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<title>Materials — Verifiable Alloy &amp; Crystal Discovery · SZL Holdings</title>
<meta name="description" content="Materials (Quechua 'Q'allariy' — the beginning/first): a live, honest, verifiable alloy &amp; crystal discovery surface. Signed crystal novelty certificate (isometry-invariant PDD fingerprint), PAC-Bayes generalization certificate, and Immune dual-use screening — each verdict signed into the shared Khipu chain. Honest labels: PDD injectivity = ROADMAP; McAllester Lean proof = SORRY; Lambda = Conjecture 1; Khipu = Conjecture 2; Neyman-Pearson immune gate = proven-backing; trust never 100%; locked-8 @ c7c0ba17."/>
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<div class="topbar">
  <span>SZL HOLDINGS</span><span class="sep">/</span><span>a11oy</span>
  <span class="live"><span class="live-dot"></span><span id="liveTag">MATERIALS · LIVE</span></span>
  <span class="switcher">
    <a class="flag active" href="/materials">Materials</a>
    <a class="flag" href="/immune">Immune</a>
    <a class="flag" href="/energy">Energy</a>
    <a class="flag" href="/fleet-c2">Fleet C2</a>
    <a class="flag" href="/living-anatomy">Living Anatomy</a>
    <a class="flag" href="/code">Code</a>
  </span>
</div>

<div class="wrap">
  <h1>Materials — Verifiable Alloy &amp; Crystal Discovery<span class="badge" id="organBadge">Q'allariy · the beginning · Khipu-signed</span></h1>
  <p class="lede">
    <b>Materials</b> (Quechua <b>Q'allariy</b> — "the first") is SZL's verifiable
    alloy &amp; crystal discovery surface. The field competes on <b>accuracy</b>; SZL competes on
    <b>verifiability</b> — every verdict below is a <b>real endpoint call</b> signed into the
    <b>shared Khipu chain</b>, re-verifiable by any judge. Three live capabilities:
    a signed <b>crystal novelty certificate</b> (isometry-invariant PDD fingerprint, answering the GNoME
    duplicate scandal), a <b>PAC-Bayes generalization certificate</b>, and <b>Immune dual-use screening</b>.
    Honest labels throughout: PDD injectivity = <b>ROADMAP</b>; McAllester Lean proof = <b>SORRY</b>;
    &Lambda; = <b>Conjecture&nbsp;1</b>; Khipu = <b>Conjecture&nbsp;2</b>; Neyman&ndash;Pearson immune gate =
    <b>proven-backing</b>. Locked-proven set unchanged at EXACTLY 8 @ kernel <code>c7c0ba17</code>;
    trust is never 100%; effectors simulated; no fabricated data.
  </p>

  <div class="cards">
    <div class="card"><div class="lbl">Novelty registry</div><div class="big" id="cRegistry">—</div><div class="sub" id="cRegistrySub">fingerprints registered</div></div>
    <div class="card"><div class="lbl">Khipu chain depth</div><div class="big" id="cChain">—</div><div class="sub" id="cChainSub">verified</div></div>
    <div class="card"><div class="lbl">PAC-Bayes</div><div class="big" id="cCertify">—</div><div class="sub">/certify endpoint</div></div>
    <div class="card"><div class="lbl">Immune screen</div><div class="big" id="cScreen">—</div><div class="sub">/screen endpoint</div></div>
  </div>

  <!-- PANEL 1 — Crystal Novelty -->
  <div class="panel">
    <h2>1 · Crystal Novelty Certificate <span class="meta" id="novEp">POST /api/a11oy/v1/materials/novelty</span></h2>
    <p class="lede" style="margin:.2rem 0 .6rem;font-size:.86rem;">
      Submit a crystal (lattice <code>a,b,c,&alpha;,&beta;,&gamma;</code> in &Aring;/degrees + fractional atom
      sites). The endpoint computes an <b>isometry-invariant Pointwise-Distance-Distribution fingerprint</b>
      (Widdowson&ndash;Kurlin PDD), compares it against an append-only registry, and signs a Khipu receipt
      (<code>SZL.Materials.NoveltyCert.v1</code>). Prefilled with the <b>Al-FCC</b> example.
      <span class="roadmap">Fingerprint INJECTIVITY is ROADMAP / CONJECTURE</span> — not proven.
    </p>
    <div>
      <span class="preset" data-p="al-fcc">Al-FCC (a=4.05)</span>
      <span class="preset" data-p="cu-fcc">Cu-FCC (a=3.61)</span>
      <span class="preset" data-p="nacl">NaCl rock-salt (a=5.64)</span>
      <span class="preset" data-p="fe-bcc">Fe-BCC (a=2.87)</span>
    </div>
    <div class="lattice-grid">
      <div><label>a (&Aring;)</label><input id="latA" value="4.05"/></div>
      <div><label>b (&Aring;)</label><input id="latB" value="4.05"/></div>
      <div><label>c (&Aring;)</label><input id="latC" value="4.05"/></div>
      <div><label>&alpha; (&deg;)</label><input id="latAl" value="90"/></div>
      <div><label>&beta; (&deg;)</label><input id="latBe" value="90"/></div>
      <div><label>&gamma; (&deg;)</label><input id="latGa" value="90"/></div>
    </div>
    <div class="fullrow">
      <label>atom sites — JSON array of {el,x,y,z} (fractional)</label>
      <textarea id="sitesInput" rows="3">[{"el":"Al","x":0,"y":0,"z":0}]</textarea>
    </div>
    <button class="run" id="runNov">Certify novelty &rarr;</button>
    <div id="novOut"></div>
  </div>

  <div class="grid2">
    <!-- PANEL 2 — PAC-Bayes -->
    <div class="panel">
      <h2>2 · PAC-Bayes Certificate <span class="meta" id="certEp">POST /api/a11oy/v1/materials/certify</span></h2>
      <p class="lede" style="margin:.2rem 0 .6rem;font-size:.86rem;">
        Compute the <b>McAllester PAC-Bayes bound</b> "with prob &ge; 1&minus;&delta;, population risk &le; bound"
        + a signed certificate. The bound <b>computation is exact</b>; the
        <span class="roadmap">McAllester Lean proof is a tracked SORRY</span> (proven-on-paper) —
        <code>Lutar/Materials/PACBayesMaterials.lean</code>.
      </p>
      <div>
        <span class="preset" data-c="alloy">alloy-regression preset</span>
        <span class="preset" data-c="tight">tight (large n)</span>
        <span class="preset" data-c="loose">loose (small n)</span>
      </div>
      <div class="fieldrow">
        <div><label>empirical_risk</label><input id="cRisk" value="0.08"/></div>
        <div><label>kl divergence</label><input id="cKl" value="2.0"/></div>
        <div><label>n (sample size)</label><input id="cN" value="5000"/></div>
        <div><label>delta</label><input id="cDelta" value="0.05"/></div>
      </div>
      <button class="run" id="runCert">Certify bound &rarr;</button>
      <div id="certOut"></div>
    </div>

    <!-- PANEL 3 — Immune Screen -->
    <div class="panel">
      <h2>3 · Immune Screen <span class="meta" id="scrEp">POST /api/a11oy/v1/materials/screen</span></h2>
      <p class="lede" style="margin:.2rem 0 .6rem;font-size:.86rem;">
        Screen a materials-inference input through the <b>Neyman&ndash;Pearson-optimal, fail-closed Immune gate</b>
        (dual-use / safety). Returns <b>allow / deny</b> + signals + a signed receipt. Falls back to
        <code>/api/a11oy/v1/immune/verdict</code> if <code>/screen</code> is not yet live.
        <span class="proven">Immune gate Lean backing is PROVEN</span> (not folded into locked-8).
      </p>
      <div>
        <span class="preset" data-s='{"action":{"cmd":"synthesize Al-Cu alloy at 600C"}}'>benign synthesis</span>
        <span class="preset" data-s='{"action":{"cmd":"rm -rf /"}}'>rm -rf /</span>
        <span class="preset" data-s='{"action":{"q":"DROP TABLE structures; --"}}'>DROP TABLE</span>
      </div>
      <div class="fullrow">
        <label>action payload (JSON: {"action":{"cmd":...}})</label>
        <textarea id="scrInput" rows="4">{"action":{"cmd":"synthesize Al-Cu alloy at 600C"}}</textarea>
      </div>
      <button class="run" id="runScr">Screen &rarr; verdict</button>
      <div id="scrOut"></div>
    </div>
  </div>

  <!-- HONEST FOOTER PANEL — claim sheet -->
  <div class="panel">
    <h2>Honest claim sheet — what is real vs roadmap <span class="meta">Doctrine v11 · trust never 100%</span></h2>
    <p class="lede" style="margin:.2rem 0 .5rem;font-size:.85rem;">
      <b>Claiming more than is real is the only unacceptable outcome.</b> Each capability is labeled with its
      exact Lean reference. The locked machine-checked proven set is <b>EXACTLY 8</b>
      {F1,F4,F7,F11,F12,F18,F19,F22} at kernel <code>c7c0ba17</code> — none of the materials capabilities are
      folded into it.
    </p>
    <table>
      <thead><tr><th>Capability</th><th>Status</th><th>Lean reference</th><th>Live endpoint</th></tr></thead>
      <tbody>
        <tr>
          <td>Crystal novelty fingerprint + signed Khipu receipt (computation + chain)</td>
          <td><span class="pill green">PROVEN by construction</span></td>
          <td><code>Lutar/Wave8/HashChain.lean</code></td>
          <td><code>/materials/novelty</code></td>
        </tr>
        <tr>
          <td>PDD fingerprint <b>injectivity</b> (distinct crystals &rArr; distinct PDD)</td>
          <td><span class="pill blue">ROADMAP</span></td>
          <td><code>Lutar/Materials/PDDInjective.lean</code> (<code>sorry</code>)</td>
          <td><code>/materials/novelty</code></td>
        </tr>
        <tr>
          <td>PAC-Bayes (McAllester) bound — <b>computation</b></td>
          <td><span class="pill green">EXACT / PROVEN-on-paper</span></td>
          <td><code>szl_formulas.pac_bayes_mcallester</code></td>
          <td><code>/materials/certify</code></td>
        </tr>
        <tr>
          <td>McAllester bound — <b>Lean proof</b> (materials specialization)</td>
          <td><span class="pill blue">ROADMAP (SORRY)</span></td>
          <td><code>Lutar/Materials/PACBayesMaterials.lean</code> (<code>sorry</code>)</td>
          <td><code>/materials/certify</code></td>
        </tr>
        <tr>
          <td>&Lambda;-aggregator uniqueness (geometric mean is unique)</td>
          <td><span class="pill yellow">CONJECTURE 1</span></td>
          <td><code>Lutar/Uniqueness.lean:215</code> (<code>sorry</code>)</td>
          <td>aggregated trust label</td>
        </tr>
        <tr>
          <td>Khipu receipt ordering + energy-measurement methodology</td>
          <td><span class="pill yellow">CONJECTURE 2</span></td>
          <td><code>Lutar/Khipu/SummationInvariant.lean</code></td>
          <td>all <code>/materials/*</code> receipts</td>
        </tr>
        <tr>
          <td>Neyman&ndash;Pearson-optimal, fail-closed Immune egress gate</td>
          <td><span class="pill green">PROVEN-backing</span></td>
          <td><code>Lutar/Wave11/ImmuneNeymanPearsonOpt.lean</code></td>
          <td><code>/materials/screen</code> &rarr; <code>/immune/verdict</code></td>
        </tr>
        <tr>
          <td>Receipt cryptographic signature</td>
          <td><span class="pill dim">DSSE_PLACEHOLDER</span></td>
          <td>Sigstore not wired into CI (chain integrity is real)</td>
          <td>all receipts</td>
        </tr>
      </tbody>
    </table>
    <div class="simnote">
      Legend: <span class="proven">PROVEN</span> = machine-checked Lean (no-<code>sorry</code>) @ <code>c7c0ba17</code> or peer-reviewed ·
      <span class="conj">CONJECTURE</span> = formally stated, not yet machine-checked ·
      <span class="roadmap">ROADMAP</span> = scaffolded statement with an explicit tracked <code>sorry</code>.
      The two new <code>Lutar/Materials/*.lean</code> files are NOT imported by <code>Lutar.lean</code> (not in <code>lake build</code>) and are NOT in the locked-8.
      <b>Trust is never 100%.</b>
    </div>
  </div>

  <div class="footnote" id="leanFoot">
    Lean refs live at github.com/szl-holdings/lutar-lean @ main. Locked-proven set = EXACTLY 8 {F1,F4,F7,F11,F12,F18,F19,F22} @ kernel c7c0ba17 — the materials Lean targets are cited, NOT folded in.
    SLSA L1/L2/L3-roadmap · 0 runtime CDN · effectors simulated · no fabricated data. This page reads only the live /api/a11oy/v1/materials/* (+ /immune/verdict fallback) endpoints. Λ = Conjecture 1; Khipu = Conjecture 2; trust never 100%.
  </div>
</div>

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const IMM = "/api/a11oy/v1/immune";

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// ---- crystal presets ----
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  "cu-fcc": {a:3.61,b:3.61,c:3.61,al:90,be:90,ga:90, sites:'[{"el":"Cu","x":0,"y":0,"z":0}]'},
  "nacl":   {a:5.64,b:5.64,c:5.64,al:90,be:90,ga:90, sites:'[{"el":"Na","x":0,"y":0,"z":0},{"el":"Cl","x":0.5,"y":0.5,"z":0.5}]'},
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};
function applyCrystal(k){
  const c = CRYSTALS[k]; if(!c) return;
  latA.value=c.a; latB.value=c.b; latC.value=c.c; latAl.value=c.al; latBe.value=c.be; latGa.value=c.ga;
  sitesInput.value=c.sites;
}

// ---- PAC-Bayes presets ----
const CERTS = {
  "alloy": {risk:0.08, kl:2.0, n:5000, delta:0.05},
  "tight": {risk:0.03, kl:1.0, n:50000, delta:0.01},
  "loose": {risk:0.18, kl:6.0, n:300, delta:0.1}
};
function applyCert(k){
  const c=CERTS[k]; if(!c) return;
  cRisk.value=c.risk; cKl.value=c.kl; cN.value=c.n; cDelta.value=c.delta;
}

// ---- summary cards ----
async function loadCards(){
  const reg = await fetchJSON(MAT + "/novelty/registry");
  if(reg.ok && reg.data){
    document.getElementById("cRegistry").textContent = (reg.data.count ?? "—");
    document.getElementById("cRegistrySub").textContent = (reg.data.receipt_type || "fingerprints registered");
    document.getElementById("cChain").textContent = (reg.data.chain_depth ?? "—");
    document.getElementById("cChainSub").textContent = (reg.data.chain_verified ? "chain verified" : "unverified");
  } else {
    document.getElementById("cRegistry").textContent = "—";
    document.getElementById("cChain").textContent = "—";
  }
  // probe optional endpoints (built in parallel); show LIVE/DEPLOYING honestly.
  // /certify has no GET-info route, so probe it with a minimal valid POST (idempotent,
  // append-only receipt; cheap). /screen liveness is reflected by the /status summary.
  const cert = await fetchJSON(MAT + "/certify", {method:"POST",headers:{"content-type":"application/json"},body:JSON.stringify({empirical_risk:0.1,kl:1.0,n:1000,delta:0.05})});
  setProbe("cCertify", cert.status);
  const scr = await fetchJSON(MAT + "/status");
  setProbe("cScreen", scr.status);
}
function setProbe(id, status){
  const el=document.getElementById(id);
  if(status===200){ el.innerHTML='<span class="proven" style="font-size:1rem">LIVE</span>'; }
  else if(status===404){ el.innerHTML='<span class="roadmap" style="font-size:1rem">DEPLOYING</span>'; }
  else { el.textContent="—"; }
}

// ---- PANEL 1: novelty ----
async function runNovelty(){
  const out = document.getElementById("novOut");
  let sites;
  try{ sites = JSON.parse(sitesInput.value); }
  catch(e){ out.innerHTML='<div class="verdict-box dup">Invalid sites JSON: '+esc(e.message)+'</div>'; return; }
  const body = {
    a:parseFloat(latA.value), b:parseFloat(latB.value), c:parseFloat(latC.value),
    alpha:parseFloat(latAl.value), beta:parseFloat(latBe.value), gamma:parseFloat(latGa.value),
    sites:sites
  };
  out.innerHTML='<div class="verdict-box">certifying…</div>';
  const r = await fetchJSON(MAT + "/novelty", {method:"POST",headers:{"content-type":"application/json"},body:JSON.stringify(body)});
  if(r.status===404){ out.innerHTML=deployingBox("novelty"); return; }
  if(!r.ok || !r.data){ out.innerHTML='<div class="verdict-box dup">endpoint unreachable — retry</div>'; return; }
  const v=r.data;
  const novel = v.novel===true;
  const cls = novel? "novel":"dup";
  const pill = novel? '<span class="pill green">NOVEL</span>' : '<span class="pill yellow">DUPLICATE</span>';
  const rec = v.receipt||{};
  out.innerHTML =
    '<div class="verdict-box '+cls+'">'+
      '<div>verdict '+pill+' &nbsp; <span style="color:var(--dim)">distance='+esc(v.distance==null?"—":v.distance)+'</span></div>'+
      '<div style="margin:.35rem 0;"><span style="color:var(--dim)">nearest match</span> <span class="v">'+esc(v.nearest_match_id||"(none)")+'</span></div>'+
      '<div><span style="color:var(--dim)">fingerprint digest</span> <span class="digest">'+esc(v.fingerprint_digest||"")+'</span></div>'+
      '<div style="margin:.25rem 0;"><span style="color:var(--dim)">fingerprint</span> <code>'+esc(v.fingerprint||"")+'</code></div>'+
      '<div><span style="color:var(--dim)">Khipu receipt</span> <span class="digest">'+esc(rec.digest||"")+'</span> '+
        '<span style="color:var(--dim)">seq '+esc(rec.seq)+' · depth '+esc(rec.chain_depth)+' · '+esc(rec.receipt_type||"SZL.Materials.NoveltyCert.v1")+'</span></div>'+
      '<div style="color:var(--dim);margin-top:.35rem"><span class="roadmap">injectivity: ROADMAP/CONJECTURE</span> · '+esc((v.honesty&&v.honesty.lean_roadmap_ref)||"Lutar/Materials/PDDInjective.lean")+' · receipt signature '+esc((v.honesty&&v.honesty.receipt_signature)||"DSSE_PLACEHOLDER")+'</div>'+
    '</div>';
  loadCards();
}

// ---- PANEL 2: PAC-Bayes certify ----
async function runCertify(){
  const out=document.getElementById("certOut");
  const body = {
    empirical_risk:parseFloat(cRisk.value), kl:parseFloat(cKl.value),
    n:parseInt(cN.value,10), delta:parseFloat(cDelta.value)
  };
  out.innerHTML='<div class="verdict-box">computing bound…</div>';
  const r = await fetchJSON(MAT + "/certify", {method:"POST",headers:{"content-type":"application/json"},body:JSON.stringify(body)});
  if(r.status===404){ out.innerHTML=deployingBox("certify"); return; }
  if(!r.ok || !r.data){ out.innerHTML='<div class="verdict-box dup">endpoint unreachable — retry</div>'; return; }
  const v=r.data;
  const bound = (v.bound ?? v.population_risk_bound ?? v.pac_bayes_bound);
  const rec = v.receipt || v.khipu_receipt || {};
  out.innerHTML =
    '<div class="verdict-box allow">'+
      '<div>PAC-Bayes bound <span class="pill green">'+esc(bound==null?"—":bound)+'</span></div>'+
      '<div style="margin:.35rem 0;color:var(--paragraph)">'+esc(v.certificate_text || ("with prob ≥ 1−"+body.delta+", population risk ≤ "+(bound==null?"—":bound)))+'</div>'+
      '<div><span style="color:var(--dim)">Khipu receipt</span> <span class="digest">'+esc(rec.digest||"")+'</span> '+
        '<span style="color:var(--dim)">seq '+esc(rec.seq)+' · '+esc(rec.receipt_type||"SZL.Materials.PACBayesCert.v1")+'</span></div>'+
      '<div style="color:var(--dim);margin-top:.35rem"><span class="roadmap">McAllester Lean proof = SORRY</span> (computation exact) · Lutar/Materials/PACBayesMaterials.lean</div>'+
    '</div>';
  loadCards();
}

// ---- PANEL 3: immune screen (fallback to /immune/verdict) ----
async function runScreen(){
  const out=document.getElementById("scrOut");
  let body;
  try{ body = JSON.parse(scrInput.value); }
  catch(e){ out.innerHTML='<div class="verdict-box deny">Invalid JSON: '+esc(e.message)+'</div>'; return; }
  out.innerHTML='<div class="verdict-box">screening…</div>';
  let r = await fetchJSON(MAT + "/screen", {method:"POST",headers:{"content-type":"application/json"},body:JSON.stringify(body)});
  let viaFallback=false;
  if(r.status===404){
    // /screen not yet live — fall back to the live immune verdict path (honest).
    r = await fetchJSON(IMM + "/verdict", {method:"POST",headers:{"content-type":"application/json"},body:JSON.stringify(body)});
    viaFallback=true;
  }
  if(r.status===404){ out.innerHTML=deployingBox("screen"); return; }
  if(!r.ok || !r.data){ out.innerHTML='<div class="verdict-box deny">endpoint unreachable — retry</div>'; return; }
  const v=r.data;
  const deny = v.decision==="deny";
  const cls = deny? "deny":"allow";
  const pill = deny? '<span class="pill red">DENY</span>' : '<span class="pill green">ALLOW</span>';
  const sigs = (v.signals||[]).map(s=>'<span class="sig">'+esc(s)+'</span>').join("") || '<span class="pill dim">no signal</span>';
  const rec = v.immune_receipt || v.khipu_receipt || v.receipt || {};
  const en = v.energy || v.energy_provenance;
  out.innerHTML =
    '<div class="verdict-box '+cls+'">'+
      '<div>decision '+pill+(viaFallback?' <span class="pill blue">via /immune/verdict</span>':'')+' &nbsp; <span style="color:var(--dim)">Λ='+esc(v.lambda_value)+' (floor '+esc(v.lambda_floor)+')</span></div>'+
      '<div style="margin:.35rem 0;color:var(--paragraph)">'+esc(v.reason||"")+'</div>'+
      '<div style="margin:.3rem 0;">signals: '+sigs+'</div>'+
      (en? '<div><span style="color:var(--dim)">energy</span> <span class="v">'+esc(JSON.stringify(en)).slice(0,120)+'</span></div>':'')+
      '<div><span style="color:var(--dim)">Khipu receipt</span> <span class="digest">'+esc(rec.digest||"")+'</span> '+
        '<span style="color:var(--dim)">seq '+esc(rec.seq)+' · '+esc(rec.receipt_type||"SZL.Immune.Verdict.v1")+'</span></div>'+
      '<div style="color:var(--dim);margin-top:.35rem"><span class="proven">Neyman–Pearson gate = PROVEN-backing</span> · fail-closed='+esc(v.fail_closed)+' · doctrine '+esc(v.doctrine||"v11")+'</div>'+
    '</div>';
}

function deployingBox(which){
  return '<div class="verdict-box deploying">'+
    '<div><span class="pill blue">ENDPOINT DEPLOYING</span></div>'+
    '<div style="margin:.35rem 0;color:var(--paragraph)">The <code>/materials/'+esc(which)+'</code> endpoint is being deployed in parallel and is not live yet (HTTP 404). '+
    'No fake result is shown — this panel will return real signed output once the backend lands. Trust never 100%.</div>'+
    '</div>';
}

document.querySelectorAll(".preset[data-p]").forEach(p=>p.addEventListener("click",()=>applyCrystal(p.getAttribute("data-p"))));
document.querySelectorAll(".preset[data-c]").forEach(p=>p.addEventListener("click",()=>applyCert(p.getAttribute("data-c"))));
document.querySelectorAll(".preset[data-s]").forEach(p=>p.addEventListener("click",()=>{ scrInput.value=p.getAttribute("data-s"); }));
document.getElementById("runNov").addEventListener("click",runNovelty);
document.getElementById("runCert").addEventListener("click",runCertify);
document.getElementById("runScr").addEventListener("click",runScreen);

loadCards();
setInterval(loadCards, 12000);
</script>
</body>
</html>