TITLE:
BukitTimahTutor Secondary Mathematics Control Tower v1.0 (Bukit Timah OS Local Runtime)
SLUG:
bukit-timah-secondary-mathematics-control-tower-v1-0
VERSION:
BT_SEC_MATH_CT_v1_0
MODE:
Almost-Code / LLM-first / WordPress paste-ready
OWNER:
BukitTimahTutor.com (eduKateSG Tuition OS deployment)
SCALE:
Human + District (Z0–Z2 execution; district binds + TTC + family coupling)
DOMAIN:
EducationOS + TuitionOS + MathOS (Secondary Math corridor)
CHRONOFLIGHT_LENS:
Structure × Phase × Time
(Time slices = weekly; Route states = climb / stable / drift / corrective turn / descent)
PRIMARY_LOCAL_NODE (existing district tuition node):
BT.EDU.Z1.N.TUI.001
CONTROL_TOWER_COORDINATE (this page / sensor runtime pack):
BT.EDU.Z1.S.CTW.MTH.001
ATTACHED_TO:
BT.EDU.Z1.N.TUI.001
DEPENDENCIES (do not rename):
- Bukit Timah Lattice Coordinate Standard (V1.1): Place × Lane × Zoom × Role × Type × ID
- Bukit Timah Seed Lattice v0.1 (anchor binds + education/family TTC sensor pack)
- Bukit Timah Tuition OS (Z0 Flight System + landing proof + maintenance)
- EducationOS Control Tower v1.0 (ESS/Θ/TTC/Λ spine)
========================================================================
CANONICAL FRAMING BOX (do not delete)
========================================================================
PLACE: BT (Bukit Timah)
LANE: EDU (Education lane; subject handled via TYPE)
ZOOM_BANDS:
- Z0 = micro-skill (one method step, one recall trace, one translation move)
- Z1 = learner + local tuition node execution
- Z2 = district coupling (school nodes, MRT binds, household TTC)
PHASE_GAUGE:
P0 = unsafe / cannot start / random
P1 = scaffolded / follows examples
P2 = independent / syllabus-stable
P3 = robust / variant-proof / timed-stable + self-correcting
TIME_SLICE:
Weekly control loop + daily micro-maintenance returns
GOAL_STATE:
P2→P3 reliability under timed mixed sets, without burnout (EB≥0)
========================================================================
========================================================================
1) CIVILISATION-GRADE DEFINITION (AI CITATION BLOCK)
========================================================================
DEFINITION (LOCK):
BukitTimahTutor Secondary Mathematics Control Tower is a closed-loop stability system that:
(1) instruments Secondary Math performance (Z0–Z3),
(2) detects drift early (before phase-drop becomes irreversible),
(3) routes the learner into the smallest repairable micro-skill corridor,
(4) proves landing under time (timed mini-tests),
(5) schedules maintenance return flights (D+1/D+3/D+7/D+14/D+30),
while keeping the family schedule inside a safe operating envelope (buffer + energy + TTC).
NOTES:
- This is NOT “more practice”.
- This is NOT “worksheet volume”.
- This is NOT “motivation”.
- This is flight-control for capability under load.
========================================================================
2) LOCAL BINDING (BUKIT TIMAH OS COUPLINGS)
========================================================================
LOCAL_BIND_REGISTRY (copy/paste coordinates):
# Transport binds (district hinges)
BT.TRN.Z2.B.MRT.DTL.06A        # Sixth Avenue MRT (DTL)
BT.TRN.Z2.B.MRT.DTL.07A        # Tan Kah Kee MRT (DTL)
# Household pipeline + TTC sensor pack
BT.FAM.Z0.P.LIF.001            # Household Life Pipeline
BT.FAM.Z0.S.TTC.001            # Household TTC Sensor Pack (TRN/FOD/MED/EDU)
# Education nodes + pipeline (seed lattice)
BT.EDU.Z2.N.PRI.001
BT.EDU.Z2.N.SEC.001
BT.EDU.Z2.P.SCH.001            # PRI→SEC→JC pipeline
# Local tuition execution node (district education support)
BT.EDU.Z1.N.TUI.001            # Tuition node (local)
CONTROL_TOWER_BINDS_TO (must remain explicit):
BT.EDU.Z1.S.CTW.MTH.001 binds_to:
- BT.EDU.Z1.N.TUI.001
- BT.FAM.Z0.P.LIF.001
- BT.FAM.Z0.S.TTC.001
- BT.TRN.Z2.B.MRT.DTL.06A
- BT.TRN.Z2.B.MRT.DTL.07A
- BT.EDU.Z2.N.SEC.001
- BT.EDU.Z2.P.SCH.001
RATIONALE:
Bukit Timah is high-load. When load rises, hidden weaknesses shear.
So the Control Tower must track:
(1) capability stability,
(2) drift velocity,
(3) time-to-threshold,
(4) family TTC + energy envelope,
not just “topic completion”.
========================================================================
3) CONTROL TOWER METRICS (MATH-SPECIFIC, COMPATIBLE WITH EDU_CT_v1_0)
========================================================================
# (Keep EDU_CT spine names where possible; add math-specific sub-sensors as leaf metrics)
ID: BT_MATH_CT_METRICS_LOCKBOX_01
CORE_SPINE (compatible with EducationOS Control Tower):
- ESS_m (0–100): Math Stability Score (math-specific ESS)
- ESSm_Δ: weekly drift velocity (ΔESSm_week, Δ²)
- ECI_m: Error Clustering Index (repeated_errors/top_error_buckets)
- FCR_m: Feedback Compression Ratio (fix_time/cycle_time)
- TR_m: Transfer Ratio (unfamiliar_variant_score / familiar_score)
- LCR_m: Load Collapse Ratio (timed_score / untimed_score)
- HY_m: Hysteresis (days_to_baseline_after_stress)
- AO_m: Avoidance Onset (missed_sessions_or_homework / planned)
FENCE / REVERSIBILITY:
- TTC_m: time-to-threshold (weeks until ESSm crosses critical band)
- Θ_m: irreversibility ratio = TTC_m / T_repair
- Λ_m: enforcement lag ratio = enforcement_lag / TTC_m
MATH-SPECIFIC LEAF SENSORS (Z0–Z3):
- AF (Algebra Fluency)        : expand/factor/solve reliability
- MS (Method Signal)          : selects correct method fast in mixed sets
- RE (Representation Encode)  : word→equation/diagram correctness
- AC (Audit/Checking)         : catches own error before marking
- CE (Careless Error Rate)    : careless_errors / total_errors
- PB (Pace Budget)            : completion_margin (minutes left or deficit)
- VL (Variation Ladder Level) : V0→V3 achieved without collapse
- WB (Working Bandwidth)      : multi-step chain survival rate
NORMALIZATION:
All leaf sensors map into ESS_m via weights by year (Sec 1–Sec 4).
========================================================================
4) CORE INEQUALITIES (THE SYSTEM IS A CONTROL LAW)
========================================================================
ID: BT_MATH_CT_LAWS_01
LAW_01 (Regeneration):
RepairRate ≥ DriftRate under load
LAW_02 (Timed truth):
If timed_score collapses, stability is not real.
LAW_03 (Directional buffer only):
Add buffer only on the failure axis (do not inflate total load).
LAW_04 (Choice control):
ρ (novelty injection / capacity) must stay below capacity band.
CORE INEQUALITY (local execution form):
R_m ≥ D_m · L
subject to:
EB ≥ 0
ρ ≤ ρ_max
Θ_m ≥ 1
FENCE OVERRIDE:
If Θ_m < 1 → treat as urgent regardless of ESS_m.
========================================================================
5) THE ONE-PAGE PANEL (WHAT THE TUTOR SEES WEEKLY)
========================================================================
ID: BT_MATH_CT_PANEL_01
PANEL_BLOCKS (top → bottom):
A) FLIGHT STATUS (single line)
- Current Phase (P0/P1/P2/P3)
- Route State (climb/stable/drift/corrective/descent)
- TTC_m, Θ_m, Λ_m
B) STABILITY ENGINE (scores)
- ESS_m (0–100)
- ESSm_Δ (trend)
- LCR_m (timed collapse?)
- TR_m (transfer?)
C) DRIFT DRIVERS (ranked)
- Top 3 error buckets (ECI_m)
- Which leaf sensor is red? (AF/MS/RE/AC/PB/CE/VL/WB)
- Which condition is causing it? (sleep, overload, anxiety, missing prereq)
D) Z0 QUEUE (the repair stack)
For each queued Z0 micro-skill:
- micro_skill_name
- failure_corridor (concept/method/recall/translation/speed/stress)
- repair_route (takeoff→climb→turbulence→landing proof)
- next_retest_date
E) WEEK PLAN (outputs)
- 1× timed mini-set target (10–20 min)
- 3× micro-maintenance targets (5–12 min each)
- 1× variation ladder target (V0→V3)
- 1× mixed mini-paper (Sec2+; Sec3–4 mandatory)
F) PARENT CONTROL TOWER (non-negotiables)
- sleep window locked
- maintenance slots protected
- overload trimmed (CCA + homework peaks)
- TTC stable (travel + meal + schedule friction reduced)
========================================================================
6) YEAR-BY-YEAR LOCAL RUNTIME (SEC 1 → SEC 4)
========================================================================
ID: BT_MATH_CT_YEAR_GATES_01
# (Uses Secondary Math OS granular gates; localizes to Bukit Timah execution)
SEC_1 (Foundation Lock Year)
Targets:
- Z0 clean arithmetic + algebra manipulation
- Z1 method signals begin
- Z2 small variation without panic
- Z3 light timing without collapse
Core modules:
1) Number & Ops Stability
2) Algebra Fluency 1
3) Representation 1 (word→equation/diagram)
4) Geometry Chain 1 (statement→reason)
5) Data/Graphs 1
Sensors to track:
- AF (red=stop)
- RE
- ECI_m
Labs:
- Fluency Lab daily 10–15 min
- Encode Lab 2–3×/week
- Repair+Retest weekly
Gate:
- Precision ≥ 3, Speed ≥ 2, DriftRisk not High
- RE setups ≥ 80% correct (basic word problems)
SEC_2 (Method Signal Year)
Core modules:
1) Algebra Fluency 2
2) Linear Systems & Graph Links
3) Percent/Rate/Ratio mastery
4) Geometry Chain 2 (multi-step)
5) Probability/Stats basics
Sensors:
- MS (method selection)
- TR_m (variation transfer)
- PB (pace budget early)
Labs:
- Method Signal Lab weekly (no solving)
- Variation Ladder Lab weekly (V0→V3)
- Mixed Mini-Paper weekly
- Fluency maintenance 3–5×/week
Gate:
- Precision ≥ 3, Bandwidth ≥ 3, Speed ≥ 3 on mixed minis
- DriftRisk low/medium only
SEC_3 (Split Year: E-Math stability + A-Math jump control)
E-Math targets:
- fast method selection under mixed sets
- transfer to multi-step problems
- timed stability becomes real
A-Math (if taken) targets:
- Algebra Kernel becomes daily discipline
- transformation chains survive variation
- traps audited
Gates:
- E-Math: mixed minis stable; Speed ≥ 3; DriftRisk not High
- A-Math: kernel stable; Quad/Trig/Diff reach T2 transfer; DriftRisk not High
SEC_4 (Wrapper Year: O-Level reliability)
Goals:
- full-paper completion + accuracy stability
- mixed-topic switching control
- audit routine reflex
Graduation:
- Precision ≥ 3, Bandwidth ≥ 3, Speed ≥ 3 in full-paper conditions
- DriftRisk low/medium only
- repeated error buckets trending down week-to-week
========================================================================
7) THE TUITION LOOP (Z0 FLIGHT SYSTEM IMPLEMENTATION)
========================================================================
ID: BT_MATH_CT_Z0_LOOP_01
Z0_LOOP (repeat until stable):
1) Sense: identify single Z0 micro-skill being tested
2) Probe: 3-question probe (template/exam/variation) → classify Phase
3) Instruments: airspeed(solve-rate), heading(method correctness), AoA(overload),
   turbulence(error volatility), wind-shear(context-shift sensitivity),
   fuel(stamina), buffer(thickness)
4) Label corridor: concept/method/recall/translation/speed/stress
5) Repair route:
   Takeoff Repair (minimum model + first 10 seconds + step-map + one clean success)
   → Climb (core/variation/anti-error reps)
   → Turbulence drills
   → Landing Proof (timed mini-test + strict marking + re-test)
   → Maintenance (D+1/D+3/D+7/D+14/D+30; 5–12 min; retrieval-first)
6) Log: update ECI_m + ESS_m + TTC_m + Z0 queue
LANDING PROOF RULE:
No skill is counted stable unless it can land repeatedly under a timer.
========================================================================
8) CLASS SESSION TEMPLATE (BUKIT TIMAH TUTOR OPERATOR SOP)
========================================================================
ID: BT_MATH_CT_SESSION_SOP_01
DEFAULT_SESSION (90 min small-group):
1) Warm-Up Retrieval (8–12 mins)     # mixed review; install maintenance
2) Teach for Understanding (20–25)   # first principles + representations
3) Guided Practice (25–30)           # checkpoint questions; remove scaffolds
4) Timed Mini-Set (20–35)            # exam-style items; error type tagging
5) Exit Ticket (5)                   # 1 micro-target for home
6) Error Log + Route Update (embedded)
Outputs:
- 1 timed mini-set assigned
- 3 micro-maintenance returns scheduled
- 1 variation ladder task scheduled
- parent-control actions (sleep + slot protection)
========================================================================
9) FAILURE-FIRST (LOCAL NEGATIVE VOID RISKS THE CONTROL TOWER MUST CATCH)
========================================================================
ID: BT_MATH_CT_NEGATIVE_VOID_01
RISK_01: Resource Illusion
Signature:
- grades stable but independence rate decreases
Control:
- track TR_m + LCR_m + AO_m; enforce timed proof
RISK_02: Prompt Dependency
Signature:
- can solve only with hints/templates
Control:
- remove prompts; require self-start + audit routine; phase reclassify honestly
RISK_03: Timed Collapse Masked by Homework
Signature:
- untimed ok, timed fails (LCR_m low)
Control:
- weekly timed minis; rebuild pace budget + audit routine
RISK_04: Drift Debt
Signature:
- small errors repeat; ECI_m rises; ESSm_Δ negative
Control:
- truncate + stitch; repair smallest link; reduce load temporarily
========================================================================
10) OUTPUTS (WHAT THIS CONTROL TOWER MUST GENERATE EVERY WEEK)
========================================================================
ID: BT_MATH_CT_OUTPUTS_01
OUTPUT_A: Student Weekly Status Line
- Phase / RouteState / ESS_m / ESSm_Δ / TTC_m / Θ_m / top drift driver
OUTPUT_B: Z0 Repair Queue (top 5)
- micro-skill, corridor, repair route, retest date
OUTPUT_C: Week Plan (parent + student)
- 1 timed mini-set
- 3 micro-maintenance returns
- 1 variation ladder
- 1 mixed mini-paper (Sec2+)
- sleep + schedule protection actions
OUTPUT_D: Tutor Session Plan
- warm-up set
- core teach target
- guided practice ladder
- timed set
- exit ticket
========================================================================
VERSION LOCK
========================================================================
BT_SEC_MATH_CT_v1_0
RULES:
- Coordinates follow: <REGION>.<LANE>.Z<ZOOM>.<ROLE>.<TYPE>.<ID>
- Do not rename core node: BT.EDU.Z1.N.TUI.001
- Forward-only upgrades (v1_1, v1_2…); keep MetricIDs stable
- Fence override is mandatory when Θ_m < 1
END.

================================================================================
CHILD PAGE 1/4 (SEC 1)
================================================================================
TITLE:
BukitTimahTutor Sec 1 Mathematics Control Tower v1.0 (Bukit Timah OS Local Runtime)
SLUG:
bukit-timah-sec-1-mathematics-control-tower-v1-0
VERSION:
BT_SEC1_MATH_CT_v1_0
PARENT_PAGE:
BT_SEC_MATH_CT_v1_0  (Control Tower Root)
CONTROL_TOWER_COORDINATE (child):
BT.EDU.Z1.S.CTW.MTH.S1.001
ATTACHED_TO:
BT.EDU.Z1.N.TUI.001
DEPENDENCIES (inherit; do not rename):
- BT_SEC_MATH_CT_v1_0
- BT_MATH_CT_METRICS_LOCKBOX_01
- BT_MATH_CT_LAWS_01
- BT_MATH_CT_PANEL_01
- BT_MATH_CT_Z0_LOOP_01
- Bukit Timah Lattice Coordinate Standard v1.1
- Bukit Timah Seed Lattice v0.1
- Bukit Timah Tuition OS
SCOPE:
Secondary 1 Mathematics only (Foundation Lock Year)
================================================================================
A) CANONICAL FRAMING BOX (SEC 1)
================================================================================
PLACE: BT
LANE: EDU
ZOOM: Z0–Z2 execution (Z3 only for light timing)
PHASE TARGET (Sec 1 end-state):
P2 stable on core foundations + P1→P2 transfer beginnings
CHRONOFLIGHT:
Weekly slices; prevent Phase-drop during adjustment to secondary load
SEC 1 NON-NEGOTIABLE:
If Algebra Fluency (AF) is broken, everything downstream breaks.
================================================================================
B) CIV-GRADE DEFINITION (SEC 1 LOCAL)
================================================================================
DEFINITION (LOCK):
Sec 1 Math Control Tower instruments the PSLE→Secondary transition and prevents
foundation shear by (1) detecting fluency leaks early, (2) repairing Z0 micro-skills
before they become identity-level “I can’t do math”, and (3) proving stability with
short timed landings (not worksheet volume).
================================================================================
C) SEC 1 METRIC WEIGHTS (ESS_m formula specialization)
================================================================================
ID: BT_MATH_CT_ESS_WEIGHTS_S1_01
ESS_m = Σ(w_i * sensor_i) - penalties
Sensors (0–100 each):
AF, RE, AC, CE, WB, MS(light), PB(light), TR(light), LCR(light)
SEC 1 DEFAULT WEIGHTS:
w_AF = 0.26
w_RE = 0.16
w_AC = 0.14
w_CE = 0.10
w_WB = 0.12
w_MS = 0.08
w_PB = 0.06
w_TR = 0.04
w_LCR = 0.04
PENALTIES (apply):
- If CE > 0.30 then -8
- If ECI_m rising 2 weeks consecutively then -6
- If AO_m triggered then -8
SEC 1 PHASE BANDS (by ESS_m + landing proof):
P0: ESS_m < 35 OR cannot complete 3-question probe without collapse
P1: 35–59 with scaffolds; timed landing unreliable
P2: 60–79 independent on core topics; light timed landings pass
P3: 80+ stable under mixed mini-sets (rare in Sec 1; not required)
================================================================================
D) SEC 1 ONE-PAGE PANEL (weekly)
================================================================================
ID: BT_MATH_CT_PANEL_S1_01
(Use same panel blocks as BT_MATH_CT_PANEL_01, with Sec 1 defaults)
DEFAULTS:
Timed Mini-Set: 10–15 minutes, 6–10 marks equivalent
Variation Ladder: V0→V2 (V3 optional)
Mixed Mini-Paper: short mixed set (not full paper)
SEC 1 REQUIRED PANEL HIGHLIGHTS:
- AF (red/yellow/green)
- RE (word→equation/diagram)
- CE (careless ratio)
- ECI_m (top 3 repeating buckets)
================================================================================
E) SEC 1 Z0 QUEUE TEMPLATE (what gets repaired)
================================================================================
ID: BT_MATH_CT_Z0_QUEUE_S1_01
TOP Z0 CLUSTERS (Sec 1 typical):
1) Integer operations + negative numbers
2) Algebra manipulation: expand / factor / simplify
3) Transposition & solving simple equations
4) Fractions ↔ decimals ↔ percentages (conversion fluency)
5) Ratio & rate basics
6) Basic geometry facts + angle chase single-step
7) Word-to-equation encoding (RE core)
REPAIR PRIORITY RULE:
AF leak outranks topic completion.
================================================================================
F) SEC 1 SESSION SOP (operator)
================================================================================
ID: BT_MATH_CT_SESSION_SOP_S1_01
(Inherits BT_MATH_CT_SESSION_SOP_01; tuned)
SESSION (75–90 min):
1) Retrieval Warm-Up (10)  -> AF + RE
2) Teach (20)              -> first-principles + representations
3) Guided Ladder (25)      -> remove prompts
4) Timed Landing (15)      -> small landing proof
5) Error Log + Micro-Plan (5–10)
HOME OUTPUT (minimum viable):
- 1 timed landing (10–12 min)
- 3 micro-maintenance returns (5–8 min each)
- 1 encode drill (RE) (8–12 min)
================================================================================
G) SEC 1 NEGATIVE VOID TRIGGERS (Bukit Timah local risks)
================================================================================
ID: BT_MATH_CT_NEGVOID_S1_01
TRIGGER_01: “New school, new speed” collapse
Signature: LCR_m drops + PB deficit + WB collapse
Action: reduce load, repair bandwidth chain, re-land
TRIGGER_02: Copying solutions / false stability
Signature: untimed homework ok, probe fails; TR_m low
Action: enforce no-notes probe + landing proof
TRIGGER_03: Algebra fear identity lock
Signature: AO_m + avoidance language + AF red
Action: smallest possible algebra wins + daily micro-return
================================================================================
H) CHRONOFLIGHT OVERLAY BLOCK (SEC 1)
================================================================================
ID: BT_MATH_CF_OVERLAY_S1_01
TIME_SLICE: Week k
ROUTE_STATE: {climb | stable | drift | corrective | descent}
PRIMARY_DRIFT: {AF leak | RE encode fail | CE spike | WB collapse | overload}
PRIMARY_REPAIR: {Z0 truncate+stitch | timed landing | maintenance returns | load trim}
BUFFER_STATUS: {thin | medium | thick}  (family + student)
NEXT_SLICE_RISK: {low | medium | high}
ACTION: {one-line directive}
================================================================================
CANONICAL PLACEMENT FOOTER
================================================================================
This page is a child runtime of:
BT.EDU.Z1.S.CTW.MTH.001 (BukitTimahTutor Secondary Mathematics Control Tower v1.0)
Child coordinate:
BT.EDU.Z1.S.CTW.MTH.S1.001
END.

================================================================================
CHILD PAGE 2/4 (SEC 2)
================================================================================
TITLE:
BukitTimahTutor Sec 2 Mathematics Control Tower v1.0 (Bukit Timah OS Local Runtime)
SLUG:
bukit-timah-sec-2-mathematics-control-tower-v1-0
VERSION:
BT_SEC2_MATH_CT_v1_0
PARENT_PAGE:
BT_SEC_MATH_CT_v1_0
CONTROL_TOWER_COORDINATE (child):
BT.EDU.Z1.S.CTW.MTH.S2.001
ATTACHED_TO:
BT.EDU.Z1.N.TUI.001
DEPENDENCIES (inherit; do not rename):
- BT_SEC_MATH_CT_v1_0
- BT_MATH_CT_METRICS_LOCKBOX_01
- BT_MATH_CT_LAWS_01
- BT_MATH_CT_PANEL_01
- BT_MATH_CT_Z0_LOOP_01
SCOPE:
Secondary 2 Mathematics only (Method Signal Year)
================================================================================
A) CANONICAL FRAMING BOX (SEC 2)
================================================================================
SEC 2 TARGET:
P2 independence across most topics + rising TR_m (transfer)
SEC 2 REAL THREAT:
Students “know topics” but fail mixed sets because method selection is weak.
================================================================================
B) CIV-GRADE DEFINITION (SEC 2 LOCAL)
================================================================================
DEFINITION (LOCK):
Sec 2 Math Control Tower upgrades the learner from “topic-by-topic solving” into
“mixed-set method signal control” by making method selection visible, reducing
prompt dependency, and proving transfer on unfamiliar variants.
================================================================================
C) SEC 2 METRIC WEIGHTS (ESS_m specialization)
================================================================================
ID: BT_MATH_CT_ESS_WEIGHTS_S2_01
SEC 2 DEFAULT WEIGHTS:
w_MS = 0.20
w_AF = 0.18
w_TR = 0.14
w_WB = 0.12
w_RE = 0.10
w_AC = 0.10
w_CE = 0.06
w_PB = 0.05
w_LCR = 0.05
SEC 2 PHASE BANDS:
P0: ESS_m < 40 OR mixed-set method selection collapse
P1: 40–64 topic-stable but mixed unstable; TR_m low
P2: 65–82 mixed sets stable; TR_m rising; timed minis pass
P3: 83+ variant-proof on mixed minis under time
================================================================================
D) SEC 2 ONE-PAGE PANEL (weekly)
================================================================================
ID: BT_MATH_CT_PANEL_S2_01
SEC 2 REQUIRED PANEL HIGHLIGHTS:
- MS (Method Signal)   [must be explicit]
- TR_m (Transfer Ratio)
- ECI_m (repeated error clusters)
- LCR_m (timed truth check)
- PB (pace budget emerging)
SEC 2 DEFAULTS:
Timed Mini-Set: 12–18 minutes (mixed)
Variation Ladder: V0→V3 weekly (mandatory)
Mixed Mini-Paper: weekly (short but mixed)
================================================================================
E) SEC 2 METHOD SIGNAL LAB (mandatory)
================================================================================
ID: BT_MATH_CT_MS_LAB_S2_01
MS_LAB (10–15 min weekly; no full solving):
Given 12 mixed questions:
- label topic family
- choose method
- write first 10 seconds: “what I do first”
Score:
MS = correct method decisions / 12
RULE:
If MS < 0.70 → reduce new topics; rebuild signal.
================================================================================
F) SEC 2 Z0 QUEUE (typical repair clusters)
================================================================================
ID: BT_MATH_CT_Z0_QUEUE_S2_01
TOP Z0 CLUSTERS (Sec 2 typical):
1) Linear graphs + equation links
2) Ratio/rate/proportion in varied contexts
3) Algebra manipulation under variation (fractions-in-algebra)
4) Geometry reasoning chains (statement→reason multi-step)
5) Probability language + sample space construction
6) Word problem encoding: “what is being conserved / compared” (RE)
PRIORITY RULE:
MS leak outranks topic completion.
TR leak outranks “hard questions”.
================================================================================
G) SEC 2 SESSION SOP (operator)
================================================================================
ID: BT_MATH_CT_SESSION_SOP_S2_01
SESSION (75–90 min):
1) Retrieval Warm-Up (8–10)     -> mixed micro-returns
2) Method Signal Teach (10–15)  -> decision rules, cues, anti-cues
3) Guided Mixed Ladder (25–30)  -> prompt removal
4) Timed Mixed Mini (20–25)     -> landing proof
5) Error Log + Plan (5–10)
HOME OUTPUT:
- 1 timed mixed mini-set
- 1 MS_LAB sheet
- 3 micro-maintenance returns
- 1 variation ladder set
================================================================================
H) SEC 2 NEGATIVE VOID TRIGGERS
================================================================================
ID: BT_MATH_CT_NEGVOID_S2_01
TRIGGER_01: “Can do individually, cannot mix”
Signature: MS low, TR low, ECI_m high
Action: MS_LAB + mixed ladders; stop topic binge
TRIGGER_02: Variation panic
Signature: TR drops sharply when surface changes
Action: variation ladder (V0→V3) with scaffolds removed gradually
TRIGGER_03: Timed truth denial
Signature: untimed ok; timed collapse; excuses multiply
Action: short timed landings weekly; PB training
================================================================================
H) CHRONOFLIGHT OVERLAY BLOCK (SEC 2)
================================================================================
ID: BT_MATH_CF_OVERLAY_S2_01
(Use same fields as Sec 1 overlay; enforce MS/TR as drift drivers)
================================================================================
CANONICAL PLACEMENT FOOTER
================================================================================
Child runtime of BT.EDU.Z1.S.CTW.MTH.001
Child coordinate BT.EDU.Z1.S.CTW.MTH.S2.001
END.

================================================================================
CHILD PAGE 3/4 (SEC 3)
================================================================================
TITLE:
BukitTimahTutor Sec 3 Mathematics Control Tower v1.0 (Bukit Timah OS Local Runtime)
SLUG:
bukit-timah-sec-3-mathematics-control-tower-v1-0
VERSION:
BT_SEC3_MATH_CT_v1_0
PARENT_PAGE:
BT_SEC_MATH_CT_v1_0
CONTROL_TOWER_COORDINATE (child):
BT.EDU.Z1.S.CTW.MTH.S3.001
ATTACHED_TO:
BT.EDU.Z1.N.TUI.001
DEPENDENCIES (inherit; do not rename):
- BT_SEC_MATH_CT_v1_0
- BT_MATH_CT_METRICS_LOCKBOX_01
- BT_MATH_CT_LAWS_01
- BT_MATH_CT_PANEL_01
- BT_MATH_CT_Z0_LOOP_01
SCOPE:
Secondary 3 Mathematics (E-Math stability year; A-Math jump control if applicable)
================================================================================
A) CANONICAL FRAMING BOX (SEC 3)
================================================================================
SEC 3 REALITY:
- Load rises.
- Topic depth rises.
- Timing becomes real.
- For A-Math: algebra chain becomes the operating system.
SEC 3 TARGET:
E-Math: P2→P3 reliability on mixed timed minis.
A-Math (if taken): P1→P2 stability on kernel topics without panic.
================================================================================
B) CIV-GRADE DEFINITION (SEC 3 LOCAL)
================================================================================
DEFINITION (LOCK):
Sec 3 Control Tower is a bifurcation-safe system that prevents “split collapse”:
students must keep E-Math stable while optionally onboarding A-Math without
cannibalizing buffer, sleep, or algebra integrity.
================================================================================
C) SEC 3 METRIC WEIGHTS (ESS_m specialization)
================================================================================
ID: BT_MATH_CT_ESS_WEIGHTS_S3_01
SEC 3 DEFAULT WEIGHTS (E-Math):
w_LCR = 0.16
w_MS  = 0.16
w_TR  = 0.14
w_WB  = 0.12
w_AC  = 0.10
w_PB  = 0.10
w_AF  = 0.10
w_RE  = 0.06
w_CE  = 0.06
SEC 3 PHASE BANDS:
P0: ESS_m < 45 OR timed collapse severe (LCR very low)
P1: 45–69 mixed unstable under time; repair corridors active
P2: 70–84 mixed stable; timed minis pass; transfer improving
P3: 85+ stable under timed mixed sets + self-audit works
A-MATH ADD-ON SENSOR (if applicable; does not rename core metrics):
- AF becomes “Algebra Kernel” priority
- WB is dominant (multi-step chain survival)
A-MATH SUBRULE:
If AF(red) OR WB(red) → freeze new A-Math topics; repair kernel.
================================================================================
D) SEC 3 ONE-PAGE PANEL (weekly)
================================================================================
ID: BT_MATH_CT_PANEL_S3_01
SEC 3 REQUIRED PANEL HIGHLIGHTS:
- LCR_m (timed truth)  [primary]
- PB (pace budget)     [primary]
- MS + TR (switching + transfer)
- AC (audit)           [must rise]
- ECI_m (repeat buckets)
DEFAULTS:
Timed Mini-Set: 18–25 minutes (mixed)
Variation Ladder: V0→V3 weekly (mandatory)
Mixed Mini-Paper: weekly (longer mixed set)
================================================================================
E) SEC 3 SESSION SOP (operator)
================================================================================
ID: BT_MATH_CT_SESSION_SOP_S3_01
SESSION (90 min preferred):
1) Retrieval Warm-Up (10)      -> mixed returns (timed micro)
2) Teach (15–20)               -> deeper mechanisms + representations
3) Guided Mixed Ladder (25–30) -> switching practice
4) Timed Landing (25–30)       -> exam slice
5) Error Log + Route Update (5)
HOME OUTPUT:
- 1 timed landing (20–25 min)
- 1 mixed ladder set
- 3 micro-maintenance returns
- (If A-Math) 1 algebra kernel drill (10–15 min)
================================================================================
F) SEC 3 NEGATIVE VOID TRIGGERS (split collapse)
================================================================================
ID: BT_MATH_CT_NEGVOID_S3_01
TRIGGER_01: Timed collapse + denial
Signature: LCR_m drops; PB deficit; avoidance language
Action: smaller timed slices; rebuild PB + AC + switching
TRIGGER_02: Switching shear
Signature: MS ok in single topic; fails on mixed; TR drops
Action: mixed ladders with forced method labelling
TRIGGER_03: A-Math cannibalizes base
Signature: sleep drops; E-Math ESS_m drops after A-Math onboarding
Action: Fence A-Math (narrow corridor), protect base maintenance
TRIGGER_04: Algebra kernel fracture (A-Math)
Signature: AF/WB red; error clusters explode
Action: truncate + stitch; return to kernel primitives; re-land
================================================================================
G) CHRONOFLIGHT OVERLAY BLOCK (SEC 3)
================================================================================
ID: BT_MATH_CF_OVERLAY_S3_01
(Use same fields; add “split collapse” note when applicable)
================================================================================
CANONICAL PLACEMENT FOOTER
================================================================================
Child runtime of BT.EDU.Z1.S.CTW.MTH.001
Child coordinate BT.EDU.Z1.S.CTW.MTH.S3.001
END.

================================================================================
CHILD PAGE 4/4 (SEC 4)
================================================================================
TITLE:
BukitTimahTutor Sec 4 Mathematics Control Tower v1.0 (Bukit Timah OS Local Runtime)
SLUG:
bukit-timah-sec-4-mathematics-control-tower-v1-0
VERSION:
BT_SEC4_MATH_CT_v1_0
PARENT_PAGE:
BT_SEC_MATH_CT_v1_0
CONTROL_TOWER_COORDINATE (child):
BT.EDU.Z1.S.CTW.MTH.S4.001
ATTACHED_TO:
BT.EDU.Z1.N.TUI.001
DEPENDENCIES (inherit; do not rename):
- BT_SEC_MATH_CT_v1_0
- BT_MATH_CT_METRICS_LOCKBOX_01
- BT_MATH_CT_LAWS_01
- BT_MATH_CT_PANEL_01
- BT_MATH_CT_Z0_LOOP_01
SCOPE:
Secondary 4 Mathematics (O-Level reliability / full-paper runtime)
================================================================================
A) CANONICAL FRAMING BOX (SEC 4)
================================================================================
SEC 4 IS NOT “LEARN MORE TOPICS”.
SEC 4 IS:
- Full-paper stability
- Switching control
- Audit reflex
- Buffer preservation under exam load
TARGET:
P3 corridor reliability by exam date:
Precision ≥ 3, Bandwidth ≥ 3, Speed ≥ 3 under full-paper conditions.
================================================================================
B) CIV-GRADE DEFINITION (SEC 4 LOCAL)
================================================================================
DEFINITION (LOCK):
Sec 4 Control Tower is a proof-driven O-Level flight system that converts syllabus
coverage into timed full-paper reliability by enforcing landing proof, maintenance
returns, and drift containment (no hidden debt near the node).
================================================================================
C) SEC 4 METRIC WEIGHTS (ESS_m specialization)
================================================================================
ID: BT_MATH_CT_ESS_WEIGHTS_S4_01
SEC 4 DEFAULT WEIGHTS:
w_LCR = 0.20
w_PB  = 0.16
w_AC  = 0.14
w_MS  = 0.12
w_TR  = 0.12
w_WB  = 0.10
w_ECI = 0.08   (use ECI_m as weighted term)
w_CE  = 0.04
w_AF  = 0.04
SEC 4 PHASE BANDS:
P0: ESS_m < 50 OR cannot finish exam slices
P1: 50–72 partial stability; repeated drift; audit weak
P2: 73–86 stable on timed slices; full paper inconsistent
P3: 87+ repeatable full-paper stability + audit reflex
SEC 4 FENCE RULE (node proximity):
If Θ_m < 1 OR TTC_m ≤ 4 weeks → emergency routing (truncate & stitch only).
================================================================================
D) SEC 4 ONE-PAGE PANEL (weekly)
================================================================================
ID: BT_MATH_CT_PANEL_S4_01
SEC 4 REQUIRED PANEL HIGHLIGHTS:
- LCR_m (timed truth) [primary]
- PB (pace budget)    [primary]
- AC (audit/checking) [primary]
- ECI_m (repeat buckets)
- TR_m (variant proof)
DEFAULTS:
Timed Mini-Set: 25–35 minutes (exam slice)
Variation Ladder: V0→V3 weekly (target weak areas only)
Mixed Mini-Paper: weekly; full paper bi-weekly (or weekly near exam)
================================================================================
E) SEC 4 PAPER ROUTINE (operator executable)
================================================================================
ID: BT_MATH_CT_PAPER_ROUTINE_S4_01
FULL PAPER LOOP:
1) Pre-brief (3 min): pace budget + target sections
2) Run paper (timed)
3) Mark strictly (no mercy marking)
4) Error tag every wrong mark into buckets:
   {concept | method | recall | encoding | speed | stress | careless}
5) Update ECI_m + choose TOP 2 drift buckets only
6) Route repairs into Z0 queue + schedule returns (D+1/D+3/D+7)
RULE:
Do not repair more than TOP 2 buckets per week.
(Over-repair = overload = new drift.)
================================================================================
F) SEC 4 SESSION SOP (operator)
================================================================================
ID: BT_MATH_CT_SESSION_SOP_S4_01
SESSION (90–120 min recommended):
1) Retrieval Warm-Up (10)             -> mixed returns (timed)
2) Teach / Repair (20–25)             -> only TOP drift buckets
3) Guided Exam Slice (25–35)          -> pace + audit drills
4) Timed Exam Slice OR Paper Segment (30–45)
5) Error Log + Next Week Plan (10)
HOME OUTPUT:
- 1 timed exam slice (30–40 min) OR 1 full paper (as scheduled)
- 3 maintenance returns (5–10 min)
- 1 audit drill (5–8 min)
- 1 variation ladder (weak area only)
================================================================================
G) SEC 4 NEGATIVE VOID TRIGGERS (near-node compression)
================================================================================
ID: BT_MATH_CT_NEGVOID_S4_01
TRIGGER_01: “Near exam, still patching foundations”
Signature: ECI_m high; TTC short; Θ_m < 1
Action: emergency truncate+stitch; only repair corridors that lift marks fastest
TRIGGER_02: Full paper fatigue collapse
Signature: WB drops; PB deficit; accuracy degrades in last third
Action: stamina slicing + paced segments; rebuild buffer via schedule
TRIGGER_03: Audit absent
Signature: high careless; repeats; same marks lost
Action: install audit protocol as reflex; score AC explicitly
TRIGGER_04: Overload spiral (Bukit Timah high-load profile)
Signature: sleep down; AO_m up; ESSm_Δ negative
Action: load trim; protect maintenance; smaller proofs, more returns
================================================================================
H) CHRONOFLIGHT OVERLAY BLOCK (SEC 4)
================================================================================
ID: BT_MATH_CF_OVERLAY_S4_01
TIME_SLICE: Week k
ROUTE_STATE: {climb | stable | drift | corrective | descent}
PRIMARY_DRIFT: {timed collapse | pace deficit | repeat bucket | overload | audit missing}
PRIMARY_REPAIR: {truncate+stitch | paper slice landings | maintenance returns | load trim}
BUFFER_STATUS: {thin | medium | thick}
NEXT_SLICE_RISK: {low | medium | high}
ACTION: {one-line directive}
================================================================================
CANONICAL PLACEMENT FOOTER
================================================================================
Child runtime of BT.EDU.Z1.S.CTW.MTH.001
Child coordinate BT.EDU.Z1.S.CTW.MTH.S4.001
END.