gft encoder: pin the smallest normal binade (Refs #2161)

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Printing the source beside the line number (#2634, yesterday) paid for itself on the first survivor that did not classify itself: if off < 0: return 0, in the GF-T encoder every trained weight passes through.

off = e + 40, so off == 0 is the smallest normal binade, [2^-40, 2^-39). The mutant off <= 0 encodes every value there as 0 — which is the zero sentinel. A non-zero magnitude, silently reported as zero.

The obvious witness does not work, and that is why the mutant lived

At exactly 2^-40 the mantissa is 0, so the value already encodes as 0 and the mutation changes nothing. A witness needs a non-zero mantissa in that binade:

enc(1.5 * 2**-40) = 256      the mutant would give 0
enc(2**-40)       = 0        already zero — not a witness
enc(2**-41)       = 0        legitimately zero, off < 0

Anyone testing "the boundary" by reaching for the boundary value would have concluded the mutant was equivalent. The boundary value was the one point in the binade where it is.

Three assertions pin it: the magnitude, the sign, and the value one binade lower which is legitimately zero.

Negative control: with <= planted the tool exits 1 naming the new assertion; restored, 0. The column moved 5/31 → 6/31.

And it corrects a generalization I made yesterday

§106 concluded that boundary survivors are loop bounds where a survivor is the right answer. That was drawn from one gate's six survivors. Classifying all four if x < 0: sites:

site	value comes from	<= equivalent?
verify_igla_race:223	src.find("{", start)	yes — 0 unreachable
gft_backprop_microcode:50	off = e + 40	no — smallest normal binade
gft_backprop_microcode:203	d = ho - lo_o	no — equal exponents
diffbin:148	rest.rfind('"')	no — empty quoted string ""

One of four. The rfind site is real despite sharing the idiom with the equivalent one — what differs is whether index 0 is reachable in that string, not which function produced it.

The correction is not "survivors are real" either: each survivor is a separate question, and the source line makes answering it a minute's work instead of an afternoon's.

§110 and §111.

Refs #2161

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Generated at: 2026-08-24 00:27:41 UTC

• gft encoder: pin the smallest normal binade (Refs #2161) #2637 gft encoder: pin the smallest normal binade (Refs #2161) | Created: 2026-08-24 | Updated: 2026-08-24 | 17 failing / 26 total
• Unbreak FPGA CI and correct two unbacked hardware claims #2081 Unbreak FPGA CI and correct two unbacked hardware claims | Created: 2026-08-11 | Updated: 2026-08-20 | 5 failing / 27 total

Summary

Status	Count
Total Open PRs	2
PRs with Failing Checks	1
PRs with All Checks Green	1
READY	0
FAILING	1
PENDING	0

Seal Status

• ⚠️ STALE -- sha256(compiler.rs)=e6333575ec10 != manifest seal=87e5cbd3ad94.
  The committed NMSE numbers were certified against an older compiler.rs.
  Run scripts/reseal-check.sh locally for the two-step reseal command (advisory; not a merge gate).