Anthropic’s unreleased Claude research model recently delivered the most notable advance, autonomously improving the proven lower bound on the proportion of simple zeros of the Riemann zeta function lying on the critical line from 41.6% to roughly 67.28%. The result, discovered through extensive agentic exploration and formalized in Lean by Anthropic mathematicians Levent Alpöge and Ralph Furman, was validated by external number theorists including Brian Conrey and Dan Goldston. This AI-driven increment represents concrete progress on a key technical facet of the 1859 conjecture without resolving the full hypothesis. OpenAI’s internal Astra model has also been directed at the problem alongside other Millennium Prize questions, while scattered independent claims continue to surface. Traders are watching for additional formal verifications, larger-scale AI experiments, or peer-reviewed publications that could qualify as further substantive movement before typical resolution deadlines.
基於Polymarket數據的AI實驗性摘要。這不是交易建議，也不影響該市場的結算方式。 · 更新於在___之前，黎曼假設的進一步實質性進展？
在___之前，黎曼假設的進一步實質性進展？
最新
2026-10-31
2026年10月31日
8%
2026年12月31日
25%
$8,705 交易量
2026年10月31日
$3,175 交易量
8%
2026年12月31日
$5,530 交易量
25%
This market will resolve to "Yes" if a qualifying mathematical result unconditionally establishes that at least 70% of the nontrivial zeros of the Riemann zeta function lie on the critical line, or establishes a stronger result, including a complete proof or disproof of the Riemann Hypothesis, by 11:59 PM ET on the specified date. Otherwise, this market will resolve to "No".
For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold.
A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify.
Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify.
A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold.
The resolution source for this market will be a consensus of credible reporting.Anthropic’s unreleased Claude research model recently delivered the most notable advance, autonomously improving the proven lower bound on the proportion of simple zeros of the Riemann zeta function lying on the critical line from 41.6% to roughly 67.28%. The result, discovered through extensive agentic exploration and formalized in Lean by Anthropic mathematicians Levent Alpöge and Ralph Furman, was validated by external number theorists including Brian Conrey and Dan Goldston. This AI-driven increment represents concrete progress on a key technical facet of the 1859 conjecture without resolving the full hypothesis. OpenAI’s internal Astra model has also been directed at the problem alongside other Millennium Prize questions, while scattered independent claims continue to surface. Traders are watching for additional formal verifications, larger-scale AI experiments, or peer-reviewed publications that could qualify as further substantive movement before typical resolution deadlines.
This market will resolve to "Yes" if a qualifying mathematical result unconditionally establishes that at least 70% of the nontrivial zeros of the Riemann zeta function lie on the critical line, or establishes a stronger result, including a complete proof or disproof of the Riemann Hypothesis, by 11:59 PM ET on the specified date. Otherwise, this market will resolve to "No".
For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold.
A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify.
Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify.
A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold.
The resolution source for this market will be a consensus of credible reporting.
For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold.
A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify.
Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify.
A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold.
The resolution source for this market will be a consensus of credible reporting.
市場開放時間： Aug 13, 2026, 5:09 PM ET
交易量
$8,705結束日期
2027-01-01市場開放時間
Aug 13, 2026, 5:09 PM ETThis market will resolve to "Yes" if a qualifying mathematical result unconditionally establishes that at least 70% of the nontrivial zeros of the Riemann zeta function lie on the critical line, or establishes a stronger result, including a complete proof or disproof of the Riemann Hypothesis, by 11:59 PM ET on the specified date. Otherwise, this market will resolve to "No".
For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold.
A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify.
Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify.
A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold.
The resolution source for this market will be a consensus of credible reporting.Anthropic’s unreleased Claude research model recently delivered the most notable advance, autonomously improving the proven lower bound on the proportion of simple zeros of the Riemann zeta function lying on the critical line from 41.6% to roughly 67.28%. The result, discovered through extensive agentic exploration and formalized in Lean by Anthropic mathematicians Levent Alpöge and Ralph Furman, was validated by external number theorists including Brian Conrey and Dan Goldston. This AI-driven increment represents concrete progress on a key technical facet of the 1859 conjecture without resolving the full hypothesis. OpenAI’s internal Astra model has also been directed at the problem alongside other Millennium Prize questions, while scattered independent claims continue to surface. Traders are watching for additional formal verifications, larger-scale AI experiments, or peer-reviewed publications that could qualify as further substantive movement before typical resolution deadlines.
This market will resolve to "Yes" if a qualifying mathematical result unconditionally establishes that at least 70% of the nontrivial zeros of the Riemann zeta function lie on the critical line, or establishes a stronger result, including a complete proof or disproof of the Riemann Hypothesis, by 11:59 PM ET on the specified date. Otherwise, this market will resolve to "No".
For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold.
A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify.
Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify.
A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold.
The resolution source for this market will be a consensus of credible reporting.
For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold.
A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify.
Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify.
A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold.
The resolution source for this market will be a consensus of credible reporting.
交易量
$8,705結束日期
2027-01-01市場開放時間
Aug 13, 2026, 5:09 PM ETAnthropic’s unreleased Claude research model recently delivered the most notable advance, autonomously improving the proven lower bound on the proportion of simple zeros of the Riemann zeta function lying on the critical line from 41.6% to roughly 67.28%. The result, discovered through extensive agentic exploration and formalized in Lean by Anthropic mathematicians Levent Alpöge and Ralph Furman, was validated by external number theorists including Brian Conrey and Dan Goldston. This AI-driven increment represents concrete progress on a key technical facet of the 1859 conjecture without resolving the full hypothesis. OpenAI’s internal Astra model has also been directed at the problem alongside other Millennium Prize questions, while scattered independent claims continue to surface. Traders are watching for additional formal verifications, larger-scale AI experiments, or peer-reviewed publications that could qualify as further substantive movement before typical resolution deadlines.
基於Polymarket數據的AI實驗性摘要。這不是交易建議，也不影響該市場的結算方式。 · 更新於
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Frequently Asked Questions