SG-SCIENCE Master Graph v0.1 (Primary → Secondary → JC) — Executable Syllabus Lattice

TITLE: SG-SCIENCE Master Graph v0.1 (Primary → Secondary → JC) — Executable Syllabus Lattice
VERSION: CivOS Unified Spec v1.x
MODE: Almost-Code / LLM-first / WordPress paste-ready
OWNER: eduKateSG Fence Learning Systems
SCOPE: Singapore Science (Primary + Secondary + JC: Physics/Chem/Bio) as a capability lattice
GOAL: Make science computable: Concepts → Mechanisms → Models → Questions → Practical → Transfer under load
CANONICAL CLAIM:
- Science failure is usually not “content volume”. It is mechanism failure:
  (1) weak concept definitions,
  (2) unstable causal chains (NIT-science),
  (3) math coupling gaps (graphs, algebra, proportional reasoning),
  (4) practical reasoning drift,
  (5) late fencing (repair arrives after exam shock).
- This graph attaches sensors + Fence rules + repair routing to reach P2/P3 reliability.
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0) GLOBAL PRIMITIVES (LOCKED)
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Phase (Reliability Under Load):
- P0 collapse: cannot explain or apply; answers become random
- P1 scaffolded: can follow notes; fails in unfamiliar questions
- P2 reliable: standard exam conditions; stable mechanism answers
- P3 stable: high-variation; novel application; fast + accurate
Zoom:
- Z0 learner, Z1 family/tutor, Z2 school, Z3 city, Z4 nation, Z5 civilisation, Z6 supranational
FenceOS:
- R = Ḋ/Ġ  (mechanism decay / repair rate)  ; stable if R<1
- Θ = T_fence / T_repair                  ; must be <1
- Λ = T_enforce / T_fence                 ; preferred <1
Science-HD Core Sensors:
- MR (Mechanism Reliability): % of explanations with correct causal chain
- DR (Definition Reliability): % of key terms defined correctly under time
- GRF (Graph/Formula Reliability): accuracy applying formulas/graphs
- PR (Practical Reliability): ability to design/interpret experiments
- NIT-S (Narrative Irreversibility Threshold—Science): point where causal chain becomes irrecoverably wrong
- TR (Transfer Reliability): performance on unfamiliar contexts
- VFR (Variation Failure Rate): failure rate on “application” questions
- BN (Backlog Nodes), TTC, SII (speed instability)
Fence Actions:
- Truncation: reduce breadth; fix definitions + mechanism chain first
- Stitching: targeted repair loop; rebuild buffer; rejoin safe trajectory (APRC)
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1) GRAPH FORMALISM (SCIENCE PIPELINE)
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Science Pipeline Lattice:
Definitions → Mechanisms → Models/Representations → Question Types → Practical → Transfer
NodeRecord := {
  ID, LevelBand, Domain, Prereq[], Outputs[],
  LoadProfile, PhaseTargetByStage,
  TransferTests[], Sensors[], FailureModes[], RepairLoops[],
  FenceRules
}
ID Grammar (LOCK):
Place×Lane×Zoom×Role×Type×ID
Place: SG
Lane: SCI
Zoom: Z0
Role: Learner / Tutor / Teacher / Operator
Type: Node / Edge / SensorPack / Protocol / Test / Panel
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2) MASTER DOMAINS (TOP-LEVEL CLUSTERS)
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Primary Science Domains (broad):
- PSK: Scientific Skills (observe, compare, classify)
- PMAT: Matter & Materials
- PENG: Energy & Forces (intro)
- PLIF: Life Processes (plants/animals/humans)
- PSYS: Systems (simple ecosystems, cycles)
- PINQ: Inquiry (fair test, variables, conclusion)
Secondary Science Domains:
- PHY: Physics (forces, energy, waves, electricity)
- CHE: Chemistry (particles, reactions, acids/bases)
- BIO: Biology (cells, transport, reproduction, ecology)
- DATA: Data handling (tables, graphs, uncertainty)
- PRAC: Practical skills (planning, technique, evaluation)
JC Science Domains:
- PHY-JC: mechanics/fields/waves/quantum (track dependent)
- CHE-JC: energetics, kinetics, equilibria, redox, organic
- BIO-JC: molecular/cell biology, genetics, homeostasis, evolution
- PRAC-JC: higher-order practical + evaluation
- MATH-COUPLING: calculus, graphs, algebra, proportionality (strong)
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3) PRIMARY SCIENCE (P3–P6 focus) — NODE SET v0.1
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3.1 INQUIRY CORE (the spine)
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Node: SG×SCI×Z0×Learner×Node×PINQ-FAIRTEST
Prereq: []
Outputs: PINQ-VARIABLES, PINQ-CONCLUDE
LoadProfile: medium
PhaseTarget: {P2 by P4, P3 by P6 top band}
TransferTests: {identify fair test vs unfair; fix experiment}
Sensors: {PR, DR}
FailureModes: {ConfuseVariableTypes}
RepairLoops: {IV/DV/Controls card + drills}
FenceRules:
- If ConfuseVariableTypes repeats → Truncate to variable sorting → Stitch fair test examples
Node: SG×SCI×Z0×Learner×Node×PINQ-VARIABLES
Prereq: [PINQ-FAIRTEST]
Outputs: PINQ-DATA, PINQ-EVALUATE
LoadProfile: high (precision)
PhaseTarget: {P2 by P6}
TransferTests: {choose variables; state controls}
Sensors: {PR}
FailureModes: {MissingControls}
RepairLoops: {control checklist}
FenceRules: enforce checklist (Λ)
Node: SG×SCI×Z0×Learner×Node×PINQ-CONCLUDE
Prereq: [PINQ-FAIRTEST]
Outputs: PINQ-EVIDENCE
LoadProfile: medium
PhaseTarget: {P2 by P6}
TransferTests: {conclusion must match DV; use evidence}
Sensors: {MR-lite}
FailureModes: {ConclusionNotLinkedToData}
RepairLoops: {data→trend→conclusion template}
FenceRules: if mismatch → truncate; stitch template
Node: SG×SCI×Z0×Learner×Node×PINQ-DATA
Prereq: [PINQ-VARIABLES]
Outputs: SEC-DATA-GRAPHS readiness
LoadProfile: medium
PhaseTarget: {P2 by P6}
TransferTests: {draw table; simple graph; interpret}
Sensors: {GRF}
FailureModes: {ReadGraphWrong}
RepairLoops: {axis/units discipline}
FenceRules: enforce units
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3.2 PRIMARY CONTENT CLUSTERS (high-level nodes)
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Node: SG×SCI×Z0×Learner×Node×PMAT-MATERIALS
Prereq: []
Outputs: SEC-CHE-PARTICLES
LoadProfile: medium
PhaseTarget: {P2 by P6}
TransferTests: {properties vs uses; change reversible/irreversible}
Sensors: {DR, MR-lite}
FailureModes: {VagueDefinitions}
RepairLoops: {definition cards + examples/nonexamples}
FenceRules: definition-first
Node: SG×SCI×Z0×Learner×Node×PENG-FORCES-ENERGY
Prereq: []
Outputs: SEC-PHY-FORCES
LoadProfile: medium
PhaseTarget: {P2 by P6}
TransferTests: {push/pull, simple energy changes}
Sensors: {MR-lite}
FailureModes: {WrongCauseEffect}
RepairLoops: {cause→effect chain practice}
FenceRules: if chain breaks → truncate to 2-link chain
Node: SG×SCI×Z0×Learner×Node×PLIF-LIFE-PROCESSES
Prereq: []
Outputs: SEC-BIO-CELLS
LoadProfile: medium
PhaseTarget: {P2 by P6}
TransferTests: {basic human systems; plants}
Sensors: {DR}
FailureModes: {TermMixUp}
RepairLoops: {term sorting + diagrams}
FenceRules: diagram-first
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4) SECONDARY SCIENCE (Sec1–Sec4/5) — NODE SET v0.1
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Secondary Science splits into PHY/CHE/BIO + shared PRAC/DATA spine.
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4.1 SHARED SPINES: DATA + PRACTICAL + MECHANISM
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Node: SG×SCI×Z0×Learner×Node×DATA-GRAPHS
Prereq: [PINQ-DATA, SG×MATH×GRAPH-LINEAR (coupling)]
Outputs: PHY-GRAPHS, CHE-RATES, BIO-TRENDS
LoadProfile: high (interpretation + accuracy)
PhaseTarget: {P2 by Sec2}
TransferTests: {gradient, intercept meaning, trend statements}
Sensors: {GRF, TR}
FailureModes: {DescribeNotExplain, UnitsMissing}
RepairLoops: {trend→evidence→mechanism template}
FenceRules: enforce units + mechanism line
Node: SG×SCI×Z0×Learner×Node×PRAC-CORE
Prereq: [PINQ-VARIABLES, PINQ-CONCLUDE]
Outputs: PRAC-EVALUATE
LoadProfile: high (multi-step + precision)
PhaseTarget: {P2 by Sec3}
TransferTests: {plan fair test; identify errors; improve method}
Sensors: {PR}
FailureModes: {NoControls, NoRepeat, NoSafety}
RepairLoops: {practical checklist + exemplars}
FenceRules: checklist enforced before marking (Λ)
Node: SG×SCI×Z0×Learner×Node×PRAC-EVALUATE
Prereq: [PRAC-CORE, DATA-GRAPHS]
Outputs: JC-PRAC readiness
LoadProfile: high
PhaseTarget: {P2 by Sec4}
TransferTests: {limitations; improvements; reliability/accuracy}
Sensors: {PR, MR}
FailureModes: {GenericEvaluation}
RepairLoops: {limitation→effect→fix template}
FenceRules: if generic repeats → truncate to one-variable-at-a-time evaluation
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4.2 PHYSICS (SEC) — CORE NODES
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Node: SG×SCI×Z0×Learner×Node×PHY-FORCES
Prereq: [PENG-FORCES-ENERGY, SG×MATH×RPP-PROPORTION]
Outputs: PHY-MOTION, PHY-PRESSURE
LoadProfile: high (vectors + proportionality)
PhaseTarget: {P2 by Sec2}
TransferTests: {draw forces; resultant; simple calculations}
Sensors: {MR, GRF}
FailureModes: {ConfuseMassWeight, DirectionBlindness}
RepairLoops: {free-body diagram protocol}
FenceRules: diagram-first enforced (Λ)
Node: SG×SCI×Z0×Learner×Node×PHY-MOTION
Prereq: [PHY-FORCES, SG×MATH×GRAPH-LINEAR]
Outputs: JC-MECHANICS readiness
LoadProfile: very high (graphs + equations)
PhaseTarget: {P2 by Sec3, P3 top band}
TransferTests: {speed-time graphs; acceleration; explain}
Sensors: {GRF, MR, VFR}
FailureModes: {GraphMeaningFailure, FormulaPluggingNoMeaning}
RepairLoops: {graph→story→equation→check loop}
FenceRules:
- If FormulaPlugging detected → truncate calculations → stitch meaning chain
Node: SG×SCI×Z0×Learner×Node×PHY-ENERGY
Prereq: [PHY-MOTION]
Outputs: PHY-POWER, CHE-ENERGETICS bridge
LoadProfile: high
PhaseTarget: {P2 by Sec4}
TransferTests: {energy changes; efficiency; conservation}
Sensors: {MR, DR}
FailureModes: {EnergyAsThingConfusion}
RepairLoops: {system boundary + before/after tables}
FenceRules: define system boundary first
Node: SG×SCI×Z0×Learner×Node×PHY-ELECTRICITY
Prereq: [SG×MATH×ALG-EQ-LINEAR (algebra coupling)]
Outputs: JC-FIELDS readiness
LoadProfile: high
PhaseTarget: {P2 by Sec4}
TransferTests: {circuits; V=IR; reasoning}
Sensors: {MR, GRF}
FailureModes: {CurrentVoltageConfusion}
RepairLoops: {water-model analogy + circuit reasoning templates}
FenceRules: concept check before formula use
Node: SG×SCI×Z0×Learner×Node×PHY-WAVES
Prereq: []
Outputs: JC-WAVES readiness
LoadProfile: medium
PhaseTarget: {P2 by Sec4}
TransferTests: {wave properties; refraction}
Sensors: {DR, MR}
FailureModes: {TermMixUp}
RepairLoops: {diagram labeling protocol}
FenceRules: diagram-first
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4.3 CHEMISTRY (SEC) — CORE NODES
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Node: SG×SCI×Z0×Learner×Node×CHE-PARTICLES
Prereq: [PMAT-MATERIALS]
Outputs: CHE-CHANGES, CHE-REACTIONS
LoadProfile: high (abstract model)
PhaseTarget: {P2 by Sec2}
TransferTests: {particle diagrams; state changes}
Sensors: {DR, MR}
FailureModes: {ModelAsPictureOnly}
RepairLoops: {particle story explanations}
FenceRules: require “because particles…” line (NIT-lite)
Node: SG×SCI×Z0×Learner×Node×CHE-REACTIONS
Prereq: [CHE-PARTICLES]
Outputs: CHE-ACIDBASE, CHE-REDOX readiness
LoadProfile: high
PhaseTarget: {P2 by Sec3}
TransferTests: {word equations; predict products (basic)}
Sensors: {DR, MR}
FailureModes: {MemoriseNoMechanism}
RepairLoops: {reactivity reasoning + pattern sets}
FenceRules: if memorise-only → truncate list; stitch reasoning
Node: SG×SCI×Z0×Learner×Node×CHE-ACIDBASE
Prereq: [CHE-REACTIONS]
Outputs: CHE-SALTS, JC-EQUIL readiness
LoadProfile: high
PhaseTarget: {P2 by Sec4}
TransferTests: {pH; indicators; neutralisation}
Sensors: {MR, GRF}
FailureModes: {pHScaleConfusion}
RepairLoops: {scale anchors + practice}
FenceRules: anchor points first
Node: SG×SCI×Z0×Learner×Node×CHE-RATES
Prereq: [DATA-GRAPHS]
Outputs: JC-KINETICS readiness
LoadProfile: high
PhaseTarget: {P2 by Sec4}
TransferTests: {factors; interpret graphs}
Sensors: {GRF, MR}
FailureModes: {Correlation≠Causation}
RepairLoops: {variable control + mechanism explanation}
FenceRules: enforce “factor→particle collision” line
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4.4 BIOLOGY (SEC) — CORE NODES
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Node: SG×SCI×Z0×Learner×Node×BIO-CELLS
Prereq: [PLIF-LIFE-PROCESSES]
Outputs: BIO-TRANSPORT, JC-CELL readiness
LoadProfile: high (terms + diagrams)
PhaseTarget: {P2 by Sec2}
TransferTests: {label; function; explain}
Sensors: {DR, MR}
FailureModes: {LabelOnlyTrap}
RepairLoops: {label→function→because-chain}
FenceRules: require function line for each label
Node: SG×SCI×Z0×Learner×Node×BIO-TRANSPORT
Prereq: [BIO-CELLS]
Outputs: BIO-HUMAN-SYS, JC-HOMEOSTASIS readiness
LoadProfile: high
PhaseTarget: {P2 by Sec3}
TransferTests: {diffusion/osmosis; application}
Sensors: {MR, VFR}
FailureModes: {DirectionConfusion}
RepairLoops: {concentration gradient diagrams + cases}
FenceRules: diagram-first + gradient statement
Node: SG×SCI×Z0×Learner×Node×BIO-ECOLOGY
Prereq: []
Outputs: JC-EVOLUTION readiness
LoadProfile: medium
PhaseTarget: {P2 by Sec4}
TransferTests: {food webs; cycles; impacts}
Sensors: {MR}
FailureModes: {StoryNoMechanism}
RepairLoops: {cause→effect→feedback loop templates}
FenceRules: enforce feedback loop statement
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5) JC SCIENCE — NODE SET v0.1 (ABSTRACTED)
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NOTE:
JC content is large; v0.1 provides the high-impact “spines” first.
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5.1 JC PHYSICS SPINE (readiness)
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Node: SG×SCI×Z0×Learner×Node×JC-PHY-MECHANICS
Prereq: [PHY-MOTION, SG×MATH×JC-CALC-DIFF (coupling)]
Outputs: JC-PHY-FIELDS, JC-PHY-WAVES
LoadProfile: extreme
PhaseTarget: {P2 by JC2, P3 top band}
TransferTests: {multi-step problems; explain assumptions}
Sensors: {MR, GRF, TR, BN}
FailureModes: {AssumptionBlindness, MathCouplingBreak}
RepairLoops: {assumption checklist + math patching}
FenceRules:
- If MathCouplingBreak → truncate physics complexity → stitch math node first (Θ control)
Node: SG×SCI×Z0×Learner×Node×JC-PHY-FIELDS
Prereq: [PHY-ELECTRICITY]
Outputs: A-level transfer
LoadProfile: extreme
Sensors: {MR, GRF}
FailureModes: {FieldForceConfusion}
RepairLoops: {field line reasoning + templates}
FenceRules: concept check before calculation
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5.2 JC CHEMISTRY SPINE (readiness)
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Node: SG×SCI×Z0×Learner×Node×JC-CHE-KINETICS
Prereq: [CHE-RATES]
Outputs: JC-CHE-EQUIL
LoadProfile: extreme
Sensors: {MR, GRF, TR}
FailureModes: {EquationChasing, NoMechanism}
RepairLoops: {rate law interpretation + mechanism line}
FenceRules: enforce mechanism explanation
Node: SG×SCI×Z0×Learner×Node×JC-CHE-EQUIL
Prereq: [CHE-ACIDBASE]
Outputs: JC-CHE-ORGANIC
LoadProfile: extreme
Sensors: {MR}
FailureModes: {LeChatelierAsMagic}
RepairLoops: {stress→shift reasoning templates}
FenceRules: require “system response” statement
Node: SG×SCI×Z0×Learner×Node×JC-CHE-ORGANIC
Prereq: [CHE-REACTIONS]
Outputs: A-level transfer
LoadProfile: extreme (memory + mechanism)
Sensors: {DR, MR, TR}
FailureModes: {MemoriseRoutes, RouteConfusion}
RepairLoops: {map-of-maps (functional groups) + pattern sets}
FenceRules: truncate to core routes first, then expand
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5.3 JC BIOLOGY SPINE (readiness)
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Node: SG×SCI×Z0×Learner×Node×JC-BIO-CELL
Prereq: [BIO-CELLS]
Outputs: JC-BIO-GENETICS, JC-BIO-HOMEOSTASIS
LoadProfile: extreme (detail + logic)
Sensors: {DR, MR, TR}
FailureModes: {DetailFloodNoStructure}
RepairLoops: {hierarchy maps + mechanism chains}
FenceRules: truncate detail; stitch structure first
Node: SG×SCI×Z0×Learner×Node×JC-BIO-GENETICS
Prereq: [JC-BIO-CELL]
Outputs: JC-BIO-EVOLUTION
LoadProfile: extreme
Sensors: {MR}
FailureModes: {ProcessConfusion}
RepairLoops: {flowchart reasoning}
FenceRules: flowchart enforced
Node: SG×SCI×Z0×Learner×Node×JC-BIO-HOMEOSTASIS
Prereq: [BIO-TRANSPORT]
Outputs: A-level transfer
LoadProfile: extreme
Sensors: {MR}
FailureModes: {FeedbackLoopFailure}
RepairLoops: {stimulus→receptor→control→effector→response}
FenceRules: require full loop statement
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6) NIT-S (SCIENCE NARRATIVE IRREVERSIBILITY THRESHOLD) — v0.1
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Definition:
NIT-S := point where the causal/mechanistic explanation becomes internally inconsistent
such that learner cannot repair it even when prompted.
NIT-S Triggers:
- uses wrong variable as cause (e.g., “mass causes weight to change with location”)
- breaks conservation logic (energy “disappears” without system boundary)
- confuses correlation with causation (rates/graphs)
- explanation contradicts earlier statement
- cannot link evidence (data) to mechanism
Fence Rule:
- If NIT-S triggers → TRUNCATE breadth; rebuild definitions + 2-link mechanism chain
- Only after MR stable → increase chain length and variation
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7) CORE EDGES (PREREQ + COUPLING) — v0.1
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Edge: SG×SCI×Z0×Operator×Edge×E-MATH→SCI-DATA
From: SG×MATH×GRAPH-LINEAR
To: DATA-GRAPHS
Weight: very high
TypicalFailure: wrong gradient meaning
RepairBridge: graph→story→equation loop
Edge: SG×SCI×Z0×Operator×Edge×E-RPP→PHY-FORCES
From: SG×MATH×RPP-PROPORTION
To: PHY-FORCES
Weight: high
TypicalFailure: proportionality errors
RepairBridge: unitary method + unit tagging
Edge: SG×SCI×Z0×Operator×Edge×E-ALG→ELECTRICITY
From: SG×MATH×ALG-EQ-LINEAR
To: PHY-ELECTRICITY
Weight: high
TypicalFailure: rearrangement/solve errors
RepairBridge: algebra patch drills
Edge: SG×SCI×Z0×Operator×Edge×E-ENG→SCI-EXPLAIN
From: SG×ENG×PARA-CORE
To: MR (Mechanism Reliability) across science
Weight: medium→high
TypicalFailure: cannot explain clearly even if knows
RepairBridge: “because-chain” writing templates
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8) CIVOS-HD SENSOR PACK (SCIENCE EDITION) — v0.1
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SensorPack: SG×SCI×Z0×Tutor×SensorPack×SENS-SCI-HD
Inputs:
- DR, MR, GRF, PR, NIT-S, TR, VFR, BN, TTC, SII
Derived:
- DriftVelocity: d(MR)/dt, d(GRF)/dt
- Fence Timing: Θ, Λ (qualitative if needed)
Triggers:
- DR < 70% on key terms → stop new topics; stitch definition pack
- MR low but DR ok → mechanism chain drills (2-link → 3-link → 5-link)
- GRF failures → patch math coupling node
- PR low → checklist + exemplar planning drills
- NIT-S triggers → truncate to core chain + system boundary definition
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9) FENCE RULES (GLOBAL STOP-LOSS) — v0.1
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FenceRules.Global:
- Definition → Mechanism → Calculation (never reverse this order).
- If calculation works but explanation fails: treat as unstable; repair mechanism.
- If TTC short and BN high:
  - truncate breadth
  - focus on high-weight nodes: {DATA-GRAPHS, PRAC-CORE, PHY-FORCES/MOTION, CHE-PARTICLES/REACTIONS, BIO-CELLS/TRANSPORT}
- Practical marks are not “extra”: they are transfer reliability sensors.
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10) CH/ai SCHEDULER HOOK (SCIENCE) — v0.1
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CH/ai.Inputs:
- TTC, HoursPerWeek, NodePhaseScores, BN
- CouplingEdges (Math/English dependencies)
- Practical schedule constraints
CH/ai.Outputs:
- WeeklyRoutePlan:
  - 2× Definitions + Mechanism sessions
  - 2× Mixed exam-style question sessions
  - 1× Data/Graphs session
  - 1× Practical planning/evaluation session
  - 1× Timed micro-simulation (only if stability reached)
- DowngradeLogic:
  1) drop low-weight extension topics
  2) keep mechanism spines + data + practical
  3) patch coupling deficits first (math/graph/algebra)
- ReTestSchedule:
  - DR weekly
  - MR weekly via explain-in-90-seconds
  - GRF weekly
  - PR biweekly
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11) REQUIRED SHORT FAILURE MODE TRACE (CANONICAL)
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Trace:
Weak definitions → wrong mechanism chain (NIT-S) → formula plugging →
graph misread → practical evaluation generic → exam variation collapse → P2→P0
Fence Repair:
Detect DR/MR/GRF drift early → truncate breadth → stitch definitions + 2-link chain →
patch math coupling → timed variation ramps → maintain P2/P3
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END: SG-SCIENCE Master Graph v0.1
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WORDPRESS PASTE-READY PAGE STRUCTURE
H1: Singapore Science Syllabus as a Lattice — SG-SCIENCE Master Graph v0.1
H2: Why “Mechanism Reliability” beats memorising chapters
H2: Phase (P0–P3) and Zoom (Z0–Z6) in Science
H2: Primary Spine: Inquiry (Fair Test → Variables → Data → Conclusion)
H2: Secondary Spines: Data+Practical + Physics + Chemistry + Biology
H2: JC Spines: Physics/Chem/Bio readiness (high-impact nodes)
H2: NIT-S (Science Irreversibility Threshold) — detect causal collapse early
H2: Coupling Edges (Math ↔ Science, English ↔ Science)
H2: CivOS-HD Sensor Pack + Fence Rules
H2: CH/ai Scheduler Hook + Downgrade Logic
H2: Failure Trace + Repair Trace