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T50: a representation that leaves its own domain pays at the boundary - #840

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T50 — a design whose internal representation differs from its interface is not complete until the conversion is inside the measured design. Comparing such a design against one that already speaks the interface attributes the conversion cost to neither, and flatters the first.

Measured, from trinity-fpga#593:

cells Fmax vs multiplier
Z[φ] layer, pair output (as measured in #592) 660 204.08 MHz 1.66× smaller, 2.95× faster
the same layer with the reconstruction inside 839 106.26 MHz 1.31× smaller, 1.54× faster

The reconstruction is shift-adds with no multiplier — and it still halves the clock. That is the honest deployable number; the earlier one compared a layer that cannot be consumed as it stands against one that can.

This narrows T49's numbers without touching its statement: unrolling does recover throughput. It was the baseline it got quoted against that was incomplete.

The refusal: the remaining advantage is real and smaller, measured on iCE40 which has no DSP blocks and so penalises the multiplier maximally. And it does not say the conversion is a loss the representation was preventing — a quantised layer requantises at its boundary regardless, and the exactness bought inside is not undone by rounding at the exit.

Ratchet 179/26 against baseline 184/27, no file gained. Audits: RU and EN PASS, 27 routes.

A design whose internal representation differs from its interface is not
complete until the conversion is inside the measured design. Comparing
it against one that already speaks the interface flatters it.

Measured: without the reconstruction the Z[phi] layer was 660 cells at
204.08 MHz against 1098 at 69.21 -- 1.66x smaller, 2.95x faster. With
the reconstruction inside it, 839 cells at 106.26 MHz: 1.31x smaller and
1.54x faster. The reconstruction is shift-adds with no multiplier and it
still halves the clock.

This narrows T49's numbers without touching its statement -- unrolling
does recover throughput; the comparison it was quoted against was
incomplete.

Audits run locally: RU and EN PASS, 27 routes.
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gHashTag merged commit ff391ea into main Aug 18, 2026
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gHashTag deleted the science/boundary-theorem branch August 18, 2026 09:39
github-actions Bot added a commit that referenced this pull request Aug 18, 2026
T50: a representation that leaves its own domain pays at the boundary (#840)

A design whose internal representation differs from its interface is not
complete until the conversion is inside the measured design. Comparing
it against one that already speaks the interface flatters it.

Measured: without the reconstruction the Z[phi] layer was 660 cells at
204.08 MHz against 1098 at 69.21 -- 1.66x smaller, 2.95x faster. With
the reconstruction inside it, 839 cells at 106.26 MHz: 1.31x smaller and
1.54x faster. The reconstruction is shift-adds with no multiplier and it
still halves the clock.

This narrows T49's numbers without touching its statement -- unrolling
does recover throughput; the comparison it was quoted against was
incomplete.

Audits run locally: RU and EN PASS, 27 routes.
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