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| <header><h1>CAffNet: theorem + neural audit</h1><p class="sub">20hdQQQrA4 · arbitrary constraints · joint null-space training · universal approximation</p></header> | |
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| <article class="card"><h2>C1 · Hard feasibility</h2><div class="metric">Arbitrary m</div><p class="formula">minimal face → feasible enumerated candidate</p><p>Penrose algebra closes for every input, rank, and finite constraint count under nonempty-feasibility assumptions.</p></article> | |
| <article class="card"><h2>C2 · Joint training</h2><div class="metric">5 seeds</div><p class="formula">dP/df = dP/dw = I-A†A</p><p>Both parameter paths receive gradients; learned null-space choice is load-bearing and hard-feasible.</p></article> | |
| <article class="card"><h2>C3 · UAT</h2><div class="metric">All finite p≥1</div><p class="formula">error ≤ (n+1)·base error</p><p>An independent Euclidean-projection candidate proof transfers underlying density while C1 preserves adherence.</p></article> | |
| <article class="card scope"><h2>Direct neural evidence</h2><p>Paper-spec width-200 Scenario A: five seeds, 50,000 epochs, mean MSE 0.00299 versus 0.0020±0.0032, zero CAffNet violations. Dimension-matched solver and non-monotone width sweep are retained with their limitations, not promoted into universal evidence.</p></article> | |
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| <footer>23/23 tests pass · all three proof DAGs valid · paper hash pinned · CPU reproduction</footer> | |
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