Pick Unit and c in minutes. Reproducible and stamped.
3.5 Lens calibration quickstart (2 minutes, reproducible)
Goal. Choose Unit and c so tanh(c*e) is informative (not saturated, not tiny), then freeze them in a manifest for apples-to-apples comparison.
Protocol (declare in manifest).
- Sample. Collect recent items’ raw terms (no PII).
- Compute provisional contrast.
e_raw := ( SUM alpha_i * P_i - SUM beta_j * N_j )
- Set Unit (normalize to dimensionless
e).
q := median(|e_raw|)
Unit := max(q, 1e-6)
e := e_raw / Unit
- Set c (single gain knob).
# start
c := 1.0
# adjust by distribution of |a| = |tanh(c*e)|
if fraction(|a| > 0.9) > 0.10: c := 0.7 * c
if fraction(|a| < 0.1) > 0.70: c := 1.3 * c
- Freeze. Stamp
Unit,c,alpha/betain the manifest and reuse across vendors.
Lane mapping (reference).
a_in := tanh( -c * e_in )
a_out := tanh( +c * e_out )
Chooser & zero-evidence guard (normative).
U_in := SUM w_i * atanh(a_in_i)
V_out := SUM w_j * atanh(a_out_j)
W_in := SUM w_i
RSI := tanh( (V_out - U_in) / max(W_in, eps_w) ) # eps_w = 1e-12
if W_in == 0: RSI := 0; band := "A0"; reason := "insufficient_evidence"
Sanity metrics (log once/day).
saturation_rate := mean( |a| > 0.9 )
dead_zone_rate := mean( |a| < 0.1 )
drift_watch := (median_RSI, band_histogram)
QA checklist (pass/fail).
• Clamps applied: a_c := clamp(a, -1+eps_a, +1-eps_a) before any atanh.
• Unit stability: recomputing Unit shifts bands < 1 step on a holdout slice.
• No-evidence path: W_in == 0 ⇒ RSI = 0, band A0, reason recorded.
• Determinism: same manifest ⇒ identical a, RSI, band on replay.
One-line takeaway. Normalize with Unit, set a single gain c, verify distribution health, then freeze and stamp—consistent lanes, comparable RSI, reproducible audits.
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