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Emerton's dimension conjecture for the full Hecke algebra at p = 2 and odd level

Theorem 1.1: for every odd $N$ , every irreducible component of $\mathrm{Spec}\,\mathbb T_2(N)$ has Krull dimension exactly $4$ . The upper bound comes from a cuspidal point of weight at least 3 on each component, a tangent bound of 3 from Newton-Thorne Selmer vanishing, and one arithmetic dimension. Only the case $p=2$ is treated; the paper does not claim the conjecture for odd $p$ .

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Oct 5, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Emerton's dimension conjecture for the full Hecke algebra at p = 2 and odd level · Emerton dimension conjecture, p = 2

Confidence: Not scored

Registry verification: unreviewed · announcement · partial

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Unreleased internal OpenAI model
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Named evidence

VibeMathed record: Emerton's dimension conjecture for the full Hecke algebra at p = 2 and odd level

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 of the October 5 manuscript was read against Emerton's Conjecture 2.9 as the paper cites it; it claims dimension exactly four for every component of the full 2-adic Hecke algebra of level $\Gamma_1(N)$ , $N$ odd, residually reducible and scalar components included. The proof was not refereed. It uses Emerton's lower bound, Chenevier's determinant laws and the Newton-Thorne adjoint Selmer vanishing theorem as external inputs. No Lean formalization exists for this family.

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Emerton's dimension conjecture for the full Hecke algebra at p = 2 and odd level

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Companion: Fontaine-Mazur modularity at the prime 2

paper · pending

paper link supplied by the VibeMathed registry.

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Companion: Unrestricted pro-modularity at the prime two

paper · pending

paper link supplied by the VibeMathed registry.

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Revised edition (October 6, 2026): Fontaine-Mazur modularity at the prime 2

paper · pending

paper link supplied by the VibeMathed registry.

Source ↗

Revised edition (October 6, 2026): Unrestricted pro-modularity at the prime two

paper · pending

paper link supplied by the VibeMathed registry.

Source ↗

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Emerton's dimension conjecture for the full Hecke algebra at p = 2 and odd level evidence for this event

Revised edition (October 6, 2026): Unrestricted pro-modularity at the prime two evidence for this event

This event attributed to Unreleased internal OpenAI model

Revised edition (October 6, 2026): Fontaine-Mazur modularity at the prime 2 evidence for this event

Companion: Fontaine-Mazur modularity at the prime 2 evidence for this event

Companion: Unrestricted pro-modularity at the prime two evidence for this event

VibeMathed record: Emerton's dimension conjecture for the full Hecke algebra at p = 2 and odd level evidence for this event

Emerton's dimension conjecture for the full Hecke algebra at p = 2 and odd level parent of this event

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