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Rationality of the Gaitsgory-Lafforgue-Raskin canonical Arthur filtration

Under the stated characteristic assumptions, the canonical Arthur filtration on finitely supported unramified automorphic functions is defined over $\mathbb Q$ , for split connected semisimple $G$ , including the noncuspidal part and every closed invariant nilpotent support. Using the companion decomposition at trivial level, each cuspidal filtration step is identified with the scalar extension of the corresponding rational summands (the common-scope form of GLR Conjectures 3.4.9 and 3.4.11). It does not treat small characteristic or nonsplit groups.

Exact FrontierDelta

Prior state unknown→proved

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Occurred: Sep 24, 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: Rationality of the Gaitsgory-Lafforgue-Raskin canonical Arthur filtration · Rationality of the canonical Arthur filtration

Confidence: Not scored

Registry verification: unreviewed · announcement · partial

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Unreleased internal OpenAI model
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VibeMathed record: Rationality of the Gaitsgory-Lafforgue-Raskin canonical Arthur filtration

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the main theorem was read against GLR Conjecture 2.7.3. It is proved for split connected semisimple groups under four explicit characteristic hypotheses (the restricted-theory assumptions), for the whole space including the noncuspidal part; outside those hypotheses the conjecture is not addressed, hence Partial. It uses the restricted geometric Langlands results and trace-of-Frobenius theorems as inputs. The proof was not refereed. No Lean formalization exists for this family.

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Rationality of the Gaitsgory-Lafforgue-Raskin canonical Arthur filtration

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

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Companion: Ramanujan-Arthur Decompositions of Cuspidal Functions at Full Finite Level

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Rationality of the Gaitsgory-Lafforgue-Raskin canonical Arthur filtration evidence for this event

Companion: Ramanujan-Arthur Decompositions of Cuspidal Functions at Full Finite Level evidence for this event

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