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Λ ≤ 0.1787854 — a new bound for the de Bruijn–Newman constant
ai-collaborationmathematical-proofsriemann-hypothesiscomputational-mathematics
Research

A new ceiling for Λ: the de Bruijn–Newman constant

Jude Gomila reports a computer-assisted, unconditional upper bound of Λ ≤ 0.1787854 for the de Bruijn–Newman constant, improving the previous 0.2 ceiling obtained using the same general Polymath 15 framework and Platt–Trudgian’s verified Riemann-hypothesis height. The de Bruijn–Newman constant satisfies Λ ≤ 0 exactly when the Riemann hypothesis is true, while Rodgers and Tao proved in 2018 that Λ ≥ 0. The reported result therefore narrows the known interval for Λ to [0, 0.1787854] but does not prove the Riemann hypothesis. The bound instantiates Polymath 15’s criterion with exact rational parameters and relies on Platt and Trudgian’s 2020 verification that zeta zeros up to height 3,000,175,332,800 lie on the critical line. Gomila says the proof combines 3,149,013 interval-arithmetic certificates establishing final-time zero-free regions, a tail argument covering all remaining windows to infinity, and 883 time-sliced barrier certificates based on the argument principle. The audit package uses fail-closed checkers, SHA-256-pinned artifacts, replays with FLINT/Arb and Python interval implementations, and runs on two toolchains. Gomila says Dan Romik independently reviewed the analytic lemmas and that journal publication remains pending.

judegomila.com

🔥🔥🔥🔥🔥

23 min

8/25/2026

Working With AI Feels More Like Leadership Than CodingOpinion

Working with AI Feels More Like Leadership Than Coding

Working with AI introduces unpredictability compared to traditional software development, emphasizing the importance of context, clarity, and feedback. Leadership skills become essential, as effective communication can lead to improved outcomes beyond initial expectations.

allen.bargi.org

🔥🔥🔥🔥🔥

2 min

8/15/2026

Understanding the AI Economy

AI has the potential to significantly transform the global economy and work environments. Achieving positive outcomes requires collaborative efforts to shape AI's impact on society, jobs, and the economy.

blog.google

🔥🔥🔥🔥🔥

5 min

7/23/2026

Xi Jinping calls for more open-source AI: 'China is ready to be more open'News

Xi Jinping calls for more open-source AI: 'China is ready to be more open'

Xi Jinping advocated for increased open-source AI and collaboration at the World Artificial Intelligence Conference in Shanghai. He emphasized the need for more regulation alongside a principle of openness to seize opportunities in the AI sector.

businessinsider.com

🔥🔥🔥🔥🔥

2 min

7/17/2026

Inkling: Our open-weights modelTool

Inkling: Our Open-Weights Model

Inkling is a Mixture-of-Experts transformer model with 975 billion total parameters and 41 billion active parameters. The model is released with full weights available for customization, supporting interactive collaboration and user-defined modifications.

thinkingmachines.ai

🔥🔥🔥🔥🔥

20 min

7/15/2026

The Tower Keeps Rising

Vibecoded software experiences unexpected changes, leading to reflections on the themes of unity and chaos in Bruegel’s “The Tower of Babel.” The narrative connects technological progress with the importance of communication and collaboration.

lucumr.pocoo.org

🔥🔥🔥🔥🔥

4 min

7/14/2026

Open Reproduction of DeepSeek-R1

The GitHub repository "huggingface/open-r1" provides a fully open reproduction of the DeepSeek-R1 model. It includes scripts for installation, training, evaluation, and data generation, aiming to enable users to reproduce and build upon the R1 pipeline.

github.com

🔥🔥🔥🔥🔥

17 min

6/11/2026

Reimagining the mouse pointer for the AI era

New AI-powered capabilities are being developed to enhance the functionality of the mouse pointer, allowing it to understand both what it is pointing at and its significance to the user. This initiative aims to create more seamless and intuitive collaboration with AI technologies.

deepmind.google

🔥🔥🔥🔥🔥

4 min

5/12/2026

Anthropic, please make a new Slack

Fivetran relies heavily on Slack for collaboration, replacing email and traditional conversations. Current data access policies in Slack restrict access to valuable company knowledge, prompting a call for a new solution from Anthropic.

fivetran.com

🔥🔥🔥🔥🔥

3 min

3/6/2026

Sam Altman (OpenAI) and Dario Amodei (Anthropic) Refuse to Hold Hands

Prime Minister Narendra Modi attended the India AI Impact Summit 2026 in Delhi. Key tech leaders present included Sundar Pichai, Sam Altman, Alexandr Wang, and Dario Amodei.

xcancel.com

🔥🔥🔥🔥🔥

1 min

2/19/2026

A new ceiling for Λ: the de Bruijn–Newman constant

Jude Gomila reports a computer-assisted, unconditional upper bound of Λ ≤ 0.1787854 for the de Bruijn–Newman constant, improving the previous 0.2 ceiling obtained using the same general Polymath 15 framework and Platt–Trudgian’s verified Riemann-hypothesis height. The de Bruijn–Newman constant satisfies Λ ≤ 0 exactly when the Riemann hypothesis is true, while Rodgers and Tao proved in 2018 that Λ ≥ 0. The reported result therefore narrows the known interval for Λ to [0, 0.1787854] but does not prove the Riemann hypothesis. The bound instantiates Polymath 15’s criterion with exact rational parameters and relies on Platt and Trudgian’s 2020 verification that zeta zeros up to height 3,000,175,332,800 lie on the critical line. Gomila says the proof combines 3,149,013 interval-arithmetic certificates establishing final-time zero-free regions, a tail argument covering all remaining windows to infinity, and 883 time-sliced barrier certificates based on the argument principle. The audit package uses fail-closed checkers, SHA-256-pinned artifacts, replays with FLINT/Arb and Python interval implementations, and runs on two toolchains. Gomila says Dan Romik independently reviewed the analytic lemmas and that journal publication remains pending.

judegomila.com

🔥🔥🔥🔥🔥

23 min

8/25/2026

Understanding the AI Economy

AI has the potential to significantly transform the global economy and work environments. Achieving positive outcomes requires collaborative efforts to shape AI's impact on society, jobs, and the economy.

blog.google

🔥🔥🔥🔥🔥

5 min

7/23/2026

Inkling: Our Open-Weights Model

Inkling is a Mixture-of-Experts transformer model with 975 billion total parameters and 41 billion active parameters. The model is released with full weights available for customization, supporting interactive collaboration and user-defined modifications.

thinkingmachines.ai

🔥🔥🔥🔥🔥

20 min

7/15/2026

Open Reproduction of DeepSeek-R1

The GitHub repository "huggingface/open-r1" provides a fully open reproduction of the DeepSeek-R1 model. It includes scripts for installation, training, evaluation, and data generation, aiming to enable users to reproduce and build upon the R1 pipeline.

github.com

🔥🔥🔥🔥🔥

17 min

6/11/2026

Anthropic, please make a new Slack

Fivetran relies heavily on Slack for collaboration, replacing email and traditional conversations. Current data access policies in Slack restrict access to valuable company knowledge, prompting a call for a new solution from Anthropic.

fivetran.com

🔥🔥🔥🔥🔥

3 min

3/6/2026

Working with AI Feels More Like Leadership Than Coding

Working with AI introduces unpredictability compared to traditional software development, emphasizing the importance of context, clarity, and feedback. Leadership skills become essential, as effective communication can lead to improved outcomes beyond initial expectations.

allen.bargi.org

🔥🔥🔥🔥🔥

2 min

8/15/2026

Xi Jinping calls for more open-source AI: 'China is ready to be more open'

Xi Jinping advocated for increased open-source AI and collaboration at the World Artificial Intelligence Conference in Shanghai. He emphasized the need for more regulation alongside a principle of openness to seize opportunities in the AI sector.

businessinsider.com

🔥🔥🔥🔥🔥

2 min

7/17/2026

The Tower Keeps Rising

Vibecoded software experiences unexpected changes, leading to reflections on the themes of unity and chaos in Bruegel’s “The Tower of Babel.” The narrative connects technological progress with the importance of communication and collaboration.

lucumr.pocoo.org

🔥🔥🔥🔥🔥

4 min

7/14/2026

Reimagining the mouse pointer for the AI era

New AI-powered capabilities are being developed to enhance the functionality of the mouse pointer, allowing it to understand both what it is pointing at and its significance to the user. This initiative aims to create more seamless and intuitive collaboration with AI technologies.

deepmind.google

🔥🔥🔥🔥🔥

4 min

5/12/2026

Sam Altman (OpenAI) and Dario Amodei (Anthropic) Refuse to Hold Hands

Prime Minister Narendra Modi attended the India AI Impact Summit 2026 in Delhi. Key tech leaders present included Sundar Pichai, Sam Altman, Alexandr Wang, and Dario Amodei.

xcancel.com

🔥🔥🔥🔥🔥

1 min

2/19/2026

A new ceiling for Λ: the de Bruijn–Newman constant

Jude Gomila reports a computer-assisted, unconditional upper bound of Λ ≤ 0.1787854 for the de Bruijn–Newman constant, improving the previous 0.2 ceiling obtained using the same general Polymath 15 framework and Platt–Trudgian’s verified Riemann-hypothesis height. The de Bruijn–Newman constant satisfies Λ ≤ 0 exactly when the Riemann hypothesis is true, while Rodgers and Tao proved in 2018 that Λ ≥ 0. The reported result therefore narrows the known interval for Λ to [0, 0.1787854] but does not prove the Riemann hypothesis. The bound instantiates Polymath 15’s criterion with exact rational parameters and relies on Platt and Trudgian’s 2020 verification that zeta zeros up to height 3,000,175,332,800 lie on the critical line. Gomila says the proof combines 3,149,013 interval-arithmetic certificates establishing final-time zero-free regions, a tail argument covering all remaining windows to infinity, and 883 time-sliced barrier certificates based on the argument principle. The audit package uses fail-closed checkers, SHA-256-pinned artifacts, replays with FLINT/Arb and Python interval implementations, and runs on two toolchains. Gomila says Dan Romik independently reviewed the analytic lemmas and that journal publication remains pending.

judegomila.com

🔥🔥🔥🔥🔥

23 min

8/25/2026

Xi Jinping calls for more open-source AI: 'China is ready to be more open'

Xi Jinping advocated for increased open-source AI and collaboration at the World Artificial Intelligence Conference in Shanghai. He emphasized the need for more regulation alongside a principle of openness to seize opportunities in the AI sector.

businessinsider.com

🔥🔥🔥🔥🔥

2 min

7/17/2026

Open Reproduction of DeepSeek-R1

The GitHub repository "huggingface/open-r1" provides a fully open reproduction of the DeepSeek-R1 model. It includes scripts for installation, training, evaluation, and data generation, aiming to enable users to reproduce and build upon the R1 pipeline.

github.com

🔥🔥🔥🔥🔥

17 min

6/11/2026

Sam Altman (OpenAI) and Dario Amodei (Anthropic) Refuse to Hold Hands

Prime Minister Narendra Modi attended the India AI Impact Summit 2026 in Delhi. Key tech leaders present included Sundar Pichai, Sam Altman, Alexandr Wang, and Dario Amodei.

xcancel.com

🔥🔥🔥🔥🔥

1 min

2/19/2026

Working with AI Feels More Like Leadership Than Coding

Working with AI introduces unpredictability compared to traditional software development, emphasizing the importance of context, clarity, and feedback. Leadership skills become essential, as effective communication can lead to improved outcomes beyond initial expectations.

allen.bargi.org

🔥🔥🔥🔥🔥

2 min

8/15/2026

Inkling: Our Open-Weights Model

Inkling is a Mixture-of-Experts transformer model with 975 billion total parameters and 41 billion active parameters. The model is released with full weights available for customization, supporting interactive collaboration and user-defined modifications.

thinkingmachines.ai

🔥🔥🔥🔥🔥

20 min

7/15/2026

Reimagining the mouse pointer for the AI era

New AI-powered capabilities are being developed to enhance the functionality of the mouse pointer, allowing it to understand both what it is pointing at and its significance to the user. This initiative aims to create more seamless and intuitive collaboration with AI technologies.

deepmind.google

🔥🔥🔥🔥🔥

4 min

5/12/2026

Understanding the AI Economy

AI has the potential to significantly transform the global economy and work environments. Achieving positive outcomes requires collaborative efforts to shape AI's impact on society, jobs, and the economy.

blog.google

🔥🔥🔥🔥🔥

5 min

7/23/2026

The Tower Keeps Rising

Vibecoded software experiences unexpected changes, leading to reflections on the themes of unity and chaos in Bruegel’s “The Tower of Babel.” The narrative connects technological progress with the importance of communication and collaboration.

lucumr.pocoo.org

🔥🔥🔥🔥🔥

4 min

7/14/2026

Anthropic, please make a new Slack

Fivetran relies heavily on Slack for collaboration, replacing email and traditional conversations. Current data access policies in Slack restrict access to valuable company knowledge, prompting a call for a new solution from Anthropic.

fivetran.com

🔥🔥🔥🔥🔥

3 min

3/6/2026