Basics
Q: Does SSMH change my numbers?
A: No. Collapse parity holds: phi((m,a)) = m, so classical outputs remain identical.
Q: Why not just add error bars?
A: Error bars are static. The lane composes through operators and streams (tanh/atanh, {U,W}), so it stays meaningful end-to-end and order-invariant.
Q: Is a a probability or confidence score?
A: No. a ∈ (-1,+1) is a bounded alignment coordinate from a declared mapping (e.g., entropy, residual). It is dimensionless, composable, and not a probability.
Q: Will streaming and batch disagree?
A: No. The {U,W} rule guarantees batch == stream == shuffled:U += w*atanh(a), W += w, a_out = tanh(U/max(W,eps_w)).
Q: Can we deploy without risk?
A: Yes. Start read-only. You gain visibility, bands, and economics without touching actuator math.
Q: Where does the biggest value appear first?
A: Ratios near zero, multi-sensor fusion, oscillatory controllers, and noisy fleet KPIs (braking, drives, DVFS, MPPT, NOC).
Q: When do we go to silicon?
A: After read-only and advisory wins persist. Semantics are identical in software and silicon; hardware mainly brings latency, power, and throughput benefits.
Math & Correctness
Q: What core equations must I honor?
A: Clamp-first and inverse map: a := clamp(a, -1+eps_a, +1-eps_a), u = atanh(a), a = tanh(u).
Streaming fuse: U += w*atanh(a), W += w, a_out = tanh(U/max(W,eps_w)).
Collapse: phi((m,a)) = m.
Q: How do multiplies/divides compose in the lane?
A: M2 identities:a_mul = tanh(atanh(a1) + atanh(a2)),a_div = tanh(atanh(a_f) - atanh(a_g)).
Q: What if W = 0 or the stream is empty?
A: Use a_out = tanh(U/max(W,eps_w)). With no samples, return the prior a_out or a declared neutral (policy); never divide by zero.
Q: What if a hits the bounds?
A: Exact |a| = 1 is disallowed by clamp; atanh(a) remains finite. Always clamp before atanh, reclamp after tanh.
Q: Does sign or magnitude affect the lane?
A: The value lane carries sign/magnitude as usual. The alignment lane a is dimensionless. If using weights, w = |m|^gamma (default gamma = 1).
Q: Division by near-zero denominators?
A: Magnitude policy is strict|meadow|soft (value lane only). The lane uses M2 (atanh difference) so it stays bounded and informative; no NaNs when clamps are honored.
Q: Do we keep associativity and commutativity?
A: Yes, for lane combine under M2 in u-space; streaming invariance follows from additive {U,W}.
Q: How do we choose band thresholds?
A: Use a simple, monotone, non-overlapping table (e.g., A++>=0.75, A+>=0.50, A0>=0.25, A->=0.10, else A--) and add hysteresis such as delta_a >= 0.05 to move up.
Numerics & Knobs
Q: What values should I use for eps_a and eps_w?
A: Defaults work: eps_a = 1e-6, eps_w = 1e-12. Tighten only if your numeric range demands it; record knobs in the manifest.
Q: How do I pick mapping parameters (entropy window, bins, k)?
A: Start with win long enough to see meaningful variation (hundreds of samples for slow KPIs), bins ∈ {16,32}, and a gentle gain k ∈ [1.5, 2.5]. Tweak to stabilize band mixes while keeping events visible.
Q: What about quantization and fixed-point?
A: Use Q-formats like Q1.15/Q5.11/Q9.7. For tanh/atanh, use LUT+polynomial with bounded error; verify with E8/E10. Enforce |a_q| <= 1 - 2^-fractionbits.
Q: Tolerances for CI?
A: Typical: tol = 1e-12 for float64 parity, q_rtol = 1e-6 for fixed-point parity. Shuffle invariance checked under a fixed seed.
Q: What happens with NaN/Inf inputs?
A: Treat as gate FAIL. Clamp discipline plus input validation should keep the lane finite and bounded.
Performance & Implementation
Q: What is the software overhead?
A: Small. Each sample adds a clamp and one atanh per cue; a flush is one divide and a tanh. Most CPUs/MCUs handle this easily for KPI rates.
Q: How about microcontrollers and FPGAs?
A: On MCUs, use LUT+poly for tanh/atanh. On FPGAs, SSM-ALU + SSACC make map/compose/inverse near-zero latency; fixed-point is recommended.
Q: Memory footprint?
A: Per KPI you keep scalars U,W and optionally a rolling window for the mapper (if needed). O(1) for fuse; O(window) for the chosen mapping.
Q: Is it deterministic and thread-safe?
A: Yes, if you maintain exact {U,W} and fixed knobs; ensure atomic updates per KPI stream.
Adoption & Ops
Q: How do we prove it works?
A: Run E1..E12 (calculator-fast). Publish manifests and stamped logs. Show batch == stream == shuffled and phi((m,a)) = m.
Q: What do operators see?
A: Value + band side-by-side: value -> band. Tooltips: m, a, band, knobs_hash, build_id.
Q: What is the rollback plan?
A: One switch disables advisory hooks; read-only logging continues. Keep manifests immutable; any knob change ⇒ new manifest.
Q: How do we interpret low a (A-/A--)?
A: As “thin evidence” or “disagreement.” Investigate; do not hide or alter the value.
Interop & Data
Q: What should we log?
A: Minimal schema: time,kpi,m,a,band,knobs_hash,build_id,site_id,unit_id,note. Add u,w,U_accum,W_accum,a_out for proofs if desired.
Q: How do we handle missing/late samples and backfills?
A: Use {U,W} with max(W,eps_w). Order does not matter; backfills produce the same a_out. Keep both wall time ts and a monotonic seq.
Q: How do we preserve integrity?
A: Use a daily anchor with manifest+bundle hashes (ASCII). Keep an append-only list of anchors.
Q: Can we mix sampling rates or resample?
A: Yes. Compute per-cue a at its native rate, then fuse via {U,W} at the reporting cadence.
Safety, Ethics, and Scope
Q: Is this a diagnostic, safety, or compliance oracle?
A: No. The lane is bounded metadata, not a medical, legal, or safety decision system.
Q: Can we gate actuators by a?
A: Not during pilots. Promotion from read-only → advisory → scoped closed loop requires evidence, training, and a documented rollback plan.
Q: Could a be gamed?
A: Any derived signal can be influenced if mappings are mis-specified. Mitigate with declared mappings, CI gates, audits, and cross-cue checks.
Planning & Economics
Q: Where do savings usually land first?
A: Fewer nuisance alarms and oscillations, more stable scheduling (energy/fuel), and reduced ops toil from clearer triage.
Q: What artifacts satisfy stakeholders?
A: Immutable manifests, stamped logs, E1..E12 reports, and operator training notes. Tie KPI deltas to finance thresholds.
Practical How-To
Q: Quickstart?
A: Set eps_a=1e-6, eps_w=1e-12. Emit (m,a) per KPI with bands. Maintain {U,W} and flush a_out. Run E1..E12. Keep the value lane untouched.
Q: Spreadsheet smoke test?
A: Compute U = SUM(ATANH(a_i)), W = COUNT(a_i), a_out = TANH(U/MAX(W,1e-12)). Reorder rows; a_out stays equal.
Q: How do we choose fusion weights?
A: Start with w = |m|^gamma (default gamma = 1). For multi-cue, pick simple ratios (e.g., 2:1) and tune to balance sensitivity (lower A--) vs stricter consensus (higher A++).
Troubleshooting & Quick Fixes (rare, fixable in minutes)
• Weak mapper window → adjust WIN, BINS, K_GAIN, or switch to residual/coverage mapper.
• Band flicker near thresholds → increase rapidity precision or widen band step/hysteresis.
• Transport quirks (CSV locales, timestamps) → normalize formatting in the harness.
• Clamp omissions → always a := clamp(a, -1+eps_a, +1-eps_a) before atanh(a); reclamp after tanh(u).
One-line recap
Add a bounded alignment lane that composes (tanh/atanh, {U,W}) while preserving numbers (phi((m,a)) = m) so operators see when evidence is thin—without changing the value lane.
Navigation
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Directory of Pages
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https://github.com/OMPSHUNYAYA/Symbolic-Mathematical-Hardware
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.
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