Shunyaya Symbolic Mathematical Hardware — Glossary (15)

  • Pair. x := (m, a) with magnitude m and bounded confidence a.
  • Value lane. The classical scalar m; all control/math on values remains unchanged.
  • Alignment lane. The dimensionless coordinate a ∈ (-1,+1) that composes through maps and streams.
  • Collapse / phi. phi((m,a)) = m; recovering the classical number from the pair.
  • Collapse-safe. Any operation preserves phi((m,a)) = m on the value lane.
  • Clamp. a := clamp(a, -1+eps_a, +1-eps_a); apply before atanh(a) and reclamp after tanh(u).
  • Rapidity (u-space). u := atanh(a); inverse map a := tanh(u); additive in u enables clean composition.
  • M2 identities. a_mul = tanh(atanh(a1)+atanh(a2)), a_div = tanh(atanh(af)-atanh(ag)).
  • U/W fusion (order-invariant). Keep U += w*atanh(a), W += w; publish a_out := tanh(U/max(W,eps_w)).
  • Streaming invariance. The lane yields batch == stream == shuffled under U/W fusion.
  • Weight (w). w := |m|^gamma (default gamma = 1) for fuse weighting.
  • Gamma. Exponent controlling how magnitude scales w in fusion; gamma = 1 by default.
  • Bands. Operator-visible thresholds A++/A+/A0/A-/A-- mapping a to cues (monotone, non-overlap).
  • Band hysteresis. Require delta_a >= step (e.g., 0.05) to move up a band; allow immediate drop to avoid flicker.
  • Gate (env gate). a_env := clamp(g_t * a_op, -1+eps_a, +1-eps_a) with m untouched; policy overlay only.
  • Canonical zero. Display (0,+1) when m == 0; value lane stays classical, lane remains bounded.
  • Division policy. Value-lane magnitude handling strict|meadow|soft; the lane uses M2 so a stays bounded.
  • eps_a / eps_w. Small positives for numeric safety: eps_a clamps a; eps_w guards divide-by-zero in U/W.
  • Q-format (fixed-point). Integer encodings like Q1.15/Q5.11/Q9.7; keep |a_q| <= 1 − 2^-fractionbits.
  • SSM-ALU. 3-stage lane ALU: clamp/map (atanh), compose (add/sub in u), inverse/re-clamp (tanh).
  • SSACC. Streaming accumulator maintaining {U,W} for order-invariant fusion.
  • Manifest. ASCII header with knobs, build, and conformance_checksum; immutable per run/release.
  • Knobs / knobs_hash. The declared numeric/policy settings and their hash; tie every row/log to its manifest.
  • Conformance gates. E1..E12 calculator-fast checks (clamp, M2, U/W, collapse, quantization, parity, invariance).
  • SSM-Clock Stamp. Daily/bundle hash anchors for ordering and integrity; append-only ASCII lines.
  • Backfill. Recomputing with identical knobs yields the same a_out due to U/W order invariance.
  • Adapters (SSMS ports). Verb-to-port mapping s_sum/s_add/s_sub/s_mul/s_div/... that consumes/produces (m,a) pairs.
  • A-MAC. Alignment-carrying multiply-accumulate for edge AI and DSP where a flows through mul and streamed sum.
  • Order-invariant. Results independent of sample order (batch, stream, shuffle) for the alignment lane.

Caution. Research/observation only. Not for operational or safety-critical use without a completed safety case and formal approvals.

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Disclaimer
The contents in the Shunyaya Symbolic Mathematical Hardware (SSMH) materials are research/observation material. They are not engineering advice, not a safety standard or certification, and not operational guidance. Do not use for safety-critical, medical, legal, or financial decisions. Use at your own discretion; no warranties are provided; results depend on correct implementation and inputs.