SSM-NET — Alignment lane (2A)

A tiny, bounded, replayable dial beside unchanged bytes

What this subsection defines (in one line).
A deterministic, transport-agnostic alignment lane that lives beside the original payload and never mutates it. The lane is bounded, replayable, and order-invariant across batch, stream, and shard-merge.

Kernel (normative, copy-ready).

# collapse parity (payload invariance)
phi((m,a)) = m


# four-step pipeline (must be in this order)
a_c := clamp(a_raw, -1+eps_a, +1-eps_a)      # safety clamp
u   := atanh(a_c)                            # move to rapidity space
U  += w * u                                  # accumulate evidence
W  += w
align := tanh( U / max(W, eps_w) )           # fuse back to bounded lane

Norms (MUST / SHOULD / MAY).

  • MUST implement the four-step pipeline with clamp before atanh.
  • MUST keep eps_a > 0, eps_w > 0 (small positive safeguards).
  • SHOULD persist (U, W) per scope so the dial is continuous across messages.
  • MAY set w := 1 if no weighting policy is declared.
  • MAY define epoch rollover for (U,W) (time or count). Rollover points SHOULD be continuity-stamped and documented in the manifest.

Determinism & invariants (clarifications).

# order-invariance across modes (within numeric tolerance)
# batch == stream == shard-merge
U_total := Σ U_i
W_total := Σ W_i
align_total := tanh( U_total / max(W_total, eps_w) )
  • Shard/merge rule. Compute per-shard (U_i, W_i) using the same eps_a, eps_w, w; fold by summation only (no re-clamp at joins).
  • Payload invariance. The lane must not alter original bytes: phi((m,a)) = m.

Recommended numeric practice (strongly encouraged).

  • Float mode. Use 64-bit floating point for reproducibility; embedded targets may use fixed-point with documented Q-format.
  • Tolerances. Target parity of ≤ 1e-6 for batch vs stream and ≤ 1e-12 for shard-merge on identical inputs/parameters.
  • Canonical decimal (if public). When exposing align publicly, also emit align_ascii as fixed-width decimal (e.g., "+0.732000") to avoid serializer drift.

Weighting guidance.

  • Equal weights. w := 1 is acceptable where no trust/sample/importance weighting is defined.
  • Declared policy. If non-trivial w is used, the manifest MUST document how w is chosen; implementations MUST apply the same rule during parity checks.

Prohibited behaviors.

  • MUST NOT apply clamp after atanh.
  • MUST NOT re-scale, re-center, or remap align outside the specified pipeline.
  • MUST NOT change eps_a, eps_w, or w within a scope without stamping a policy/manifest change.

Why it matters (human terms).
This tiny lane turns drifting, vendor-specific interpretations into a bounded, comparable dial that any receiver can recompute and verify—while your payload remains byte-for-byte intact.

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