Shunyaya Symbolic Mathematical Hardware – Display & Practical Gains (1.10–1.11)

1.10 — Display and bands (quick reference)

  • Canonical display for a. Show 4–5 decimals; always clamp before display: a := clamp(a, -1+eps_a, +1-eps_a).
  • Bands (global defaults — normative).
    A++: a >= +0.90
    A+ : +0.60 <= a < +0.90
    A0 : -0.60 < a < +0.60
    A- : -0.90 < a <= -0.60
    A--: a <= -0.90
    Overrides must be declared explicitly.
  • Zero convention. (0,+1) may be used as the canonical fully-certain zero when policy requires; otherwise preserve the reported a.
  • Operator cues. Prefer compact badges (A++…A–) near values; surface low-confidence segments on timelines without hiding numbers.

1.11 — What this buys you in practice (summary)

  • Stability near zeros. Ratios stop “exploding”; fragility is exposed via the lane, not leaked into m.
  • Order-free fusion. batch == stream == shuffled via the U/W rule: U += w*atanh(a) ; W += w ; a_out := tanh(U / max(W, eps_w)).
  • Zero-friction rollout. Publish the lane read-only beside 3–5 KPIs; dashboards and schedulers get smarter instantly.
  • Hardware-ready path. Identical semantics later compile to a tiny SSM-ALU and SSACC {U,W} tile for speed.
  • Auditability. Bands, stamps, and fixed knobs yield reproducible PASS/WARN/FAIL gates for QA and post-mortems.
  • Policy independence. Classical outputs remain identical by collapse: phi((m,a)) = m.

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