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<!doctype html>
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<meta charset="utf-8">
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<title>Shannon-Prime — long-context KV memory you can run</title>
<meta name="description" content="A four-tier auditable memory hierarchy for frozen transformers (Ring 1/2/2′/3), XBAR (a token-free latent crossbar with an O(1)-in-context KV cache), and KAIROS (a resident 12B daemon that rewinds at the metal). Receipts-first: every number reproduces from a command, honest negatives kept attached.">
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<div class="wrap">
<header>
<h1>Auditable memory for a frozen transformer — a latent crossbar between models, and a resident daemon that rewinds at the metal.</h1>
<p class="lede">A 12B's KV cache made <strong class="good">O(1) in context</strong> — <strong>8k↔16k flat within ~50 MiB</strong>, the needle surviving at every depth. A 12B steered by <strong>direct KV-cache transplant, no tokens</strong> — 15/15, receipted. A resident 12B daemon that holds <strong>disciplined silence</strong> and shears its cache by an <strong>O(1) byte-exact rewind</strong> (48 layers, diffs = 0).</p>
<p class="sub">A memory-and-agency architecture that attaches to a frozen pretrained transformer and preserves its outputs — bit-exact when disabled. Proof-of-mechanism on one dev host: the <strong>0.6B</strong> carries the memory ladder, the <strong>12B</strong> (Gemma-3-12B QAT 4-bit) carries the XBAR and KAIROS results. Every number reproduces from a command, and the misses stay published (the composed 32k retrieval MISSed; ledger 01-R9).</p>
</header>
<h2>Run the composed pipeline</h2>
<div class="run">
<pre id="cmd">git clone https://github.com/nihilistau/Position_Is_Arithmetic.git && cd Position_Is_Arithmetic/papers/01-two-ring-memory/repro
./run_r9_32k_needle.ps1 -Model Qwen3-0.6B-f16.gguf -Drive F:\ -Corpus wiki.test.raw</pre>
<button onclick="navigator.clipboard.writeText(document.getElementById('cmd').innerText)">copy</button>
</div>
<p class="sub">You'll watch the cold KV path serve a 32k context off a drive, in ~1.8 GB of RAM. Honest scope: at the full composed 32k budget (64× selection) the retrieval itself <strong>MISSed</strong> (ledger 01-R9, kept on purpose) — the <strong>512-position retrieval is the proven claim</strong>, and the off-drive machinery (poison-gated, zero silent fallbacks over 16.3 h) is real either way. Correctness reproduces on any NVMe; the latency figure needs Optane.</p>
<h2>Three walls, three mechanisms</h2>
<div class="grid">
<div class="card"><p class="k">Memory wall</p><p class="v">910×</p><p class="d">resident KV cache shrunk (8.3 MB vs 7.5 GB at 32k) via a two-ring offload to byte-addressable storage.</p></div>
<div class="card"><p class="k">Intelligence wall</p><p class="v">+0.69%</p><p class="d">perplexity at 8× sparsification — four pinned attention-sink tokens; 2× and 4× go negative.</p></div>
<div class="card"><p class="k">Compute wall</p><p class="v">O(N)</p><p class="d">a ±1 projection router + quickselect: directional recall at 32 bytes/token, linear selection.</p></div>
</div>
<h2>The receipts</h2>
<table>
<tr><th>Claim</th><th>Number</th><th>Caveat</th></tr>
<tr><td>Quality at 8× sparsification</td><td>+0.69% PPL <span class="c">(2× −0.71, 4× −0.92)</span></td><td><span class="c">0.6B, 2k, one corpus</span></td></tr>
<tr><td>Needle retrieval, no recency bias</td><td>HIT at depth 10 / 50 / 90</td><td><span class="c">one model, one needle type</span></td></tr>
<tr><td>KV served off physical Optane</td><td>HIT off NVMe, poison-gated</td><td><span class="c">512 proven; composed 32k MISSed at the 64× budget (01-R9)</span></td></tr>
<tr><td>Random-read latency</td><td>7.57 µs / read</td><td><span class="c">Optane-specific</span></td></tr>
<tr><td>KV-RAM footprint</td><td>910× cache · 1.8 GB live</td><td><span class="c">net ~8×, router-index-dominated</span></td></tr>
<tr><td>Bit-exact when disabled</td><td>argmax-identical to the stock model</td><td><span class="c">the invariant under everything</span></td></tr>
<tr><td>12B GPU decode + quality, RTX 2060 12GB</td><td>26.1 tok/s at wikitext PPL 5.12</td><td><span class="c">gated + citable (06-R10); llama.cpp 31.29 tok/s at PPL 192–506 — broken artifacts (06-R8)</span></td></tr>
<tr><td>gemma-4 ecosystem finding</td><td>true PPL 4.68 vs GGUFs 192–506</td><td><span class="c">engine-independent (06-R8); fix tutorial in-repo</span></td></tr>
<tr><td>Latent crossbar probe (XBAR P1)</td><td>15/15 incorporation, 15/15 selectivity, 3.69 orders max rank pull</td><td><span class="c">12B steered by direct KV transplant, no tokens; gold-instrument coherence (X-R1)</span></td></tr>
<tr><td>O(1) KV decoupled from context (12B)</td><td>learned 512×32 LSH router <span class="good">+0.47% PPL @8×</span>; VRAM 8k↔16k flat ~50 MiB; needle survives 10/50/90%</td><td><span class="c">oracle −0.08%, frozen +4.17%; frozen-router control MISSES; KV term is O(1) (X-R2)</span></td></tr>
<tr><td>Resident 12B daemon: silence + O(1) rewind</td><td>24-tick crucible perfect (0 false / 0 missed / 0 drift); rewind byte-identical 48 layers; metal 0.0073 vs grow 0.924 s/action</td><td><span class="c">scripted tape; 0.6B control collapses; ≥24 h soak IN-FLIGHT, no verdict yet (KAIROS-01/02)</span></td></tr>
<tr><td>The Memo curator drives the crossbar autonomously</td><td>inert when off (PPL 4.6665 bit-identical); 256-bit LSH / integer-Hamming address; promote matched <span class="good">+0.000%</span> / discard corrupted +40106%</td><td><span class="c">float→discrete course-correction (sign-binarize collapses at r=32, ship r=256); 2-episode registry; Ring-2 verbatim recall (X-C2)</span></td></tr>
<tr><td>O(1) bit-exact rewind of latent memory</td><td>replay load-bearing (zeroed reads back all-zero); rewind resets prefix byte-identical (layer-diffs=0), 12B + E2B + SWA-ring wrap</td><td><span class="c">the §4-trap guarantee made mechanical; O(1) in byte-count (latency slope = KAIROS-02/03) (X-222)</span></td></tr>
<tr><td>Parameter-free Ring-3 consolidation (VSA/HRR, zero training)</td><td>recall@1=1.0 to N=32; loss a step function (hit +0.000% / miss +8.04% caught by 2% gate); idle GC 349.8 MB → 16.3 KB index</td><td><span class="c">retrieve-and-verify (P2.b top-5 honored); VSA retrieve host-numpy, Z_q/NTT port a follow-on; Path B budget-gated (X-R3VSA)</span></td></tr>
<tr><td>The organism breathes: real audio → episodic memory</td><td>audio-conditioned KV → canonical Ring-2 episode; signature separates (self 211/256, margin +79); round-trip clean</td><td><span class="c">step 1; the +1989% deflection is foreign-by-design (cross-context reject signal), not an audio-recall quality claim (X-ORG)</span></td></tr>
</table>
<h2>The system: four tiers and a crossbar</h2>
<p class="sub">The two-ring design grew into a four-tier hierarchy with an inter-model lane on top — each component carries its status:</p>
<table>
<tr><th>Component</th><th>What it is</th><th>Status</th></tr>
<tr><td><strong>Ring 1</strong></td><td>working KV window — the live turn</td><td><span class="good">PROVEN</span> <span class="c">(the stock model path)</span></td></tr>
<tr><td><strong>Ring 2</strong></td><td>verbatim episodic store on byte-addressable storage — the "hippocampus"</td><td><span class="good">PROVEN</span> <span class="c">(on Optane, poison-gated; bounded — the 64×-budget 32k MISS is why)</span></td></tr>
<tr><td><strong>Ring 2′</strong> (shadow)</td><td>transient staging: the curator proposes, a coherence gate promotes or rewinds — the audit mechanism</td><td>WIRED <span class="c">(C1-lite curator, exercised on real recall)</span></td></tr>
<tr><td><strong>Ring 3</strong></td><td>adapter-compressed consolidated store — the "neocortex"</td><td>DESIGN <span class="c">(under the irreversible-aware G-R3-LOSS gate)</span></td></tr>
<tr><td><strong>XBAR</strong></td><td>the Auditable Latent Crossbar: Exec + Memo share memory through latent state, no tokens — every write receipted, gated, rewindable; the cache itself <strong class="good">O(1) in context</strong></td><td><span class="good">PROVEN</span> <span class="c">(probe P1 X-R1; O(1) KV + learned router X-R2)</span></td></tr>
<tr><td><strong>KAIROS</strong></td><td>the time / agency axis: a resident 12B daemon — disciplined silence (NO_OP) + coherent action, with an O(1) byte-exact cache rewind to cold-evict idle thoughts</td><td><span class="good">PROVEN</span> <span class="c">(crucible KAIROS-01; metal rewind KAIROS-02; ≥24 h soak IN-FLIGHT)</span></td></tr>
<tr><td><strong>NIGHTSHIFT</strong></td><td>offline idle-time consolidation: Ring 2 → adapter → Ring 2′ → gate → Ring 3 — a synthetic subconscious whose dreams are auditable</td><td>DESIGN</td></tr>
</table>
<p class="sub">Full map with the architecture diagram: <a href="https://github.com/nihilistau/Position_Is_Arithmetic#the-system-a-four-tier-memory-hierarchy-plus-a-latent-crossbar">README — The system</a>.</p>
<h2>Honest scope</h2>
<div class="note">
Proof-of-mechanism on <strong>one dev host</strong> (RTX 2060, 12 GB) — not a scaling study, not multi-model, not independently reproduced yet. The <strong>0.6B</strong> (Qwen3-0.6B) carries the two-ring memory ladder; the <strong>12B</strong> (Gemma-3-12B, QAT 4-bit) carries the XBAR and KAIROS results. The CPU decode is <strong>~1.34× behind</strong> a tuned llama.cpp at the same quantization: the value here is the <strong>memory-and-agency envelope, not raw throughput</strong>. The <strong>≥24 h KAIROS endurance soak is in-flight, not passed</strong> — we do not call a verdict from a mid-run log. We keep the unflattering numbers in the papers on purpose — a result with its caveats attached is one you can trust.
</div>
<h2>Read more</h2>
<div class="doors">
<a class="door" href="https://github.com/nihilistau/Position_Is_Arithmetic/tree/main/papers/01-two-ring-memory"><p class="t">The systems paper →</p><p class="d">Every mechanism as idea → receipt → payoff → implementation. The receipts, in full.</p></a>
<a class="door" href="https://github.com/nihilistau/Position_Is_Arithmetic/blob/main/COMPANION-THEORY.md"><p class="t">The algebraic companion →</p><p class="d">The elliptic-curve framework that motivated the design. Not required to run or validate anything. A door for the curious.</p></a>
</div>
<h2>Get involved</h2>
<p class="sub">The biggest open question is scale: the O(1) KV result holds 8× at +0.47% PPL on the 12B (X-R2) — does it hold past 12B, and on other architectures? Other one-person-can't-do-it asks: independent repros on your own drive (the Linux path especially), and the ≥24 h KAIROS soak reproduced on a card that <em>can</em> lock its memory clock (ours can't — see the methodology). See <a href="https://github.com/nihilistau/Position_Is_Arithmetic/blob/main/CONTRIBUTING.md">CONTRIBUTING</a>.</p>
<footer>
A receipts-first series · 06 (computing on the zip file) complete + citable; 04/05 written; 02/03 staged; 07/08/10 staged drafts; 09 (KAIROS) staged — release gated on the in-flight ≥24 h soak; 12–15 (the orchestration tier: Memo curator, O(1) rewind, parameter-free Ring-3, the audio→memory organism) written + citable. Citable ledger rows now include XBAR X-R1 (latent write), X-R2 (O(1) KV), X-R3 (replay-write), X-C2/X-222/X-R3VSA/X-ORG (the orchestration tier) and KAIROS-01/02/04. ·
Cite: <a href="https://github.com/nihilistau/Position_Is_Arithmetic/blob/main/CITATION.cff">CITATION.cff</a> · License: <a href="https://github.com/nihilistau/Position_Is_Arithmetic/blob/main/LICENSE">MIT</a> · Every number traces to <a href="https://github.com/nihilistau/Position_Is_Arithmetic/blob/main/LEDGER.md">the ledger</a>.
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