eduKateSG.IC.Poster.StabilityInequality.v1.0

1) Stability Inequality + Control Knobs Poster v1.0

ID: eduKateSG.IC.Poster.StabilityInequality.v1.0
Type: One-poster control law (math compressed)
Goal: A single equation operators can run + the knobs they can turn

The One Inequality (Education Stability Law)

Define:

Ḋ(t) = total damage / drift / shortcut rate
Ġ(t) = total repair / verification / transfer rate

Stability condition (must hold weekly): $\dot{G} (t) > \dot{D} (t)$ G˙(t) > D˙(t)

If violated → Phase drops (P3→P2→P1→P0).

What Is Ḋ(t) (Damage Rate)

			
DamageRate_Ḋ:
  Components:
    Overload:          w1 * d_overload
    StressShock:       w2 * d_stress
    FalseCompetence:   w3 * u_A * (1 - V)
    BufferDecay:       w4 * (1 - B1) + w5 * (1 - B2) + w6 * (1 - B3)

		

Interpretation:

More load and stress raises damage.
AI use without verification raises damage fast.
Weak routines, weak teachers, bad routing raise damage steadily.

What Is Ġ(t) (Repair Rate)

			
RepairRate_Ġ:
  Components:
    RepairLoop:        k1 * u_R
    Verification:      k2 * u_V
    Transfer:          k3 * u_X * min(D,S)
    BufferSupport:     k4 * (B1 + B2 + B3)

		

Interpretation:

Repair loops directly rebuild foundations.
Verification drains false competence.
Transfer only works if depth + stability exist.
Buffers (routine, bandwidth, routing) amplify everything.

The 5 Control Knobs (Operator Levers)

			
ControlKnobs:
  u_R: "Repair intensity (Truncation+Stitching)"
  u_L: "Load level (reduce spikes)"
  u_X: "Transfer frequency (weekly new context)"
  u_V: "Verification enforcement (logs + tests)"
  B1:  "Routine buffer (sleep/device/home stability)"

		

Fastest lever in emergencies:

reduce u_L (scope)
increase u_V (verification)
run u_R (repair corridor)

Phase Gate (P3 Requirement)

			
P3Gate:
  requires:
    D >= θD
    S >= θS
    T >= θT
    V >= θV
  plus:
    weekly: "Ġ > Ḋ"

		

The Modern Collapse Shortcut

			
ShortcutCollapse:
  If: u_A rises and u_V falls
  Then: FalseCompetence explodes → Ḋ spikes → inequality breaks

Emergency Stop-Loss (Fence Behaviour)

			
EmergencyFence:
  Trigger: "Ġ <= Ḋ for 2 weeks OR VerificationCompliance drops sharply"
  Actions:
    - "Freeze innovations (Δ = 0)"
    - "Cut scope (u_L down)"
    - "Mandatory verification logs (u_V up)"
    - "RepairLoop only (u_R up)"
    - "Keep 1 small transfer task/week (u_X minimal)"

		

2) Minimal Dataset Schema for Real Dashboard v1.0

ID: eduKateSG.IC.DataSchema.MinDashboard.v1.0
Type: Tables + fields (run immediately)
Goal: Smallest database that supports CFCS + Interstellar-Core metrics

A) Table: Learner

			
Table: Learner
PrimaryKey: learner_id
Fields:
  learner_id: string
  name_alias: string
  dob: date
  age: int
  stage: enum(A1,A2,A3,A4,A5,A6,A7)
  cohort_id: string
  start_date: date
  active: bool

		

B) Table: WeeklyState (Z0 core)

One row per learner per week.

			
Table: WeeklyState
PrimaryKey: (learner_id, week_start)
Fields:
  learner_id: string
  week_start: date
  Depth_D: float        # 0..1
  Stability_S: float    # 0..1
  Transfer_T: float     # 0..1
  Verification_V: float # 0..1
  Coordination_C: float # 0..1
  StressSignal: enum(Low,Med,High)
  TimedStabilityIndex: float  # 0..1
  TransferIndex: float        # 0..1
  VerificationLogCount: int
  Phase: enum(P0,P1,P2,P3)
  Notes_1sentence: string

		

C) Table: DriftEvent

Tracks detected drift + classification.

			
Table: DriftEvent
PrimaryKey: drift_id
Fields:
  drift_id: string
  learner_id: string
  date: date
  drift_type: enum(FoundationBreak,StabilityDrop,TransferFail,VerificationDrop,StressRise)
  severity: enum(Low,Med,High)
  error_cluster: string
  classified_by: staff_id
  action_triggered: enum(None,RepairLoop,StopLoss,ParentAction,OracleReview)

		

D) Table: Intervention (Repair / Transfer / Verification)

			
Table: Intervention
PrimaryKey: intervention_id
Fields:
  intervention_id: string
  learner_id: string
  start_date: date
  end_date: date
  type: enum(RepairLoop,TransferProgram,VerificationProgram,StressStabilityProgram)
  u_R: float
  u_L: float
  u_X: float
  u_V: float
  u_A: float
  owner_staff_id: staff_id
  outcome: enum(Improved,NoChange,Worse,Pending)
  failure_trace: string

		

E) Table: FamilyBuffer (Z1 simplified)

			
Table: FamilyBuffer
PrimaryKey: (learner_id, week_start)
Fields:
  learner_id: string
  week_start: date
  RoutineStability_B1: float  # 0..1
  SleepSignal: enum(Good,OK,Poor)
  DeviceLoad: enum(Low,Med,High)
  ConflictSignal: enum(Low,Med,High)

		

F) Table: Staff + Role (AVOO)

			
Table: Staff
PrimaryKey: staff_id
Fields:
  staff_id: string
  name_alias: string
  role: enum(Operator,Oracle,Visionary,Architect)
  certification_level: enum(None,Operator,Oracle,Visionary,Architect)
  active: bool

		

G) Table: Audit (Z2/Z3 integrity)

			
Table: Audit
PrimaryKey: audit_id
Fields:
  audit_id: string
  site_id: string
  date: date
  audited_by: staff_id
  RecordCompleteness: float
  VerificationCompliance: float
  TransferDensity: float
  CollapseRate: float
  P3Fraction: float
  flags: string
  actions_next: string

		

3) Derived Metrics (computed weekly)

Cohort Metrics

			
Derived_Cohort:
  P3Fraction = count(Phase==P3)/count(active)
  CollapseRate = count(Phase==P0)/count(active)
  VerificationCompliance = avg(Verification_V)
  TransferDensity = avg(Transfer_T)

		

Stability Check (poster inequality)

			
Derived_Stability:
  DamageRate_Ḋ = w1*Overload + w2*Stress + w3*u_A*(1-V) + w4*(1-B1)
  RepairRate_Ġ = k1*u_R + k2*u_V + k3*u_X*min(D,S) + k4*B1
  Stable = (Ġ > Ḋ)

4) Minimal “Run It Tomorrow” Workflow

			
Workflow:
  Weekly:
    - fill WeeklyState for each learner (5 numbers + phase + 1 sentence)
    - log DriftEvents
    - assign Interventions when needed
    - compute cohort metrics
    - run Audit checklist monthly

		

Version Lock

			
VersionLock:
  Poster: "eduKateSG.IC.Poster.StabilityInequality.v1.0"
  Schema: "eduKateSG.IC.DataSchema.MinDashboard.v1.0"
  Policy: "Forward-only updates; fields never renamed"