Chad St Thomas
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<title>The Dose-Window Hypothesis — order, calibration, and externalised knowledge in small language models</title>
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<meta name="description" content="A proposed and partially tested hypothesis on training order, quantisation calibration, and external knowledge in small language models — with every number from frozen instruments and paired controls.">
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<header class="top">
<p class="eyebrow">Preprint &nbsp;·&nbsp; a hypothesis with measured corollaries</p>
<h1>The Dose-Window Hypothesis</h1>
<p class="subtitle">Order, calibration, and externalised knowledge in small
language models — a hypothesis with measured corollaries</p>
<p class="author">Chad St Thomas <span class="affil">· CuriousGene / Tablinum</span></p>
<p class="byline">
<span><b>Substrate:</b> Qwen3-0.6B · LFM2.5-1.2B · Qwen3.5-2B · Nanbeige-4.2-3B · LFM2.5-8B-A1B</span>
<span><b>Compute:</b> one 6 GB laptop GPU</span>
</p>
</header>
<div class="abstract">
<span class="lbl">Abstract</span>
<p>This paper proposes and partially tests the <b>Dose-Window
Hypothesis</b>: for a model of size <em>N</em> and a behaviour <em>B</em>,
there is an interval <code>[W_install, W_harm]</code> in effective training
exposure — examples × epochs, measured against the model's existing format
lock — below which <em>B</em> does not install, and above which it saturates
into template memorisation and erodes complementary behaviours, nearest
neighbours first. The hypothesis emerged from an eight-week program training
small language models (0.3B–8B) to investigate — answer from evidence,
challenge false premises, abstain when evidence is absent, cite what each
claim rests on — on a single 6 GB laptop GPU, with every score produced by
frozen, deterministic instruments and paired controls.</p>
<p>Four measured corollaries support it and stand independently of it.
<b>(1) Order beats ingredients:</b> the same category data cost 0.081 mixed
into a base mixture and gained 0.016 as an isolated pulse followed by a
format re-lock, at identical compute. <b>(2) The quantisation floor is
calibration, not bits:</b> two 2-bit builds of one model, identical in file
size and bit width, scored 0.014 and 0.708. <b>(3) Knowledge divides
cleanly:</b> a static, runtime-editable fact table supplies the content half
— lifting premise correction 4–5× at zero training, with a single 8B
reaching 0.959 on the bench and 0.90 on a blind holdout — while the polarity
half remains the model's job and fails below roughly 2B regardless of what
the table supplies. <b>(4) Interfaces leak:</b> giving the model a retrieval
tool scored 0.510–0.633 against 0.939 for retrieving before inference,
through three separable failure modes.</p>
<p>The hypothesis is stated with its untested predictions; section 7
gives the applications at scale and the open agenda, and section 9 states
what remains unestablished. The evaluation harness and CLI are released as
open source.</p>
</div>
<!-- ================================================================= -->
<section>
<h2><span class="n">1</span>Measurement infrastructure</h2>
<p class="lead">Every score in this paper comes from a frozen instrument with a
deterministic grader and a paired control. This section defines what that
means, how answers are graded, and how the reported numbers are bounded.</p>
<figure>
<div class="figbox"><!--FIG:pipeline-->
<svg viewBox="0 0 760 250" width="100%" role="img" xmlns="http://www.w3.org/2000/svg" style="display:block"><text x="0.0" y="26.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="12" font-weight="700" fill="#1E3A8A" text-anchor="start">I · INSTRUMENT</text><rect x="0.0" y="40.0" width="236.0" height="158.0" fill="#F8FAFC" stroke="#E2E8F0" stroke-width="1" rx="6"/><rect x="14.0" y="56.0" width="208.0" height="36.0" fill="#FFFFFF" stroke="#E2E8F0" stroke-width="1" rx="4"/><text x="24.0" y="71.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="600" fill="#1F2933" text-anchor="start">frozen test set</text><text x="24.0" y="84.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9" font-weight="normal" fill="#64748B" text-anchor="start">written and sealed</text><rect x="14.0" y="104.0" width="208.0" height="36.0" fill="#FFFFFF" stroke="#E2E8F0" stroke-width="1" rx="4"/><text x="24.0" y="119.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="600" fill="#1F2933" text-anchor="start">deterministic grader</text><text x="24.0" y="132.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9" font-weight="normal" fill="#64748B" text-anchor="start">match · tail · entailment</text><rect x="14.0" y="152.0" width="208.0" height="36.0" fill="#FFFFFF" stroke="#E2E8F0" stroke-width="1" rx="4"/><text x="24.0" y="167.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="600" fill="#1F2933" text-anchor="start">oracle + shortcut check</text><text x="24.0" y="180.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9" font-weight="normal" fill="#64748B" text-anchor="start">trivial baseline &lt; 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<!--/FIG:pipeline--></div>
<figcaption><b>Figure 1.</b> The three phases of the method. Instruments are
frozen before any training run. Deployment failures are fed back as new
instrument items, closing the loop.</figcaption>
</figure>
<h3>1.1 What an instrument is</h3>
<p>A question set with a deterministic grader, written and sealed before any
training run and never trained on. Four disciplines apply: the file, its
generator, and its build seed are committed together and never rebuilt in
place; training corpora are checked for shared gold values against every frozen
set; every item's gold target grades against itself at 1.0 by construction; and
compared conditions share item identities exactly, so the comparison is
paired.</p>
<div class="box">
<span class="lbl">Standing guard</span>
<p><code>shortcut_check</code> runs on every new premise or entailment set
before it is trusted. It fits simple baselines — length ratio, lexical
overlap, answer position — and fails the set if any exceeds 0.90. Backfilled
across eight frozen instruments, the values were 0.783–0.867.</p>
</div>
<h3>1.2 Controls and contamination</h3>
<p>Every condition reported in this paper is paired with its control on
identical items — an uplift without its baseline is not a result. Training
corpora are re-graded for instrument overlap before every run, and the office
evaluation instruments are deliberately <em>not</em> published, because a
published evaluation set becomes a training set.</p>
<h3>1.3 The grader</h3>
<p>The production grader is strictly additive across three stages: exact and
substring gold-value matching under a rejection lexicon, with unit
normalisation; the same test applied to a tail window of the raw answer; and an
NLI entailment check with the gold fact as premise and the answer as hypothesis,
requiring <code>P(entail) ≥ 0.80</code>. Calibration: 0.991 entailment on a tight
paraphrase, 0.715 on a vague one, correctly declined. Tests pin the bar at
exactly 0.8.</p>
<h3>1.4 Statistical treatment</h3>
<p>For independent bounded scores, simultaneous two-sided intervals for each of
<code>m</code> axis means use Hoeffding's inequality with a union bound:</p>
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<use xlink:href="#Cmr10-3d" transform="translate(961.984375 0.273438)"/>
<use xlink:href="#Cmr10-5b" transform="translate(1057.228516 0.273438)"/>
<use xlink:href="#Cmr10-6d" transform="translate(1084.914062 0.273438)"/>
<use xlink:href="#Cmr10-61" transform="translate(1168.214844 0.273438)"/>
<use xlink:href="#Cmr10-78" transform="translate(1218.214844 0.273438)"/>
<use xlink:href="#Cmr10-28" transform="translate(1270.900391 0.273438)"/>
<use xlink:href="#Cmr10-30" transform="translate(1309.71875 0.273438)"/>
<use xlink:href="#Cmmi10-3b" transform="translate(1359.71875 0.273438)"/>
<use xlink:href="#Cmr10-b9" transform="translate(1415.342285 1.445312)"/>
<use xlink:href="#Cmmi10-78" transform="translate(1404.962891 0.273438)"/>
<use xlink:href="#Cmsy10-a1" transform="translate(1479.601562 0.273438)"/>
<use xlink:href="#Cmmi10-72" transform="translate(1574.845703 0.273438)"/>
<use xlink:href="#Cmr10-29" transform="translate(1619.962891 0.273438)"/>
<use xlink:href="#Cmmi10-3b" transform="translate(1658.78125 0.273438)"/>
<use xlink:href="#Cmr10-6d" transform="translate(1728.412521 0.273438)"/>
<use xlink:href="#Cmr10-69" transform="translate(1811.713303 0.273438)"/>
<use xlink:href="#Cmr10-6e" transform="translate(1839.39885 0.273438)"/>
<use xlink:href="#Cmr10-28" transform="translate(1894.916428 0.273438)"/>
<use xlink:href="#Cmr10-31" transform="translate(1933.734787 0.273438)"/>
<use xlink:href="#Cmmi10-3b" transform="translate(1983.734787 0.273438)"/>
<use xlink:href="#Cmr10-b9" transform="translate(2039.358322 1.445312)"/>
<use xlink:href="#Cmmi10-78" transform="translate(2028.978928 0.273438)"/>
<use xlink:href="#Cmr10-2b" transform="translate(2103.6176 0.273438)"/>
<use xlink:href="#Cmmi10-72" transform="translate(2198.86174 0.273438)"/>
<use xlink:href="#Cmr10-29" transform="translate(2243.978928 0.273438)"/>
<use xlink:href="#Cmr10-5d" transform="translate(2282.797287 0.273438)"/>
<path d="M 257.873047 132.5
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</span>
<!--/EQ:hoeffding-->
<span class="eqnum">(1)</span>
</div>
<p>At <code>α = 0.05</code>, all four intervals jointly cover their population
means with probability ≥ 0.95. Dependence between axes is permitted; independence
of sampled questions is required. This is a conservative finite-sample bound, not
a power calculation — with a perfect mean it needs ≥ 254 items per axis for the
lower endpoint to reach 0.90. For paired comparisons on identical items,
<code>D_i = candidate_i − baseline_i</code> in [−1, 1], and the radius doubles
because the range width doubles.</p>
<p>Two further constraints on inference were measured. Identical
<code>prompt_sha256</code> produced only 3 of 30 byte-identical answers across
server restarts, giving a ≈2-item noise band on n = 30 across server lifetimes;
within-server comparisons are robust, absolute values are ±0.07. And scores are
compared within a backend only, because kernel numerics can flip an argmax at the
margin — cross-backend cells agree within ≤2 items, so curves are read
within-sweep.</p>
</section>
<!-- ================================================================= -->
<section>
<h2><span class="n">2</span>The dose window</h2>
<p class="lead">The order in which a behaviour is trained matters more than the
data used to train it. Installing one behaviour by mixing its data into the base
mixture cost score twice; applying the same data as an isolated pulse followed by
a format re-lock produced the program's best result.</p>
<figure>
<div class="figbox"><!--FIG:dose-->
<svg viewBox="0 0 760 330" width="100%" role="img" xmlns="http://www.w3.org/2000/svg" style="display:block"><text x="149.1" y="54.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="normal" fill="#64748B" text-anchor="middle">too little</text><text x="343.2" y="54.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="700" fill="#0F766E" text-anchor="middle">the window</text><text x="612.4" y="54.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="600" fill="#BE123C" text-anchor="middle">too much</text><rect x="224.2" y="64.0" width="237.9" height="186.0" fill="#0F766E" opacity="0.08"/><line x1="224.2" y1="64.0" x2="224.2" y2="250.0" stroke="#0F766E" stroke-width="1.1" stroke-dasharray="4 3"/><line x1="462.1" y1="64.0" x2="462.1" y2="250.0" stroke="#0F766E" stroke-width="1.1" stroke-dasharray="4 3"/><line x1="74.0" y1="250.0" x2="700.0" y2="250.0" stroke="#1F2933" stroke-width="1.2"/><line x1="74.0" y1="64.0" x2="74.0" y2="250.0" stroke="#1F2933" stroke-width="1.2"/><line x1="70.0" y1="250.0" x2="74.0" y2="250.0" stroke="#1F2933" stroke-width="1"/><text x="66.0" y="254.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.00</text><line x1="70.0" y1="203.5" x2="74.0" y2="203.5" stroke="#1F2933" stroke-width="1"/><text x="66.0" y="207.5" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.25</text><line x1="70.0" y1="157.0" x2="74.0" y2="157.0" stroke="#1F2933" stroke-width="1"/><text x="66.0" y="161.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.50</text><line x1="70.0" y1="110.5" x2="74.0" y2="110.5" stroke="#1F2933" stroke-width="1"/><text x="66.0" y="114.5" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.75</text><line x1="70.0" y1="64.0" x2="74.0" y2="64.0" stroke="#1F2933" stroke-width="1"/><text x="66.0" y="68.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">1.00</text><text x="66.0" y="54.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="normal" fill="#64748B" text-anchor="end">score</text><text x="700.0" y="268.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="normal" fill="#64748B" text-anchor="end">effective exposure (examples × epochs)</text><text x="218.2" y="244.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="600" fill="#0F766E" text-anchor="end">W_install</text><text x="468.1" y="244.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="600" fill="#BE123C" text-anchor="start">W_harm</text><path d="M 74.0 220.2 L 136.6 205.4 L 224.2 164.4 L 311.9 136.5 L 387.0 119.8 L 462.1 112.4 L 537.2 110.5 L 612.4 114.2 L 700.0 119.8" stroke="#0F766E" stroke-width="2.2" fill="none" stroke-linejoin="round"/><path d="M 74.0 78.9 L 174.2 80.7 L 261.8 84.5 L 349.4 93.8 L 424.6 108.6 L 499.7 145.8 L 574.8 181.2 L 649.9 201.6 L 700.0 209.1" stroke="#BE123C" stroke-width="2.2" fill="none" stroke-linejoin="round"/><text x="261.8" y="194.2" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="600" fill="#0F766E" text-anchor="middle">target behaviour installs</text><text x="562.3" y="194.2" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="600" fill="#BE123C" text-anchor="middle">protected axes eroded</text><circle cx="130.3" cy="100.5" r="4.0" fill="#64748B" stroke="#FFFFFF" stroke-width="1.4"/><text x="130.3" y="90.5" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">v18 0.804</text><circle cx="336.9" cy="107.2" r="4.0" fill="#64748B" stroke="#FFFFFF" stroke-width="1.4"/><circle cx="437.1" cy="115.5" r="4.0" fill="#64748B" stroke="#FFFFFF" stroke-width="1.4"/><text x="74.0" y="288.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start" font-style="italic">mixing the behaviour data into the base mix:</text><text x="74.0" y="304.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">v19 0.768 v20 0.723</text><circle cx="524.7" cy="97.5" r="5.5" fill="#1E3A8A" stroke="#FFFFFF" stroke-width="1.6"/><text x="543.5" y="93.8" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#1E3A8A" text-anchor="start">v21 0.820</text><text x="543.5" y="108.6" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#1E3A8A" text-anchor="start">pulse, then re-lock</text><path d="M 524.7 112.4 L 524.7 101.2" stroke="#1E3A8A" stroke-width="1.4" fill="none" stroke-dasharray="3 3" stroke-linejoin="round"/></svg>
<!--/FIG:dose--></div>
<figcaption><b>Figure 2.</b> The dose window. Below <code>W_install</code> the
target behaviour does not install; above <code>W_harm</code> it saturates into
template memorisation and erodes the protected axes, nearest neighbours first.
Measured arms are placed by their construction.</figcaption>
</figure>
<h3>2.1 The experiment</h3>
<div class="tblwrap">
<table>
<caption><b>Table 1.</b> Same data, same compute class, same base. The only
variable is order and replay structure.</caption>
<thead><tr><th>arm</th><th>construction</th><th class="num">overall</th><th class="num">Δ baseline</th></tr></thead>
<tbody>
<tr><td>v18</td><td>format-locked baseline</td><td class="num">0.804</td><td class="num">—</td></tr>
<tr><td>v19</td><td>34% SQuAD-v2 + premise, mixed into the main mix</td><td class="num">0.768</td><td class="num">−0.036</td></tr>
<tr><td>v20</td><td>12% abstain-only, mixed into the main mix</td><td class="num">0.723</td><td class="num">−0.081</td></tr>
<tr><td><b>v21</b></td><td><b>same category data, staged pulse → format re-lock</b></td><td class="num"><b>0.820</b></td><td class="num"><b>+0.016</b></td></tr>
</tbody>
</table>
</div>
<div class="box">
<span class="lbl">Dose-window hypothesis</span>
<p>For a model of size <em>N</em> and behaviour <em>B</em>, there exists an
interval <code>[W_install, W_harm]</code> in effective exposure — examples ×
epochs, measured against the model's existing format lock — such that below
<code>W_install</code> the behaviour does not install, and above
<code>W_harm</code> it saturates into template memorisation and erodes
complementary behaviours, nearest neighbours first.</p>
<p style="margin-top:10px"><b>Status of its predictions.</b>
P1, windows widen with scale: supported at one size pair (0.6B →
1.2B, same recipe), untested beyond. P2, damage is dose-driven rather
than data-driven: supported (v19/v20 vs v21; swapped-order control
collapsed to 0.497). P3, recovery asymmetry between formats and
behaviours: confirmed (Table 2). The mechanism — gradient-level
interference between category batches — is unmeasured; the
correlation structure in Figure 3b is descriptive only. The
hypothesis is therefore a hypothesis: two confirmed predictions, one
partially confirmed, mechanism open.</p>
</div>
<h3>2.2 Recovery asymmetry</h3>
<p>A deliberately over-dosed abstention pulse (300 steps, ≈7 epochs over 343
examples) produced a clean damage map. One epoch-equivalent of re-locking then
repaired the structural damage while the newly installed behaviour survived:</p>
<div class="tblwrap">
<table>
<caption><b>Table 2.</b> Damage and repair. Formats install deep and leave last;
behavioural skills are fragile during installation and durable once
super-saturated.</caption>
<thead><tr><th>axis</th><th class="num">before</th><th class="num">after over-dose</th><th class="num">after re-lock</th></tr></thead>
<tbody>
<tr><td>grounding</td><td class="num">0.887</td><td class="num">0.025</td><td class="num">0.863</td></tr>
<tr><td>premise</td><td class="num">0.733</td><td class="num">0.533</td><td class="num">—</td></tr>
<tr><td>abstention</td><td class="num">0.633</td><td class="num">0.567</td><td class="num"><b>0.833</b></td></tr>
<tr><td>provenance</td><td class="num">0.980</td><td class="num">0.940</td><td class="num">held</td></tr>
</tbody>
</table>
</div>
<p>Grounding was erased and restored almost completely <em>while the newly
installed abstention behaviour survived</em>. At 1.2B the same recipe held
abstention at 1.000 and grounding at 0.975 simultaneously — a combination no
0.6B arm reached. <b>The window widens with scale.</b></p>
<h3>2.3 The per-epoch damage ledger</h3>
<figure>
<div class="figbox"><!--FIG:ledger-->
<svg viewBox="0 0 760 250" width="100%" role="img" xmlns="http://www.w3.org/2000/svg" style="display:block"><text x="0.0" y="12.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="12" font-weight="700" fill="#1F2933" text-anchor="start">(a) sub-score damage per epoch</text><text x="0.0" y="27.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">0.2-epoch pulse, 0.6B · normalised weights feed the loss</text><text x="108.0" y="63.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="normal" fill="#1F2933" text-anchor="end">abstention</text><rect x="118.0" y="48.0" width="214.0" height="22.0" fill="#F8FAFC" stroke="#E2E8F0" stroke-width="1" rx="3"/><rect x="118.0" y="48.0" width="214.0" height="22.0" fill="#0F766E" rx="3" opacity="0.92"/><text x="344.0" y="63.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="11.5" font-weight="700" fill="#1F2933" text-anchor="start">2.50</text><text x="390.0" y="63.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10.5" font-weight="normal" fill="#64748B" text-anchor="start">d̃ 0.458</text><text x="108.0" y="105.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="normal" fill="#1F2933" text-anchor="end">grounding</text><rect x="118.0" y="90.0" width="214.0" height="22.0" fill="#F8FAFC" stroke="#E2E8F0" stroke-width="1" rx="3"/><rect x="118.0" y="90.0" width="90.7" height="22.0" fill="#0F766E" rx="3" opacity="0.92"/><text x="344.0" y="105.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="11.5" font-weight="700" fill="#1F2933" text-anchor="start">1.06</text><text x="390.0" y="105.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10.5" font-weight="normal" fill="#64748B" text-anchor="start">d̃ 0.194</text><text x="108.0" y="147.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="normal" fill="#1F2933" text-anchor="end">premise</text><rect x="118.0" y="132.0" width="214.0" height="22.0" fill="#F8FAFC" stroke="#E2E8F0" stroke-width="1" rx="3"/><rect x="118.0" y="132.0" width="85.6" height="22.0" fill="#0F766E" rx="3" opacity="0.92"/><text x="344.0" y="147.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="11.5" font-weight="700" fill="#1F2933" text-anchor="start">1.00</text><text x="390.0" y="147.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10.5" font-weight="normal" fill="#64748B" text-anchor="start">d̃ 0.183</text><text x="108.0" y="189.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="normal" fill="#1F2933" text-anchor="end">provenance</text><rect x="118.0" y="174.0" width="214.0" height="22.0" fill="#F8FAFC" stroke="#E2E8F0" stroke-width="1" rx="3"/><rect x="118.0" y="174.0" width="77.0" height="22.0" fill="#0F766E" rx="3" opacity="0.92"/><text x="344.0" y="189.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="11.5" font-weight="700" fill="#1F2933" text-anchor="start">0.90</text><text x="390.0" y="189.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10.5" font-weight="normal" fill="#64748B" text-anchor="start">d̃ 0.165</text><text x="118.0" y="224.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10.5" font-weight="normal" fill="#64748B" text-anchor="start">total 5.46 / epoch</text><text x="470.0" y="12.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="12" font-weight="700" fill="#1F2933" text-anchor="start">(b) interference structure</text><text x="470.0" y="27.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">Spearman over 8 runs · descriptive, not causal</text><text x="470.0" 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fill="#1F2933" text-anchor="start">provenance ↔ overall</text><rect x="531.9" y="174.0" width="56.1" height="16.0" fill="#BE123C" rx="2" opacity="0.9"/><text x="524.9" y="186.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10.5" font-weight="700" fill="#BE123C" text-anchor="end">-0.61</text><line x1="588.0" y1="54.0" x2="588.0" y2="214.0" stroke="#CBD5E1" stroke-width="1"/><text x="588.0" y="48.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">0</text><text x="470.0" y="230.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start" font-style="italic">negative = the axis moves against overall score</text></svg>
<!--/FIG:ledger--></div>
<figcaption><b>Figure 3.</b> (a) Sub-score damage per epoch, measured on a
0.2-epoch pulse at 0.6B, with the normalised weights the objective uses.
(b) Interference structure across eight sequentially selected runs —
descriptive, not causal.</figcaption>
</figure>
<h3>2.4 The objective: damage-aware OPD</h3>
<p>Inherited from MiniCPM5: specialist teachers, a reverse-KL teacher signal used
as a per-token advantage, and distillation prompt reuse. That pipeline has no
notion of cross-behaviour interference during consolidation. This program
measured exactly that interference; DA-OPD is the synthesis.</p>
<p>The sampled token advantage, unbiased at the behaviour policy:</p>
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<!--/EQ:advantage-->
<span class="eqnum">(2)</span>
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<p>The consolidation loss:</p>
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<!-- $\mathcal{L}(\theta) = -\,\mathbb{E}_{\tau \sim \pi_\theta}\left[ \mathrm{mean}_{t \in \tau_a}\, \rho_t \cdot \mathrm{sg}(A_t) \right] + \beta \sum_c \tilde{d}_c\, \mathbb{E}_{\tau \sim \mathcal{D}_c}\left[ \mathrm{KL}(\pi_{\mathrm{ref}} \,\|\, \pi_\theta) \right]$ -->
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<span class="eqnum">(3)</span>
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<p>where the importance ratio is</p>
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<span class="eqnum">(4)</span>
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<p>The first term is the unmodified on-policy distillation objective. The second
term is the addition: while a teacher's domain is being consolidated, every
protected category pays an anchor-KL penalty to a frozen reference, weighted by
how expensive that category is to damage. The reference is the common SFT
initialisation, with <code>β = 0.25</code> as the prior. Setting
<code>β = 0</code> recovers vanilla OPD and is the control arm.</p>
<p>The measured comparison: <code>β = 0.25</code> anchored beat
<code>β = 0</code> control in <b>3 of 3 student seeds</b> on overall and every
protected axis at equal transfer (0.816 vs 0.791). Premise preservation failed in
all six arm-seeds, and the <code>β = 0.5</code> screen fired STOP per its frozen
rule because the β response is non-monotone.</p>
<h3>2.5 Dose allocation as a linear program</h3>
<p>Teacher routing is solved before any run rather than tuned after it:</p>
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<span class="eqnum">(5)</span>
</div>
<p>where <code>g_c</code> is own-category installation gain per epoch,
<code>D_{c→c'}</code> is the expected sub-score change in <code>c'</code> per
epoch of category-<code>c</code> exposure, <code>Ŵ_harm,c</code> is the measured
harm threshold, and <code>K</code> is the total update budget. Unmeasured rows
default to the mean measured damage and are flagged. The output — per-teacher
budgets and predicted per-category deltas — is falsifiable against the run's
actual deltas.</p>
<h3>2.6 Recipes are per-substrate</h3>
<p>Three measured points on the same recipe family: at 0.6B the recipe trains
behaviours up and MMLU rose 3.7 points; at 1.2B the same recipe preserves the
cost but damages MMLU monotonically with dose (42.34 → 40.72); at Qwen3.5-2B the
recipe <em>regressed</em> against a strong base across every variant measured
(−0.08 overall, −5.22 MMLU). The dilution law is measured, not inferred. Recipe
choice is an experimental variable per substrate, not a transferred
constant.</p>
</section>
<!-- ================================================================= -->
<section>
<h2><span class="n">3</span>Compression: calibration, not bits</h2>
<p class="lead">Two 2-bit builds of one model, identical in file size and bit
width, scored 0.014 and 0.708. The variable was not how far the model was
compressed but what the compressor was told to protect.</p>
<h3>3.1 The estimand</h3>
<p>The quantisation gap of a lineage at a rung is</p>
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<!--/EQ:gap-->
<span class="eqnum">(6)</span>
</div>
<p>measured at identical evaluation, protocol, seed, and decode settings.
Matched-quant deltas only: <code>candidate_rung − base_rung</code> is reportable;
<code>candidate_rung − base_bf16</code> is never reported as a delta. Each rung
is a frozen estimand with its own lock entry.</p>
<figure>
<div class="figbox"><!--FIG:parity-->
<svg viewBox="0 0 760 300" width="100%" role="img" xmlns="http://www.w3.org/2000/svg" style="display:block"><text x="0.0" y="12.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="12" font-weight="700" fill="#1F2933" text-anchor="start">(a) dense / looped 3B · 2.6 GB</text><text x="0.0" y="27.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">score by rung; calibrated Q2 matches Q4 at 73% of the size</text><line x1="60.0" y1="236.0" x2="380.0" y2="236.0" stroke="#1F2933" stroke-width="1.2"/><line x1="60.0" y1="44.0" x2="60.0" y2="236.0" stroke="#1F2933" stroke-width="1.2"/><line x1="56.0" y1="236.0" x2="60.0" y2="236.0" stroke="#1F2933" stroke-width="1"/><text x="52.0" y="240.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.0</text><line x1="56.0" y1="140.0" x2="60.0" y2="140.0" stroke="#1F2933" stroke-width="1"/><text x="52.0" y="144.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.5</text><line x1="56.0" y1="44.0" x2="60.0" y2="44.0" stroke="#1F2933" stroke-width="1"/><text x="52.0" y="48.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">1.0</text><text x="52.0" y="36.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="normal" fill="#64748B" text-anchor="end">v3</text><text x="220.0" y="268.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="middle">artifact size (GB)</text><line x1="60.0" y1="97.4" x2="380.0" y2="97.4" stroke="#B45309" stroke-width="1.3" stroke-dasharray="4 3"/><text x="64.0" y="89.4" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#B45309" text-anchor="start">Q4 = 0.722</text><circle cx="345.7" cy="97.4" r="5.5" fill="#0F766E" stroke="#FFFFFF" stroke-width="1.4"/><circle cx="199.4" cy="100.1" r="5.5" fill="#0F766E" stroke="#FFFFFF" stroke-width="1.4"/><circle cx="87.4" cy="222.8" r="5.5" fill="#BE123C" stroke="#FFFFFF" stroke-width="1.4"/><circle cx="199.4" cy="233.3" r="5.5" fill="#BE123C" stroke="#FFFFFF" stroke-width="1.4"/><text x="345.7" y="83.4" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#1F2933" text-anchor="end">Q4_K_M</text><text x="199.4" y="86.1" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#0F766E" text-anchor="middle">Q2 + imatrix 0.708</text><text x="199.4" y="221.3" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#BE123C" text-anchor="middle">Q2 naive 0.014</text><text x="87.4" y="200.8" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#BE123C" text-anchor="middle">IQ1_M 0.069</text><text x="220.0" y="284.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="700" fill="#1F2933" text-anchor="middle">same bits, same size: ≈50× apart</text><text x="220.0" y="298.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="middle" font-style="italic">the variable is the calibration corpus</text><text x="440.0" y="12.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="12" font-weight="700" fill="#1F2933" text-anchor="start">(b) MoE 7.9B / 1.3B active</text><text x="440.0" y="27.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">2-bit retention where the dense substrate collapsed</text><line x1="484.0" y1="236.0" x2="740.0" y2="236.0" stroke="#1F2933" stroke-width="1.2"/><line x1="484.0" y1="44.0" x2="484.0" y2="236.0" stroke="#1F2933" stroke-width="1.2"/><line x1="480.0" y1="236.0" x2="484.0" y2="236.0" stroke="#1F2933" stroke-width="1"/><text x="476.0" y="240.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.0</text><line x1="480.0" y1="140.0" x2="484.0" y2="140.0" stroke="#1F2933" stroke-width="1"/><text x="476.0" y="144.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.5</text><line x1="480.0" y1="44.0" x2="484.0" y2="44.0" stroke="#1F2933" stroke-width="1"/><text x="476.0" y="48.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">1.0</text><path d="M 532.0 73.4 L 616.0 83.9 L 700.0 86.6" stroke="#0F766E" stroke-width="1.8" fill="none" stroke-linejoin="round"/><circle cx="532.0" cy="73.4" r="5.5" fill="#0F766E" stroke="#FFFFFF" stroke-width="1.4"/><text x="532.0" y="61.4" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#1F2933" text-anchor="middle">0.847</text><text x="532.0" y="252.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="normal" fill="#1F2933" text-anchor="middle">Q4_K_M</text><circle cx="616.0" cy="83.9" r="5.5" fill="#0F766E" stroke="#FFFFFF" stroke-width="1.4"/><text x="616.0" y="71.9" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#1F2933" text-anchor="middle">0.792</text><text x="616.0" y="252.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="normal" fill="#1F2933" text-anchor="middle">IQ2_M</text><circle cx="700.0" cy="86.6" r="5.5" fill="#0F766E" stroke="#FFFFFF" stroke-width="1.4"/><text x="700.0" y="74.6" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#1F2933" text-anchor="middle">0.778</text><text x="700.0" y="252.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="normal" fill="#1F2933" text-anchor="middle">Q2_K</text><text x="712.0" y="104.6" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11" font-weight="700" fill="#0F766E" text-anchor="end">93% of Q4</text><line x1="484.0" y1="222.8" x2="740.0" y2="222.8" stroke="#BE123C" stroke-width="1.2" stroke-dasharray="4 3"/><text x="490.0" y="214.8" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#BE123C" text-anchor="start">dense at Q2 / IQ1: 0.014 – 0.069</text><text x="612.0" y="284.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="middle" font-style="italic">expert redundancy is the quantisation armour</text></svg>
<!--/FIG:parity--></div>
<figcaption><b>Figure 4.</b> (a) The parity column on one dense/looped
substrate. Calibrated Q2 sits within noise of Q4 at 73% of the file size;
naive Q2 collapses; IQ1 destroys the polarity capability itself. (b) An MoE
retains 92–93% of its Q4 score at 2 bits, where the dense substrate
collapsed.</figcaption>
</figure>
<h3>3.2 The 50× swing, and the mechanism</h3>
<div class="tblwrap">
<table>
<caption><b>Table 3.</b> One substrate, four rungs, greedy decode, paired
controls. The two Q2 builds are identical in size and bit width.</caption>
<thead><tr><th>rung</th><th class="num">size</th><th class="num">engram v3</th><th class="num">control v3</th><th class="num">uplift</th></tr></thead>
<tbody>
<tr><td>Q4_K_M</td><td class="num">2.40 GB</td><td class="num">0.722</td><td class="num">0.056</td><td class="num">13×</td></tr>
<tr><td><b>Q2_K, imatrix-calibrated</b></td><td class="num"><b>1.76 GB</b></td><td class="num"><b>0.708</b></td><td class="num">0.111</td><td class="num">6.4×</td></tr>
<tr><td><b>Q2_K, naive</b></td><td class="num"><b>1.76 GB</b></td><td class="num"><b>0.014</b></td><td class="num">0.000</td><td class="num">collapsed</td></tr>
<tr><td>IQ1_M, imatrix-calibrated</td><td class="num">1.27 GB</td><td class="num">0.069</td><td class="num">0.014</td><td class="num">5× on a collapsed base</td></tr>
</tbody>
</table>
</div>
<p>The mechanism is standard tooling, not an invention here.
<code>llama-imatrix</code> runs a calibration corpus through the model and
accumulates, per weight, an importance estimate derived from the expected squared
activation flowing through it — the diagonal of an empirical Hessian/Fisher-type
quantity. <code>llama-quantize --imatrix</code> then allocates bit precision by
that importance: weights the calibration data exercises heavily keep resolution,
weights it rarely touches are squeezed harder.</p>
<p><b>The contribution is the calibration corpus choice.</b> The imatrix was
built from this program's own corpora. A generic calibration set does not know
which weights a given domain depends on. The consequence is practical: if a rung
collapses, the first variable to fix is <em>what you calibrated against</em>,
not the rung.</p>
<h3>3.3 The parity ladder, and the IQ1 verdict</h3>
<p>The deployable artifact is a matched pair <code>(rung, table)</code>, and the
product claim is a curve: composite score stays flat as weights shrink, with the
table growing slightly to compensate. Pre-registered gates: at every rung there
exists a table size scoring within 0.05 of the top-rung reference, and a larger
table never hurts.</p>
<p><code>IQ1_M</code>, calibrated from our own corpora, was measured on both
architecture classes: dense <b>0.069</b>, MoE <b>0.097</b>. Both collapsed. The
compression destroys the <em>polarity</em> capability itself, and the division of
labour in §4 says the table cannot replace the model's reject half. IQ1 + engram
parity with an uncompressed base fails on both classes; <b>the ladder floor is
calibrated 2-bit</b>.</p>
<h3>3.4 MoE quantisation armour</h3>
<p>A 7.9B/A1.3B mixture-of-experts held 92–93% of its Q4 score at 2 bits, where
the dense looped substrate measured 0.014–0.069. Expert redundancy functions as
quantisation armour. This is one measured cell on one instrument, not a general
claim about MoE architectures.</p>
<h3>3.5 Tables are quantisation-immune</h3>
<p>On one trained 1.2B substrate the same fact table scored <b>0.767 at F16 and
0.767 at Q4_K_M — bit-for-bit identical</b> — and retained 70% of its uplift at
Q2_K (0.533, against a 0.383 floor) at one fifth the file size. Facts in a table
survive compression; facts in the weights do not.</p>
<div class="box bad">
<span class="lbl">Published numbers are not admissible references</span>
<p>A model advertised at ~84–85 MMLU scored <b>48.2</b> on this harness. The
gap is protocol, not model: 0-shot letter-loglikelihood here against 5-shot
generative on the full set, an offset of roughly 36 points that cannot be
modelled away. Vendor benchmark numbers are inadmissible as base references on
this harness; base-only runs of our own are the references, and a
generation-based public bench is the cleaner external anchor.</p>
</div>
</section>
<!-- ================================================================= -->
<section>
<h2><span class="n">4</span>The engram: division of labour</h2>
<p class="lead">An engram here is a static, runtime-editable fact table — a few
hundred to a few thousand rows, each with source provenance — whose retrieved
hits are injected into the prompt. No architecture change, no training. The task
splits cleanly into a half only the model can supply and a half a table supplies
better than training can.</p>
<h3>4.1 The decomposition</h3>
<p>Fine-grained grading separates three outcomes on reject-polarity items:
<em>corrected</em> (rejected the premise and stated the true fact),
<em>affirmed</em> (accepted a false premise), and <em>rejected without
content</em> (rejected but could not state the fact). All arms share the same six
retrieval misses, so the residual decomposes cleanly.</p>
<figure>
<div class="figbox"><!--FIG:division-->
<svg viewBox="0 0 760 258" width="100%" role="img" xmlns="http://www.w3.org/2000/svg" style="display:block"><text x="190.0" y="12.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="12" font-weight="700" fill="#1F2933" text-anchor="start">outcome on 60 reject-polarity items, hard bench</text><text x="190.0" y="27.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">every arm shares the same six retrieval misses</text><text x="178.0" y="65.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="normal" fill="#1F2933" text-anchor="end">Qwen3-0.6B dense</text><rect x="190.0" y="46.0" width="46.7" height="26.0" fill="#0F766E" opacity="0.92"/><text x="213.3" y="64.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10.5" font-weight="700" fill="#FFFFFF" text-anchor="middle">7</text><rect x="236.7" y="46.0" width="20.0" height="26.0" 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y="184.0" width="73.3" height="26.0" fill="#B45309" opacity="0.92"/><text x="513.3" y="202.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10.5" font-weight="700" fill="#FFFFFF" text-anchor="middle">11</text><rect x="550.0" y="184.0" width="40.0" height="26.0" fill="#BE123C" opacity="0.92"/><text x="570.0" y="202.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10.5" font-weight="700" fill="#FFFFFF" text-anchor="middle">6</text><text x="602.0" y="202.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10.5" font-weight="normal" fill="#64748B" text-anchor="start">content</text><rect x="190.0" y="246.0" width="11.0" height="11.0" fill="#0F766E" rx="2" opacity="0.92"/><text x="207.0" y="256.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">corrected</text><rect x="292.1" y="246.0" width="11.0" height="11.0" fill="#B45309" rx="2" opacity="0.92"/><text x="309.1" y="256.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">rejected, no content</text><rect x="454.1" y="246.0" width="11.0" height="11.0" fill="#BE123C" rx="2" opacity="0.92"/><text x="471.1" y="256.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">affirmed a false premise</text></svg>
<!--/FIG:division--></div>
<figcaption><b>Figure 5.</b> Outcome decomposition on 60 reject-polarity
items. The failure mode is not one thing: below roughly 2B, models affirm false
premises even when the true fact is supplied, and no amount of additional
facts repairs that.</figcaption>
</figure>
<p><b>Polarity is the model's job.</b> Accept or reject. At 0.6B, 50 of 60
reject items failed this way. Below roughly 2B the model affirms a false premise
even when handed the true fact — a judgement limit, not a knowledge limit.</p>
<p><b>Content is the table's job.</b> What the true fact <em>is</em>. Supply it
and content failures nearly vanish; at 1.2B the model restates an injected fact
89% of the time when it rejects.</p>
<h3>4.2 Uplift, and why its shape matters</h3>
<figure>
<div class="figbox"><!--FIG:uplift-->
<svg viewBox="0 0 760 268" width="100%" role="img" xmlns="http://www.w3.org/2000/svg" style="display:block"><text x="0.0" y="12.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="12" font-weight="700" fill="#1F2933" text-anchor="start">(a) paired uplift across the model ladder</text><text x="0.0" y="27.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">engram ÷ paired control, hard bench</text><line x1="56.0" y1="196.0" x2="350.0" y2="196.0" stroke="#1F2933" stroke-width="1.2"/><line x1="56.0" y1="46.0" x2="56.0" y2="196.0" stroke="#1F2933" stroke-width="1.2"/><rect x="67.8" y="165.2" width="25.5" height="30.8" fill="#64748B" rx="2" opacity="0.9"/><text x="80.5" y="159.2" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#1F2933" text-anchor="middle">3.7×</text><text x="80.5" y="211.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="middle">0.6B</text><rect x="116.8" y="54.3" width="25.5" height="141.7" fill="#0F766E" rx="2" opacity="0.9"/><text x="129.5" y="48.3" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#1F2933" text-anchor="middle">17×</text><text x="129.5" y="211.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="middle">1.2B</text><rect x="165.8" y="136.8" width="25.5" height="59.2" fill="#64748B" rx="2" opacity="0.9"/><text x="178.5" y="130.8" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#1F2933" text-anchor="middle">7.1×</text><text x="178.5" y="211.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="middle">2B</text><rect x="214.8" y="87.7" width="25.5" height="108.3" fill="#64748B" rx="2" opacity="0.9"/><text x="227.5" y="81.7" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#1F2933" text-anchor="middle">13×</text><text x="227.5" y="211.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="middle">loop</text><rect x="263.8" y="153.5" width="25.5" height="42.5" fill="#64748B" rx="2" opacity="0.9"/><text x="276.5" y="147.5" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#1F2933" text-anchor="middle">5.1×</text><text x="276.5" y="211.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="middle">Ling</text><rect x="312.8" y="156.8" width="25.5" height="39.2" fill="#64748B" rx="2" opacity="0.9"/><text x="325.5" y="150.8" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="700" fill="#1F2933" text-anchor="middle">4.7×</text><text x="325.5" y="211.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="middle">8B</text><text x="46.0" y="38.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="normal" fill="#64748B" text-anchor="end">×</text><line x1="52.0" y1="154.3" x2="56.0" y2="154.3" stroke="#1F2933" stroke-width="1"/><text x="48.0" y="158.3" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">5</text><line x1="52.0" y1="112.7" x2="56.0" y2="112.7" stroke="#1F2933" stroke-width="1"/><text x="48.0" y="116.7" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">10</text><line x1="52.0" y1="71.0" x2="56.0" y2="71.0" stroke="#1F2933" stroke-width="1"/><text x="48.0" y="75.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">15</text><text x="203.0" y="230.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="middle">input model size</text><text x="350.0" y="50.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="600" fill="#0F766E" text-anchor="end">peaks mid-ladder, then declines</text><text x="400.0" y="12.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="12" font-weight="700" fill="#1F2933" text-anchor="start">(b) engram-size scaling by architecture class</text><text x="400.0" y="27.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">hard bench, engram condition</text><line x1="440.0" y1="196.0" x2="664.0" y2="196.0" stroke="#1F2933" stroke-width="1.2"/><line x1="440.0" y1="46.0" x2="440.0" y2="196.0" stroke="#1F2933" stroke-width="1.2"/><line x1="436.0" y1="150.3" x2="440.0" y2="150.3" stroke="#1F2933" stroke-width="1"/><text x="432.0" y="154.3" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.4</text><line x1="436.0" y1="113.7" x2="440.0" y2="113.7" stroke="#1F2933" stroke-width="1"/><text x="432.0" y="117.7" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.6</text><line x1="436.0" y1="77.1" x2="440.0" y2="77.1" stroke="#1F2933" stroke-width="1"/><text x="432.0" y="81.1" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.8</text><text x="440.0" y="211.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">310</text><text x="552.0" y="211.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">1K</text><text x="664.0" y="211.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">3K</text><text x="552.0" y="230.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="middle">facts in the table</text><path d="M 440.0 55.7 L 552.0 53.1 L 664.0 53.1" stroke="#1E3A8A" stroke-width="1.8" fill="none" stroke-linejoin="round"/><circle cx="440.0" cy="55.7" r="3.6" fill="#1E3A8A"/><circle cx="552.0" cy="53.1" r="3.6" fill="#1E3A8A"/><circle cx="664.0" cy="53.1" r="3.6" fill="#1E3A8A"/><path d="M 440.0 65.9 L 552.0 58.3 L 664.0 58.3" stroke="#6D28D9" stroke-width="1.8" fill="none" stroke-linejoin="round"/><circle cx="440.0" cy="65.9" r="3.6" fill="#6D28D9"/><circle cx="552.0" cy="58.3" r="3.6" fill="#6D28D9"/><circle cx="664.0" cy="58.3" r="3.6" fill="#6D28D9"/><path d="M 440.0 78.6 L 552.0 73.6 L 664.0 71.1" stroke="#0F766E" stroke-width="1.8" fill="none" stroke-linejoin="round"/><circle cx="440.0" cy="78.6" r="3.6" fill="#0F766E"/><circle cx="552.0" cy="73.6" r="3.6" fill="#0F766E"/><circle cx="664.0" cy="71.1" r="3.6" fill="#0F766E"/><path d="M 440.0 86.2 L 552.0 86.2 L 664.0 86.2" stroke="#64748B" stroke-width="1.8" fill="none" stroke-linejoin="round"/><circle cx="440.0" cy="86.2" r="3.6" fill="#64748B"/><circle cx="552.0" cy="86.2" r="3.6" fill="#64748B"/><circle cx="664.0" cy="86.2" r="3.6" fill="#64748B"/><line x1="672.0" y1="53.0" x2="686.0" y2="53.0" stroke="#1E3A8A" stroke-width="1.8"/><text x="691.0" y="56.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="600" fill="#1E3A8A" text-anchor="start">8B-A1B</text><line x1="672.0" y1="73.0" x2="686.0" y2="73.0" stroke="#6D28D9" stroke-width="1.8"/><text x="691.0" y="76.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="600" fill="#6D28D9" text-anchor="start">Ling</text><line x1="672.0" y1="93.0" x2="686.0" y2="93.0" stroke="#0F766E" stroke-width="1.8"/><text x="691.0" y="96.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="600" fill="#0F766E" text-anchor="start">2B dense</text><line x1="672.0" y1="113.0" x2="686.0" y2="113.0" stroke="#64748B" stroke-width="1.8"/><text x="691.0" y="116.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="600" fill="#64748B" text-anchor="start">loop 3B</text><text x="440.0" y="38.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">v3</text></svg>
<!--/FIG:uplift--></div>
<figcaption><b>Figure 6.</b> (a) Paired uplift across the model ladder peaks
where a model has enough judgement to use a fact and not enough knowledge to
already contain it, then declines as the control floor rises. (b) Engram-size
scaling separates by architecture class: both MoEs saturate near 1,000 facts
while the dense 2B is still rising and the 0.6B is flat.</figcaption>
</figure>
<p>Uplift is defined as the ratio of the engram condition to its paired control.
The first true paired table in the program's history: 3.7× at 0.6B, <b>17× at
1.2B</b>, 7.1× at 2B, 13× on the looped substrate at Q4, 5.1× and 4.7× on the two
MoEs.</p>
<p><b>Uplift is non-monotone.</b> It peaks mid-ladder and declines at the top as
the control floor rises. The declining tail is the first measured support for the
prediction that a substrate carrying knowledge natively has less headroom.</p>
<p>A related result: a gate that decides <em>whether</em> to supply the fact was
falsified on both scales. Always-inject beats gated-inject, because injected
facts help true-premise items too, and withholding costs more than the gate's
reject decision adds.</p>
<h3>4.3 Saturation arrives near a thousand facts</h3>
<p>Growing a table from 310 to 3,000 facts bought +0.02 to +0.04 — a real gain,
not a step change. Gate reads: within-class consistency passed (both MoEs trend
identically), between-class difference passed (MoE saturates at 1,000, dense-2B
still rising, 0.6B flat), and the capacity signature is supported but shallow.
Anti-cheat guard: table growth uses generator-grown, provenance-recorded facts
only, never bench-derived; golds stay frozen and hit@1 is re-measured at every
size.</p>
<h3>4.4 Table quality beats table volume</h3>
<p>Twenty items were authored from the frozen table's corpus facts — its actual
distribution, disjoint from the bench's end-user topics — and committed
<b>before any retrieval probing at all</b>.</p>
<figure>
<div class="figbox"><!--FIG:holdout-->
<svg viewBox="0 0 760 268" width="100%" role="img" xmlns="http://www.w3.org/2000/svg" style="display:block"><text x="0.0" y="12.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="12" font-weight="700" fill="#1F2933" text-anchor="start">(a) blind holdout: the first table was overfitted</text><text x="0.0" y="27.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">offline probe · both tables include the holdout gold rows</text><line x1="56.0" y1="194.0" x2="400.0" y2="194.0" stroke="#1F2933" stroke-width="1.2"/><line x1="56.0" y1="48.0" x2="56.0" y2="194.0" stroke="#1F2933" stroke-width="1.2"/><line x1="52.0" y1="121.0" x2="56.0" y2="121.0" stroke="#1F2933" stroke-width="1"/><text x="48.0" y="125.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">0.5</text><line x1="52.0" y1="48.0" x2="56.0" y2="48.0" stroke="#1F2933" stroke-width="1"/><text x="48.0" y="52.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="end">1.0</text><rect x="83.5" y="65.8" width="51.6" height="128.2" fill="#BE123C" rx="2" opacity="0.9"/><text x="109.3" y="60.8" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="700" fill="#1F2933" text-anchor="middle">0.88</text><rect x="148.9" y="50.9" width="51.6" height="143.1" fill="#0F766E" rx="2" opacity="0.9"/><text x="174.7" y="45.9" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="700" fill="#1F2933" text-anchor="middle">0.98</text><text x="142.0" y="210.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">bench</text><text x="142.0" y="222.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">hit@1</text><rect x="255.5" y="113.7" width="51.6" height="80.3" fill="#BE123C" rx="2" opacity="0.9"/><text x="281.3" y="108.7" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="700" fill="#1F2933" text-anchor="middle">0.55</text><rect x="320.9" y="69.9" width="51.6" height="124.1" fill="#0F766E" rx="2" opacity="0.9"/><text x="346.7" y="64.9" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="700" fill="#1F2933" text-anchor="middle">0.85</text><text x="314.0" y="210.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">holdout</text><text x="314.0" y="222.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">hit@1</text><rect x="56.0" y="240.0" width="10.0" height="10.0" fill="#BE123C" rx="2" opacity="0.9"/><text x="71.0" y="249.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="start">frozen (28,425)</text><rect x="172.0" y="240.0" width="10.0" height="10.0" fill="#0F766E" rx="2" opacity="0.9"/><text x="187.0" y="249.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="start">challenger (2,445)</text><text x="440.0" y="12.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="12" font-weight="700" fill="#1F2933" text-anchor="start">(b) volume against performance</text><text x="440.0" y="27.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">2,445 facts is 8.6% of 28,405</text><text x="440.0" y="58.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="normal" fill="#64748B" text-anchor="start">hand-curated · 28,405 facts</text><rect x="440.0" y="66.0" width="290.0" height="24.0" fill="#BE123C" rx="3" opacity="0.9"/><text x="440.0" y="106.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="11" font-weight="700" fill="#BE123C" text-anchor="start">hit@1 0.55</text><text x="440.0" y="146.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10.5" font-weight="normal" fill="#64748B" text-anchor="start">mechanical hygiene · 2,445 facts</text><rect x="440.0" y="154.0" width="25.0" height="24.0" fill="#0F766E" rx="3" opacity="0.9"/><text x="473.0" y="172.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="11" font-weight="700" fill="#0F766E" text-anchor="start">hit@1 0.85</text><text x="440.0" y="206.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="700" fill="#1F2933" text-anchor="start">≈ 8.6% of the volume</text><text x="440.0" y="224.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11" font-weight="700" fill="#0F766E" text-anchor="start">+0.30 holdout hit@1</text><text x="440.0" y="240.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11" font-weight="700" fill="#0F766E" text-anchor="start">+0.40 holdout v3</text><text x="440.0" y="258.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="start" font-style="italic">every residual miss traced to same-topic near-duplicates</text></svg>
<!--/FIG:holdout--></div>
<figcaption><b>Figure 7.</b> The blind holdout exposed the first table as
overfitted to its bench. Offline retrieval probe; both tables include
the holdout gold rows, so the comparison is like-for-like. A mechanically
filtered table at 8.6% of the volume outperformed it on both benches.</figcaption>
</figure>
<div class="tblwrap">
<table>
<caption><b>Table 4.</b> Retrieval quality, offline probe. Both tables include
the twenty holdout gold rows, so the comparison is like-for-like; hit@1 /
hit@3.</caption>
<thead><tr><th>table</th><th class="num">bench</th><th class="num">holdout</th></tr></thead>
<tbody>
<tr><td>frozen, hand-curated (28,425 rows)</td><td class="num">0.878 / 0.959</td><td class="num">0.550 / 0.750</td></tr>
<tr><td><b>challenger, mechanical (2,445 rows)</b></td><td class="num"><b>0.980 / 1.000</b></td><td class="num"><b>0.850 / 0.900</b></td></tr>
</tbody>
</table>
</div>
<p>Without the holdout rows merged, the frozen table's holdout retrieval
collapsed further — hit@1 <b>0.30</b>, v3 0.50 — so the probe above flatters
it. Every residual miss on the large table traced to same-topic
near-duplicates that the mechanical hygiene pass never admits. Volume was the
disease.</p>
<p>Final gates on the challenger, single 8B-A1B, pool 50, top-k 1, no keyword
tiebreak: bench <b>0.959</b> at the strict stage-1 grader (0.980 on grader
v2), blind holdout <b>0.900</b> (18/20, on-hit conversion 17/17). The 0.9 gate
passes on a single model, on both the original bench and the blind
holdout.</p>
<h3>4.5 Retrieval geometry</h3>
<figure>
<div class="figbox"><!--FIG:retrieval-->
<svg viewBox="0 0 760 218" width="100%" role="img" xmlns="http://www.w3.org/2000/svg" style="display:block"><text x="196.0" y="12.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="12" font-weight="700" fill="#1F2933" text-anchor="start">retrieval hit@1 at 18K facts</text><text x="196.0" y="27.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">three-leg retrieval, measured cumulatively</text><text x="182.0" y="67.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="normal" fill="#1F2933" text-anchor="end">keyword overlap</text><rect x="196.0" y="48.0" width="372.0" height="26.0" fill="#F8FAFC" stroke="#E2E8F0" stroke-width="1" rx="3"/><rect x="196.0" y="48.0" width="182.3" height="26.0" fill="#BE123C" rx="3" opacity="0.92"/><text x="580.0" y="67.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="11.5" font-weight="700" fill="#1F2933" text-anchor="start">0.490</text><text x="182.0" y="115.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="normal" fill="#1F2933" text-anchor="end">+ bge-small embeddings</text><rect x="196.0" y="96.0" width="372.0" height="26.0" fill="#F8FAFC" stroke="#E2E8F0" stroke-width="1" rx="3"/><rect x="196.0" y="96.0" width="280.9" height="26.0" fill="#B45309" rx="3" opacity="0.92"/><text x="580.0" y="115.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="11.5" font-weight="700" fill="#1F2933" text-anchor="start">0.755</text><text x="634.0" y="115.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="11" font-weight="700" fill="#B45309" text-anchor="start">+0.265</text><text x="182.0" y="163.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="normal" fill="#1F2933" text-anchor="end">+ cross-encoder re-rank</text><rect x="196.0" y="144.0" width="372.0" height="26.0" fill="#F8FAFC" stroke="#E2E8F0" stroke-width="1" rx="3"/><rect x="196.0" y="144.0" width="334.1" height="26.0" fill="#0F766E" rx="3" opacity="0.92"/><text x="580.0" y="163.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="11.5" font-weight="700" fill="#1F2933" text-anchor="start">0.898</text><text x="634.0" y="163.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="11" font-weight="700" fill="#0F766E" text-anchor="start">+0.143</text><text x="196.0" y="200.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start" font-style="italic">Embeddings fix conversational collisions; exact-token re-ranking fixes the numeral-differing</text><text x="196.0" y="214.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start" font-style="italic">distractors embeddings cannot separate. A hybrid, not a swap.</text></svg>
<!--/FIG:retrieval--></div>
<figcaption><b>Figure 8.</b> The retrieval ladder at 18K facts. Dense
embeddings fix the conversational-collision problem that kills keyword search
above roughly a thousand facts; exact-token re-ranking fixes the
numeral-differing distractors embeddings cannot separate.</figcaption>
</figure>
<p>Conflict-aware distillation is the named next lever: two facts, same
topic, different numbers — keep the document-pinned one.</p>
<h3>4.6 Cross-vertical transfer</h3>
<p>The formula was run on three verticals, reported on one basis
(stage-1 / grader v2): M365 0.959 / 0.980, SQL Server 0.878 / 0.878,
PowerShell 0.781 / 0.829. On PowerShell the <b>model leg transferred
unchanged</b> — on-hit conversion 0.96–1.00, replicating the M365 result
including on affirm items — while the retrieval leg was bound by table quality
(0.585 hit@1 against M365's 0.898). The gap on a new vertical is a table-quality
problem, not a method problem.</p>
</section>
<!-- ================================================================= -->
<section>
<h2><span class="n">5</span>Interface: where the knowledge enters</h2>
<p class="lead">Giving the model a retrieval tool made it worse than retrieving
before inference — at both scales measured, through three separable failure
modes.</p>
<figure>
<div class="figbox"><!--FIG:leaks-->
<svg viewBox="0 0 760 226" width="100%" role="img" xmlns="http://www.w3.org/2000/svg" style="display:block"><rect x="0.0" y="44.0" width="158.0" height="96.0" fill="#0F766E" rx="6" opacity="0.93"/><text x="79.0" y="86.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="22" font-weight="800" fill="#FFFFFF" text-anchor="middle">1.000</text><text x="79.0" y="108.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="600" fill="#FFFFFF" text-anchor="middle">pre-injection</text><text x="79.0" y="124.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="9.5" font-weight="normal" fill="#FFFFFF" text-anchor="middle" opacity="0.85">on-hit conversion</text><text x="190.0" y="50.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="700" fill="#1F2933" text-anchor="start">1 · initiation</text><text x="190.0" y="66.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">does the model ask?</text><rect x="190.0" y="78.0" width="158.0" height="62.0" fill="#F8FAFC" stroke="#E2E8F0" stroke-width="1" rx="5"/><rect x="190.0" y="78.0" width="158.0" height="62.0" fill="#BE123C" rx="5" opacity="0.1"/><text x="269.0" y="112.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="21" font-weight="800" fill="#BE123C" text-anchor="middle">0.367</text><text x="269.0" y="129.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">8B, unprompted</text><line x1="352.0" y1="109.0" x2="372.0" y2="109.0" stroke="#64748B" stroke-width="1.2"/><path d="M 372 109 l -5 -3 l 0 6 z" stroke="#64748B" stroke-width="0" fill="#64748B" stroke-linejoin="round"/><text x="380.0" y="50.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="700" fill="#1F2933" text-anchor="start">2 · query quality</text><text x="380.0" y="66.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">does the query find it?</text><rect x="380.0" y="78.0" width="158.0" height="62.0" fill="#F8FAFC" stroke="#E2E8F0" stroke-width="1" rx="5"/><rect x="380.0" y="78.0" width="158.0" height="62.0" fill="#BE123C" rx="5" opacity="0.1"/><text x="459.0" y="112.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="21" font-weight="800" fill="#BE123C" text-anchor="middle">0.490</text><text x="459.0" y="129.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">keyword hit@1</text><line x1="542.0" y1="109.0" x2="562.0" y2="109.0" stroke="#64748B" stroke-width="1.2"/><path d="M 562 109 l -5 -3 l 0 6 z" stroke="#64748B" stroke-width="0" fill="#64748B" stroke-linejoin="round"/><text x="570.0" y="50.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11.5" font-weight="700" fill="#1F2933" text-anchor="start">3 · round trip</text><text x="570.0" y="66.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="10" font-weight="normal" fill="#64748B" text-anchor="start">does it convert?</text><rect x="570.0" y="78.0" width="158.0" height="62.0" fill="#F8FAFC" stroke="#E2E8F0" stroke-width="1" rx="5"/><rect x="570.0" y="78.0" width="158.0" height="62.0" fill="#BE123C" rx="5" opacity="0.1"/><text x="649.0" y="112.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="21" font-weight="800" fill="#BE123C" text-anchor="middle">0.722</text><text x="649.0" y="129.0" font-family="'JetBrains Mono', ui-monospace, Consolas, monospace" font-size="9.5" font-weight="normal" fill="#64748B" text-anchor="middle">on-call conversion</text><text x="0.0" y="172.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11" font-weight="normal" fill="#1F2933" text-anchor="start">Three leaks, measured separately and compounding. Pre-injection risks none of them.</text><text x="0.0" y="190.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11" font-weight="normal" fill="#1F2933" text-anchor="start">At 350M the constraint is stage 3, not stage 1: the tool is called on 96–98% of items and the</text><text x="0.0" y="208.0" font-family="Inter, system-ui, 'Segoe UI', sans-serif" font-size="11" font-weight="normal" fill="#1F2933" text-anchor="start">model still affirms the false premise when handed the correct fact.</text></svg>
<!--/FIG:leaks--></div>
<figcaption><b>Figure 9.</b> The three leaks. Pre-injection risks none of
them: by the time the model sees the question, the fact is already in
context.</figcaption>
</figure>
<div class="tblwrap">
<table>
<caption><b>Table 5.</b> Same questions, same grader, same model — all four
arms on one basis.</caption>
<thead><tr><th>arm</th><th class="num">tool-call rate</th><th class="num">on-call conversion</th><th class="num">v3, 8B</th><th class="num">v3, 350M</th></tr></thead>
<tbody>
<tr><td><b>pre-injection</b></td><td class="num">n/a</td><td class="num">1.000 on-hit</td><td class="num"><b>0.939</b></td><td class="num"><b>0.327</b></td></tr>
<tr><td>tool available, model chooses</td><td class="num">36.7%</td><td class="num">0.722</td><td class="num">0.510</td><td class="num">0.265</td></tr>
<tr><td>tool call, model writes the query</td><td class="num">98.0%</td><td class="num">0.625</td><td class="num">0.633</td><td class="num">0.061</td></tr>
</tbody>
</table>
</div>
<p>The three leaks are independent and they compound. <b>Initiation</b>: with the
tool merely available, the 8B calls it on barely a third of items and answers
blind the rest of the way. <b>Query quality</b>: with explicit framing the call
rate reaches 98%, but the model's keyword queries hit the right fact only ~49% of
the time. <b>Round-trip conversion</b>: even when the perfect fact is returned,
conversion through the tool result is 0.722 against 1.000 for pre-injection.</p>
<div class="box bad">
<span class="lbl">The product reading</span>
<p>An MCP surface does not make a small model competent. At 350M the tool is
called on 96–98% of items and conversion is still 0.27 with the perfect fact
handed back — the misses are <em>affirmed</em>. The binding constraint at that
scale is conversion, not access. For a bounded product scope, pre-injection is
strictly better; tool-calling remains interesting only for open-ended retrieval
the engram cannot anticipate.</p>
</div>
<h3>The arithmetic wall</h3>
<p>One-shot multi-row spreadsheet aggregation failed at every scale measured,
including 1.2B with harness arithmetic supplied — asserting 102,000 against
15,834.36. Scale bought document quality, not the composition skill. The product
answer is a deterministic harness that evaluates formulas against a harvested cell
grid and prints exact totals regardless of model state. The measured boundary in
the trained 350M: three rows 1.000, seven rows 0.167.</p>
<!-- ================================================================= -->
<section>
<h2><span class="n">6</span>The artifact</h2>
<p>The deployable object is not a model. It is a triple: a <b>table</b> carrying
the facts with per-row provenance, editable and versioned without retraining and
bit-identical at every rung; a <b>substrate</b> carrying the judgement — accept,
reject, abstain, cite — large enough for the polarity half; and a <b>rung</b>, a
measured choice with a measured cliff, printed on the card next to the win.</p>
<p>Config rules are per-vertical because retrieval geometry is: topic-diverse
corpora want a wide candidate pool with top-1 and no tiebreak; narrow corpora
want a narrow pool with top-3, and measured <em>worse</em> at the wider setting.
The optimisation question changes accordingly — not <em>how small can the model
be</em>, but <em>which half of the problem am I fixing</em>.</p>
</section>
<!-- ================================================================= -->
<section>
<h2><span class="n">7</span>At scale, and where to go next</h2>
<p class="lead">The measurements above were taken at 0.3B–8B on one 6 GB GPU.
This section separates what they <em>predict</em> at scale from what remains
open, and names the experiments the hypothesis most needs. Everything here is
intended as open-source knowledge: the harness is released so each item can be
run, checked, or falsified by someone else.</p>
<h3>7.1 What the dose window predicts for large-model practice</h3>
<p>If windows widen with scale — and P1 is confirmed at only one size pair —
two consequences follow for fine-tuning at scale. First, targeted behavioural
patching should become relatively cheaper as models grow: a pulse-then-re-lock
curriculum sized against a damage ledger, rather than category data mixed into
the base mixture. Second, multi-teacher consolidation should weight anchor
replay by measured per-category damage — the DA-OPD anchor term, equation (3) —
rather than uniformly. Both are extrapolations from the measured interval, not
results.</p>
<h3>7.2 What the calibration result changes at serving scale</h3>
<p>Build the importance matrix from deployment-domain text, not a generic
corpus, and ship quantisation rungs as measured pairs with their table. The
measured rungs: calibrated 2-bit at parity with Q4 at 73% of the size on one
dense substrate, and 92–93% retention at 2 bits on one MoE. If the MoE result
holds across the class, 2-bit MoE serving is roughly a further 40% memory
reduction at near-parity — the cheapest untested capacity lever in this
paper.</p>
<h3>7.3 What the division of labour changes about knowledge management</h3>
<p>Perishable knowledge belongs in tables, not weights: per-vertical tables of
roughly a thousand facts with per-row provenance, refreshed without retraining.
The self-populating pipeline — search, distill a cited fact, answer — measured
0.800 against a 0.000 control on post-cutoff questions, at n = 5: a
demonstration, not a result. Private enterprise knowledge is the axis on which
external tables <em>compose with</em> rather than compete against large
n-gram-table architectures: those tables freeze at pretraining;
runtime-editable tables with provenance are structurally absent from
them.</p>
<h3>7.4 An open agenda</h3>
<p>The experiments this hypothesis most needs, in the order a small team can
run them:</p>
<ol>
<li><b>Scale test.</b> The same pulse / re-lock pair at 7B–14B: two arms
decide whether <code>W_harm</code> keeps widening.</li>
<li><b>Mechanism test.</b> Gradient cosine similarity between category
batches during the pulse — the causal test the correlation matrix in
Figure 3b cannot substitute for.</li>
<li><b>Public replication.</b> The calibration finding on a
generation-based public bench, with the imatrix corpora published.</li>
<li><b>Conflict-aware distillation.</b> The named residual: two facts, same
topic, different numbers — keep the document-pinned one.</li>
<li><b>Multi-seed the headline cells</b> and report paired intervals;
several single-run cells here are point estimates.</li>
<li><b>Instrument mirrors.</b> Publish public versions of the frozen
instruments — fresh items, same generators — so results are reproducible
without contaminating the private sets.</li>
</ol>
<div class="box good">
<span class="lbl">Open source</span>
<p>The evaluation harness, corpus builders, retrieval pipeline, and
command-line tooling described here are released as open source at
<a href="https://github.com/chadstthomas-svg/cowork-cli"
>github.com/chadstthomas-svg/cowork-cli</a>, together with the
frozen-instrument generators. Licenses: code Apache-2.0; catalog sources
CC-BY-4.0; NLI grader MIT; training corpus under the Tablinum Dataset
License v1.0. Every number recomputes from a committed run record — the
intent is that you can check, and falsify.</p>
</div>
</section>
<!-- ================================================================= -->
<!-- ================================================================= -->
<section>
<h2><span class="n">8</span>Method rules this program adopted</h2>
<ol>
<li><b>Freeze instruments before training.</b> A published evaluation set
becomes a training set.</li>
<li><b>Run a shortcut check on every new instrument.</b> A trivial baseline
above 0.90 means the instrument measures the shortcut.</li>
<li><b>Pair every condition with a control.</b> An uplift without a baseline is
not a result.</li>
<li><b>Report per-polarity.</b> Reject and affirm are never blended.</li>
<li><b>Structure-true testing.</b> No pattern crosses an architecture class
without its own cell; a cross-structure pattern may reflect the corpus rather
than the architecture.</li>
<li><b>A custom grader is a hypothesis until probed.</b> Grade the grader.</li>
<li><b>Read the generations, not the exit codes.</b></li>
<li><b>Smoke gates check speed, not just completion.</b> A gate that passed at
150 s/step implied a 47-hour run.</li>
<li><b>Within-server comparisons are robust; absolute values across server
restarts are not.</b> Ship the comparison, annotate the absolute.</li>
<li><b>State the failure mode next to the win.</b></li>
</ol>
</section>
<!-- ================================================================= -->
<section>
<h2><span class="n">9</span>What remains unestablished</h2>
<ul>
<li><b>Production-scale quality assurance.</b> Whether a ≥2B substrate with a
fixed table clears 0.9 on genuinely real-world questions is predicted, not
measured. The deciding cell has not run.</li>
<li><b>Below calibrated 2-bit.</b> The cliff is measured on two architecture
classes; whether some class has cheaper redundancy is untested.</li>
<li><b>Domain generality.</b> One successful transfer on the model leg is a
data point. The method's behaviour on a domain with different retrieval
geometry is unknown.</li>
<li><b>Conflict.</b> The named residual — two facts, same topic, different
numbers — has no measured solution. Conflict-aware distillation is a
proposal.</li>
<li><b>Cross-lineage anchoring.</b> Same-initialisation self-anchoring is
measured; anchoring a student to a different lineage's checkpoint is not.</li>
<li><b>The causal reading of the interference matrix.</b> The correlation
structure in Figure 3b is descriptive across eight sequentially selected runs.
Gradient-level measurement is the named test and has not been run.</li>
</ul>
</section>
<footer>
<p><span class="mark">TABLINUM</span></p>
<p>Every number here recomputes from a committed run record. Instruments are
frozen; controls are paired. Code and harness are open source; this paper
is intended to be reused, extended, and falsified.</p>
</footer>
</div>
</body>
</html>