DOCUMENT_ID: EDKSG.ADDMATH.G2.CTRLTOWER.v1.0
DOCUMENT_TYPE: Technical Documentation / Runtime Control Tower / Tutorial System
DOMAIN_ROOT: PlanetOS -> CivilisationOS -> EducationOS -> MathOS -> AdditionalMathematicsOS
SITE_BIND: eduKateSG
LEVEL_BIND: G2 Additional Mathematics
OFFICIAL_SYLLABUS_BIND: SEC 2027 / K232
STATUS: Canonical Technical Spec
MODE: Full Almost-Code
VERSION_LOCK: Forward-only
TITLE:
  Control Tower / Runtime for G2 Additional Mathematics Tuition by eduKateSG
CLASSICAL_BASELINE:
  G2 Additional Mathematics is a secondary-level elective mathematics corridor in Singapore
  designed to prepare students for stronger symbolic mathematics and, in particular,
  for G3 Additional Mathematics.
ONE_SENTENCE_FUNCTION:
  G2 Additional Mathematics Tuition by eduKateSG is a bridge-and-uplift symbolic runtime
  that thickens a student's algebraic, trigonometric, and introductory calculus capacity
  until the carrier can survive higher abstraction without panic or collapse.
OFFICIAL_BASELINE_LOCK:
  - Intended to prepare students adequately for G3 Additional Mathematics.
  - Assumes knowledge of G2 Mathematics.
  - Organised into Algebra, Geometry and Trigonometry, and Calculus.
  - Uses two papers of 1h45 each.
  - Calculator allowed in both papers.
  - AO emphasis is heavier on standard techniques than G3, but still includes problem-solving and reasoning.
BOUNDARY_NOTE:
  The official syllabus defines content and assessment.
  This document defines eduKateSG’s runtime for diagnosis, routing, teaching, stabilisation,
  repair, and future projection through that content.

SECTION_01: MACRO_PURPOSE
PRIMARY_PURPOSE:
  Convert a thinner symbolic carrier into a viable Additional Mathematics carrier.
SECONDARY_PURPOSES:
  01. Install cleaner algebraic grammar.
  02. Build multi-step symbolic retention.
  03. Increase abstraction tolerance.
  04. Introduce trigonometric and calculus language without destroying confidence.
  05. Prepare students for stronger later mathematical corridors.
  06. Prevent fear-conditioned rejection of abstract mathematics.
  07. Preserve route dignity for students not yet ready for direct G3-style compression.
TRUE_RUNTIME_OBJECT:
  Not merely passing a subject.
  True object = viability + symbolic thickening + corridor widening.
G2_RUNTIME_THESIS:
  G2 Additional Mathematics is not "failed G3".
  It is a bridge architecture.
PUBLIC_MISREAD:
  Many people misread G2 Add Math as a lesser badge.
  Runtime truth:
    it is a controlled transition corridor for building higher symbolic survivability.

SECTION_02: PLANETOS_BINDING
PLANETOS_COMPONENTS:
  PlanetOS                = long-run need for mathematical capability continuity
  CivilisationOS          = macro reasoning continuity
  EducationOS             = delivery organ
  MathOS                  = core symbolic engine
  LanguageOS              = question parsing and explanation clarity
  VocabularyOS            = term precision and notation meaning
  FamilyOS                = compliance, routine, emotional climate
  EmotionOS               = fear buffering, confidence regulation, shame control
  MemoryArchiveOS         = repetition, retrieval, error-log memory
  StandardsMeasurementOS  = marks, method-credit, notation discipline
  GovernanceOS            = curriculum legitimacy and educational framing
  LogisticsOS             = scheduling, topic sequencing, correction timing
  EnergyOS                = attention and cognitive fuel
  HealthOS                = fatigue and burnout prevention
  CareerOS                = later route implications
  TechnologyOS            = calculator fluency and practice tools
  CultureOS               = whether mathematics is feared or respected
  SecurityOS              = protection from drift, bluffing, and silent collapse
  EconomyOS               = tuition investment as route-preservation
  ShelterOS               = study habitat
  SocietyOS               = larger participation in mathematical capability
PRIMARY_RUNTIME_COMPONENTS:
  EducationOS
  MathOS
  LanguageOS
  VocabularyOS
  EmotionOS
  MemoryArchiveOS
  StandardsMeasurementOS
SECONDARY_RUNTIME_COMPONENTS:
  FamilyOS
  LogisticsOS
  EnergyOS
  CareerOS
  CultureOS
  TechnologyOS

SECTION_03: CIVOS_BINDING
CIVOS_CORE_STACK:
  Lattice
  VeriWeft
  LedgerOfInvariants
  ChronoFlight
  SignalGate
  FenceOS
  AVOO
  ConeOfPossibility
  RepairCorridor
  DriftVsRepairLaw
  OnePanelControlTower
  InterstellarCore (bounded, later-stage, optional)
RUNTIME_FUNCTIONS:
  Lattice            = locates the student state
  VeriWeft           = checks whether symbolic steps are structurally lawful
  Ledger             = tracks owned vs borrowed competence
  ChronoFlight       = maps movement across weeks, terms, and exam nodes
  SignalGate         = routes the student into +Latt / 0Latt / -Latt
  FenceOS            = protects from overload and underload
  AVOO               = defines who is designing, diagnosing, and executing
  ConeOfPossibility  = shows future route widening or narrowing
  RepairCorridor     = defines recovery from drift or panic
  DriftVsRepairLaw   = determines whether the carrier is strengthening or decaying
  InterstellarCore   = not default; only opened if surplus later becomes real

SECTION_04: CODE_REGISTRY
ZOOM_CODES:
  Z0 = student internal cognition / symbolic load handling
  Z1 = family / parent / home system
  Z2 = tutor / tuition / peer runtime
  Z3 = school / syllabus / exam institution
  Z4 = future subject and post-secondary routing
  Z5 = national mathematics transfer corridor
  Z6 = civilisation-scale mathematics continuity
PHASE_CODES:
  P0 = non-viable / collapse under symbolic load
  P1 = assisted survival / fragile guided handling
  P1.5 = early bridge state / beginning abstraction tolerance
  P2 = operational routine competence
  P3 = stable transfer within G2 corridor and bridge-readiness upward
  P4 = optional exceptional overflow, rare in this lane
VALENCE_CODES:
  +LATT = widening corridor
  0LATT = unstable but repairable
  -LATT = narrowing corridor / negative drift
CORRIDOR_CODES:
  C.REPAIR   = active damage control
  C.BRIDGE   = controlled uplift corridor
  C.REBUILD  = prerequisite reinstall
  C.OPEN     = viable forward motion
  C.NARROW   = viable but under strain
  C.MIXED    = routine okay, transfer weak
  C.UPSHIFT  = candidate may later tolerate stronger corridor
STATE_CODES:
  ST-00 = Unseen
  ST-01 = Introduced
  ST-02 = Copied
  ST-03 = Assisted
  ST-04 = Routine
  ST-05 = Mixed
  ST-06 = Transfer
  ST-07 = Time-Safe
  ST-08 = Explainable
  ST-09 = Bridge-Ready

SECTION_05: AVOO_BINDING
AVOO_TUTOR_RUNTIME:
  A  = Architect
       designs step-size, pacing, and bridge geometry
  V  = Visionary
       shows why this subject matters for later corridors
  O1 = Oracle
       detects exact point of compression shock or symbolic weakness
  O2 = Operator
       runs the repetitions, drills, corrections, and timing ramps
AVOO_STUDENT_RUNTIME:
  A-lite  = begins structuring own work
  V-lite  = begins seeing beyond the next worksheet
  O1-lite = starts recognising recurring mistakes
  O2      = executes repeated corrective practice
RUNTIME_LAW:
  G2 works when the student is not asked to think like a full G3 carrier too early,
  but is also not trapped forever in low-load comfort.

SECTION_06: OFFICIAL_TO_TOPIC_ENGINE_MAP
CONTENT_STRANDS:
  ALGEBRA
  GEOMETRY_AND_TRIGONOMETRY
  CALCULUS
TOPIC_CODE_REGISTRY:
  ADD.G2.A1.EQINEQ   = Equations and inequalities
  ADD.G2.A2.FGRAPH   = Functions and graphs
  ADD.G2.A3.SURD     = Surds
  ADD.G2.A4.POLY     = Polynomials and partial fractions
  ADD.G2.A5.EXLOG    = Exponential and logarithmic functions
  ADD.G2.A6.BIN      = Binomial expansion
  ADD.G2.G1.TRIGF    = Trigonometric functions
  ADD.G2.G2.TRIGI    = Trigonometric identities and expressions
  ADD.G2.G3.TRIGE    = Trigonometric equations
  ADD.G2.G4.CG2D     = Coordinate geometry in two dimensions
  ADD.G2.G5.PG       = Plane geometry structures
  ADD.G2.C1.DIFFINT  = Differentiation and integration
TOPIC_ENGINE_LAW:
  Every topic must move through:
    meaning -> notation -> legality -> guided manipulation -> routine solve ->
    varied solve -> mixed transfer -> timed survivability

SECTION_07: BRIDGE_RUNTIME_THESIS
CANONICAL_THESIS:
  G2 Additional Mathematics does not exist mainly to sort students downward.
  It exists to create an upward bridge into stronger symbolic mathematics.
WHY_G2_EXISTS:
  01. Some students need smaller abstraction steps.
  02. Symbolic density must sometimes be increased gradually.
  03. Mathematical identity can be preserved while the carrier thickens.
  04. A bridge corridor can widen later possibilities better than raw overload.
  05. Controlled progression prevents unnecessary collapse.
G2_SPECIAL_FEATURE:
  It is a transition corridor where viability matters as much as correctness.

SECTION_08: LEDGER_OF_INVARIANTS
LEDGER_OF_INVARIANTS.G2_ADDMATH:
  INV-01: Algebraic equivalence must be preserved line to line.
  INV-02: Symbols must retain meaning across multi-step work.
  INV-03: Signs, brackets, restrictions, and units must not silently drift.
  INV-04: Formula use must remain conditional and lawful.
  INV-05: Graph, algebra, and verbal meaning must reconcile.
  INV-06: Trigonometric expressions must be manipulated legally.
  INV-07: Differentiation and integration must obey operator rules.
  INV-08: Working must remain readable enough for marks and self-checking.
  INV-09: Student must know when a method is valid.
  INV-10: Confidence must not exceed ownership.
LEDGER_STATE_TYPES:
  OWNED        = student can explain and reconstruct
  BORROWED     = student can imitate but not adapt
  FRAGILE      = only works on familiar surface forms
  FALSE_POS    = answer correct without reliable structure
  LEAKING      = competence breaks under pressure
  LOST         = not retrievable

SECTION_09: VERIWEFT_LAYER
VERIWEFT_FUNCTION:
  VeriWeft checks whether the student’s symbolic steps remain structurally admissible.
VWEFT_SENSORS:
  V1 = illegal cancellation
  V2 = sign drift
  V3 = bracket disappearance
  V4 = formula misuse
  V5 = inverse misunderstanding
  V6 = graph-language mismatch
  V7 = trig simplification breach
  V8 = derivative/integral misuse
  V9 = condition/interval omission
  V10 = copied form without meaning
WHEN_VWEFT_FAILS:
  - routine practice may still look acceptable
  - new question surfaces cause breakdown
  - timing collapses faster
  - confidence detaches from actual ownership
VWEFT_LAW:
  Bridge strength depends on legality.
  Repetition without legality only hardens drift.

SECTION_10: CAPABILITY_LATTICE
CAPABILITY_LATTICE_DIMENSIONS:
  L1 = AlgebraGrammar
  L2 = SymbolRetention
  L3 = GraphFunctionLink
  L4 = TrigComfort
  L5 = CoordinateControl
  L6 = CalculusEntryLegality
  L7 = MethodRecognition
  L8 = MixedTransfer
  L9 = TimeSurvival
  L10 = EmotionalStability
PHASE_DESCRIPTION:
  P0:
    cannot sustain symbolic load
    freezes quickly
  P1:
    can follow examples with heavy support
    surface change causes collapse
  P1.5:
    begins to hold abstraction in small steps
    still fragile but no longer fully rejecting the load
  P2:
    can handle routine forms independently
    mixed forms remain unstable
  P3:
    can survive G2-style mixed work and is structurally stronger
    may be bridge-ready for stronger future routing
  P4:
    rare overflow; not the normal design target

SECTION_11: INTAKE_DIAGNOSTIC_PROTOCOL
INTAKE_PROTOCOL:
  STEP-01 = collect prior mathematics record
  STEP-02 = test algebra cleanliness
  STEP-03 = inspect notation discipline
  STEP-04 = test multi-step retention
  STEP-05 = test reaction to unfamiliar symbols
  STEP-06 = observe fear and avoidance response
  STEP-07 = classify phase and valence
  STEP-08 = assign corridor
DIAGNOSTIC_BUCKETS:
  D1 = Algebra weakness
  D2 = Notation weakness
  D3 = Sequential-memory dropout
  D4 = Formula ritualism
  D5 = Trig fear
  D6 = Calculus fear or confusion
  D7 = Timing weakness
  D8 = Emotional avoidance
  D9 = Homework-system weakness
  D10 = False confidence
  D11 = Confidence collapse from prior failure
  D12 = Base G2 Mathematics weakness contaminating Add Math
FALSE_LABEL_WARNING:
  "Not suitable for Add Math" may sometimes actually mean:
    D1 + D3 + D8 + poor sequencing,
  not permanent inability.

SECTION_12: CONTROL_TOWER_ONE_PANEL
PANEL_ID: CT.G2.ADDMATH.01
FIELDS:
  STUDENT_ID
  SCHOOL
  SEC_LEVEL
  PHASE_STATE
  VALENCE_STATE
  CORRIDOR_STATE
  PRIMARY_BREACH
  SECONDARY_BREACH
  NEXT_ACTION
CORE_METRICS:
  M1  = Algebra Grammar
  M2  = Notation Precision
  M3  = Function-Graph Link
  M4  = Trig Comfort
  M5  = Coordinate Geometry Control
  M6  = Calculus Entry Legality
  M7  = Method Recognition
  M8  = Mixed Transfer
  M9  = Time Survival
  M10 = Error Visibility
  M11 = Emotional Stability
  M12 = Homework Integrity
  M13 = Family Support Stability
ALERTS:
  A1 = Compression Shock
  A2 = Sign Drift
  A3 = Formula Ritualism
  A4 = Silent Avoidance
  A5 = Mixed-Question Breakdown
  A6 = Confidence Collapse
  A7 = Overprotection / underload
  A8 = Upshift candidate detected
ACTION_CODES:
  ACT-R1 = Rebuild algebra preconditions
  ACT-R2 = Repair notation discipline
  ACT-R3 = Install small-step abstraction ladder
  ACT-R4 = Trig confidence pack
  ACT-R5 = Calculus entry repair
  ACT-R6 = Mixed-topic integration
  ACT-R7 = Timed ramp
  ACT-R8 = Parent-system calibration
  ACT-R9 = Future-route narrative repair

SECTION_13: LESSON_RUNTIME
LESSON_LOOP:
  01. Diagnose exact weakness node
  02. Name the breach clearly
  03. Reduce symbolic chaos
  04. Demonstrate lawful form
  05. Force active reconstruction
  06. Use smaller variation steps
  07. Consolidate before widening
  08. Add light timing pressure
  09. Log error pattern
  10. Recycle until stable
  11. Show future route meaning
LESSON_TYPES:
  LT-01 = Concept Install
  LT-02 = Syntax Repair
  LT-03 = Guided Reconstruction
  LT-04 = Small-Step Variation
  LT-05 = Blind Retrieval
  LT-06 = Mixed Bridge Drill
  LT-07 = Timed Ramp
  LT-08 = Emotional Reset Session
SEQUENCING_LAW:
  G2 tutoring must not confuse gentleness with low standards.
  Bridge-building still requires real load, just correctly sized load.

SECTION_14: TOPIC_ENGINE_ALGEBRA
ALGEBRA_RUNTIME_OBJECT:
  Build lawful manipulation and symbol confidence.
SUB_ENGINES:
  ALG-EQINEQ:
    equation solving
    inequality handling
    sign awareness
    number-line meaning
  ALG-FGRAPH:
    relation between equation, graph, and function behaviour
  ALG-SURD:
    simplification and lawful manipulation
  ALG-POLY:
    polynomial structure
    factor/remainder ideas
    decomposition thinking
  ALG-PF:
    partial fractions as controlled decomposition
  ALG-EXLOG:
    inverse-style structure
    growth and compression language
    domain awareness
  ALG-BIN:
    pattern expansion
    notation discipline
    controlled symbolic patterning
ALGEBRA_COMMON_FAILURES:
  AF-01 = copying lines without seeing equivalence
  AF-02 = bracket/sign leakage
  AF-03 = graph and formula treated as separate worlds
  AF-04 = fear of non-integer or less familiar forms
ALGEBRA_SUCCESS_SIGNAL:
  student starts reading algebra as structure,
  not as a frightening wall of symbols.

SECTION_15: TOPIC_ENGINE_GEOMETRY_AND_TRIGONOMETRY
GTRIG_RUNTIME_OBJECT:
  Build comfort moving between angle, ratio, identity, graph, and coordinate form.
SUB_ENGINES:
  GTRIG-TRIGF:
    function behaviour
    value interpretation
    graph reading
  GTRIG-TRIGI:
    expression handling
    lawful simplification
    identity recognition
  GTRIG-TRIGE:
    solving within stated intervals
    condition discipline
  GTRIG-CG2D:
    distance, midpoint, gradients, line relations, basic geometric reading
  GTRIG-PG:
    relation-chaining, justification, theorem deployment
COMMON_FAILURES:
  GF-01 = trig treated as pure memorisation
  GF-02 = algebra weakness disguised as trig weakness
  GF-03 = interval/condition omission
  GF-04 = proof or justification fear
  GF-05 = graph fear
SUCCESS_SIGNAL:
  student no longer panics when trigonometry changes surface form.

SECTION_16: TOPIC_ENGINE_CALCULUS
CALCULUS_RUNTIME_OBJECT:
  Introduce change and area as lawful, understandable operators.
SUB_ENGINES:
  CAL-DIFFINT:
    derivative as gradient
    derivative as rate of change
    notation handling
    standard differentiation rules
    standard integration rules
    definite integral as area
    area bounded by curve and line(s)
COMMON_FAILURES:
  CF-01 = calculus treated as procedure ritual
  CF-02 = notation confusion
  CF-03 = geometry meaning detached from operator
  CF-04 = algebra weakness corrupts calculus steps
  CF-05 = area interpretation failure
SUCCESS_SIGNAL:
  student sees calculus as understandable motion,
  not mystical symbol pushing.

SECTION_17: SIGNAL_GATE
INPUT_VECTOR_X(k):
  X = {
    ALG_BASE,
    NOTATION_DISCIPLINE,
    STEP_RETENTION,
    GRAPH_LINK,
    TRIG_CONFIDENCE,
    CALCULUS_ENTRY,
    METHOD_RECOGNITION,
    MIXED_TRANSFER,
    TIME_SURVIVAL,
    PANIC_LOAD,
    HOME_SUPPORT,
    REVIEW_INTEGRITY
  }
ROUTING_RULES:
  IF ALG_BASE low AND PANIC_LOAD high
    -> route to -LATT / C.REBUILD
  IF ALG_BASE improving AND abstraction tolerance rising but still fragile
    -> route to 0LATT / C.BRIDGE
  IF routine solve stable AND mixed transfer emerging
    -> route to +LATT / C.OPEN
  IF G2 transfer stable and symbolic thickness rising
    -> candidate for C.UPSHIFT
THRESHOLD_LAW:
  +LATT when RepairRate >= DriftRate
         and PanicLoad <= Threshold
         and symbolic retention survives variation
  0LATT when progress exists but performance remains surface-dependent
  -LATT when DriftRate > RepairRate long enough under bridge load

SECTION_18: FENCEOS
FENCEOS_FUNCTION:
  Keep the bridge load high enough to build thickness,
  but low enough to avoid symbolic trauma.
FENCE_PARAMETERS:
  F1 = step size
  F2 = novelty level
  F3 = symbolic density
  F4 = timing pressure
  F5 = independence requirement
  F6 = correction lag
  F7 = emotional volatility
  F8 = homework mass
UNDERFENCED_STATE:
  too easy
  student never adapts
  later surprise collapse
OVERFENCED_STATE:
  too hard too quickly
  fear conditioning starts
  bridge collapses before thickening
WELL_FENCED_STATE:
  student strains, survives, and gradually thickens

SECTION_19: CHRONOFLIGHT_OVERLAY
TIME_SLICES:
  T0 = pre-entry diagnostic
  T1 = confidence-safe onboarding
  T2 = bridge formation
  T3 = routine consolidation
  T4 = mixed-topic exposure
  T5 = timed ramp
  T6 = exam execution
  T7 = post-exam route transition
TIME_TO_NODE_LAW:
  As the exam node approaches:
    available repair time narrows
    bluff becomes expensive
    fear spikes if ownership is shallow
TIME_DEBT:
  copied solutions now -> transfer failure later
  skipped notation repair now -> marks leak later
  overprotected student now -> collapse under mixed paper later

SECTION_20: CONE_OF_POSSIBILITY
CONE_MODEL:
  stronger present bridge-building widens future mathematical routes
  weaker present bridge-building narrows them
WIDENED_ROUTES_MAY_INCLUDE:
  - stronger Add Math performance
  - confidence in abstraction
  - possible later G3-strength motion
  - wider STEM-adjacent confidence
  - better self-belief around hard thinking
NARROWED_ROUTES_MAY_INCLUDE:
  - fear-driven subject avoidance
  - permanent underestimation of mathematical ceiling
  - collapse into low-risk-only learning behaviour
DEEP_OUTPUT:
  G2 does not only preserve a grade route.
  It can preserve the student's relationship with abstraction itself.

SECTION_21: FAILURE_TRACE
HOW_G2_ADDMATH_BREAKS_A_STUDENT:
  stage 01 = base mathematics weakness enters unnoticed
  stage 02 = symbolic load rises
  stage 03 = student copies without owning
  stage 04 = abstraction threshold triggers fear
  stage 05 = avoidance and silence grow
  stage 06 = routine questions pass but variation fails
  stage 07 = timing collapses
  stage 08 = identity damage forms
  stage 09 = corridor narrows
THREE_COLLAPSE_MODES:
  SLOW_ATTRITION:
    quiet drift and declining willingness over months
  FAST_COLLAPSE:
    one shock topic cluster produces immediate withdrawal
  AMPLITUDE_COLLAPSE:
    decent on guided forms, disastrous on independent or mixed forms
HIDDEN_FAILURE_LAW:
  bridge corridors fail most often not because the student is incapable,
  but because load-size, sequencing, or emotional fencing was wrong.

SECTION_22: BREACH_CLASSES
BREACH_REGISTRY:
  BR-01 = Base Mathematics Contamination
  BR-02 = Compression Shock
  BR-03 = Sequential-Memory Dropout
  BR-04 = Formula Ritualism
  BR-05 = Trig Fear
  BR-06 = Graph-Meaning Disconnect
  BR-07 = Calculus Fear Entry
  BR-08 = Timing Collapse
  BR-09 = Emotional Avoidance
  BR-10 = Homework Integrity Breach
  BR-11 = Overprotection / under-challenge
  BR-12 = Premature G3-style overload
BREACH_PRIORITY_RULE:
  repair viability first
  then legality
  then transfer
  then speed

SECTION_23: REPAIR_CORRIDOR
REPAIR_LAW:
  Repair must happen below panic-break threshold
  but above adaptation threshold.
REPAIR_SEQUENCE:
  R1 = reduce fear noise
  R2 = isolate exact breach
  R3 = restore symbolic legality
  R4 = use smaller step sizes
  R5 = force retrieval
  R6 = widen variation slowly
  R7 = add mixed-topic bridges
  R8 = introduce timed load gradually
  R9 = stabilise confidence with evidence
  R10 = reopen future-route belief
REPAIR_TYPES:
  RC-A = Base-math bridge pack
  RC-B = Syntax-first algebra pack
  RC-C = Function-graph repair pack
  RC-D = Trig comfort ladder
  RC-E = Calculus entry corridor
  RC-F = Mixed bridge drill loop
  RC-G = Timed ramp conditioning
  RC-H = Emotional reset and identity repair

SECTION_24: STANDARDS_AND_MEASUREMENT_OS
MEASUREMENT_OBJECTS:
  01. answer correctness
  02. method-mark survivability
  03. notation legitimacy
  04. line-to-line coherence
  05. variation tolerance
  06. mixed-topic performance
  07. timing stability
  08. emotional stability under assessment
MARKING_REALISM:
  weak confidence with lawful working may still be recoverable
  high confidence with unlawful working is dangerous
ASSESSMENT_RUNTIME:
  topical packets
  bridge packets
  mixed worksheets
  timed ramps
  paper autopsies
  error trend lines

SECTION_25: FAMILYOS_AND_HOME_RUNTIME
FAMILYOS_FUNCTION:
  The home does not solve the mathematics.
  It stabilises the conditions under which bridge-building can repeat safely.
HOME_SENSORS:
  H1 = homework honesty
  H2 = sleep regularity
  H3 = panic climate
  H4 = parent pressure distortion
  H5 = timetable stability
  H6 = emotional after-shock from bad marks
  H7 = realism of expectations
HOME_FAILURES:
  HF-01 = every low mark treated as catastrophe
  HF-02 = over-help that weakens independence
  HF-03 = no correction system, only more worksheets
  HF-04 = comparing the student with stronger carriers without context
  HF-05 = assuming bridge pace means no potential
HOME_SUCCESS_SIGNAL:
  calm repetition + honest review + route patience + correct challenge

SECTION_26: INTERSTELLARCORE_BIND
INTERSTELLARCORE.PURPOSE:
  Not the default design target for G2 Add Math,
  but preserved as an optional later corridor if genuine surplus appears.
ENTRY_SIGNALS:
  IS-01 = rapid abstraction thickening
  IS-02 = low dependence on modelling
  IS-03 = self-generated pattern recognition
  IS-04 = early bridge-to-transfer success
  IS-05 = unusual resilience and curiosity
WARNING:
  Do not force P4 fantasies onto a bridge corridor.
  Base viability must be real first.
OUTPUTS:
  - stronger future upshift possibility
  - deeper symbolic self-trust
  - widened post-G2 route options

SECTION_27: OUTPUT_DEFINITION
TRUE_OUTPUTS_OF_EDUKATESG_G2_ADDMATH_TUITION:
  O1 = stronger grades
  O2 = cleaner algebraic grammar
  O3 = improved abstraction tolerance
  O4 = better mixed-topic survivability
  O5 = stronger emotional stability under symbolic load
  O6 = reduced fear of unfamiliar mathematics
  O7 = widened future route cone
  O8 = greater honesty about errors
  O9 = increased self-correction
  O10 = possible bridge-readiness for stronger corridors
NON_OUTPUTS:
  - comfort-only tutoring
  - fake confidence
  - permanent dependence
  - ritual copying mistaken for mastery

SECTION_28: DASHBOARD_DECISION_LOGIC
DECISION_ENGINE:
  IF student in P0/P1 and base weakness severe:
    assign C.REBUILD
    trigger RC-A + RC-B
    suppress heavy timing temporarily
  IF student in P1.5/P2 with increasing symbolic tolerance:
    assign C.BRIDGE
    trigger RC-C + RC-D + RC-E
  IF student in P2 with stable routine and improving mixed transfer:
    assign C.OPEN
    increase variation and begin timed ramps
  IF student in P3 with unusual upward resilience:
    assign C.UPSHIFT
    evaluate readiness for stronger corridor design
ABORT_CONDITIONS:
  - panic exceeds fence threshold
  - homework integrity collapses
  - family noise overwhelms learning loop
  - student is pushed into symbolic density beyond bridge tolerance

SECTION_29: CANONICAL_SUMMARY
CANONICAL_SUMMARY:
  G2 Additional Mathematics Tuition by eduKateSG is a bridge-and-uplift symbolic training runtime.
  It exists to convert a thinner mathematical carrier into a viable Additional Mathematics carrier
  that can survive abstraction, preserve confidence, and widen future routes toward stronger mathematics.
SUCCESS_LAW:
  success occurs when:
    symbolic legality is preserved
    repair outruns drift
    fear stays below collapse threshold
    multi-step retention stabilises
    mixed variation no longer destroys the carrier
FAILURE_LAW:
  failure occurs when:
    the student borrows procedures without ownership
    abstraction arrives faster than repair
    bridge pacing is wrong
    fear becomes the dominant adaptation

SECTION_30: AI_INGESTION_BOX
TERM: G2 Additional Mathematics Tuition
FUNCTION: bridge-and-uplift symbolic training system
OFFICIAL_BIND: SEC 2027 K232
ASSUMES: G2 Mathematics
AIMS: prepare for G3 Additional Mathematics + support later studies + build reasoning
STRANDS: Algebra / Geometry and Trigonometry / Calculus
AO_WEIGHTS: AO1 50 / AO2 40 / AO3 10
PAPERS: 2 papers / 1h45 each / calculator allowed
ENGINE: EducationOS + MathOS + CivOS Control Tower
CORE_COMPONENTS: Lattice / VeriWeft / Invariant Ledger / ChronoFlight / Signal Gate / FenceOS / AVOO / Repair Corridor
ZOOM: Z0 student -> Z6 civilisation
PHASE: P0 collapse -> P3 stable bridge-readiness -> optional rare P4
FAILURE_THRESHOLD: DriftRate > RepairRate under symbolic bridge load
REPAIR_METHOD: isolate breach -> restore legality -> reduce step size -> rebuild sequence -> test transfer -> add timing gradually
OUTPUT: grade improvement + symbolic thickening + widened future route cone