feat(rng): one press unlocks a bulk RNG health test on an uninitialized device

[BitHighlander]

Scope, up front: this enables RNG health testing, not entropy measurement. No output analysis can bound the entropy of an RNG's internal state — a strong PRNG seeded with 40 bits emits a stream that passes every test below by construction. See "What this does and does not prove".

Why

ENTROPY_FREE_BUDGET (64 KB/boot, added in 2f9269f64) is too small for the health test it exists to enable — because the positive control cannot run at that size.

A zero-collision result proves nothing on its own: a detector that never fires also returns zero. So the scan must also run at a width where collisions are expected and their count checked against theory. 32-bit collisions over N blocks expect N²/2³³:

sample	expected 32-bit collisions	positive control
64 KB	0.03	cannot run
1 MB	8	weak
8 MB	512	tight (±4.4%)

8 MB is the first size at which the result carries information. Under the old cap, reaching it cost 128 manual replugs.

The cap was also asymmetric in the wrong direction: it never stopped a patient remote attacker — host malware simply waits for the replugs that happen anyway and accumulates 64 KB at a time — while it fully priced out the honest auditor. The original comment concedes the failure mode ("so nobody ever checked").

What

Gate the bulk path on a single explicit press rather than a byte count, and only before initialization:

• One confirm per boot unlocks unmetered draws. A remote host cannot forge a press — the property the byte cap was only approximating.
• Uninitialized only. No seed exists, so there is no key material to correlate against. Keeping bulk export off initialized devices also denies a covert exfiltration channel: compromised firmware could otherwise encode a seed into bytes that still look random.

Initialized devices are unchanged: 64 KB, then a confirm on every draw.

Hardware validation

Flashed to an uninitialized device. 8.00 MB in 345 s (23.7 KB/s, 8192 calls, mean 42 ms/chunk), with exactly one stall — chunk 65, 17.4 s, the press — at exactly the 64 KB boundary.

 8-byte birthday  N=1048576  expected 2.98e-08  observed 0     PASS
 6-byte birthday  N=1398101  expected 0.00347   observed 0     PASS
 4-byte birthday  N=2097152  expected 512       observed 490   PASS  (z=-0.97, positive control)
 adjacent equal 32-bit words                    0              PASS
 duplicate 1 KB chunks                          0              PASS
 longest identical-byte run                     4              PASS
 byte chi-square   278.2 (df=255, 4s 165-345)                  PASS
 Shannon entropy   7.999976 bits/byte (empirical, of sample)   PASS
 monobit           z=0.665                                     PASS
 lag-1 autocorr    -0.000289 (bound 0.00138)                   PASS

sha256(sample) 32178de71a1083bb79d9c1fa891b081066632d7403bd99bfdfb8f6dae9cb484c

What this does and does not prove

Does: rules out stuck or badly biased output, repeated buffers, transport caching, gross correlation, and — via the 32-bit control — a collision detector that silently does nothing.

Does not: bound the entropy of the RNG's internal state. Specifically:

• "Detects ≤39 bits" would be wrong. A 64-bit scan over N=2²⁰ expects one collision at a 39-bit support, but P(0 collisions) is then e⁻¹ = 37%. Zero collisions excludes only ≤37.4 bits at 95% confidence (≤36.8 at 99%). The table reads "1 expected collision at k bits" for this reason.
• A low-entropy state behind a strong expander is invisible here, by construction.
• 7.999976 bits/byte is empirical Shannon entropy of the sample, not cryptographic min-entropy. NIST SP 800-90B assesses the raw noise source and wants continuous RCT/APT health tests — separate future work, tracked below.

Follow-ups (not in this PR)

• Continuous RCT/APT per SP 800-90B on unconditioned noise. The STM32 SEIS/CECS seed-and-clock error bits give partial coverage today (reset_rng() on fault).
• Report device model, firmware build hash, tool version and sample digest alongside results.
• Force a fresh reseed / power cycle between audit and ResetDevice so wallet generation never continues the audited stream.
• Consider Trezor-style entropy-check at setup (commit/reveal over discarded rounds), which verifies the seed-generation path itself rather than a stream.

Cost

One static bool and two branches. Device build green across all variants.