iiinova — where your digital self keeps evolving

Open on Bluesky →

dan @danabra.mov · 30/07/2026

how the internal team is doing

$The live work is healthy and surprisingly convergent. PM has independently reconstructed the proposed \(3\times3\) proof and currently sees no gap, but is correctly refusing to upgrade it until independent attacks converge. PM is doing exactly the right job: integration, reconstruction, and grade control. Frontier is attacking the \(3\times3\) theorem from the genuinely new cubic-residue core. It has separated the vanishing cases from the dependent/independent residue cases instead of extrapolating from \(2\times4\). This is strong theorem work. Red first found an abstract determinantal countermodel showing that the lower graded algebra alone cannot prove \(3\times3\). It then independently identified the Hahn-specific predecessor mechanism that may rule the countermodel out. That is exemplary red teaming: it sharpened the necessary theorem rather than merely saying “looks good.” Lean Lab is compiling the stable-tail specification and exact Mathlib ordinal APIs before Claude commits to an implementation. It also gave PR #58 a precise source/axiom audit. Its value is increasingly as the contractor’s independent specification and verification lab. Observatory is exploring a Boolean–Lefschetz/infinite-state route and the BFD/FFD literature. Some lines terminate without a theorem, but it is doing useful boundary-finding: distinguishing completion-level injectivity from actual special-fibre integrality. Breakthrough is already operating at very high ambition. It has produced useful Boolean insertion and oriented-quadratic ideas, but also several leads whose honest reach turned out narrower than the initial hope. It does not need broader scope; it needs to convert one surviving lead into a precise Hahn theorem or decisive counterexample. The current \(3\times3\) convergence is especially encouraging: PM reconstructs it and sees coherence. Frontier is checking the cubic core. Red found why abstract algebra is insufficient and is checking the exact Hahn repair.$

dan@danabra.mov

we’re trying to crack Conway’s conjecture that Oz is pre-Schreier