP.SPEED_BUILD.v0_1
Z2_CONTROL:
- EKS.SEC2MATH.Z2.NODE.EXAM_FORMAT_TRANSFER.v0_1
Z3_OUTPUT:
- EKS.SEC2MATH.Z3.P3.NODE.SEC2_STABILITY_LOCK.v0_1

PAGE: EKS.EMATH.DIR.LANE.v0_1
TITLE: E-Mathematics — O-Level Lane Directory
FOCUS:
- full-syllabus execution + exam strategy + speed + checking
Z0_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_1
Z1_LOOPS:
- EKS.EMATH.Z1.LOOP.TEN_YEAR_SERIES.v0_1
- EKS.EMATH.Z1.LOOP.CARELESSNESS_ZEROING.v0_1
Z2_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_1
TITLE: A-Mathematics — O-Level Lane Directory
FOCUS:
- algebraic power + calculus + trig identities; high-precision execution
Z0_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_1
Z1_LOOPS:
- EKS.AMATH.Z1.LOOP.SKILL_DRILLS_TO_VARIATION.v0_1
- EKS.AMATH.Z1.LOOP.EXAM_SPEED_PRECISION.v0_1
Z2_CONTROL:
- EKS.AMATH.Z2.NODE.TOPIC_DEPENDENCY_ROUTER.v0_1
Z3_OUTPUT:
- EKS.AMATH.Z3.P3.NODE.OLEVEL_AMATH_A1_STABILITY.v0_1

DIR: EKS.SECMATH.DIR.TESTS.v0_1
TESTS:
- 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_1
PASS: ≥80% correct with zero hints on mixed set
FAIL: needs prompts/rescues or only works on “same-format” questions

TEST: EKS.SECMATH.TEST.SPEED_TAIL.v0_1
PASS: tail time bounded (no time sink questions)
FAIL: a few questions consume most time → paper collapses

DIR: EKS.SECMATH.DIR.BINDS.v0_1
BINDS:
- 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_1
CLAIM:
Secondary Maths stability reduces household load and prevents P0 education collapse.

CLAIM: EKS.SECMATH.CLAIM.CANONICAL.v0_1
Secondary Mathematics works when Z0 execution becomes P3 under time + variation,
and repair loops prevent false competence from snapping into exam collapse.