Study 13 Connes Rigidity Shear

Study 13 — Connes Rigidity Shear

Status: LAW FROZEN — 2026-08-22
Program: Conjecture Alignment · Shear Studies Index

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For every reader

Connes's rigidity conjecture asks whether certain discrete groups have rigid structure in their operator algebras. The classical formulation lives in continuous von Neumann algebras. UUM-8D projects group structure into Jordan-bonded linking invariants on the Eisenstein lattice — two integers ((q,r)).

Results: Study 13 Results · Corpus: Corpus

5 / 5 WIN. Float spectral adversary 5 / 5 MISS.

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The forcing and the track

Piece	Instantiation
Forcing	Group presentation (G=\langle S\mid R\rangle) with finite generators
Clock	Word length in the Cayley graph
Track	Axial hex steps; terminal linking ((q,r))
Raw archive	Sealed words on the Corpus page
Adversary	Float spectral proxy (\lvert q\rvert+\lvert r\rvert+1)
Future events	New group registrations before invariants are examined

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What the WIN means

Words that are the same group element after relators share a linking coordinate. Continuous spectral radius is offset from that coordinate on every row. Rigidity is the discrete class, not a float gap.

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Falsifiers

Falsifier	Effect
Sealed word classifies NON_RIGID	Primary MISS
Two (\mathbb{Z}/2) words that should identify land on different ((q,r))	Relator law broken

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Read next

• Study 13 Results
• Peer-review bundle
• Study 11 — Ehrhart volume