BTT.AMATH — BukitTimahTutor.com Additional Mathematics Overlay (Z0–Z3)

(Almost-Code Canonical · Unified Spec v1.0)

This attaches Additional Mathematics (A-Math) as a high-symbol-density, high-transfer, high-speed lane under BukitTimahTutor’s repair router.


BTT×AMATH — Lane Registry

[SITE]
Domain: bukittimahtutor.com
Place: SGP.SG.BT
Lane: EDU.MATH.AMATH
Role: Repair Router (Truncation + Stitching)
Zoom: Z0–Z3
v: v1.0

1) A-Math Lock (What A-Math Really Tests)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z3×V×LOCK×BTT.AMATH.PURPOSE×v1.0:
txt: "A-Math is an acceleration test of symbol control + abstraction + transfer under time; BukitTimahTutor repairs primitives first, then restores speed."
[EDGE]
binds_to:
SGP.SG.BT×EDU.MATH×Z3×R×PROTOCOL×BTT.MATH.REPAIR×v1.0
SGP.SG.BT×EDU×Z3×S×LAW×BTT.ACCEL_MISMATCH×v1.0

2) A-Math Core Primitives (Below Topics)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z0×L×PRIM×AMATH.SYMBOL_FLUENCY×v1.0:
def: "fast, accurate manipulation of symbols without losing meaning"
[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z0×L×PRIM×AMATH.FUNCTION_SENSE×v1.0:
def: "seeing expressions as functions/objects; understanding input-output and transformation"
[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z1×L×PRIM×AMATH.IDENTITY_CONTROL×v1.0:
def: "algebraic identity manipulation with constraint awareness"
[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z1×L×PRIM×AMATH.ERROR_RESILIENCE×v1.0:
def: "self-correction under dense multi-step chains"
[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z2×L×PRIM×AMATH.TRANSFER_UNDER_VARIATION×v1.0:
def: "selecting correct method when the question is unfamiliar"
[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z2×L×PRIM×AMATH.TIME_COMPRESSION×v1.0:
def: "executing long chains with speed without collapse"

3) A-Math Phase Definitions (P0–P3) (Operational)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z3×S×PHASE×P0P3.AMATH×v1.0:
P3:
- "chooses method correctly under novelty"
- "executes symbol chains cleanly"
- "checks constraints automatically"
- "stable under time"
P2:
- "can do standard forms"
- "brittle under twists"
- "errors accumulate in long chains"
P1:
- "memorises procedures"
- "drops marks to careless algebra"
- "panic when stuck; time collapse"
P0:
- "cannot start; avoidance; shutdown"

4) A-Math Failure Mode Trace (Required)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z3×R×TRACE×BTT.AMATH.FAILURE_MODE×v1.0:
chain:
- "Z0: weak symbol fluency → slow + errors"
- "Z0: missing function sense → treats expressions as static"
- "Z1: identity manipulation without constraints → nonsense steps"
- "Z1: error loop externalised → cannot repair mid-chain"
- "Z2: transfer failure → wrong method chosen"
- "Z2: time compression collapse → panic → blanking"
phase_drift:
- "P2 → P1 → P0 under acceleration mismatch"
repair_route:
- "truncate speed → rebuild primitives → restore transfer → add time last → P1→P2→P3"

5) Topic Blocks (as Capability Objects, not Syllabus)

These are expressed as objects with failure signatures and repair binds.

5.1 Algebraic Manipulation (All of A-Math lives here)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z1×L×MODULE×AMATH.ALGEBRA_ENGINE×v1.0:
requires:
- AMATH.SYMBOL_FLUENCY
- AMATH.IDENTITY_CONTROL
- AMATH.ERROR_RESILIENCE
failure_signature:
- "sign errors"
- "lost brackets"
- "illegal cancellation"
- "equation solved with unstated restrictions"
repair_bind:
- "force constraint checks + localisation rituals + short-chain mastery before long chains"

5.2 Functions & Graphs (Method selection + interpretation)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z2×L×MODULE×AMATH.FUNCTIONS_GRAPHS×v1.0:
requires:
- AMATH.FUNCTION_SENSE
- AMATH.TRANSFER_UNDER_VARIATION
failure_signature:
- "cannot interpret graph meaning"
- "treats transformations as memorised shifts"
repair_bind:
- "map every expression to input-output + effect of parameter change"

5.3 Trigonometry (Identity discipline + constraints)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z2×L×MODULE×AMATH.TRIG_ENGINE×v1.0:
requires:
- AMATH.IDENTITY_CONTROL
- AMATH.ERROR_RESILIENCE
- AMATH.TRANSFER_UNDER_VARIATION
failure_signature:
- "wrong identities"
- "angle/radian confusion (if present)"
- "forgets domain restrictions"
repair_bind:
- "identity ladder + constraint guardrails + verification by substitution"

5.4 Logarithms & Indices (Rule correctness under speed)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z2×L×MODULE×AMATH.LOGS_INDICES×v1.0:
requires:
- AMATH.SYMBOL_FLUENCY
- AMATH.ERROR_RESILIENCE
failure_signature:
- "illegal log rules"
- "base confusion"
- "domain mistakes"
repair_bind:
- "rule boundary training + counterexample checks"

5.5 Differentiation & Integration (Chain control + interpretation)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z2×L×MODULE×AMATH.CALCULUS_ENGINE×v1.0:
requires:
- AMATH.FUNCTION_SENSE
- AMATH.SYMBOL_FLUENCY
- AMATH.ERROR_RESILIENCE
- AMATH.TRANSFER_UNDER_VARIATION
failure_signature:
- "wrong differentiation rules"
- "lost chain rule"
- "cannot connect derivative to meaning (gradient/rate)"
repair_bind:
- "rule mastery + meaning checks + method selection drills"

6) A-Math Diagnostic Router (Fast Classification)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z3×R×PROTOCOL×BTT.AMATH.DIAG_ROUTER×v1.0:
if:
- "errors are mostly algebraic" → route_to: AMATH.ALGEBRA_ENGINE
- "stuck at start" → route_to: AMATH.FUNCTIONS_GRAPHS (representation + decomposition)
- "twist questions fail" → route_to: AMATH.TRANSFER_UNDER_VARIATION
- "time runs out" → route_to: AMATH.TIME_COMPRESSION with speed-last rule
- "panic/avoidance" → route_to: TRUNCATION + S6.STABILITY repair

7) A-Math Repair Protocol (Strict Order, Speed-Last)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z3×R×PROTOCOL×BTT.AMATH.REPAIR×v1.0:
TRUNCATE:
- "stop long problem chains"
- "reduce speed demand"
- "repair confidence via competence"
REBUILD:
- "symbol fluency (short chains)"
- "constraint guardrails (domain/restrictions)"
- "error localisation protocol"
- "function sense (interpretation)"
- "transfer ladder (variation training)"
TIME:
- "time budgeting"
- "first-step speed"
- "accuracy under mild time"
SPEED LAST:
- "increase velocity gradually only after variance low"

8) A-Math Sensors (What BukitTimahTutor Measures)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z0×R×METRIC×BTT.AMATH.SENSOR.SYMBOL_ERROR_RATE×v1.0:
def: "symbol manipulation error frequency per chain"
[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z2×R×METRIC×BTT.AMATH.SENSOR.METHOD_SELECTION_ERROR×v1.0:
def: "wrong-method chosen rate on unfamiliar problems"
[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z2×R×METRIC×BTT.AMATH.SENSOR.TIME_COLLAPSE_RATE×v1.0:
def: "probability of blanking/panic under timed load"

9) A1 Meaning in A-Math (P3 Definition)

[NODE]
SGP.SG.BT×EDU.MATH.AMATH×Z3×V×LOCK×BTT.AMATH.A1_MEANING×v1.0:
txt: "A1 in A-Math means P3: correct method selection + clean symbol chains + automatic constraint checks + stable speed."

10) Canonical Copy/Paste Lock Block (A-Math)

[LOCKBLOCK:BTT.AMATH.v1.0]
A-Math is symbol-density + transfer + time-compression.
BTT repairs primitives first: symbol fluency → constraints → error loop → function sense → transfer → time → speed last.
Target is P3 (robust under novelty + time), not P1 cram.

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