Title: Secondary 3 Additional Mathematics (A-Math) — The Pipeline That Ruptures Under Load
Coordinate: BTT.MAT.Z2.N.AM3.001

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Definition Lock

Secondary 3 A-Math is not “harder math.”
It is a load transition node where students fail because their execution pipeline is not regenerative.

A-Math “works” only when the student can:

• execute algebraic control at speed,
• manage symbolic manipulation without prompts,
• check under time pressure,
• and recover from errors without collapsing.

If the pipeline is weak, Sec 3 A-Math becomes a rupture point.

What This Page Is

This is a lattice node page. It maps:

• what Sec 3 A-Math demands (system function),
• what fails mechanically (pipeline failure),
• which Z0 pockets must be stable,
• which sensors detect drift early,
• and how to recover without rescue loops.

It is not a topic list.
It is a capability reliability map.

The Sec 3 A-Math Load Step (Why rupture happens here)

Sec 3 A-Math increases load in three ways at once:

1. Speed (time pressure becomes real)
2. Abstraction (symbol control becomes non-negotiable)
3. Variation (questions mutate; pattern-matching fails)

Students who “were fine before” often collapse here because earlier stages allowed:

• prompts,
• scaffolding,
• repetitive drills,
• or rescue marking schemes.

A-Math exposes whether control is real.

Core Z0 Execution Pipelines (Non-negotiable)

If these are weak, Sec 3 A-Math becomes random guessing.

1) Algebra Control Pipeline

Coordinate: BTT.MAT.Z0.P.ALG.001
Slug: /btt-mat-z0-p-alg-001-algebra-control-pipeline/

A-Math is mostly algebra, disguised.

Failure signatures

• cannot rearrange reliably
• drops negative signs
• loses brackets
• cannot isolate variables cleanly
• cannot keep expressions coherent across steps

2) Differentiation Execution Pipeline

Coordinate: BTT.MAT.Z0.P.DIF.001
Slug: /btt-mat-z0-p-dif-001-differentiation-execution-pipeline/

Differentiation is the first “speed + variation” operator-heavy pocket.

Failure signatures

• rule confusion under mixed forms
• incorrect chain rule triggers
• cannot simplify before applying rules
• does not check with reasonableness tests

3) Geometry Control Pipeline (support pocket, often hidden)

Coordinate: BTT.MAT.Z0.P.GEO.001
Slug: /btt-mat-z0-p-geo-001-geometry-control-pipeline/

Appears through graphs, gradients, tangents, rates, and modelling.

Sensors (How to detect failure early — before exams)

These sensors make this page system-aware and not generic.

A) Student TTC / Time Pressure Sensor

Coordinate: BTT.SEN.Z0.S.TTC.001
Slug: /btt-sen-z0-s-ttc-001-student-ttc-sensor/

Interpretation:
If TTC variance spikes, the student is no longer executing — they are compensating.

B) Prompt Dependency Sensor

Coordinate: BTT.SEN.Z1.S.DEP.001
Slug: /btt-sen-z1-s-dep-001-prompt-dependency-sensor/

Interpretation:
If the student needs “what do I do first?” often, independence has collapsed.

C) False Competence Gauge

Coordinate: BTT.SEN.Z1.S.FCG.001
Slug: /btt-sen-z1-s-false-competence-gauge/

Interpretation:
Looks fine on homework; ruptures on timed mixed papers.

D) Error Pattern Sensor

Coordinate: BTT.MAT.Z0.S.ERR.001
Slug: /btt-mat-z0-s-err-001-error-pattern-sensor/

Interpretation:
Most A-Math failure is not “concept.” It is error-class dominance:

• slips,
• transformation errors,
• checking failure,
• or control collapse under speed.

Exam Pipeline Bind (What this node feeds into)

Sec 3 A-Math is part of the Secondary exam pipeline:

• BTT.EXM.Z2.P.SEC.001 — Secondary Exam Pipeline
• BTT.EXM.Z2.B.OLEV.001 — O-Level Bind

Meaning:
If you don’t stabilise Sec 3, Sec 4 becomes rescue-mode and O-Levels become a cliff.

The Common Failure Modes (Mechanical, not emotional)

Failure Mode 1 — Algebra collapse masked by “topic learning”

Student thinks they are learning differentiation, but actually can’t control algebra.
So every question becomes impossible.

Failure Mode 2 — Time pressure reveals non-regenerative skill

Student can do it slowly with prompts. Under time, the pipeline collapses.

Failure Mode 3 — Tuition becomes rescue

The student is walked through steps. They feel progress.
But dependency rises, and the next paper ruptures harder.

Recovery Protocol (P1→P3 for a student)

P1 — Stabilise (stop the bleeding)

• isolate the failing Z0 pocket (usually algebra control)
• remove mixed-topic overload temporarily
• rebuild checking habits under low speed

P2 — Adapt (build independence)

• fade prompts aggressively
• force “first step selection” practice
• introduce variation sets (same skill, different wrapping)

P3 — Excellence (reliable under exam load)

• timed mixed practice with strict checking loops
• reduce TTC variance
• errors become rare and recoverable
• student can execute without prompts

Lattice Coordinates Referenced (Required)

• BTT.MAT.Z2.N.AM3.001
• BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z0.P.DIF.001
• BTT.MAT.Z0.P.GEO.001
• BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z1.S.FCG.001
• BTT.MAT.Z0.S.ERR.001
• BTT.EXM.Z2.P.SEC.001
• BTT.EXM.Z2.B.OLEV.001
• SG.EDU.Z3.B.EXM.001

Edges Created (BindsTo / Impacts)

• BTT.MAT.Z2.N.AM3.001 BindsTo BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z2.N.AM3.001 BindsTo BTT.MAT.Z0.P.DIF.001
• BTT.SEN.Z1.S.DEP.001 Impacts BTT.EXM.Z2.P.SEC.001
• BTT.SEN.Z0.S.TTC.001 Observes BTT.MAT.Z2.N.AM3.001
• BTT.MAT.Z2.N.AM3.001 Impacts BTT.EXM.Z2.B.OLEV.001

Sensors Mentioned

• BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z1.S.FCG.001
• BTT.MAT.Z0.S.ERR.001

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Algebra Control Pipeline (BTT.MAT.Z0.P.ALG.001) — Z0 Execution Page (V1.1, Publish-Ready)

Title: Algebra Control Pipeline — The Hidden Engine Behind All Secondary & A-Math
Coordinate: BTT.MAT.Z0.P.ALG.001

Definition Lock

Algebra Control is the ability to reliably transform expressions and equations under time pressure without losing structure (signs, brackets, equivalence).
It is not “algebra topic knowledge.” It is execution control.

Mathematics “works” only when algebra control is:

• fast enough,
• consistent enough,
• and self-checking under load.

If algebra control is weak, every topic becomes random.

What This Page Is

This is a Z0 execution pipeline page.
It defines the atomic pockets that must regenerate for Secondary Math and A-Math to be reliable.

Algebra Control is the common failure root behind:

• A-Math collapse,
• differentiation mistakes,
• equation solving failures,
• and “I understand but I can’t do” syndrome.

The Algebra Control Pipeline (Z0) — Atomic Pockets

You do not “revise algebra.” You stabilise these pockets.

Pocket A — Expression Integrity (Structure Preservation)

Goal: keep expressions intact while manipulating.

Failure signatures

• loses brackets
• changes signs incorrectly
• merges unlike terms
• treats multiplication like addition

Under-load inversion test

• If the student cannot expand and simplify flawlessly in 30–60 seconds, the pipeline is not stable.

Pocket B — Transformation Rules (Legal Moves)

Goal: only do equivalence-preserving moves.

Examples of legal moves

• add/subtract same term both sides
• multiply/divide both sides by same non-zero constant
• factorise then cancel only when factor is shared

Failure signatures

• cancels terms incorrectly
• divides by a term that could be zero without considering
• “moves” a term across equals sign without applying the operation properly

Pocket C — Rearrangement Control (Isolate Variable Reliably)

Goal: isolate any variable without hesitation.

Failure signatures

• gets stuck choosing the first step
• makes multiple simultaneous moves and loses track
• ends with variable on both sides and panics

Key rule
Rearrangement is a sequence of legal moves. Under load, the student must choose the next move instantly.

Pocket D — Fraction + Negative Sign Discipline

Goal: eliminate fraction chaos and sign chaos.

Failure signatures

• common denominator errors
• sign flips lost during distribution
• minus outside bracket ignored
• reciprocal mistakes

Under-load inversion test
Give 5 fraction equations. If 3+ are wrong due to sign/fraction handling, the pipeline is not yet functional.

Pocket E — Factorisation as Control (Not “pattern spotting”)

Goal: factorisation is used to control structure (simplify, solve, cancel), not as isolated trick.

Failure signatures

• factorises wrongly
• factorises then doesn’t know what to do next
• expands when should factorise (or vice versa)

Pocket F — Substitution Control (Multi-step integrity)

Goal: substitute without corrupting structure.

Failure signatures

• substitutes only part of an expression
• forgets brackets during substitution
• simplifies incorrectly after substitution

This is where A-Math and modelling problems collapse.

The Three Most Common Algebra Failure Classes

Use these to diagnose quickly.

1. Slip dominance (careless sign/bracket errors)
2. Transformation illegality (doing illegal moves)
3. Checking failure (no verification loop, errors persist)

If you don’t classify the failure, you can’t fix it.

Checking Protocol (Algebra Must Be Self-Repairing)

Algebra “works” only if it repairs itself. That means checking is built in.

Check 1 — Reverse Move Check

If you “moved” something, can you reverse the operation and return to the original?

Check 2 — Substitution Check (equations)

Pick a simple value and verify both sides remain equal after each major step.

Check 3 — Structure Check

Before simplifying, ask:

• “Did I change the expression structure illegally?”
• “Did any bracket/sign get lost?”

Variation Sets (How you actually stabilise Algebra)

Algebra stabilises by controlled variation, not by doing 100 similar questions.

Variation Set 1 — Rearrangement ladder

Same goal (isolate x), but different structures:

• fractions
• brackets
• variables both sides
• powers
• parameters

Variation Set 2 — Expand/Simplify under constraint

Same expansion skill but with traps:

• nested brackets
• negative outside brackets
• mixed like/unlike terms
• fractional coefficients

Variation Set 3 — Factorise → Solve chain

Not just factorising, but completing the full chain:
factorise → set each factor to 0 → solve → check.

Where This Pipeline Binds (Downstream Dependencies)

Algebra Control binds into almost everything, but especially:

• Secondary 3 A-Math node
  BTT.MAT.Z2.N.AM3.001
/btt-mat-z2-n-am3-001-secondary-3-amath/
• Differentiation pipeline
  BTT.MAT.Z0.P.DIF.001
  (create next)
• Secondary Exam pipeline
  BTT.EXM.Z2.P.SEC.001
  (create soon)

If algebra is unstable, students think differentiation is the problem. It usually isn’t.

Sensors (How to know the pipeline is failing)

Student TTC Sensor

BTT.SEN.Z0.S.TTC.001
If time spikes during algebra steps, control is not automatic.

Error Pattern Sensor

BTT.MAT.Z0.S.ERR.001
Classify whether errors are:

• sign/bracket slips,
• illegal transformations,
• simplification mistakes,
• or checking failure.

Recovery Protocol (P1 → P3 for Algebra)

P1 — Stabilise legality and structure

• slow down
• force single-step legal moves
• check after each major transform

P2 — Build speed with variation

• timed micro-sets (5–8 minutes)
• variation ladders
• enforce “first step selection” practice

P3 — Automaticity under exam load

• mixed timed sets
• minimal prompts
• checking becomes reflex
• TTC variance falls

Lattice Coordinates Referenced (Required)

• BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z2.N.AM3.001
• BTT.MAT.Z0.P.DIF.001
• BTT.EXM.Z2.P.SEC.001
• BTT.SEN.Z0.S.TTC.001
• BTT.MAT.Z0.S.ERR.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z1.S.FCG.001

Edges Created (BindsTo / Impacts)

• BTT.MAT.Z0.P.ALG.001 BindsTo BTT.MAT.Z2.N.AM3.001
• BTT.MAT.Z0.P.ALG.001 BindsTo BTT.MAT.Z0.P.DIF.001
• BTT.SEN.Z0.S.TTC.001 Observes BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z0.S.ERR.001 Observes BTT.MAT.Z0.P.ALG.001
• BTT.SEN.Z1.S.DEP.001 Impacts BTT.EXM.Z2.P.SEC.001 (dependency prevents algebra becoming automatic under load)

Sensors Mentioned

• BTT.SEN.Z0.S.TTC.001
• BTT.MAT.Z0.S.ERR.001

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Differentiation Execution Pipeline (BTT.MAT.Z0.P.DIF.001) — Z0 Execution Page (V1.1, Publish-Ready)

Title: Differentiation Execution Pipeline — The First True “Speed + Variation” Operator Test
Slug: /btt-mat-z0-p-dif-001-differentiation-execution-pipeline/
Coordinate: BTT.MAT.Z0.P.DIF.001

Definition Lock

Differentiation (Execution) is the ability to reliably convert a function into its derivative under time pressure, across mixed forms, without prompts — and to keep algebraic control intact throughout.

Differentiation “works” only when:

• rule selection is automatic,
• algebra simplification is controlled,
• chain structure is preserved,
• and checking is built in.

Most students don’t “not understand differentiation.”
They rupture because their execution pipeline is not regenerative.

What This Page Is

This is a Z0 execution pipeline page.
It maps the atomic pockets that must regenerate for differentiation to be reliable in Secondary 3–4 A-Math.

Differentiation is where students first experience:

• mixed-rule variation,
• speed pressure,
• and algebraic fragility.

So this page is built to prevent that rupture.

Differentiation Pipeline (Z0) — Atomic Pockets

Pocket A — Form Recognition (Identify the structure fast)

Goal: classify the function form instantly.

Common forms:

• polynomial / power form
• product
• quotient
• composite (chain)
• mixed (composite + product/quotient)

Failure signatures

• uses the wrong rule
• misses that something is composite
• treats a product as a power
• differentiates term-by-term when structure is not additive

Under-load inversion test
If the student cannot label the correct rule(s) in <10 seconds, they are not execution-ready.

Pocket B — Rule Triggering (Choose the correct operator)

Goal: apply the correct differentiation operator without hesitation.

Core triggers:

• power rule
• constant multiple
• sum rule
• product rule
• quotient rule
• chain rule

Failure signatures

• chain rule applied too little or too much
• product/quotient used when simplification would remove need
• forgets constant multiple
• differentiates inside and outside inconsistently

Pocket C — Chain Structure Integrity (Do not destroy the function)

Goal: preserve the “outer function” and multiply by derivative of inner.

Failure signatures

• differentiates inside only (forgets outer)
• differentiates outer only (forgets inner)
• loses brackets during chain expansion
• collapses when there are nested composites

Key execution rule
Write “outer derivative × inner derivative” explicitly before simplifying.

Pocket D — Algebra Control During Differentiation (Non-negotiable)

Goal: simplification and rearrangement must remain legal and clean.

This binds directly to:

• BTT.MAT.Z0.P.ALG.001 (Algebra Control Pipeline)

Failure signatures

• sign slips while simplifying
• incorrect factorisation
• cancels incorrectly
• expands and creates chaos unnecessarily

Differentiation often “fails” because algebra control collapses after correct rule selection.

Pocket E — Simplify-before-rule Decision (Time efficiency)

Goal: decide whether to simplify first.

Example logic:

• If simplifying converts product/quotient into power → simplify first.
• If simplification increases risk (fractions/signs chaos) → apply rule first.

Failure signatures

• always applies product/quotient blindly
• wastes time expanding large expressions unnecessarily
• introduces avoidable algebra errors

Pocket F — Interpretation Bind (Derivative as meaning)

Differentiation is also used as:

• gradient of tangent
• rate of change
• stationary points

This is where “execution-only” students often break because they do not connect derivative results to graphs/meaning under exam variation.

This pocket is supported by:

• BTT.MAT.Z0.P.GEO.001 (Geometry/Graph control)

The 4 Most Common Differentiation Failure Classes (Mechanical)

1. Rule mis-selection (wrong operator)
2. Chain collapse (structure broken)
3. Algebra corruption (correct derivative ruined)
4. No checking loop (errors persist into final answer)

Checking Protocol (Differentiation must self-repair)

Differentiation becomes regenerative only when checking exists.

Check 1 — Structure sanity check

Does the derivative look “simpler” than the original in the right way?
If original grows fast, derivative should reflect that.

Check 2 — Plug-in numeric check (quick)

Pick a simple x (e.g., x=1 or x=0 where defined).
Compare slope intuition (approx) or compare derivative forms for obvious impossibilities.

Check 3 — Units/meaning check (rates/graphs)

If asked for gradient at a point, does the sign and magnitude make sense from the graph context?

Variation Sets (How you actually stabilise differentiation)

Differentiation is mastered via controlled variation, not repetition.

Variation Set 1 — Rule identification drills (no computation)

20 quick functions: label rules only.
Goal: automatic classification.

Variation Set 2 — Chain ladders

Start simple:

• (ax+b)^n
  then:
• (ax+b)^n (cx+d)^m
  then:
• nested forms
  Goal: preserve structure.

Variation Set 3 — Simplify-or-not decision sets

Pairs of questions where simplifying first saves time vs where it creates risk.
Goal: build judgement.

Variation Set 4 — Mixed exam sets (timed)

Short timed sets combining:

• differentiation + algebra solve + interpret (stationary points / tangents)
  Goal: reduce TTC variance.

Where This Pipeline Binds (Downstream Dependencies)

Differentiation binds into Sec 3–4 A-Math nodes and exam pipelines:

• BTT.MAT.Z2.N.AM3.001 — Sec 3 A-Math node
• BTT.MAT.Z2.N.AM4.001 — Sec 4 A-Math node
• BTT.EXM.Z2.P.SEC.001 — Secondary Exam Pipeline
• BTT.EXM.Z2.B.OLEV.001 — O-Level Bind

If differentiation is non-regenerative, the student collapses under mixed papers.

Sensors (How to detect drift early)

Student TTC Sensor

BTT.SEN.Z0.S.TTC.001
If differentiation time spikes unpredictably, rule selection or algebra integrity is unstable.

Error Pattern Sensor

BTT.MAT.Z0.S.ERR.001
Use it to classify:

• rule errors vs algebra corruption vs chain collapse.

Dependency Sensor (support loop failure)

BTT.SEN.Z1.S.DEP.001
If the student needs prompting for first step, they will rupture under exam load.

Recovery Protocol (P1 → P3 for Differentiation)

P1 — Stabilise rule selection + chain integrity

• rule ID drills
• explicit outer×inner writing
• slow simplification with legality checks

P2 — Adapt with variation

• chain ladders
• simplify-or-not judgement drills
• mixed micro-sets timed lightly

P3 — Exam reliability

• timed mixed papers
• minimal prompts
• checking becomes automatic
• TTC variance collapses downward (stability)

Lattice Coordinates Referenced (Required)

• BTT.MAT.Z0.P.DIF.001
• BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z0.P.GEO.001
• BTT.MAT.Z2.N.AM3.001
• BTT.MAT.Z2.N.AM4.001
• BTT.EXM.Z2.P.SEC.001
• BTT.EXM.Z2.B.OLEV.001
• BTT.SEN.Z0.S.TTC.001
• BTT.MAT.Z0.S.ERR.001
• BTT.SEN.Z1.S.DEP.001

Edges Created (BindsTo / Impacts)

• BTT.MAT.Z0.P.DIF.001 BindsTo BTT.MAT.Z2.N.AM3.001
• BTT.MAT.Z0.P.DIF.001 BindsTo BTT.MAT.Z2.N.AM4.001
• BTT.MAT.Z0.P.ALG.001 BindsTo BTT.MAT.Z0.P.DIF.001
• BTT.SEN.Z0.S.TTC.001 Observes BTT.MAT.Z0.P.DIF.001
• BTT.MAT.Z0.S.ERR.001 Observes BTT.MAT.Z0.P.DIF.001
• BTT.SEN.Z1.S.DEP.001 Impacts BTT.EXM.Z2.P.SEC.001

Sensors Mentioned

• BTT.SEN.Z0.S.TTC.001
• BTT.MAT.Z0.S.ERR.001
• BTT.SEN.Z1.S.DEP.001

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Student TTC Sensor (BTT.SEN.Z0.S.TTC.001) — Diagnostic Page (V1.1, Publish-Ready)

Title: Student TTC (Time-to-Complete) Sensor — The Fastest Way to Detect Math Collapse Early
Slug: /btt-sen-z0-s-ttc-001-student-ttc-sensor/
Coordinate: BTT.SEN.Z0.S.TTC.001

Definition Lock

Student TTC (Time-to-Complete) Sensor is the measurement of how long a student takes to execute core math pockets (Z0) under realistic time pressure — and how that time changes under variation.

TTC is not “speed.”
TTC is a stability sensor.

Math is stable when TTC is:

• predictable,
• low variance,
• and resilient under mixed question sets.

Math collapses when TTC variance rises and stays high.

What This Page Is

This is a diagnostic node page.
It gives a clean, measurable method to detect failure early, before grades collapse.

Most students don’t notice drift until:

• timed papers rupture,
• exam scores collapse,
• confidence breaks.

TTC detects drift weeks to months earlier.

Why TTC Matters (The Real Failure Mechanism)

Students fail exams because:

• execution time exceeds exam time,
• and the student compensates by rushing,
• which increases errors,
• which increases rework,
• which increases TTC further.

This is a feedback loop:

High TTC → rushed steps → errors → rework → higher TTC

When TTC crosses a threshold, performance collapses mechanically.

What TTC Measures (Three components)

TTC is made of:

1. Execution time (doing the steps)
2. Decision time (choosing the first step / selecting rules)
3. Recovery time (what happens after an error or confusion)

A strong student has:

• low decision time,
• low recovery time,
• and stable execution time.

A weak student often has:

• long decision time (“what do I do?”),
• long recovery time (stuck, panic, prompt dependency),
• and wildly unstable execution time under variation.

TTC Variance is the Key (Not the average)

A student can be “fast sometimes” and still be unstable.

Stable: TTC stays similar across different wrappers of the same skill.
Unstable: TTC spikes unpredictably when the question changes form.

That is the signature of non-regenerative capability.

How to Use the TTC Sensor (Simple Protocol)

You need 10–15 minutes. No fancy tools.

Step 1 — Choose 3 core pockets (Z0)

Use these default pockets:

• Algebra Control pocket test
  BTT.MAT.Z0.P.ALG.001
• Differentiation pocket test
  BTT.MAT.Z0.P.DIF.001
• Mixed short set (variation) test
  tied to grade node:
  BTT.MAT.Z2.N.AM3.001

Step 2 — Time each question (realistic conditions)

• no hints
• no “half marks”
• strict timekeeping
• stop only when final answer is reached (or they give up)

Step 3 — Record TTC and failure mode

For each question, record:

• TTC seconds/minutes
• whether they got stuck
• whether they asked for prompts
• whether they made slips and had to rework

This ties directly to:

• Dependency sensor (BTT.SEN.Z1.S.DEP.001)
• Error sensor (BTT.MAT.Z0.S.ERR.001)

TTC Threshold Bands (Practical Bands)

Use these as diagnostic bands, not rigid rules.

Band A — Stable

• TTC is consistent
• student completes within expected exam tempo
• errors are rare and recoverable

Band B — Drift

• TTC spikes on variation
• student slows down noticeably on mixed sets
• checking disappears when time pressure rises

Band C — Collapse Corridor

• TTC consistently exceeds exam tempo
• student rushes, makes errors, reworks
• prompts become frequent
• score collapses even if “they understand”

TTC tells you which corridor the student is in.

TTC + Prompts (Critical coupling)

A student can “finish” if guided — but that doesn’t count.

If TTC is only low when the tutor prompts:

• independence is not real,
• and exam performance will rupture.

That is captured by:

• BTT.SEN.Z1.S.DEP.001 (Prompt Dependency Sensor)

TTC + Error Rework (Why students spiral)

The most dangerous TTC profile is:

• moderate speed,
• high error rate,
• large rework time.

This creates the hidden sink:

• student “studies a lot”
• but performance does not improve
  because time is being spent on rework rather than skill regeneration.

This is detected by:

• BTT.MAT.Z0.S.ERR.001 (Error Pattern Sensor)

TTC as Early Warning for Sec 3 A-Math Rupture

Sec 3 A-Math is a load step node:

• BTT.MAT.Z2.N.AM3.001

If TTC variance is already high in early Sec 3:

• the student is in a collapse corridor for Sec 4 and O-Levels.

This is why TTC is the highest ROI diagnostic:

• it predicts future rupture.

Recovery Actions Based on TTC Profile

If TTC spikes because of decision time:

• do rule-identification drills (no computation)
• reduce prompt dependency
• practise “first step selection”

If TTC spikes because of algebra corruption:

• stabilise Algebra Control Pipeline (BTT.MAT.Z0.P.ALG.001)
• enforce structure checks

If TTC spikes because of recovery time:

• reduce variation temporarily
• train micro-recovery loops (one-step backtracking)
• build checking reflex

TTC doesn’t just detect. It tells you what to fix first.

Lattice Coordinates Referenced (Required)

• BTT.SEN.Z0.S.TTC.001
• BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z0.P.DIF.001
• BTT.MAT.Z2.N.AM3.001
• BTT.SEN.Z1.S.DEP.001
• BTT.MAT.Z0.S.ERR.001
• BTT.EXM.Z2.P.SEC.001
• BTT.EXM.Z2.B.OLEV.001

Edges Created (BindsTo / Impacts / Observes)

• BTT.SEN.Z0.S.TTC.001 Observes BTT.MAT.Z0.P.ALG.001
• BTT.SEN.Z0.S.TTC.001 Observes BTT.MAT.Z0.P.DIF.001
• BTT.SEN.Z0.S.TTC.001 Observes BTT.MAT.Z2.N.AM3.001
• BTT.SEN.Z0.S.TTC.001 Impacts BTT.EXM.Z2.P.SEC.001 (TTC corridor predicts exam rupture)
• BTT.SEN.Z1.S.DEP.001 Impacts TTC stability (dependency increases TTC variance)

Sensors Mentioned

• BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001
• BTT.MAT.Z0.S.ERR.001

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Prompt Dependency Sensor (BTT.SEN.Z1.S.DEP.001) — Diagnostic Page (V1.1, Publish-Ready)

Title: Prompt Dependency Sensor — Why Tuition “Works” Until It Suddenly Doesn’t
Slug: /btt-sen-z1-s-dep-001-prompt-dependency-sensor/
Coordinate: BTT.SEN.Z1.S.DEP.001

Definition Lock

Prompt Dependency is the condition where a student’s execution only functions when external cues are present (hints, leading questions, step-by-step guidance).

Prompt dependency is not laziness.
It is pipeline coupling failure.

A student is independent only when they can:

• select the first step unprompted,
• continue without mid-course rescue,
• and recover from errors alone.

If prompts are required, the pipeline will rupture under exam load.

What This Page Is

This is a Z1 diagnostic sensor page.
It explains why students appear to improve in tuition sessions but collapse in exams.

Prompt dependency lives in the support loop, not the skill pocket:

• Z0 may look “okay” when guided,
• Z1 silently rots,
• Z2 collapses at exams.

This sensor exposes that hidden decay.

Where Prompt Dependency Comes From (Mechanically)

Prompt dependency forms when:

1. tutors supply first steps too quickly
2. parents rescue before struggle completes
3. marking rewards partial structure without execution
4. speed pressure is removed during practice
5. variation is reduced too aggressively

Over time, the student learns:

“I don’t need to decide. Someone will tell me.”

That is catastrophic for exams.

What Prompt Dependency Looks Like (Clear Signatures)

You will see:

• “I know this, but I don’t know how to start”
• long pauses before the first step
• frequent confirmation-seeking
• progress only when guided
• collapse when question structure changes

Key tell:
TTC drops only when prompts are present.

That links directly to:

• BTT.SEN.Z0.S.TTC.001 (Student TTC Sensor)

Prompt Dependency vs Understanding (Critical Distinction)

A student can:

• explain a method verbally,
• recognise the topic,
• follow steps shown,

and still be completely non-executable.

Understanding ≠ execution.
Execution requires autonomous step selection.

Prompt dependency means the student’s control loop is external.

How Prompt Dependency Breaks Exams

Exams remove:

• prompts,
• reassurance,
• mid-course correction.

So the pipeline sequence becomes:

1. long decision pause
2. panic or random start
3. error early
4. no recovery
5. TTC spikes
6. score collapses

This is why exam failure feels “sudden.”

How to Detect Prompt Dependency (Simple Tests)

Test 1 — Silent Start Test

Give a question. Say nothing.

If the student:

• asks “what do I do?”
• stares without writing
• waits for confirmation

→ prompt dependency detected.

Test 2 — First-Step Delay Timing

Measure time to first written step.

If:

• execution starts only after prompting,
• or delay is excessive,

→ dependency exists even if later steps are correct.

Interaction With Other Sensors

Prompt Dependency rarely exists alone.

With TTC Sensor

• Prompts artificially reduce TTC.
• Remove prompts → TTC spikes.

With Error Sensor

• Errors persist because recovery is outsourced.
• Student waits for correction instead of self-checking.

This is why dependency is so destructive long-term.

Where Prompt Dependency Impacts the Lattice

Prompt dependency directly impacts:

• Secondary Exam Pipeline
  BTT.EXM.Z2.P.SEC.001
• O-Level Bind
  BTT.EXM.Z2.B.OLEV.001
• Grade nodes such as
  BTT.MAT.Z2.N.AM3.001

A dependent student will always rupture at Z2.

Recovery Protocol (P1 → P3)

Prompt dependency must be broken deliberately.

P1 — Containment (Stop creating dependency)

• stop supplying first steps
• allow productive struggle
• remove verbal scaffolding

P2 — Independence Training

• first-step-only drills
• “write anything legal” rules
• delayed feedback (not immediate rescue)

P3 — Exam Simulation

• silent timed sets
• no hints
• strict checking protocols
• TTC monitored for stability

Dependency breaks only when independence is enforced.

What Parents & Tutors Must Not Do

• Do not finish sentences
• Do not suggest the next step
• Do not confirm prematurely
• Do not rescue after 10 seconds of silence

Silence is not failure.
Silence is the decision phase rebuilding.

Lattice Coordinates Referenced (Required)

• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z0.S.TTC.001
• BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z0.P.DIF.001
• BTT.MAT.Z2.N.AM3.001
• BTT.EXM.Z2.P.SEC.001
• BTT.EXM.Z2.B.OLEV.001
• BTT.MAT.Z0.S.ERR.001

Edges Created (BindsTo / Impacts / Observes)

• BTT.SEN.Z1.S.DEP.001 Impacts BTT.EXM.Z2.P.SEC.001
• BTT.SEN.Z1.S.DEP.001 Impacts BTT.EXM.Z2.B.OLEV.001
• BTT.SEN.Z1.S.DEP.001 Impacts BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001 Impacts BTT.MAT.Z0.S.ERR.001
• BTT.SEN.Z1.S.DEP.001 Observes first-step delay at BTT.MAT.Z2.N.AM3.001

Sensors Mentioned

• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z0.S.TTC.001
• BTT.MAT.Z0.S.ERR.001

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False Competence Gauge (BTT.SEN.Z1.S.FCG.001) — Diagnostic Page (V1.1, Publish-Ready)

Title: False Competence Gauge — When Math Looks Fine Until the Load Spike Ruptures It
Slug: /btt-sen-z1-s-false-competence-gauge/
Coordinate: BTT.SEN.Z1.S.FCG.001

Definition Lock

False Competence is the condition where a student appears to be progressing (homework completed, tuition worksheets done, school marks acceptable) but the capability is not regenerative and collapses under the first serious load spike (speed, abstraction, variation).

False competence is not a personality problem.
It is measurement failure.

This gauge detects when the student’s visible “performance” is being produced by:

• prompts,
• repetition,
• low variation,
• slow practice,
• or answer-following,
  instead of real execution under exam conditions.

What This Page Is

This is a Z1 diagnostic sensor page.
It exists to answer one question:

“If my child is scoring okay now, why do they suddenly fail later?”

Because the pipeline was never stable.
The measurement just didn’t trigger the load that reveals it.

Why False Competence Happens (Mechanically)

Most daily practice environments are below threshold:

• unlimited time
• predictable questions
• guided solutions
• small topic slices
• generous partial credit

This produces the illusion of competence.

But exams are:

• timed,
• mixed,
• high variation,
• prompt-free,
• and unforgiving.

So the system “looks fine” until it hits real load.

The False Competence Law (Simple)

If performance requires:

• low speed,
• low variation,
• or external prompts,

then competence is false.

Real competence must survive:

• speed + variation + no prompts.

What False Competence Looks Like (Common Signatures)

You will see:

• “He can do it at home but fails in exam”
• “She understands when I explain”
• “Worksheets all correct, but timed paper low”
• “Fine in tuition, weak in school test”
• “Can follow steps, cannot start alone”

This usually means the student has:

• prompt dependency (BTT.SEN.Z1.S.DEP.001)
• unstable TTC (BTT.SEN.Z0.S.TTC.001)
• and unclassified error dominance (BTT.MAT.Z0.S.ERR.001)

The Three Triggers That Reveal False Competence

False competence reveals itself when any one of these load spikes occur:

Trigger 1 — Time pressure (Speed)

TTC crosses exam tempo thresholds:

• BTT.SEN.Z0.S.TTC.001

Trigger 2 — Variation (Wrapper change)

Same skill, different packaging.
Student collapses because recognition ≠ execution.

Trigger 3 — Prompt removal (Independence)

Student cannot select first step without help:

• BTT.SEN.Z1.S.DEP.001

If any trigger causes collapse, the competence was not real.

How to Measure False Competence (The Gauge Protocol)

You can run this in 15–20 minutes.

Step A — Pick 2 Z0 pockets

Use:

• BTT.MAT.Z0.P.ALG.001 (algebra control)
• BTT.MAT.Z0.P.DIF.001 (differentiation)

Step B — Run two modes

Mode 1: Comfort Mode (below threshold)

• un-timed
• single-topic
• familiar pattern

Mode 2: Load Mode (above threshold)

• timed
• mixed or varied wrapper
• no prompts

Step C — Compare

If results collapse from Mode 1 to Mode 2:

• competence was false.

This gauge is the fastest way to stop wasting months.

Why False Competence Is Dangerous (It delays repair)

False competence does not just “mislead.”

It causes delayed intervention:

• parents keep the same strategy
• tuition continues rescue patterns
• school feedback stays superficial
• the student reaches Sec 3/4 and ruptures

By the time O-Levels arrive, repair cost is much higher.

This is why false competence is a phase drift problem.

Where False Competence Hits Hardest (Sec 3 A-Math rupture node)

The most common rupture corridor is:

• BTT.MAT.Z2.N.AM3.001 (Sec 3 A-Math)

A-Math increases:

• speed
• variation
• algebra control demand

So false competence becomes visible brutally here.

Recovery Protocol (P1 → P3)

False competence cannot be “motivated away.” It must be rebuilt.

P1 — Expose the truth safely

• introduce low-stakes timed work
• remove prompts
• increase variation gradually
• measure TTC and dependency

P2 — Rebuild regenerative pockets

• stabilise Algebra Control (BTT.MAT.Z0.P.ALG.001)
• stabilise Differentiation execution (BTT.MAT.Z0.P.DIF.001)
• train checking and recovery loops

P3 — Confirm under real load

• timed mixed sets
• strict no-prompt policy
• TTC variance falls
• errors become recoverable

Only then is competence real.

Lattice Coordinates Referenced (Required)

• BTT.SEN.Z1.S.FCG.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z0.S.TTC.001
• BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z0.P.DIF.001
• BTT.MAT.Z2.N.AM3.001
• BTT.EXM.Z2.P.SEC.001
• BTT.EXM.Z2.B.OLEV.001
• BTT.MAT.Z0.S.ERR.001

Edges Created (BindsTo / Impacts / Observes)

• BTT.SEN.Z1.S.FCG.001 Observes collapse between Comfort Mode and Load Mode
• BTT.SEN.Z1.S.FCG.001 Impacts BTT.EXM.Z2.P.SEC.001 (predicts rupture risk under exam load)
• BTT.SEN.Z1.S.FCG.001 BindsTo BTT.SEN.Z0.S.TTC.001 (time pressure reveals false competence)
• BTT.SEN.Z1.S.FCG.001 BindsTo BTT.SEN.Z1.S.DEP.001 (prompt removal reveals false competence)
• BTT.SEN.Z1.S.FCG.001 Observes BTT.MAT.Z2.N.AM3.001 (transition rupture node)

Sensors Mentioned

• BTT.SEN.Z1.S.FCG.001
• BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001
• BTT.MAT.Z0.S.ERR.001

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Error Pattern Sensor (BTT.MAT.Z0.S.ERR.001) — Diagnostic Page (V1.1, Publish-Ready)

Title: Error Pattern Sensor — Stop Saying “Careless” and Fix the Real Failure Class
Slug: /btt-mat-z0-s-err-001-error-pattern-sensor/
Coordinate: BTT.MAT.Z0.S.ERR.001

Definition Lock

Error Pattern Sensor classifies a student’s mistakes into a small number of repeatable failure classes, so repair targets the right mechanism instead of repeating more practice.

“Careless” is not a diagnosis.
It is a label that hides the true failure mode.

Math becomes regenerative only when:

• errors are classified,
• repairs are targeted,
• and the same error class stops recurring.

What This Page Is

This is a Z0 diagnostic sensor page.
It turns messy mistakes into structured repair categories.

Most students do not have “many random mistakes.”
They have one dominant error class that keeps recurring under load.

Fix the class → performance jumps.

The 5 Core Error Classes (Canonical)

Use these. Do not invent new ones unless necessary.

Class 1 — Slip Errors (micro execution slips)

What it is:
Signs, arithmetic, copying, small misreads.

Signature

• wrong but close
• steps are mostly correct
• error is a single micro-break

Common cause

• rushing because TTC is too high
  (BTT.SEN.Z0.S.TTC.001)

Class 2 — Transformation Errors (illegal algebra)

What it is:
Student performs an illegal manipulation.

Signature

• equation becomes non-equivalent
• cancellation done wrongly
• dividing by expressions without conditions
• bracket/sign rules violated

Strong linkage

• Algebra Control Pipeline unstable
  (BTT.MAT.Z0.P.ALG.001)

Class 3 — Rule Selection Errors (wrong method)

What it is:
Wrong operator or wrong approach.

Signature

• starts correctly then uses wrong rule
• product vs chain confusion
• wrong formula triggered

Strong linkage

• Differentiation execution instability
  (BTT.MAT.Z0.P.DIF.001)
• and/or prompt dependency (they can’t choose first step)
  (BTT.SEN.Z1.S.DEP.001)

Class 4 — Structure Loss (brackets, nesting, substitution integrity)

What it is:
Student loses structure during multi-step manipulation.

Signature

• missing brackets after substitution
• expands inconsistently
• expression “mutates” and becomes unrecognisable

Strong linkage

• Algebra control + structure preservation pocket weak
  (BTT.MAT.Z0.P.ALG.001)

Class 5 — Checking Failure (no self-repair loop)

What it is:
Student could catch errors, but doesn’t check or checks incorrectly.

Signature

• errors remain in final line
• repeated wrong answers even when steps seem plausible
• student says “I didn’t see it”

Strong linkage

• TTC pressure (rushing eliminates checking)
  (BTT.SEN.Z0.S.TTC.001)
• false competence masking (no exam-style conditions)
  (BTT.SEN.Z1.S.FCG.001)

How to Use the Error Pattern Sensor (Fast Protocol)

Step 1 — Collect 10 mistakes

From:

• homework,
• a timed paper,
• or a mixed practice set.

Step 2 — Label each mistake (one class only)

Do not label “careless.”
Force one class.

Step 3 — Find the dominant class

If 6/10 belong to one class → that is the repair target.

This makes tuition and revision stop being random.

Error Classes and Their Fix (One-to-One Repair Mapping)

If dominant class is Slip Errors:

• reduce TTC pressure first
• use timed micro-sets + calm checking

If dominant class is Transformation Errors:

• rebuild Algebra Control pipeline (BTT.MAT.Z0.P.ALG.001)
• enforce “legal move only” rules

If dominant class is Rule Selection Errors:

• do rule-identification drills (no computation)
• train “first step selection” without prompts

If dominant class is Structure Loss:

• bracket discipline drills
• substitution integrity drills
• reduce step-size (single-step transformations)

If dominant class is Checking Failure:

• install 2-step checking protocol
• require at least 1 check per question
• train reverse-move checks and substitution checks

Why This Sensor Predicts Exam Rupture

Exams don’t punish you for “not understanding.”
They punish error accumulation under time.

If error class dominance persists:

• TTC rises (rework),
• prompts increase (dependency),
• confidence collapses,
• and the student enters a collapse corridor.

This is how:

• BTT.EXM.Z2.P.SEC.001 degrades,
  especially at:
• BTT.EXM.Z2.B.OLEV.001.

Where This Sensor Lives in the Lattice

This sensor is referenced by:

• grade nodes (Sec 1–4, A-Math)
• Z0 execution pipelines (Algebra/Differentiation)
• and exam pipeline pages

It is the “diagnostic glue” that turns content into an OS.

Lattice Coordinates Referenced (Required)

• BTT.MAT.Z0.S.ERR.001
• BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z1.S.FCG.001
• BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z0.P.DIF.001
• BTT.MAT.Z2.N.AM3.001
• BTT.EXM.Z2.P.SEC.001
• BTT.EXM.Z2.B.OLEV.001

Edges Created (BindsTo / Impacts / Observes)

• BTT.MAT.Z0.S.ERR.001 Observes BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z0.S.ERR.001 Observes BTT.MAT.Z0.P.DIF.001
• BTT.MAT.Z0.S.ERR.001 Observes BTT.MAT.Z2.N.AM3.001
• Dominant error class Impacts BTT.SEN.Z0.S.TTC.001 (rework increases TTC)
• Dominant error class Impacts BTT.EXM.Z2.P.SEC.001 (persistent error class predicts exam rupture)

Sensors Mentioned

• BTT.MAT.Z0.S.ERR.001
• BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z1.S.FCG.001

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Secondary Exam Pipeline (Sec 1→Sec 4) (BTT.EXM.Z2.P.SEC.001) — Z2 Pipeline Page (V1.1, Publish-Ready)

Title: Secondary Exam Pipeline — Why Students Collapse at WA/EOY/O-Levels Even When They “Know” the Work
Slug: /btt-exm-z2-p-sec-001-secondary-exam-pipeline/
Coordinate: BTT.EXM.Z2.P.SEC.001

Definition Lock

Secondary Exam Pipeline is the Z2 load corridor that converts Z0 skill pockets into outcomes under strict constraints:

• time pressure,
• mixed variation,
• no prompts,
• high consequence scoring.

Exams do not measure understanding.
They measure execution reliability under load.

A student fails exams when the pipeline is non-regenerative:

• TTC rises,
• errors compound,
• prompts are missing,
• recovery fails,
• and the student exits the lane.

What This Page Is

This is the Z2 pipeline page that binds the entire BukitTimahTutor lattice into one mechanism:

Z0 execution + Z1 support loops → Z2 exam outcome

This page tells parents and students the truth:

• exam failure is mechanical,
• predictable,
• and fixable with correct routing.

The Exam Load Model (What exams actually do)

Exams apply three loads simultaneously:

1. Speed (time constraint)
2. Variation (mixed topics + wrapper changes)
3. Independence (no prompts, no rescue)

If any one of these is weak, the student ruptures.

The Core Failure Loop (Exam Collapse Physics)

Most collapses follow this loop:

1. TTC exceeds tempo (BTT.SEN.Z0.S.TTC.001)
2. student rushes → slip errors spike (BTT.MAT.Z0.S.ERR.001)
3. rework increases TTC further
4. checking disappears
5. confusion triggers prompt-seeking (BTT.SEN.Z1.S.DEP.001)
6. prompts absent in exam → freeze
7. score collapses

This is why exam failure feels “sudden.”
It isn’t. The sensor signatures were present earlier.

What Feeds the Exam Pipeline (Z0 must be stable)

Exams are downstream. If Z0 is unstable, Z2 cannot work.

Core Z0 dependencies:

• Algebra Control Pipeline — BTT.MAT.Z0.P.ALG.001
• Differentiation Execution Pipeline — BTT.MAT.Z0.P.DIF.001
• Geometry Control Pipeline — BTT.MAT.Z0.P.GEO.001

If algebra fails, everything else fails secondarily.

Support Loop Coupling (Z1 decides whether skill becomes independent)

Exams require independence. So Z1 must be healthy.

Z1 dependencies:

• Prompt Dependency Sensor — BTT.SEN.Z1.S.DEP.001
• False Competence Gauge — BTT.SEN.Z1.S.FCG.001

Key rule:
If tuition/homework reduces struggle too aggressively, exam collapse becomes inevitable.

The Three Hidden Exam Traps (Why “practice” doesn’t transfer)

Trap 1 — Topic slicing

Students practise single-topic sets.
Exams are mixed. They fail “selection” not “knowledge.”

Trap 2 — Unlimited time practice

Students can do questions slowly.
Exams punish TTC variance and long decision time.

Trap 3 — Prompted environments

Students always get first-step cues.
Exams remove cues.

These traps create false competence until WA/EOY/O-Level hits.

Transition Rupture Corridor (Sec 3 is the cliff)

The most common collapse corridor is:

• Sec 3 A-Math node — BTT.MAT.Z2.N.AM3.001
  → (if unstable) impacts
• O-Level bind — BTT.EXM.Z2.B.OLEV.001

Because Sec 3 increases:

• symbolic control demand
• speed and variation
• complexity of multi-step chains

If you wait until Sec 4, repair cost increases sharply.

How to Repair the Exam Pipeline (P1→P3)

P1 — Stabilise (stop bleeding)

• measure TTC (don’t guess): BTT.SEN.Z0.S.TTC.001
• classify dominant error class: BTT.MAT.Z0.S.ERR.001
• remove prompt rescue patterns: BTT.SEN.Z1.S.DEP.001
• rebuild algebra pocket first: BTT.MAT.Z0.P.ALG.001

P2 — Adapt (convert knowledge into independent execution)

• controlled variation sets (same skill, different wrappers)
• “first-step selection” drills
• checking protocols become mandatory
• timed micro-sets (not full papers yet)

P3 — Excellence (exam-proof)

• timed mixed sets
• strict no-prompt policy
• recovery loops installed
• TTC variance falls and stays low
• performance becomes predictable

What This Pipeline Produces (Output)

A stable exam pipeline produces:

• confidence that is real (predictive),
• repeatable scores,
• and independence.

An unstable pipeline produces:

• random scores,
• “I did it before but I can’t now,”
• and panic under time.

Lattice Coordinates Referenced (Required)

• BTT.EXM.Z2.P.SEC.001
• BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z0.P.DIF.001
• BTT.MAT.Z0.P.GEO.001
• BTT.SEN.Z0.S.TTC.001
• BTT.MAT.Z0.S.ERR.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z1.S.FCG.001
• BTT.MAT.Z2.N.AM3.001
• BTT.EXM.Z2.B.OLEV.001
• SG.EDU.Z3.B.EXM.001

Edges Created (BindsTo / Impacts / Observes)

• BTT.EXM.Z2.P.SEC.001 BindsTo BTT.MAT.Z0.P.ALG.001
• BTT.EXM.Z2.P.SEC.001 BindsTo BTT.MAT.Z0.P.DIF.001
• BTT.SEN.Z0.S.TTC.001 Observes BTT.EXM.Z2.P.SEC.001
• BTT.SEN.Z1.S.DEP.001 Impacts BTT.EXM.Z2.P.SEC.001
• BTT.SEN.Z1.S.FCG.001 Impacts BTT.EXM.Z2.P.SEC.001
• BTT.MAT.Z2.N.AM3.001 Impacts BTT.EXM.Z2.B.OLEV.001

Sensors Mentioned

• BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z1.S.FCG.001
• BTT.MAT.Z0.S.ERR.001

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O-Level Bind (BTT.EXM.Z2.B.OLEV.001) — Z2 Bind / Interface Page (V1.1, Publish-Ready)

Title: O-Level Bind — The Interface Where Weak Pipelines Collapse and Strong Pipelines Lock In
Slug: /btt-exm-z2-b-olev-001-o-level-bind/
Coordinate: BTT.EXM.Z2.B.OLEV.001

Definition Lock

O-Level Bind is the Z2 constraint interface that compresses the entire Secondary pipeline into a single high-consequence outcome under:

• strict time pressure,
• mixed variation,
• zero prompts,
• and scoring penalties for unrecoverable errors.

O-Levels are not “harder topics.”
O-Levels are a bind that amplifies whatever is already true about the student’s pipeline.

If the pipeline is stable, the bind locks excellence.
If the pipeline is unstable, the bind forces rupture.

What This Page Is

This is an interface/bind page.

It explains:

• why O-Level performance feels “sudden,”
• why “I can do it at home” fails here,
• which hidden sensors predict success/failure,
• and how to route recovery before the bind clamps shut.

What a Bind Does (System Mechanics)

A bind is not a new topic.
A bind is a constraint that converts small weaknesses into large outcomes.

O-Level bind applies:

• time compression (TTC matters)
• variation compression (selection matters)
• independence compression (no prompts)
• error compounding (one wrong move can poison the whole chain)

So O-Levels are an amplifier.

Why Students Collapse at O-Levels (The 4 Amplifiers)

Amplifier 1 — TTC threshold crossing

If TTC exceeds exam tempo, collapse becomes mechanical.

Sensor:

• BTT.SEN.Z0.S.TTC.001

Amplifier 2 — Dependency removal

If the student needs prompts, the bind removes them.

Sensor:

• BTT.SEN.Z1.S.DEP.001

Amplifier 3 — False competence reveal

If competence was produced by low variation + un-timed practice, the bind exposes it.

Sensor:

• BTT.SEN.Z1.S.FCG.001

Amplifier 4 — Error class compounding

One dominant error class under pressure can destroy the entire paper.

Sensor:

• BTT.MAT.Z0.S.ERR.001

What O-Levels Actually Test (Underneath the Topics)

O-Levels test whether the student can:

1. select the first step without guidance
2. execute Z0 pockets reliably under time
3. recover from errors without external correction
4. sustain performance across a full paper without fatigue collapse

This is why “understanding” doesn’t save students here.

Where the O-Level Bind Sits in the Lattice

O-Level bind clamps onto the Secondary exam pipeline:

• Secondary Exam Pipeline
  BTT.EXM.Z2.P.SEC.001

And it is most sensitive to rupture corridors such as:

• Sec 3 A-Math node
  BTT.MAT.Z2.N.AM3.001

Because that is where the pipeline usually first becomes non-regenerative.

What the O-Level Bind Requires (Minimum stability conditions)

A student does not need perfection. They need stability.

Minimum stability conditions:

• Algebra control is stable: BTT.MAT.Z0.P.ALG.001
• Differentiation execution is stable (for A-Math): BTT.MAT.Z0.P.DIF.001
• TTC variance is controlled: BTT.SEN.Z0.S.TTC.001
• Dependency is low: BTT.SEN.Z1.S.DEP.001
• error dominance is identified and repaired: BTT.MAT.Z0.S.ERR.001

If these are not true, O-Level bind becomes a clamp.

Recovery Timing (The harsh truth)

There are two recovery regimes:

Regime A — Early recovery (P2 possible)

If detected in Sec 3 (or early Sec 4), repair can be clean and regenerative.

Regime B — Late recovery (P1 emergency repair)

If detected near O-Levels, repair becomes triage:

• patch visible gaps,
• reduce catastrophic errors,
• maximise scoring under constraint.

Both can work — but early recovery is cheaper and more stable.

This is why TTC and dependency sensors matter: they detect drift early.

Recovery Protocol (P1 → P3 under the O-Level bind)

P1 — Stabilise (prevent catastrophic collapse)

• stop major illegal algebra errors
• reduce TTC spikes with micro-timed sets
• enforce checking for high-risk steps
• remove prompt rescue

P2 — Adapt (convert into exam-proof execution)

• mixed variation sets
• first-step selection drills
• controlled paper fragments (not full papers yet)
• repair dominant error class first

P3 — Excellence (bind locks in)

• timed full papers
• stable TTC
• low error rate
• reliable recovery loops
• confidence becomes predictive

Lattice Coordinates Referenced (Required)

• BTT.EXM.Z2.B.OLEV.001
• BTT.EXM.Z2.P.SEC.001
• BTT.MAT.Z2.N.AM3.001
• BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z0.P.DIF.001
• BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z1.S.FCG.001
• BTT.MAT.Z0.S.ERR.001
• SG.EDU.Z3.B.EXM.001

Edges Created (BindsTo / Impacts / Observes)

• BTT.EXM.Z2.B.OLEV.001 BindsTo BTT.EXM.Z2.P.SEC.001
• BTT.SEN.Z0.S.TTC.001 Observes O-Level risk at BTT.EXM.Z2.B.OLEV.001
• BTT.SEN.Z1.S.DEP.001 Impacts BTT.EXM.Z2.B.OLEV.001
• BTT.SEN.Z1.S.FCG.001 Impacts BTT.EXM.Z2.B.OLEV.001
• BTT.MAT.Z2.N.AM3.001 Impacts BTT.EXM.Z2.B.OLEV.001

Sensors Mentioned

• BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z1.S.FCG.001
• BTT.MAT.Z0.S.ERR.001

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Secondary 4 A-Math (BTT.MAT.Z2.N.AM4.001) — Grade Node Page (V1.1, Publish-Ready)

Title: Secondary 4 Additional Mathematics (A-Math) — The Final Pipeline Stabilisation Before O-Levels
Slug: /btt-mat-z2-n-am4-001-secondary-4-amath/
Coordinate: BTT.MAT.Z2.N.AM4.001

Definition Lock

Secondary 4 A-Math is not “more topics.”
It is the final stabilisation window where execution must become exam-proof before the O-Level bind clamps.

Sec 4 A-Math “works” only when the student can:

• execute core Z0 pockets under strict time,
• select first steps without prompts,
• recover from errors alone,
• and sustain performance across full mixed papers.

If not, the student enters emergency repair mode — and results become volatile.

What This Page Is

This is a lattice node page.
It maps:

• what Sec 4 A-Math demands as a system node,
• what collapses mechanically,
• which Z0 pockets must be stable,
• which sensors must be controlled,
• and how to route recovery before O-Levels.

Why Sec 4 Feels Brutal (It’s not the content)

Sec 4 is brutal because:

• the O-Level bind is near,
• full-paper stamina matters,
• mixed variation dominates,
• time pressure is non-negotiable,
• and there is no runway to “slowly understand.”

So weaknesses that were survivable in Sec 3 become fatal in Sec 4.

The Sec 4 A-Math Load Step (What increases)

Sec 4 increases load in three ways:

1. Paper integration (mixed question chains)
2. Time compression (TTC must drop)
3. Penalty amplification (one error can poison a whole solution)

This is why “I can do it after seeing the solution” stops working.

Core Z0 Execution Pipelines (Must be stable)

If any of these are unstable, Sec 4 becomes rescue.

1) Algebra Control Pipeline

BTT.MAT.Z0.P.ALG.001
/btt-mat-z0-p-alg-001-algebra-control-pipeline/

Sec 4 A-Math is still mostly algebra, disguised.

2) Differentiation Execution Pipeline

BTT.MAT.Z0.P.DIF.001
/btt-mat-z0-p-dif-001-differentiation-execution-pipeline/

Differentiation questions become longer chains under time.

3) Geometry/Graph Control Pipeline

BTT.MAT.Z0.P.GEO.001
(create next if needed; supports tangents/gradients/modelling)

The 4 Sec 4 Collapse Modes (Mechanical, predictable)

Collapse Mode 1 — TTC corridor breach

Student cannot finish paper without rushing.

Sensor:

• BTT.SEN.Z0.S.TTC.001

Collapse Mode 2 — Prompt dependence persists

Student still needs “what do I do first?”

Sensor:

• BTT.SEN.Z1.S.DEP.001

Collapse Mode 3 — False competence still present

Student looks fine in practice, collapses in timed mixed papers.

Sensor:

• BTT.SEN.Z1.S.FCG.001

Collapse Mode 4 — Dominant error class not repaired

Repeated error class keeps recurring and compounding.

Sensor:

• BTT.MAT.Z0.S.ERR.001

Sec 4 is where these finally become visible and unavoidable.

Where Sec 4 A-Math Binds (The O-Level clamp)

Sec 4 A-Math binds directly into:

• Secondary Exam Pipeline
  BTT.EXM.Z2.P.SEC.001
• O-Level Bind
  BTT.EXM.Z2.B.OLEV.001

Meaning:
Sec 4 is the last chance to stabilise before the bind amplifies everything.

Recovery Protocol (Two regimes: early vs late)

Regime A — Early Sec 4 (true repair possible)

Goal: convert into regenerative execution.

• rebuild Algebra Control first (BTT.MAT.Z0.P.ALG.001)
• reduce dependency (silent starts)
• install checking loops
• timed micro-sets → half-papers → full papers

Regime B — Late Sec 4 (triage, but still can win)

Goal: prevent catastrophic collapse under bind.

• fix the single dominant error class first (BTT.MAT.Z0.S.ERR.001)
• reduce TTC variance with targeted timed sets (BTT.SEN.Z0.S.TTC.001)
• lock 1–2 reliable methods per major question type
• avoid prompt dependence by enforcing first-step selection

Both regimes can improve outcomes, but the earlier regime produces stable confidence.

What “Good Sec 4” Looks Like (P3 signature)

A Sec 4 A-Math student is P3 when:

• TTC is stable (low variance) under mixed papers
• first step selection is automatic
• checking catches most mistakes
• errors are recoverable and don’t cascade
• performance is predictable across papers

That is what O-Levels reward.

Lattice Coordinates Referenced (Required)

• BTT.MAT.Z2.N.AM4.001
• BTT.MAT.Z2.N.AM3.001
• BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z0.P.DIF.001
• BTT.MAT.Z0.P.GEO.001
• BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z1.S.FCG.001
• BTT.MAT.Z0.S.ERR.001
• BTT.EXM.Z2.P.SEC.001
• BTT.EXM.Z2.B.OLEV.001
• SG.EDU.Z3.B.EXM.001

Edges Created (BindsTo / Impacts / Observes)

• BTT.MAT.Z2.N.AM4.001 BindsTo BTT.MAT.Z0.P.ALG.001
• BTT.MAT.Z2.N.AM4.001 BindsTo BTT.MAT.Z0.P.DIF.001
• BTT.MAT.Z2.N.AM4.001 Impacts BTT.EXM.Z2.B.OLEV.001
• BTT.SEN.Z0.S.TTC.001 Observes BTT.MAT.Z2.N.AM4.001
• BTT.SEN.Z1.S.DEP.001 Impacts BTT.EXM.Z2.P.SEC.001

Sensors Mentioned

• BTT.SEN.Z0.S.TTC.001
• BTT.SEN.Z1.S.DEP.001
• BTT.SEN.Z1.S.FCG.001
• BTT.MAT.Z0.S.ERR.001

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