Operational Definitions Pack v1.0

SYSTEM: World Education OS
MODULE: Operational Definitions Pack
VERSION: v1.0
SCOPE:
  - G-M2 (Tail Thickness)
  - G-M3 (Repair Latency)
  - G-M7 (Masking Proxy)
  - TAP (Transfer Audit Pack)
REFERENCE:
  - P-S1..P-S5
  - W4 GF Library
  - W5 GR Library
STATUS: LIVE (definition-level)

METRIC: G-M2 Tail Thickness
OBJECT:
  Measure how “heavy” the failure tail is (bottom performance mass)
  under a defined stability condition, not a single score.
TAIL SET:
  Choose ONE standard default for public reporting:
  OPTION A (Quantile Tail):
    Tail = bottom 20% of cohort by stability score S
  OPTION B (Hard Threshold Tail):
    Tail = all learners with S < S_min (defined below)
DEFAULT:
  Use OPTION A (bottom 20%) for comparability across cities.

STABILITY SCORE S (default):
  S = w1*(P-S1 retrieval) 
    + w2*(1 - normalized error rate from P-S2)
    + w3*(1 - normalized time volatility from P-S3/P-S5)
    + w4*(transfer robustness from P-S4)
DEFAULT WEIGHTS:
  w1=0.25, w2=0.25, w3=0.25, w4=0.25

TAIL THICKNESS OUTPUTS:
  G-M2a: Tail mean stability (mean S in tail)
  G-M2b: Tail volatility (std(S) in tail)
  G-M2c: Tail persistence (fraction staying in tail for ≥K windows)
DEFAULT WINDOW:
  window = 4 weeks
  K = 2 windows (≥8 weeks persistence)

INTERPRETATION:
  - If G-M2c high: tail is "sticky" → needs GR9 + GR7 + GR6
  - If G-M2b high: tail is unstable → needs GR4 + GR11 + GR8
  - If G-M2a low: tail is deep → needs GR1 + GR2 baseline closure

METRIC: G-M3 Repair Latency
OBJECT:
  Measure time-to-closure for a defined failure mode GFx.
  Latency is measured from first detection to verified closure.
EVENT:
  detection_time = first window where GF flag triggers
  closure_time   = first window where GF flag remains OFF for J windows
DEFAULT:
  J = 2 windows (8 weeks of stable closure)

GF TRIGGER RULE (generic):
  A GFx is ON when its sensor proxy exceeds threshold for 2 consecutive checks.
DEFAULT CHECK FREQUENCY:
  weekly checks; aggregate to 4-week windows for reporting.

REPAIR LATENCY OUTPUTS:
  G-M3a: median latency per GF
  G-M3b: 80th percentile latency per GF (tail latency)
  G-M3c: relapse rate (GF returns within R windows after closure)
DEFAULT:
  R = 3 windows (12 weeks)

INTERPRETATION:
  - High G-M3a: repair system too slow → add GR10 protocols + GR8 triggers
  - High G-M3b: tails not served → add GR9 targeting + GR7 visibility
  - High relapse: repair not structural → add GR6 continuity + GR1 buffers

METRIC: G-M7 Masking Proxy
OBJECT:
  Detect when observed performance is inflated by scaffolds that do not transfer.
MASKING = performance gap between:
  A) INDEPENDENT PROOF (no scaffold)
  B) SCAFFOLDED OUTPUT (with typical supports)
DEFAULT PROXIES:
  - independent timed task (no hints / no templates)
  - independent novel-wrapper transfer task (TAP-2 or TAP-3)

MASKING SCORE M:
  M = Score(scaffolded) - Score(independent)
REPORT:
  G-M7a: mean masking score M
  G-M7b: masking tail (top 20% M)
  G-M7c: masking persistence (stays in top 20% M for ≥K windows)
DEFAULT:
  K = 2 windows

INTERPRETATION:
  - High G-M7a: system-wide masking → enforce GR7 + GR3 transfer audits
  - High G-M7b: pockets of extreme masking → GR9 cluster targeting
  - High G-M7c: chronic masking → rewrite protocols (GR10) + continuity (GR6)

MODULE: TAP (Transfer Audit Pack)
TAP contains 4 tests:
  TAP-1: same skill, same wrapper (baseline)
  TAP-2: same skill, new wrapper (novel context)
  TAP-3: same skill, adversarial wrapper (misleading cues)
  TAP-4: same skill, time constraint (timed transfer)
OUTPUTS:
  - transfer_gap = Score(TAP-1) - Score(TAP-2/3/4)
  - robustness = 1 - normalized transfer_gap

PASS RULE (default):
  robust_transfer = TRUE if:
    transfer_gap ≤ 10% (absolute points) in ≥2 of {TAP-2, TAP-3, TAP-4}

TAP LINKS:
  TAP impacts:
    - P-S4 transfer under wrapper variation
    - G-M6 transfer gap under novelty
    - contributes to stability score S in G-M2

CITY LIVE PROMOTION (minimal publish set):
  Publish at least:
    - G-M2a, G-M2c (tails + persistence)
    - G-M3a, G-M3b (latency + tail latency)
    - G-M7a (masking mean) + definition of independent proof
    - TAP definition + one city-specific wrapper set example
  Attach ≥1 W3 comparative with proof requirements referencing these metrics.

NATION LIVE PROMOTION (minimal publish set):
  Publish at least:
    - nation-level G-M2 + G-M3 (aggregated across composed cities)
    - national gate timing windows (not just slots)
    - ≥1 nation comparative OR ≥2 city comparatives