Shannon Prime Lattice

A couple of corrections for the record, a way to reproduce the work, and a licensing note.

Tightening two numbers from my last post. In the spirit of the receipts-first discipline I keep claiming, I conflated two separate gates and undersold a third:

• The 8/8 is the router in isolation — the ±1 Rademacher projection scored 8/8 needles at cosine 1.0 against an adversarial decoy set (B=64, r=16). Separately, the end-to-end NIAH decode gate retrieves the needle at depth 10%, 50%, and 90% (no recency bias). Two different gates; I ran them together last time.

• The latency I quoted (18.86 µs) was an intermediate stage. The final IOCP + FILE_FLAG_NO_BUFFERING path is 7.57 µs/read. I undersold it.

For completeness, the rest of the envelope at 32k context: 910× resident KV-cache shrink (7.5 GB → 8.3 MB), 8× KV sparsification at +0.69% perplexity (measured at 2k context on one corpus; 2× and 4× go negative), and a reducing transcode that makes the on-disk model ~50% smaller with a bit-identical forward on both Gemma-3 and Qwen3.

Reproduce it from a command. I’ve put the work up as a receipts-first paper series — the rule is no number without a runnable command:

github.com

GitHub - nihilistau/Position_Is_Arithmetic: Prime Power Transformer: A Number-Theoretic...

Prime Power Transformer: A Number-Theoretic Architecture for Compute

git clone https://github.com/nihilistau/Position_Is_Arithmetic.git
cd Position_Is_Arithmetic
# 02 — the reducing loader: reproduces green now (6/6 format gates,
#      bit-faithful forward on gemma-3 + qwen3). See papers/02-reducing-loader/repro/
# 01 — two-ring memory: the needle-retrieval harness is in
#      papers/01-two-ring-memory/repro/ ; the 32k headline figures
#      land as that run completes.

Each paper carries its own repro/ with the exact invocation and an EXPECTED.md. Correctness reproduces on any NVMe; the latency figure is the only Optane-specific part.

Licensing. The AGPL-3.0 line in the top post is stale — we’re moving everything to MIT across all the repos. The papers repo above is already MIT; the code repos are following.

And thanks, Agerico — the closure pressure was the right thing to push on, even though the answer turned out to be “keep the lattice purely mechanical and let the disk do the remembering.”