Formal Methods / Mathematical Verification

What to call it: formal proof, structural invariants, nilpotency-based non-collapsibility proof.

Real evidence

• Theorem 1 (d-separation via do-calculus), Theorem 2 (schema floor integrity), Corollary 3.1 (nilpotency of a strictly lower-triangular matrix — T⁴=0), Proposition 1.3 (Data Processing Inequality argument) — all independently checked line by line and confirmed valid given their definitions.
• Test 5's reconstruction — original script not located, but a faithful, independently-tuned reconstruction reproduced the cited magnitude, with the actual mechanism explained (why tuning closes the gap), not just the number matched.

Honest calibration

The proof itself is real, checked math, not hand-waving. Test 5 was reconstructed and independently verified to match the cited magnitude — resolved, not open. T0.1, T0.2, and T0.3 are a genuinely different, still-unresolved state: never reconstructed, never checked, no script located for any of them. Worth being precise about that distinction with anyone technical — one empirical citation is now backed by real, rerunnable code; three others still aren't.