NODE.ID: HISOS-00
NODE.TYPE: canonical_supply_lane
SUBOS.ID: HISOS
SUBOS.NAME: History OS
PARENT.OS: EDUOS
SUBOS.CLASS: capability_supply_line
SUBOS.PURPOSE: regenerate_error_memory_and_collapse_avoidance_capability_across_generations
AXIS: time
VERSION: v0.1

DEF.HISOS:
  History OS is the education-supplied capability pipeline that regenerates
  civilisation’s error-memory: structured recall of prior failures, constraints,
  and recovery routes, enabling societies to avoid rediscovery loops, detect
  repeating collapse patterns, and preserve institutional continuity across time.
RULE:
  history is not primarily chronology; it is civilisation’s error-memory system.

HISOS.ORIGIN.DRIVERS:
  - repeated_failure_is_costly_or_fatal
  - memory_dies_with_individuals
  - drift_rewrites_truth (myths replace lessons)
  - power_requires_legitimacy (narratives form)
  - coordination_requires_shared_past (identity + rules)
EMERGENCE_CHAIN:
  failures -> stories -> records -> archives -> curricula -> applied lessons

HISOS.FUNC.1: capture (record events + conditions)
HISOS.FUNC.2: compress (extract lessons, patterns, constraints)
HISOS.FUNC.3: preserve (protect against loss + distortion)
HISOS.FUNC.4: transmit (teach across cohorts)
HISOS.FUNC.5: compare (pattern match to present)
HISOS.FUNC.6: warn (early signals of repeating failure)
HISOS.FUNC.7: route (recommend repair/recovery actions)

history must produce actionable constraints, not only narratives

DEP.LANE.1: GOVOS (institutional memory, legitimacy, policy traps)
DEP.LANE.2: SECOS (conflict cycles, law breakdown patterns)
DEP.LANE.3: FINOS (bubbles, panic cycles, debt traps)
DEP.LANE.4: EDUOS (curriculum selection: what must never be forgotten)
DEP.LANE.5: CIVOS (collapse modes, rate-dominance patterns)

weak_hisos -> rediscovery_loops↑ -> repeat_collapse_probability↑

HISOS.STAGES:
  H0: recall (basic facts)
  H1: context (conditions, constraints)
  H2: causality (mechanisms vs coincidence)
  H3: pattern (recurrence detection)
  H4: comparative_reasoning (map past->present)
  H5: warning_signals (early indicators)
  H6: recovery_routes (what worked, what failed)
  H7: institutional_memory (handover + continuity systems)

H4-H7 are what civilisation needs; H0-H1 alone is trivia storage.

HISOS.PHASES:
  P0: collapse (history unusable; pure myth/propaganda)
  P1: unstable (selective memory; inconsistent lessons)
  P2: functional_leaky (some lessons; poor transfer to decisions)
  P3: stable_mastery (clear constraints + repeatable application)
KEY:
  history capability = reliability of lesson transfer into decisions under pressure

FAIL.H1: myth_dominance (stories replace constraints)
FAIL.H2: selective_amnesia (uncomfortable lessons erased)
FAIL.H3: archive_loss (records vanish)
FAIL.H4: context_stripping (facts without conditions)
FAIL.H5: politicised_distortion (truth drift)
FAIL.H6: non-application (lessons known but ignored)
FAIL.H7: handover_break (institutions forget why rules exist)

SENSOR.HS1: rediscovery_rate (repeat same failure patterns)
SENSOR.HS2: policy_cycle_repeat (same traps recur)
SENSOR.HS3: narrative_variance (high drift across cohorts)
SENSOR.HS4: lesson_to_action_rate (do decisions reflect lessons?)
SENSOR.HS5: archive_integrity_proxy (records accessible + used)
SENSOR.HS6: institutional_handover_integrity (why-rules-exist preserved)

high_rediscovery_rate => HISOS transfer failure likely

IF HISOS degrades at population scale THEN:
  - societies repeat known traps
  - brittle myths replace constraints
  - governance loses institutional memory
  - recovery routes forgotten
  -> HRL thins
  -> Civλ effective increases
  -> dark-age probability rises (pipeline failure)

HISOS.IMPL:
  - oral_tradition
  - chronicles_archives
  - museums_records
  - school_history
  - civic_education
  - tuition_history (intervention_route)
RULE:
  implementation != root

LINK.PREV.1: EDUOS-00 (pillar)
LINK.PREV.2: EDUOS-02 (anti-decay)
LINK.PREV.3: EDUOSxHISOS-01 (dark ages as pipeline failure)
LINK.NEXT.1: EDUOS-IMPL-01 (schools as implementation layer)
LINK.NEXT.2: EDUOS-IMPL-02 (tuition as intervention router)
LINK.NEXT.3: GOVOS-bridge (history stabilizes institutional memory)

LOCK:
  History is civilisation’s error-memory supply line.
  It prevents rediscovery loops and preserves institutional lessons across time.
  Chronology without constraints is not History OS; it is data storage.

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.