3.10 — Test E8: Quantization sanity (first-order envelope)
- Setup. Rapidities span
[-atanh(1-1e-6), +atanh(1-1e-6)] = [-7.254328619247669, +7.254328619247669]. - 16-bit step.
delta_u = 14.508657238495339 / 65536 = 2.2138454038231413e-04. - At a = 0.5.
u_true = 0.5493061443340548,u_q = 0.5492550446885214,|delta_u_obs| = 5.10996455334e-05;a_true = 0.5,a_q = 0.499961674286668,|delta_a_obs| = 3.83257133320e-05. - Envelope.
sech^2(u_true)*|delta_u_obs| = (1 - tanh^2(u_true))*|delta_u_obs| = 0.75 * 5.10996455334e-05 ≈ 3.83247e-05. - Verdict. PASS (observed
|delta_a_obs|≤ envelope; errors shrink away fromu ≈ 0).
3.11 — Test E9: Environment gate (alignment-only, preserves collapse)
- Inputs.
a_op = 0.75,g_t = 0.6,eps_a = 1e-6. - Apply.
a_env = clamp( g_t * a_op, -0.999999, +0.999999 ) = clamp(0.45, ...) = 0.45; magnitude untouched. - Verdict. PASS.
3.12 — 90-second spreadsheet template (quick reproduction)
- Columns.
a,w,u := ATANH(a). - Totals.
U := SUM(w*u),W := SUM(w),a_out := TANH( U / MAX(W, 1e-12) ). - Shuffle test. Reorder rows; confirm
a_outidentical (batch == stream == shuffled). - M2 check. Add
a1,a2; computeTANH(ATANH(a1)+ATANH(a2))and(a1+a2)/(1+a1*a2); confirm equality withintol.
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