(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.comPlace: SGP.SG.BTLane: EDU.MATH.AMATHRole: Repair Router (Truncation + Stitching)Zoom: Z0–Z3v: 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.
Recommended Internal Links (Spine)
Recommended Internal Links (Spine)
- Sholpan Upgrade Training Lattice (SholpUTL): https://edukatesg.com/sholpan-upgrade-training-lattice-sholputl/
- https://edukatesg.com/human-regenerative-lattice-3d-geometry-of-civilisation/
- https://edukatesg.com/new-york-z2-institutional-lattice-civos-index-page-master-hub/
- https://edukatesg.com/civilisation-lattice/
- https://edukatesg.com/civ-os-classification/
- https://edukatesg.com/civos-classification-systems/
- https://edukatesg.com/how-civilization-works/
- https://edukatesg.com/civos-lattice-coordinates-of-students-worldwide/
- https://edukatesg.com/civos-worldwide-student-lattice-case-articles-part-1/
- https://edukatesg.com/new-york-z2-institutional-lattice-civos-index-page-master-hub/
- https://edukatesg.com/advantages-of-using-civos-start-here-stack-z0-z3-for-humans-ai/
- Education OS (How Education Works): https://edukatesg.com/education-os-how-education-works-the-regenerative-machine-behind-learning/
- Tuition OS: https://edukatesg.com/tuition-os-edukateos-civos/
- Civilisation OS kernel: https://edukatesg.com/civilisation-os/
- Root definition: What is Civilisation?
- Control mechanism: Civilisation as a Control System
- First principles index: Index: First Principles of Civilisation
- Regeneration Engine: The Full Education OS Map
- The Civilisation OS Instrument Panel (Sensors & Metrics) + Weekly Scan + Recovery Schedule (30 / 90 / 365)
- Inversion Atlas Super Index: Full Inversion CivOS Inversion
Start Here:
- https://edukatesg.com/government-os-general-government-lane-almost-code-canonical/
- https://edukatesg.com/healthcare-os-general-healthcare-lane-almost-code-canonical/
- https://edukatesg.com/education-os-general-education-lane-almost-code-canonical/
- https://edukatesg.com/finance-os-general-finance-banking-lane-almost-code-canonical/
- https://edukatesg.com/transport-os-general-transport-transit-lane-almost-code-canonical/
- https://edukatesg.com/food-os-general-food-supply-chain-lane-almost-code-canonical/
- https://edukatesg.com/security-os-general-security-justice-rule-of-law-lane-almost-code-canonical/
- https://edukatesg.com/housing-os-general-housing-urban-operations-lane-almost-code-canonical/
- https://edukatesg.com/community-os-general-community-third-places-social-cohesion-lane-almost-code-canonical/
- https://edukatesg.com/energy-os-general-energy-power-grid-lane-almost-code-canonical/
- https://edukatesg.com/community-os-general-community-third-places-social-cohesion-lane-almost-code-canonical/
- https://edukatesg.com/water-os-general-water-wastewater-lane-almost-code-canonical/
- https://edukatesg.com/communications-os-general-telecom-internet-information-transport-lane-almost-code-canonical/
- https://edukatesg.com/media-os-general-media-information-integrity-narrative-coordination-lane-almost-code-canonical/
- https://edukatesg.com/waste-os-general-waste-sanitation-public-cleanliness-lane-almost-code-canonical/
- https://edukatesg.com/manufacturing-os-general-manufacturing-production-systems-lane-almost-code-canonical/
- https://edukatesg.com/logistics-os-general-logistics-warehousing-supply-routing-lane-almost-code-canonical/
- https://edukatesg.com/construction-os-general-construction-built-environment-delivery-lane-almost-code-canonical/
- https://edukatesg.com/science-os-general-science-rd-knowledge-production-lane-almost-code-canonical/
- https://edukatesg.com/religion-os-general-religion-meaning-systems-moral-coordination-lane-almost-code-canonical/
- https://edukatesg.com/finance-os-general-finance-money-credit-coordination-lane-almost-code-canonical/
- https://edukatesg.com/family-os-general-family-household-regenerative-unit-almost-code-canonical/