NODE.ID: EDUOS-MATHOS-SEC2-00
NODE.TYPE: intervention_router_level
LEVEL: secondary_2
SITE: edukatesg
PARENT.OS: EDUOS
SUBOS: MATHOS
PURPOSE: stabilise_algebra_chains_ratio_rate_percent_graphs_and_multi_step_problem_execution
VERSION: v0.1

DEF.SEC2_ROUTER:
  Secondary 2 is where algebra becomes longer-chain, speed becomes binding,
  and representation alignment (tables/graphs/equations/words) starts to decide
  performance. This node routes learners to seal leaks, reduce variance, and
  reach stable execution under time pressure.

CAP.SEC2.T1: algebra_chain_integrity (expand/factor/simplify entry-level)
CAP.SEC2.T2: equations_and_inequalities (multi-step, form control)
CAP.SEC2.T3: ratio_rate_percent_mastery (scaling + real-world modelling)
CAP.SEC2.T4: linear_graphs_alignment (table <-> graph <-> equation)
CAP.SEC2.T5: word_problem_translation (LANGOS dependency)
CAP.SEC2.T6: checking_protocols (careless-error kill switch)
CAP.SEC2.T7: time_to_execution (fluency + latency reduction)

FAIL.SEC2.F1: algebraic_manipulation_leaks (sign errors, term loss)
FAIL.SEC2.F2: chain_break_under_length (step skipping, reordering)
FAIL.SEC2.F3: fraction_percent_ratio_confusion (unit/scaling drift)
FAIL.SEC2.F4: graph_misalignment (cannot map equation to slope/intercept)
FAIL.SEC2.F5: word_to_algebra_gap (cannot define variables correctly)
FAIL.SEC2.F6: checking_absence (no verification, careless cascades)
FAIL.SEC2.F7: time_pressure_collapse (slow recall; panic)
FAIL.SEC2.F8: bio_load_misalignment (fatigue/stress -> variance spikes)

F4 often reveals representation failure, not "graph topic weakness".
F7 often reveals fluency + confidence collapse, not concept absence.

ROUTE.SEC2.P0: re_entry
  - restore basic algebra + number fundamentals
  - rebuild confidence via minimum viable chains
ROUTE.SEC2.P1: stabilise
  - reduce swings; eliminate repeated error clusters
  - restore retention (7d/14d)
ROUTE.SEC2.P2: seal_leaks
  - speed + checking + representation alignment
  - increase novel transfer rate
ROUTE.SEC2.P3: maintain_upgrade
  - reduce slip rate to near-zero
  - handle twist questions and mixed-topic sets

PROTO.SEC2.1: chain_template_library
  - standard forms for manipulation + solving (no freestyle drift)
PROTO.SEC2.2: sign_error_firewall
  - explicit negative/term tracking + micro-checks
PROTO.SEC2.3: ratio_rate_percent_unification
  - one scaling model across contexts (units + multipliers)
PROTO.SEC2.4: representation_alignment_drills
  - equation <-> table <-> graph <-> words mapping loops
PROTO.SEC2.5: variable_definition_protocol (LANGOS bridge)
  - define variables with units + referents before solving
PROTO.SEC2.6: checking_protocol_always_on
  - substitution check, boundary check, reasonableness check
PROTO.SEC2.7: timed_fluency_loops
  - reduce time-to-first-step + stabilize under pressure
PROTO.SEC2.8: spaced_retrieval_consolidation (BIOOS bridge)
  - short cycles, frequent recall, rest integration

SENSOR.SEC2.S1: algebra_sign_error_rate
SENSOR.SEC2.S2: multi_step_chain_integrity (step loss rate)
SENSOR.SEC2.S3: ratio_rate_percent_accuracy (unit consistency)
SENSOR.SEC2.S4: graph_alignment_accuracy (slope/intercept recognition)
SENSOR.SEC2.S5: variable_definition_quality (clarity + correctness)
SENSOR.SEC2.S6: checking_rate (verification frequency)
SENSOR.SEC2.S7: time_to_first_step (latency)
SENSOR.SEC2.S8: variance_under_time_pressure
SENSOR.SEC2.S9: retention_7d_14d

(S1,S2,S6 improve) AND (S7 decreases) AND (S8 decreases) AND retention stable
=> phase shift toward P3

OUT.SEC2.1: stable_execution_of_algebra_chains
OUT.SEC2.2: consistent_scaling_model_across_ratio_rate_percent
OUT.SEC2.3: reliable_graph_equation_translation
OUT.SEC2.4: low_careless_error_density
OUT.SEC2.5: improved_novel_transfer_in_mixed_sets

LINK.PARENT: EDUOS-MATHOS-SEC-00
LINK.SIBLING.PREV: EDUOS-MATHOS-SEC1-00
LINK.SIBLING.NEXT: EDUOS-MATHOS-SEC3-00
LINK.UP: EDUOS-00, EDUOS-02, MATHOS-00
LINK.SIDE: LANGOS-00 (word-problem translation), EDUOSxBIOOS-01 (load/consolidation)
LINK.IMPL: EDUOS-IMPL-02 (tuition as intervention router)

LOCK:
  Secondary 2 is where chain length + speed + representation alignment decide outcomes.
  Seal leaks (signs, steps, scaling, graphs) and enforce checking to reach P3 reliability.

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.