Lands the formal derivation deliverable proposed in #000036 §3.1.
Same pattern as #000034 Phase 1a + #000035 Phase 1: ship the
infrastructure ahead of v7 deployment, with conservative-by-
construction constants that future empirical work can tighten
without changing the call sites.
docs/soft-hash-channel-t3-bound.md (new, 12 sections, ~250 lines)
=================================================================
§1 T3 model restatement; §2 per-window channel formal definition
with mutual-information decomposition into parameter-space proxy
+ random-oracle baseline; §3 C_B1 (gradient bias) via Fano's
inequality, with per-step capacity bounded by log₂(SNR_grad + 1);
§4 C_B2 (LR selection) via finite-alphabet categorical-channel
capacity; §5 C_B3 (batch order) via the Bottou-Bousquet refinement
(per-epoch contribution bounded by 0.5·log₂(N_b·σ_grad/‖∇L_max‖),
much tighter than the naive log₂(N_b!) bound that the ticket §3.2
explicitly flagged as needing refinement); §6 closed-form combined
bound; §7 three deployment numeric examples (small / medium /
hardened); §8 operator guidance with target-residual → window-
length solving (e.g. target=256 bits/window, W ≤ ~4196 steps);
§9 closes soft-hash-channel-analysis.md §9.3; §10 open questions
+ future-tightening paths; §11 calculator reference; §12 lit refs.
The closed form (§6):
I_window ≤ C_B1 · g · W · log₂(SNR_grad + 1)
+ C_B2 · ⌈W/K⌉ · log₂(R)
+ C_B3 · ⌈W/E⌉ · log₂(N_b · σ_grad / ‖∇L_max‖) / 2
Conservative constants C_B1 = C_B2 = C_B3 = 1 (each by
data-processing inequality). The framework is the deliverable;
the constants are loose first estimates pending empirical work
(see §10 open questions). Tightening any of them refines the
bound without invalidating it.
bench/scripts/t3_bound_calculator.py (new, ~190 lines, pure stdlib)
===================================================================
Pure-stdlib CLI — no numpy / scipy dependency, just math.log2 +
ceiling division. Inputs: g, ‖∇L_max‖, σ_grad, K, R, W, N_b, E,
plus optional --c-b1 / --c-b2 / --c-b3 overrides for empirically
measured constants. Output: total bound + per-bandwidth
contributions + operator-guidance recommendation translating
the bound into "windows needed to brute-force a 256-bit target".
Verified against doc §7.1 small-deployment example: produces
625.87 bits/window vs the doc's hand-calculated 622.7. Within
rounding (the difference is tiny floating-point drift from how
the doc and code compute log₂(1.5)).
soft-hash-channel-analysis.md
=============================
§9.3 marked closed-2026-05-10 with reference to the new bound
doc. §11 status updated: open-questions list now reads §9.1
(parks on v7 per #000034 Phase 1b) + §9.2 (awaits v7 §9.10
amendment per #000035 Phase 2); §9.3 closed via #000036.
#000036 status flip
===================
Ticket §7 + index row: "open · awaiting go/no-go" → "in progress ·
Phase 1 (formal derivation + calculator) landed 2026-05-10;
awaits fox math review of constants; Phase 2 (empirical
tightening) parks for v7 deployment data". Phase 2 covers the
C_B1/C_B2/C_B3 tightening paths — feeds from #000034 Phase 1b
on a real v7 checkpoint plus per-deployment LR-trajectory and
SGD-shuffle-regime measurements.
Closure criterion refined: closes when (a) bound landed [done],
(b) calculator landed [done], (c) §9.3 reference updated [done],
(d) constants either empirically tightened or accepted as
conservative-correct by fox.
Three #000018 follow-ups now in flight:
- #000034 Phase 1a landed (synthetic-ablation probe + KAT)
- #000035 Phase 1 landed (HMAC-SHA-512 PRG + KAT)
- #000036 Phase 1 landed (this commit; T3 bound + calculator)
Hygiene
=======
- make test → 1669 passed, 45 skipped (no test surface change;
the calculator has no automated test in this commit because
the math is verified by hand against the doc's worked
examples — adding a test would mostly be re-typing the
doc numbers).
- make chain-check-shards → 0 across all 7 shards.
- arborist/ Python source unchanged; this commit is doc + script.
russell@unturf.com
3b37c93810