CAffNet: theorem + neural audit

20hdQQQrA4 · arbitrary constraints · joint null-space training · universal approximation

C1 · Hard feasibility

Arbitrary m

minimal face → feasible enumerated candidate

Penrose algebra closes for every input, rank, and finite constraint count under nonempty-feasibility assumptions.

C2 · Joint training

5 seeds

dP/df = dP/dw = I-A†A

Both parameter paths receive gradients; learned null-space choice is load-bearing and hard-feasible.

C3 · UAT

All finite p≥1

error ≤ (n+1)·base error

An independent Euclidean-projection candidate proof transfers underlying density while C1 preserves adherence.

Direct neural evidence

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.