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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Andrey Pluzhnik — independent research</title>
<meta name="description" content="Independent verification of machine-learned physics. Instruments, audits, honest failures.">
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<body>
<div class="col">
<header>
<div class="eyebrow">Independent researcher · verification of AI-derived science</div>
<h1>Andrey Pluzhnik</h1>
<p class="lede">I build instruments that check what machine learning claims about physics —
and publish the measurements, the calibration floors, and the failed runs alongside the
successes. Work produced with an AI agent under one hard rule: the agent never gets to mark
its own work as verified.</p>
<div class="idline">
<span>ORCID <a href="https://orcid.org/0009-0005-5660-2603">0009-0005-5660-2603</a></span>
<span>GitHub <a href="https://github.com/AndreiPLK">@AndreiPLK</a></span>
<span>Zenodo <a href="https://zenodo.org/records/21915627">archive</a></span>
</div>
</header>
<hr class="hair">
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<div class="layout">
<aside class="side">
<div class="eyebrow" style="font-size:10.5px">Status · 3 Sep 2026</div>
<p class="sfacts"><b>6 works</b>, newest released today<br>
<b>the 4/5 floor under Newton's inequality</b> — proved in full, sharp<br>
<b>Sibuya's 1988 conjecture</b> — proved over most of its range, one corner open and named<br>
<b>two adversarial reviews</b> on release day; one derivation repaired, reports published<br>
<b>4,705</b> certified grid steps, worst margin 1.9×10<sup>−10</sup><br>
<b>every failed route</b> kept with its reason</p>
<a class="sthumb" href="works/newton-excess/">
<img src="assets/newton-floor-3d.png" alt="The floor 4/5 under the Newton excess" style="background:#fff">
<span>The new result as terrain: the excess surface over every case, and the floor
4/5 beneath it. The lowest ridge settles onto the floor only at infinity.</span>
</a>
<a class="sthumb" href="works/lab-note-2026-08-17/index.html">
<img src="works/lab-note-2026-08-17/whole-story.png" alt="The shore of gravity">
<span>The programme on one terrain: the floor is allowed gravity, the wall is
forbidden, the string stands exactly on the edge at 23 dimensions.</span>
</a>
<a class="sthumb" href="works/lab-note-2026-08-17/index.html">
<img src="works/lab-note-2026-08-17/almost-positive.png" alt="Almost positive">
<span>Where the proof is stuck: one big positive hump, dipping under zero by
two ten-thousandths. A loop with no dip proves the theorem.</span>
</a>
<p class="sfacts" style="border-top:1px solid var(--rule);padding-top:10px">
<b>Open:</b> one corner of Sibuya's conjecture, where the two sides of the inequality
agree to leading order. Not more computing — a new idea. The exact shape of the
obstruction is written down in the package.</p>
<p class="sfacts"><a href="works/lab-note-2026-08-17/index.html">Full lab note,
including every error caught →</a></p>
</aside>
<main style="display:flex;flex-direction:column;gap:40px;min-width:0">
<section style="display:flex;flex-direction:column;gap:22px;">
<h2 style="font-size:clamp(22px,2.4vw,30px);margin:0 0 4px">Published work</h2>
<article class="card">
<div class="body">
<span class="kind">preprint + machine-checked proof · 2026-09-03</span>
<h2><a href="works/newton-excess/">A floor under Newton's inequality: four fifths, never less</a></h2>
<p>Newton said the staircase never has a dent; he never said by how much. For the list
of numbers that decides whether a deformed string amplitude stays physical, the margin
is exactly 4/5 — sharp, for every case, proved in five machine-checked pieces. And a
1988 conjecture nobody had cited in thirty-eight years, proved over most of its range,
with the open corner stated honestly. Two adversarial reviews on release day; one
derivation caught and repaired, both reports in the package.</p>
<div class="facts">
<span>2026-09</span>
<span>MIT</span>
<span>627-rung ladder + 3 certificates, each independently validated</span>
<span>Sibuya 1988: j ≤ 1000, θ ≤ 0.9, ≤ 802 missing</span>
</div>
<div class="links">
<a class="btn primary" href="works/newton-excess/">Read the one-pager</a>
<a class="btn" href="https://github.com/AndreiPLK/newton-excess/blob/main/ARTICLE.md">Article</a>
<a class="btn" href="https://github.com/AndreiPLK/newton-excess">Code, logs & reviews</a>
<a class="btn" href="https://doi.org/10.5281/zenodo.22282840">DOI</a>
</div>
</div>
<a class="pic" href="works/newton-excess/" aria-label="Open the one-pager">
<img src="assets/newton-floor-3d.png"
alt="The Newton excess surface over the (n,t) plane with the floor 4/5 drawn beneath it; the surface never dips through.">
</a>
</article>
<article class="card">
<div class="body">
<span class="kind">lab note · 2026-08-17</span>
<h2><a href="works/lab-note-2026-08-17/index.html">One day of being wrong productively</a></h2>
<p>The problem shrank tenfold, five of my own errors were caught before they left the
building — one looked briefly like the collapse of the main theorem — and by
evening the exact missing mathematics had a name. Unpolished on purpose.</p>
<div class="facts"><span>28 hypotheses killed</span><span>1,634 certified cells</span><span>227,040 exact checks</span></div>
<div class="links"><a class="btn primary" href="works/lab-note-2026-08-17/index.html">Read the note</a></div>
</div>
<div class="pic"><img src="works/lab-note-2026-08-17/almost-positive.png" alt="Almost positive"></div>
</article>
<article class="card">
<div class="body">
<span class="kind">preprint + machine-checked proof</span>
<h2><a href="works/qg-blade-theorem/">Checking is not knowing: the blades, proved</a></h2>
<p>Sequel to the master formula. What three million exact checks suggested is
now a theorem: no kill-window of the second knife ever cuts below the shore
— even though at infinity the fleet of blades sails exactly tangent to
it. 1,047 certificates, two independent provers, and one real bug caught by
adversarial review, fixed, and told in the paper.</p>
<div class="facts">
<span>2026-08</span>
<span>MIT + CC BY 4.0</span>
<span>1,047 certificate cells, both provers exit 0</span>
<span>exact tangency at ρ=1+1/√3</span>
</div>
<div class="links">
<a class="btn primary" href="works/qg-blade-theorem/">Read the one-pager</a>
<a class="btn" href="works/qg-blade-theorem/paper.pdf">Paper (PDF)</a>
<a class="btn" href="https://github.com/AndreiPLK/qg-blade-theorem">Code & data</a>
</div>
</div>
<a class="pic" href="works/qg-blade-theorem/" aria-label="Open the one-pager">
<img src="assets/tangent-fleet.png"
alt="The blade cone touching the shore line at exactly one tangency point, with the window zone ending strictly before it.">
</a>
</article>
<article class="card">
<div class="body">
<span class="kind">counterexample + dependency-free check</span>
<h2><a href="https://github.com/AndreiPLK/rlc-selfconvolution-counterexample">A statement with strong numerical support turns out to be false</a></h2>
<p>Some sequences are log-concave: each term beats the geometric mean of its
neighbours. A stronger property asks the same of the sequence of <em>ratios</em>.
The question was whether that survives a particular averaging. It does not —
five numbers break it, twice, well inside the range in question. The margin is
written out as an exact fraction, so the refutation is checkable by hand.</p>
<div class="facts">
<span>2026-09</span>
<span>MIT + CC BY 4.0</span>
<span>48 of 193 inputs break it</span>
<span>verified four independent ways</span>
</div>
<div class="links">
<a class="btn primary" href="https://github.com/AndreiPLK/rlc-selfconvolution-counterexample">Read the note</a>
<a class="btn" href="https://github.com/AndreiPLK/rlc-selfconvolution-counterexample/releases/tag/v1.0.0">Release v1.0.0</a>
<a class="btn" href="https://github.com/AndreiPLK/rlc-selfconvolution-counterexample/blob/master/verify.py">Check it yourself</a>
</div>
</div>
<a class="pic" href="https://github.com/AndreiPLK/rlc-selfconvolution-counterexample" aria-label="Open the note">
<img src="assets/rlc-counterexample.png"
alt="Two overlapping histograms of how far apart the inputs are spread: the cases where the statement holds and the cases where it fails overlap almost entirely, so spread alone does not explain the failures.">
</a>
</article>
<article class="card">
<div class="body">
<span class="kind">preprint + exact-arithmetic code</span>
<h2><a href="works/qg-master-formula/">Every way gravity can fail, in one formula</a></h2>
<p>Sequel to the shore paper. One closed formula gives the sign of every
Regge-trajectory partial wave of the CHR graviton family; each extra
constraint turns out to cut a finite “window” of dimensions that
floats strictly above the shore. Derived, adversarially reviewed, and checked
on 3,053,832 exact points: not one cut into the allowed region.</p>
<div class="facts">
<span>2026-08</span>
<span>MIT + CC BY 4.0</span>
<span>3,053,832 exact verdicts, 0 hits</span>
<span>independently re-derived theorem</span>
</div>
<div class="links">
<a class="btn primary" href="works/qg-master-formula/">Read the one-pager</a>
<a class="btn" href="works/qg-master-formula/paper.pdf">Paper (PDF)</a>
<a class="btn" href="https://github.com/AndreiPLK/qg-master-formula">Code & data</a>
</div>
</div>
<a class="pic" href="works/qg-master-formula/" aria-label="Open the one-pager">
<img src="assets/knives-above-shore.png"
alt="Blade-shaped kill windows floating strictly above the cyan shore line dividing living land from dead land; the string sits on the shore at D=23.">
</a>
</article>
<article class="card">
<div class="body">
<span class="kind">preprint + exact-arithmetic code</span>
<h2><a href="works/qg-gravity-shore/">The shore of closed-string gravity</a></h2>
<p>Graviton amplitudes containing textbook string theory are killed, as spacetime
dimensions grow, by one quantum rule: probabilities can never be negative. This work
derives the killing boundary as a formula. It switches on at 9 dimensions, passes
exactly through the string at 23, and straightens onto D = (12+4√3)λ.
In our own four dimensions, nothing in the family dies at all.</p>
<div class="facts">
<span>2026-08</span>
<span>MIT + CC BY 4.0</span>
<span>494/494 exact verdicts, 0 alarms</span>
<span>independently re-derived theorem</span>
</div>
<div class="links">
<a class="btn primary" href="works/qg-gravity-shore/">Read the one-pager</a>
<a class="btn" href="works/qg-gravity-shore/paper.pdf">Paper (PDF)</a>
<a class="btn" href="https://github.com/AndreiPLK/qg-gravity-shore">Code & data</a>
</div>
</div>
<a class="pic" href="works/qg-gravity-shore/" aria-label="Open the one-pager">
<img src="assets/gravity-cliff-3d.png"
alt="3D landscape: cyan plateau of surviving gravity candidates, a cliff wall falling along the derived formula, and the string walking the plateau to the cliff edge at D=23.">
</a>
</article>
<article class="card">
<div class="body">
<span class="kind">preprint + exact-arithmetic code</span>
<h2><a href="works/qg-island-edges/">The island of string theories has edges</a></h2>
<p>The allowed island of Veneziano-type string amplitudes was known only as a
computer scan. This work derives its boundary in closed form: an exclusion edge
valid in every dimension, explicit curves for the rest, and a clock for how fast
q > 1 deformations die. 11,994 exact verdicts, zero unexplained
mismatches; adversarially reviewed; matches a rival method where they overlap.</p>
<div class="facts">
<span>2026-08</span>
<span>MIT + CC BY 4.0</span>
<span>from-scratch validation: PASS 5/5</span>
<span>DOI 10.5281/zenodo.21934462</span>
</div>
<div class="links">
<a class="btn primary" href="works/qg-island-edges/">Read the one-pager</a>
<a class="btn" href="works/qg-island-edges/paper.pdf">Paper (PDF)</a>
<a class="btn" href="https://github.com/AndreiPLK/qg-island-edges">Code & data</a>
</div>
</div>
<a class="pic" href="works/qg-island-edges/" aria-label="Open the one-pager">
<img src="assets/qg-island-atlas.png"
alt="Seven positivity islands for seven mass shifts, each with the same analytic exclusion edge overlaid.">
</a>
</article>
<article class="card">
<div class="body">
<span class="kind">software + reproducibility study</span>
<h2><a href="works/spacetime-verifier/">Checking an AI's black holes</a></h2>
<p>An independent curvature evaluator for machine-learned spacetimes, and the first
audit run with it: five retrainings of a published neural black-hole configuration.
The exotic geometry reproduced five times out of five; the Einstein equation itself
held in two of five — and the model's own loss could not tell the difference.</p>
<div class="facts">
<span>2026-08</span>
<span>DOI 10.5281/zenodo.21915627</span>
<span>MIT</span>
<span>20 known-answer tests, CI on Linux/Windows</span>
</div>
<div class="links">
<a class="btn primary" href="works/spacetime-verifier/">Read the one-pager</a>
<a class="btn" href="works/spacetime-verifier/note.pdf">Technical note (PDF)</a>
<a class="btn" href="https://github.com/AndreiPLK/spacetime-verifier">Code & data</a>
<a class="btn" href="https://doi.org/10.5281/zenodo.21915627">DOI</a>
<a class="btn" href="https://github.com/AndreiPLK/spacetime-verifier/blob/main/docs/RELEASE_REPORT.md">Full audit report</a>
</div>
</div>
<a class="pic" href="works/spacetime-verifier/" aria-label="Open the one-pager">
<img src="assets/seed-variability.png"
alt="Bar chart: five training runs of the same configuration; two pass the pre-frozen vacuum limit, three fail, while their training losses barely differ.">
</a>
</article>
</section>
<section class="soon">
<div class="eyebrow">In progress</div>
<h2>How did the universe grow its first supermassive black holes?</h2>
<p>JWST sees billion-solar-mass black holes less than a billion years after the Big Bang —
seemingly too big, too early. Next up: an open, honestly-calibrated testbed that runs every
proposed growth channel through one instrument and checks them against the public JWST
catalogues. Small papers, published as they land.</p>
<p style="margin:0;font-family:var(--data);font-size:12px;">Also queued: JOSS submission of
the verifier (eligible 2027-02, after six months of public history — their rule, a fair one).</p>
</section>
<hr class="hair">
<p class="foot">Everything here traces to files with recorded SHA-256 checksums, failed runs
included. AI involvement is disclosed in full in each repository. andypluzhnik@gmail.com</p>
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