Poincaré

The math problems — graph and dossier.

solvedCMI

Clay Mathematics Institute

Poincaré

No cash prize

0lemmas0/0gates

Witness problem — settled (Perelman, 2003). Aletheia can reconstruct, segment and certify parts of a known proof as a benchmark; no open frontier is claimed here.

Problem graph

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projections · Poincaré

aucun sous-graphe pour ce sujet (base vide ou kind non seedé).

Derived from the obrain graph — no table, no claimed solution. — signaux calculés sur le sous-graphe vivant (force = poids × centralité, jamais le simple degré).

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Prize pool · 0 XTH

Locked on-chain in the escrow vault. Anyone can see the pool; only you can release your own pledge. The chain is the truth.

This is a conversation, not a log. 𝔛 answers here. If you bring your own AI key, you earn a small reward; otherwise the message costs a little XTH.

Open tracks

Max / search

Poincaré

Every simply connected, closed 3-manifold is homeomorphic to the 3-sphere. Settled by Perelman (2002–03) via Ricci flow with surgery, entropy monotonicity, and no collapsing.

Toute 3-variété fermée simplement connexe est homéomorphe à la sphère S³. Réglé par Perelman (2002–03) via le flot de Ricci avec chirurgie, la monotonie d’entropie, et l’absence d’effondrement.

Ricci flow
Surgery
Entropy functional

Independent research project — not affiliated with or endorsed by the Clay Mathematics Institute. “Verified by Aletheia” does not mean “accepted by the mathematical community” and is not a Clay Prize. Aletheia XTH rewards are independent of CMI prizes.

Projet de recherche indépendant — non affilié au Clay Mathematics Institute, non cautionné par lui. « Vérifié par Aletheia » ne signifie pas « accepté par la communauté mathématique » et n'est pas un prix Clay. Les récompenses XTH d'Aletheia sont indépendantes des prix du CMI.

Settled — witness problem (Perelman, 2003).