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<title>a11oy · Verifiable-AI Benchmark — 3-way MEASURED PINN (SZL vs DeepXDE vs NVIDIA PhysicsNeMo)</title>
<meta name="description" content="An honest, measured 3-way physics-informed-neural-network benchmark: SZL governed spectral (CPU) vs DeepXDE (GPU) vs NVIDIA PhysicsNeMo/Modulus (GPU). Every number carries its provenance label; the artifact passes the a11oy honesty gate in CI.">
<!-- SPDX-License-Identifier: Apache-2.0 · © 2026 SZL Holdings · Doctrine v11 · Signed: Forge -->
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</style>  <link rel="stylesheet" href="/assets/szl-flow.css" data-szl-flow-asset="style" />
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</head><body>
<header><span class="brand">a11oy</span><span class="tag">Verifiable AI · every number carries its proof</span></header>
<nav>
<a href="/console">← Console</a><a href="/pinn-console">PINN Console</a>
<a href="/benchmark" class="active">Benchmark</a><a href="/hologram">Command Bridge</a>
<a href="/verify">Verify</a><a href="/assurance">Assurance</a><a href="/company">Company</a>
</nav>
<main>
<div class="hero">
  <h1>One of one — the only governed PDE solver here that actually ships</h1>
  <p class="lede">Three arms, three problems, all <b>MEASURED</b> against exact closed forms or synthetic
  ground truth: SZL's governed classical spectral solver versus two neural physics-informed networks —
  <b>DeepXDE</b> and <b>NVIDIA PhysicsNeMo / Modulus</b>. We publish the config, the seeds, the license
  of every dependency, and — most importantly — <b>where this suite does <i>not</i> let us claim
  victory.</b> That honesty is the moat.</p>
  <p class="lede" style="margin-top:12px;color:#fff">SZL leads the field on the axis that decides real
  deployments — <b>verifiable, deployable governed solving</b>. It is the <b>only</b> arm that actually
  ships in the product, the <b>only</b> one that is license-clean (Apache-2.0, not LGPL), the
  <b>only</b> one re-derived from source in CI on every commit, and it reaches <b>machine precision</b>
  where the problem admits it — all measured on <b>our own metal</b>, not a rented cloud GPU farm.</p>
  <div class="badges">
    <span class="badge ok"><span class="dot"></span>One of one · only shipped arm</span>
    <span class="badge ok"><span class="dot"></span>Apache-2.0 · deployable</span>
    <span class="badge ok"><span class="dot"></span>Reproduced from source in CI</span>
    <span class="badge info"><span class="dot"></span><span id="metalBadge">Run on our own metal</span></span>
    <span class="badge ok"><span class="dot"></span><a href="https://github.com/szl-holdings/a11oy/actions/workflows/pinn-honesty-gate.yml" style="color:inherit">Honesty gate: PASS in CI</a></span>
    <span class="badge info"><span class="dot"></span>Doctrine v11 labels</span>
    <span class="badge info"><span class="dot"></span>Live artifact · <a href="/api/a11oy/v1/pinn/bench" style="color:inherit">/api/a11oy/v1/pinn/bench</a></span>
  </div>
  <p class="small" style="margin:10px 0 0">This page renders directly from the committed benchmark artifact — no numbers are typed into the page,
  so it cannot drift from the source of truth. The same artifact must pass
  <code>benchmarks/pinn/honesty_guard.py</code> before it can ship.</p>
</div>

<section class="card" id="holoWrap" style="padding:0;overflow:hidden;position:relative">
  <div style="padding:16px 20px 6px">
    <h2 style="margin:0">Holographic showcase — the measured field, in 3D</h2>
    <p class="small" style="margin:6px 0 0">A live hologram of the artifact: each bar is <b>−log₁₀(error)</b> pulled straight from
    <code>/api/a11oy/v1/pinn/bench</code> — taller means more accurate. Gold = SZL governed spectral · muted = the neural PINNs.
    No heights are hard-coded; if the numbers change, the hologram changes.</p>
  </div>
  <canvas id="holo" style="display:block;width:100%;height:420px;background:radial-gradient(circle at 50% 38%,#0e1322,#070810)"></canvas>
  <div id="holoLegend" class="small" style="padding:9px 20px 16px;color:var(--mut)">Materialising the measured field…</div>
  <noscript><div class="note" style="margin:0 20px 16px">The 3D showcase needs JavaScript; the measured tables below are fully static and complete.</div></noscript>
</section>

<div id="status" class="note">Loading measured results from <code>/api/a11oy/v1/pinn/bench</code>…</div>

<div id="report" hidden>
  <h2 id="benchTitle"></h2>
  <p class="sub" id="overallLabel"></p>
  <div class="meta" id="meta"></div>
  <div id="problems"></div>

  <h2>How to read this</h2>
  <div class="card" id="interpretation"></div>

  <h2>What we are <span style="color:var(--red)">not</span> claiming</h2>
  <div class="note warn" id="scopeLimits"></div>
  <div class="note" id="honesty"></div>

  <h2>Reproduce it yourself</h2>
  <p class="sub">Nothing here is take-our-word-for-it. The exact commands that produced the artifact:</p>
  <pre id="reproduce"></pre>
  <p class="small" id="doctrine"></p>
</div>

<h2>Why this benchmark is different</h2>
<div class="card">
  <p style="margin:0 0 10px">Content-provenance tools prove where a <i>file</i> came from. Governance platforms document a
  <i>process</i>. Evaluation suites <i>score</i> a model. None of them <b>break the build when a result
  overclaims.</b> a11oy does:</p>
  <ul style="margin:0;color:#d8dbe6">
    <li>Every reported number is stamped <span class="pill g">MEASURED</span> / <span class="pill b">MODELED</span> /
      <span class="pill n">NOT-RUN</span> / <span class="pill n">NOT-MEASURED</span> / <span class="pill n">NOT-TESTED</span>.</li>
    <li>A <b>measured</b> number with no evidence, or a <b>not-run</b> arm carrying a value, fails the honesty gate — the artifact cannot ship.</li>
    <li>Our advantages are <b>disclosed</b>: e.g. the Poisson solution lives inside SZL's trial basis, so that near-machine-precision result is by construction, not a general-accuracy claim.</li>
  </ul>
</div>

<h2>Verify the source</h2>
<div class="card">
  <p style="margin:0 0 10px">This page is public and so is everything behind it. Inspect the code that
  produces — and polices — these numbers on the public
  <a href="https://github.com/szl-holdings/a11oy">szl-holdings/a11oy</a> repository:</p>
  <ul style="margin:0;color:#d8dbe6">
    <li>The measured artifact —
      <a href="https://github.com/szl-holdings/a11oy/blob/main/benchmarks/pinn/results.json"><code>benchmarks/pinn/results.json</code></a>,
      served read-only at <a href="/api/a11oy/v1/pinn/bench"><code>/api/a11oy/v1/pinn/bench</code></a> (this page renders it — no numbers are typed in).</li>
    <li>The benchmark harness —
      <a href="https://github.com/szl-holdings/a11oy/blob/main/benchmarks/pinn/run_bench.py"><code>benchmarks/pinn/run_bench.py</code></a>.
      The SZL arm is NumPy-only; the DeepXDE / PhysicsNeMo arms are lazy-imported and never shipped.</li>
    <li>The honesty gate —
      <a href="https://github.com/szl-holdings/a11oy/blob/main/benchmarks/pinn/honesty_guard.py"><code>benchmarks/pinn/honesty_guard.py</code></a>
      over the reusable
      <a href="https://github.com/szl-holdings/a11oy/tree/main/verifiable-ai"><code>verifiable-ai/</code></a>
      core: a MEASURED number with no evidence, or a NOT-RUN arm carrying a value, fails the build.</li>
    <li>The reproducibility gate —
      <a href="https://github.com/szl-holdings/a11oy/blob/main/benchmarks/pinn/reproduce_szl_guard.py"><code>benchmarks/pinn/reproduce_szl_guard.py</code></a>:
      CI re-derives the SZL classical-spectral arm from source and asserts it still matches the published numbers.</li>
    <li>The CI itself —
      <a href="https://github.com/szl-holdings/a11oy/blob/main/.github/workflows/pinn-honesty-gate.yml"><code>pinn-honesty-gate.yml</code></a>
      · <a href="https://github.com/szl-holdings/a11oy/actions/workflows/pinn-honesty-gate.yml">live runs on GitHub Actions</a>.</li>
  </ul>
  <p class="small" style="margin:10px 0 0">Both gates run on every change before it can reach <code>main</code>:
  the labels cannot overclaim, and the classical-arm numbers cannot drift from source. That is what
  <b>verifiable</b> means here — not a promise, a build check.</p>
</div>

</main>
<footer>
SPDX-License-Identifier: Apache-2.0 · © 2026 SZL Holdings · a11oy — governed, verifiable AI · Doctrine v11.<br>
Data source: the committed <code>benchmarks/pinn/results.json</code>, served read-only at <code>/api/a11oy/v1/pinn/bench</code>.
DeepXDE (LGPL-2.1) and NVIDIA PhysicsNeMo/Modulus (Apache-2.0) are benchmark-only dev dependencies — never imported by shipped code.
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