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| <title>Λ Gate — Conjecture 1, never a theorem · SZL Holdings</title> | |
| <meta name="description" content="The Λ (Lambda) governance-trust gate is CONJECTURE 1 — never proven, never green. Its status is fetched live from the machine-checked szl-formula-ledger. The unproven-ness is the whole point."/> | |
| <!-- 0 runtime CDN. System fonts only. The Λ status is read LIVE from the public | |
| szl-formula-ledger (ledger.json + formulas/corpus.json on raw.githubusercontent.com). | |
| Λ = Conjecture 1 is a LOCKED doctrine invariant: it is stated even when the ledger is | |
| unreachable. The live fetch only DISPLAYS the ledger's machine-check record, labelled | |
| REPORTED (from ledger) / UNAVAILABLE. Λ is NEVER shown as proven / green. --> | |
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| </style> | |
| </head> | |
| <body> | |
| <div class="wrap"> | |
| <header> | |
| <div class="eyebrow">SZL Holdings · governance-trust gate · holographic roadmap surface</div> | |
| <div class="glyph">Λ</div> | |
| <h1>The Λ gate is <span class="neg">Conjecture 1</span> — never a theorem, never green.</h1> | |
| <p class="lede">Λ (Lambda) is the advisory governance-trust quantity that gates every action | |
| in the estate. Its central claim — that Λ is the <em>unique</em> honest aggregator — is an | |
| open conjecture. The unproven-ness is the point: a governance number that pretends to be | |
| proven would be the dishonest one. Status below is read live from the machine-checked | |
| <code>szl-formula-ledger</code>.</p> | |
| <div class="badges"> | |
| <span id="status" class="wait">Reading the ledger…</span> | |
| <span class="badge">status <b>CONJECTURE-1</b></span> | |
| <span class="badge">trust ceiling <b>0.97</b> · never 100%</span> | |
| <span class="badge">unconditional uniqueness <b>machine-checked FALSE</b></span> | |
| <span class="badge">0 runtime CDN</span> | |
| </div> | |
| </header> | |
| <section class="hero"> | |
| <span class="k">Ledger entry <span id="entry-id">TH_L1-lambda-uniqueness</span> — the statement, verbatim</span> | |
| <p class="statement" id="statement">Loading the exact statement from the ledger…</p> | |
| <div class="src" id="source"></div> | |
| <span class="verdict" id="verdict">CONJECTURE-1 (never a theorem)</span> | |
| </section> | |
| <h2>What is actually checked (and what is not)</h2> | |
| <div class="ledger" id="ledger"> | |
| <div class="lrow"><div class="mark conj">⬡</div><div> | |
| <p class="t">Loading machine-check records…</p> | |
| <p class="d">Fetching <code>ledger.json</code> + <code>corpus.json</code> from the public repo.</p> | |
| </div></div> | |
| </div> | |
| <p class="note" id="honest-note"> | |
| <b>Why never green.</b> Λ = Conjecture 1 is a locked doctrine invariant: no amount of | |
| engineering upgrades it to a theorem, and its trust ceiling is fixed at 0.97, never 100%. | |
| A machine check has already shown its <em>unconditional</em> uniqueness is FALSE | |
| (a <code>maxAgg</code> counterexample); only a <em>conditional</em> Theorem U is proven. | |
| If the ledger is unreachable this page says <b>UNAVAILABLE</b> — but Λ's conjecture status, | |
| being doctrine, still stands. | |
| </p> | |
| <footer> | |
| <div>Live source (keyless): <a id="ledger-link" href="https://github.com/szl-holdings/szl-formula-ledger" target="_blank" rel="noopener">szl-formula-ledger</a> · <code>ledger.json</code> + <code>formulas/corpus.json</code>, relayed <b>REPORTED</b>.</div> | |
| <div>SZL Holdings · governed AI you can prove · <a href="https://a-11-oy.com" target="_blank" rel="noopener">a-11-oy.com</a> · <a href="https://github.com/szl-holdings/lutar-lean" target="_blank" rel="noopener">lutar-lean</a> · Λ = Conjecture 1, never a theorem · trust ceiling 0.97.</div> | |
| </footer> | |
| </div> | |
| <script> | |
| const RAW = "https://raw.githubusercontent.com/szl-holdings/szl-formula-ledger/main"; | |
| const CORPUS = RAW + "/formulas/corpus.json"; | |
| const LEDGER = RAW + "/ledger.json"; | |
| const ID = "TH_L1-lambda-uniqueness"; | |
| const $ = s => document.querySelector(s); | |
| const esc = s => String(s==null?"":s).replace(/[&<>"]/g,c=>({"&":"&","<":"<",">":">",'"':"""}[c])); | |
| function setStatus(cls,txt){const el=$("#status");el.className=cls;el.textContent=txt;} | |
| // The four honest facts about Λ, keyed to real ledger/corpus ids so each row cites its source. | |
| function buildRows(corpusById, ledgerById){ | |
| const conj = corpusById[ID] || {}; | |
| const conjLed = ledgerById[ID] || {}; | |
| const dim = ledgerById["lambda-score-dimensionless"] || {}; | |
| return [ | |
| {mark:"conj", cls:"conj", | |
| t:"Λ uniqueness — OPEN CONJECTURE 1", | |
| d:(conj.reported_status||"CONJECTURE-1 (never a theorem)")+". Ledger machine-check: "+ | |
| (conjLed.status||"UNCHECKABLE")+" — "+(conjLed.method||"stays Conjecture-1 (never CHECKED)."), | |
| tag:"class "+(conj.class||"CONJECTURE")+" · id "+ID}, | |
| {mark:"false", cls:"false", | |
| t:"Unconditional uniqueness — machine-checked FALSE", | |
| d:"A maxAgg counterexample refutes unconditional uniqueness. This is a real negative result, kept honestly on the record — not hidden.", | |
| tag:"lutar-lean Uniqueness.lean · F23"}, | |
| {mark:"part", cls:"part", | |
| t:"Conditional Theorem U — PROVEN (axiom-free)", | |
| d:"Under its stated conditions, uniqueness is proven and machine-checked. That is strictly weaker than the conjecture — and never rounded up to it.", | |
| tag:"conditional · proven"}, | |
| {mark:"ok", cls:"ok", | |
| t:"Λ is dimensionless — CHECKED", | |
| d:(dim.method||"trust axes are ratios in [0,1] (dimensionless); weighted geo-mean of dimensionless axes stays dimensionless")+".", | |
| tag:"class "+(dim.class||"DIMENSIONAL")+" · status "+(dim.status||"CHECKED")} | |
| ]; | |
| } | |
| function renderRows(rows){ | |
| $("#ledger").innerHTML = rows.map(r=>` | |
| <div class="lrow"> | |
| <div class="mark ${r.cls}">${r.mark==="ok"?"✓":r.mark==="false"?"✗":r.mark==="part"?"◐":"⬡"}</div> | |
| <div> | |
| <p class="t">${esc(r.t)}</p> | |
| <p class="d">${esc(r.d)}</p> | |
| <span class="tag">${esc(r.tag)}</span> | |
| </div> | |
| </div>`).join(""); | |
| } | |
| function toMap(arr){const m={};(arr||[]).forEach(x=>{if(x&&x.id)m[x.id]=x;});return m;} | |
| async function grab(url){ | |
| const ctl = new AbortController(); | |
| const t = setTimeout(()=>ctl.abort(), 12000); | |
| try{ | |
| const r = await fetch(url,{signal:ctl.signal,cache:"no-store"}); | |
| if(!r.ok) throw new Error("HTTP "+r.status); | |
| return await r.json(); | |
| } finally { clearTimeout(t); } | |
| } | |
| async function load(){ | |
| try{ | |
| const [corpus, ledger] = await Promise.all([grab(CORPUS), grab(LEDGER)]); | |
| const corpusItems = corpus.formulas || corpus.corpus || (Array.isArray(corpus)?corpus:[]); | |
| const corpusById = toMap(corpusItems); | |
| const ledgerById = toMap(ledger.ledger || ledger); | |
| const conj = corpusById[ID]; | |
| if(conj){ | |
| $("#statement").textContent = conj.statement || "(statement missing from ledger)"; | |
| $("#source").innerHTML = "source: "+esc(conj.source||"—"); | |
| $("#verdict").textContent = conj.reported_status || "CONJECTURE-1 (never a theorem)"; | |
| } else { | |
| $("#statement").textContent = "Entry "+ID+" not found in the ledger corpus."; | |
| } | |
| renderRows(buildRows(corpusById, ledgerById)); | |
| const gen = ledger.generated_at ? (" · ledger "+esc(ledger.generated_at.slice(0,10))) : ""; | |
| setStatus("ok","REPORTED from ledger"+gen); | |
| }catch(e){ | |
| setStatus("bad","UNAVAILABLE — ledger unreachable"); | |
| $("#statement").innerHTML = "<b style='color:var(--warn)'>UNAVAILABLE.</b> Could not read the "+ | |
| "szl-formula-ledger (<code>"+esc(String(e.message||e))+"</code>). No cached ledger values are shown. "+ | |
| "Λ's status is unchanged regardless: it remains <b>Conjecture 1</b> by doctrine — never a theorem, never green."; | |
| $("#verdict").textContent = "CONJECTURE-1 (doctrine invariant)"; | |
| $("#ledger").innerHTML = '<div class="lrow"><div class="mark conj">⬡</div><div>'+ | |
| '<p class="t">Live ledger records UNAVAILABLE</p>'+ | |
| '<p class="d">The machine-check detail could not be fetched. The invariant still holds: '+ | |
| 'Λ uniqueness is Conjecture 1, unconditional uniqueness is machine-checked FALSE, only a '+ | |
| 'conditional Theorem U is proven, and Λ is dimensionless.</p>'+ | |
| '<span class="tag">doctrine invariant · source down</span></div></div>'; | |
| } | |
| } | |
| load(); | |
| </script> | |
| </body> | |
| </html> | |
| <!-- static build refreshed 2026-07-10T01:39Z (redeploy: initial static deploy was stale on the empty first commit) --> | |