Shannon Prime Lattice

Update — the receipts-first paper series grew three papers, and one of them required indicting an ecosystem

A lot has happened since the opening post. The short version: the public, receipts-first paper series at https://github.com/nihilistau/Position_Is_Arithmetic now carries papers 04, 05 and 06 — and finishing 06 forced us to root-cause something the whole local-inference community is currently sitting on: every Gemma-4 GGUF we could measure, including the post-fix rebuilds, carries broken weights.

The series discipline hasn’t changed: every number is a row in a shared ledger with a command behind it, honest negatives stay on the record, and no throughput number is citable without a quality gate on the same artifact. That last rule is the reason this update exists.

Paper 04 — The Oracle & the Teacher (oracle-grounded backend verification)

• What it solves: porting a complex architecture to new silicon without the weeks-long divergence hunt — and, it turns out, defending yourself when the reference implementation itself is wrong.
• How: extract a bit-faithful CPU oracle from the reference first (scalar, readable, f64-accumulating), grade every backend against the oracle and never against a prior port, and gate autoregressive decode by teacher-forcing (the oracle re-predicts the port’s own generated stream). Receipt: a 35-layer variable-geometry MatFormer (per-layer attention widths, shared KV, proportional RoPE, softcap) matched its oracle at max KL 2.663e-10 (argmax 12/12), both live runs green first-try, 38/38.
• How it fits: this is the verification layer for everything in §1 of the opening post — “byte-exact, not small-KL” is only meaningful if the thing you’re byte-exact against is itself proven. The paper’s case study is the strongest demonstration we have: when llama.cpp scored wikitext PPL 397–506 on Gemma-4-12B and the ecosystem normalized it, a from-scratch forward written off the official safetensors + config alone measured 4.6776 — the model was healthy, llama.cpp’s forward was exonerated (two independent engines agree per-artifact), and the GGUF artifacts themselves were convicted. An oracle is not a porting tool; it’s the only defense against a poisoned reference frame.

Paper 05 — The Probe Suite (bisection, isolation & benchmark hygiene as one set)

• What it solves: the fact that correct numbers about computing systems are not read off — they are manufactured. The suite is how.
• How: truncated-parity bisection, isolation sweeps, benchmark hygiene and oracle-rank telemetry, used together. Documented kills: a 12.65× phantom speedup (three stacked artifacts), a 2.8e-3 wrong-arithmetic localized in two probe runs, a mixed-precision 0/256 bug the isolated bench passed at 1.34e-7, and a per-vector activation-quant collapse at oracle-rank 205,596 on outlier-heavy activations (fixed with per-block scales aligned to the kernel’s 128-bit loads).
• How it fits: the second half turns the same toolset outward, at ecosystem scale — tensor-class swap bisection over the broken GGUFs (restoring just the per-layer scale class recovered PPL 364→97; restoring norms made it worse , proving the matmul weights damaged too), per-layer cosine forensics (no permutation; in-place damage with a period-6 layer signature), and simulate-before-build : six quantization recipes simulated through the proven reference forward before a line of CUDA existed — and the built artifact then matched the simulation to four decimal places (5.1259), with the GPU kernel agreeing as a third instrument (5.1160).

Paper 06 — Computing on the Zip File (the dp4a bandwidth ladder — complete, gated, citable)

• What it solves: memory-bound decode on consumer silicon. The weights’ byte count is the speed of light, but only if you compute directly on the packed integer codes — dequantizing to f32 scratch first measured 3× slower than plain f32.
• How: warp-per-row __dp4a GEMV, 128-bit loads, in-ALU nibble unpack (~7% tax), exact integer accumulation, one Frobenius lift at the end — the isolated ladder runs f32 1× → int8 ~3.8× → Q4 ~7.06×, hugging the byte ratios. New this round: the OK_Q4B format (per-32-block f16 scales, store-then-derive discipline) where one weight block is exactly one 128-bit chunk in the kernel — zero extra code-bus traffic — and the sovereign quantization pipeline: artifact values come from the official safetensors checkpoint, never from a GGUF, and every artifact gates against the paper-04 oracle before any throughput number is taken.
• The headline, stated honestly: Gemma-4-12B at 26.1 tok/s and wikitext PPL 5.12 on an RTX 2060 12GB (graph path bit-exact, decode 256/256 top-1, 24/24 gates, clocks pinned). llama.cpp-CUDA on the same card does 31.29 tok/s — at PPL 192–506, because its artifacts are broken. Engine-for-engine we move +18% more bytes/s (245 vs 207 GB/s effective); our artifact is heavier because it is the only mathematically intact 4-bit Gemma-4-12B in existence. And in the spirit of the series: an earlier 34.2 tok/s headline is formally retired in the ledger — it was measured on an artifact that later failed the PPL gate. The rule caught our own number first.

For anyone hitting the Gemma-4 quant weirdness themselves: we published a standalone walkthrough — verify the breakage in ~30 minutes with an engine-independent method, plus the quantization recipe that actually works on this PTQ-hostile model (blanket 4-bit costs +45% PPL; 4-bit on the FFN gate/up pair only with 8-bit elsewhere costs +9.6%): https://github.com/nihilistau/Position_Is_Arithmetic/blob/main/GEMMA4-QUANT-FIX.md All forensic instruments are MIT, ~130-line numpy/torch scripts, no GPU required for the verification.

How this fits the lattice overall: the opening post’s thesis was that floating-point drift and un-provable identity are entropy bleeding into the hardware, and that a discrete substrate makes correctness a property you prove rather than estimate. This round extended that doctrine one level up the stack — to the artifacts. The same discipline that makes a kernel byte-exact (oracle, gates, receipts) is what caught an interchange format silently destroying weights while every smoke test stayed green. The supply chain is now part of the math.

Papers, ledger, methodology, instruments: nihilistau/Position_Is_Arithmetic

As always — the unflattering numbers are kept attached on purpose.