Shunyaya Symbolic Mathematical Hardware – Acceptance, Failures & Ops Meaning (3.13–3.16)

3.13 — Acceptance gates (bring-up sheet)

  • G1 — Clamp safety. E1 PASS.
  • G2 — M2 identities. E2 and E3 PASS.
  • G3 — Streaming associativity. E5 PASS.
  • G4 — Collapse parity. E6 PASS.
  • G5 — Quantization envelope. E8 within declared budget.
  • G6 — Gate behavior. E9 PASS.
  • Result rule. ACCEPT if all PASS; WARN if any diff <= 1e-9 but not 1e-12; FAIL otherwise.

3.14 — Common failure modes and fixes

  • Symptom. atanh overflow or NaN.
    Cause. Missing clamp.
    Fix. Enforce a := clamp(a, -1+eps_a, +1-eps_a) everywhere.
  • Symptom. Batch/stream mismatch.
    Cause. Missing U/W rule or inconsistent weights.
    Fix. Maintain {U,W} exactly; publish a_out := tanh( U / max(W, eps_w) ).
  • Symptom. Collapse mismatch with classical output.
    Cause. Lane leaked into magnitude path.
    Fix. Preserve phi((m,a)) = m at every boundary.
  • Symptom. Noisy bands from quantization.
    Cause. delta_u too coarse near u ≈ 0.
    Fix. Increase u precision or adjust band granularity.

3.15 — Conformance vectors

  • Constants. eps_a = 1e-6, eps_w = 1e-12, denom_soft_min = 1e-9, tol = 1e-12.
  • Vectors.
    • Multiply/divide. (a1,a2) = (+0.8,+0.2) -> a_mul = 0.8620689655172413; (a_f,a_g) = (+0.8,+0.2) -> a_div = 0.7142857142857144.
    • Streaming. a = {0.2, 0.5, -0.3}, w = 1 → a_out = 0.14644577359353203.
    • Reciprocal. a = +0.5 → a_(1/x) = -0.5.
    • Collapse parity. (m1,a1) = (2.0, +0.5), (m2,a2) = (3.0, -0.4) → phi = 6.0.
    • Quantization. Umax = 7.254328619247669, delta_u = 2.2138454038231413e-04, at a = 0.5 → |delta_a_obs| ≈ 3.83257e-05.

3.16 — What “passes here” means in operations

  • Safer numerics. No NaN/Inf, no edge blow-ups.
  • Predictable fusion. Batch, live stream, and backfill agree.
  • Auditable confidence. Each KPI gains a bounded, reproducible strength indicator.
  • Hardware-ready. Same checks serve as silicon bring-up gates with explicit tolerances.

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