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  "path": "/t/shannon-prime-lattice/176466#post_6",
  "publishedAt": "2026-06-03T07:21:38.000Z",
  "site": "https://discuss.huggingface.co",
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    "GitHub - nihilistau/Position_Is_Arithmetic: Prime Power Transformer: A Number-Theoretic..."
  ],
  "textContent": "A couple of corrections for the record, a way to reproduce the work, and a licensing note.\n\n**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:\n\n  * 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.\n\n  * 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.\n\n\n\n\nFor 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.\n\n**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:\n\ngithub.com\n\n### GitHub - nihilistau/Position_Is_Arithmetic: Prime Power Transformer: A Number-Theoretic...\n\nPrime Power Transformer: A Number-Theoretic Architecture for Compute\n\n\n    git clone https://github.com/nihilistau/Position_Is_Arithmetic.git\n    cd Position_Is_Arithmetic\n    # 02 — the reducing loader: reproduces green now (6/6 format gates,\n    #      bit-faithful forward on gemma-3 + qwen3). See papers/02-reducing-loader/repro/\n    # 01 — two-ring memory: the needle-retrieval harness is in\n    #      papers/01-two-ring-memory/repro/ ; the 32k headline figures\n    #      land as that run completes.\n\n\n\nEach 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.\n\n**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.\n\nAnd 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.”",
  "title": "Shannon Prime Lattice"
}