Study 13 Connes Rigidity Corpus

Study 13 — Corpus: group words on the Eisenstein lattice

Status: CORPUS SEALED — 2026-08-22
Charter: Study 13 · Results: Results

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Generator pin

Letter	Inverse	Axial step ((q,r))
a	A	(1, 0)
b	B	(0, 1)
A	a	(−1, 0)
B	b	(0, −1)

Free reduction cancels adjacent inverse pairs. Presentations then apply:

Presentation	Relator
cyclicZ2	(a^2=1) — fold a/A to a parity; keep b
freeAbelianZ2	(ab=ba) — net counts of (a) and (b)
symmetricS3	free reduction only; bound (\lvert q\rvert+\lvert r\rvert\le 4)

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Sealed words

ID	Letters	Presentation
Z2_a2b	aab	cyclic (\mathbb{Z}/2)
Z2_aba	aba	cyclic (\mathbb{Z}/2)
Z2_abAB	abAB	free abelian (\mathbb{Z}^2)
Z2_ba	ba	free abelian (\mathbb{Z}^2)
S3_abab	abab	(S_3) fragment

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Machine ledger

Artifact	Path
Grade script	corpus/study-13/study13_grade.py
Sealed ledger JSON	corpus/study-13/study13_ledger.json

python3 corpus/study-13/study13_grade.py

Expected summary: primary_win: 5, primary_total: 5, adversary_miss: 5.

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Gaps (VOID)

Slot	Reason
Property-(T) infinite presentations	Prospective registry OPEN — this seal is the finite linking pin
Full von Neumann (L(G)) reconstruction	REFUSED — continuous operator algebra is the adversary, not the corpus