NODE.ID: LANGOS-00
NODE.TYPE: canonical_supply_lane
SUBOS.ID: LANGOS
SUBOS.NAME: Language OS
PARENT.OS: EDUOS
SUBOS.CLASS: capability_supply_line
SUBOS.PURPOSE: regenerate_coordination_abstraction_contractual_reasoning_across_generations
AXIS: time
VERSION: v0.1

DEF.LANGOS:
  Language OS is the education-supplied capability pipeline that regenerates
  shared meaning, coordination protocols, abstraction, and contract-level
  reasoning needed for civilisation to function (governance, trade, law,
  science, education itself) across generations.
RULE:
  language is not primarily a school subject; it is civilisation’s coordination layer.

LANGOS.ORIGIN.DRIVERS:
  - coordination_of_group_action (hunt, build, defend)
  - role_assignment (who does what, when)
  - norm_transmission (what is allowed/forbidden)
  - error_prevention (warnings, taboos, procedures)
  - long-range cooperation (trade, alliances)
  - memory_compression (stories, rules, names)
EMERGENCE_CHAIN:
  coordination_pressure -> signals -> shared_meaning -> norms -> institutions

LANGOS.FUNC.1: meaning_alignment (shared definitions)
LANGOS.FUNC.2: instruction_execution (procedures, sequences, checks)
LANGOS.FUNC.3: abstraction (concept formation, categorization)
LANGOS.FUNC.4: negotiation (trade-offs, agreements)
LANGOS.FUNC.5: contract_reasoning (rules, obligations, enforcement)
LANGOS.FUNC.6: error_memory (narrative transfer, lessons)
LANGOS.FUNC.7: knowledge_transfer (education itself depends on language)

DEP.LANE.1: GOVOS (law, legitimacy, policy communication)
DEP.LANE.2: SECOS (rules, compliance, investigation, testimony)
DEP.LANE.3: FINOS (contracts, disclosure, risk communication)
DEP.LANE.4: TROS  (routing instructions, signage, protocols)
DEP.LANE.5: SCIOS (definitions, hypotheses, explanations)
DEP.LANE.6: EDUOS (teaching, testing, feedback loops)

weak_langos -> coordination_entropy↑ -> institutional_drift↑

LANGOS.STAGES:
  L0: basic_signals + turn-taking (coordination readiness)
  L1: vocabulary + naming (shared reference readiness)
  L2: grammar + sentence logic (instruction readiness)
  L3: reading_comprehension (extract meaning from text)
  L4: writing_clarity (encode meaning for others)
  L5: argumentation (reasoning, evidence, structure)
  L6: contract_logic (rules, obligations, exceptions)
  L7: abstraction_systems (technical language, formal definitions)

L3-L5 map strongly to "secondary literacy" competence.
L6-L7 explain law/science/governance failure modes.

LANGOS.PHASES:
  P0: collapse (cannot decode/encode reliably; avoidance)
  P1: unstable (misreads, inconsistent writing, high variance)
  P2: functional_leaky (understands basics; fails on nuance/time)
  P3: stable_mastery (durable comprehension; clear expression; low drift)
KEY:
  language capability = reliability of meaning transfer under load

FAIL.L1: definition_drift (same word different meanings)
FAIL.L2: instruction_failure (cannot follow multi-step text)
FAIL.L3: ambiguity (unclear writing causes coordination errors)
FAIL.L4: weak_inference (cannot infer implied meaning)
FAIL.L5: low_argument_integrity (claims without structure/evidence)
FAIL.L6: contract_misread (exceptions/conditions ignored)
FAIL.L7: low_transfer (can do drills; fails on real documents)

SENSOR.LS1: misread_rate (detail loss)
SENSOR.LS2: inference_accuracy (implicit meaning)
SENSOR.LS3: instruction_follow_through (multi-step compliance)
SENSOR.LS4: clarity_score_proxy (ambiguity markers, missing referents)
SENSOR.LS5: argument_structure_presence (claim->evidence->reason)
SENSOR.LS6: definition_consistency (same term, same meaning)

high_definition_drift => governance/science coordination failures likely

IF LANGOS degrades at population scale THEN:
  - rules misinterpreted
  - contracts fail
  - policy compliance drops
  - scientific communication degrades
  - institutional drift rises
  -> coordination entropy increases
  -> HRL thins
  -> Civλ effective increases

LANGOS.IMPL:
  - oral_tradition
  - literacy_schools
  - reading_programs
  - writing_workshops
  - tuition_language (intervention_route)
RULE:
  implementation != root

LINK.PREV.1: EDUOS-00 (pillar)
LINK.PREV.2: EDUOS-02 (anti-decay)
LINK.NEXT.1: SCIOS-00 (science as prediction/control supply line)
LINK.NEXT.2: HISOS-00 (history as error-memory supply line)
LINK.NEXT.3: GOVOS-bridge (language drives governance reliability)
LINK.NEXT.4: EDUOS-IMPL-01 (schools as implementation)
LINK.NEXT.5: EDUOS-IMPL-02 (tuition as intervention router)

LOCK:
  Language is civilisation’s coordination + abstraction supply line.
  Education OS must regenerate meaning-transfer reliability under load (P0–P3).
  Weak language causes definition drift, contract failures, and governance entropy.

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.