W1.4: softmax error bounds in owned code — from hard-max legs to bounded-approximation claims

[AtlantisPleb]

Workstream W1 deliverable 4 of the unified research plan
(openagents docs/tassadar/RESEARCH_PLAN.md); a stated boundary in the
lane README ("No softmax").

Problem

All five executor legs are hard-max (exact integer argmax with
latest-write tie-breaking and near-miss refusal). Percepta's full
construction runs under real softmax attention with exponentially small,
provably bounded carry-over error (scores scaled by a large constant
approximate hard-max). Until those bounds exist in owned code, every
claim this lane makes is conditioned on hard-max, and the H3 experiment
(can trained models preserve the geometry under softmax temperature?)
lacks its analytic baseline.

Scope

1. A softmax execution leg over the existing parabolic-key geometry with
   an explicit scale parameter and a derived, machine-checked error bound
   per lookup (carry-over mass from non-winning keys).
2. Differential-harness integration: the softmax leg agrees with the
   exact legs within the stated bound, or refuses, across the generated
   graph corpus — making the bound itself a tested artifact.
3. The bound's interaction with the f64 numeric window (2^53 exactness
   envelope) documented: at what trace lengths and scales does
   accumulated carry-over threaten integer rounding.

Acceptance

A sixth leg in the bounded check harness with typed bound-violation
refusals; the lane README's "No softmax" boundary replaced by a
quantified one; the H3 training experiments (W3 baseline c) unblocked
with an analytic initialization whose tolerance is known.