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Record W2953250233 · doi:10.1090/mbk/154/30

The Generalized Riemann Hypothesis

2025· book-chapter· en· W2953250233 on OpenAlex

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueAmerican Mathematical Society eBooks · 2025
Typebook-chapter
Languageen
FieldMathematics
TopicAnalytic Number Theory Research
Canadian institutionsUniversité de Montréal
Fundersnot available
KeywordsGoldbach's conjectureRiemann hypothesisMathematicsRiemann zeta functionConjectureRiemann Xi functionPure mathematicsNumber theoryAnalytic number theoryDirichlet L-functionDirichlet distributionDirichlet seriesMathematical analysis

Abstract

fetched live from OpenAlex

(Generalized) Riemann Hypothesis (that all non-trivial zeros of the (Dirichlet L-function) zeta function have real part one-half) is arguably the most important unsolved problem in contemporary mathematics due to its deep relation to the fundamental building blocks of the integers, the primes. The proof of the Riemann hypothesis will immediately verify a slew of dependent theorems ([BRW], [SA]). In this paper, we give a proof of Generalized Riemann Hypothesis which implies the proof of Riemann Hypothesis and Goldbach’s weak conjecture (also known as the odd Goldbach conjecture) one of the oldest and bestknown unsolved problems in number theory and in all of mathematics.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.002
metaresearch head score (Gemma)0.001
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesMeta-epidemiology (narrow), Science and technology studies, Insufficient payload (model declined to judge)
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: Theoretical or conceptual
GenreCandidate signal: Other · Consensus signal: Other
Teacher disagreement score0.062
Threshold uncertainty score1.000

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0020.001
Meta-epidemiology (narrow)0.0010.001
Meta-epidemiology (broad)0.0020.002
Bibliometrics0.0000.000
Science and technology studies0.0010.004
Scholarly communication0.0000.000
Open science0.0010.001
Research integrity0.0000.001
Insufficient payload (model declined to judge)0.0010.001

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.051
GPT teacher head0.319
Teacher spread0.268 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it