Science Markets
Markets / Mathematics / Number theory

The Riemann hypothesis is true.

A proposed pattern in the zeta function would explain how prime numbers are distributed. This market asks whether that pattern can be proved.

Live

Price history

Last reading Nov 14, 2026 07:41 PM EST.

How to read this chart

Each dot is one recorded reading, thinned to hourly for readability; the underlying samples are every few minutes. The line between two dots is not a measurement. A round published before the first recorded price stays off the chart, because there was no market to read; you can still open it from the round list. How the AI estimate is made.

Buy YES or NO

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YES 60¢current price
Pool depth
$149
Buy YES  60¢
Token address
J74AaZHMedNFY5Emh8kCgwaV8VLYFAgCYnCFpSf3THJh
NO 40¢current price
Pool depth
$101
Buy NO  40¢
Token address
6Tp4qYNWqLPzHaiYgrekK1SZt2NALAnECFHtm2YR5arv

Verify the market on-chain ↗ · Reading is open to everyone. Trading is subject to the terms and the access rules.

Weekly AI estimate

60% This week · Nov 10, 2026 09:23 PM EST

The average of three models reading the same evidence. It is an estimate, not proof the hypothesis holds, and it does not set the pool price.

Range
3–90%
Verdict
Undecided

The panel's confident binary this round Undecided the models did not all agree

0% 25% 50% 75% 100%
OpenAI 90% Anthropic 3% xAI 86% Average 60%
Market definition · YES, NO and evidence rules

This is the frozen contract wording. Read the YES and NO tests, the evidence requirements and the undecided cases before taking a position.

Canonical title

The Riemann hypothesis is true.

Exact hypothesis · technical wording

Every zero s of the analytic continuation of the Riemann zeta function with 0 < Re(s) < 1 has Re(s) = 1/2. This is the classical Riemann hypothesis, not its generalized version.

Each round reads the evidence that was public at a stated cutoff. Later evidence goes into a later round; the market itself has no expiry date.

How the evidence cutoff is fixed

A round only counts evidence published before its own cutoff time, and the round's number is that timestamp. So a round cannot borrow a later cutoff, and an earlier round's judgment cannot be reused for a later one. The hypothesis wording, the resolution criteria and the methodology identifier were hashed into the market account at creation, which is what stops any of them being edited afterwards.

Resolution criteria

YES: A complete unconditional proof in ZFC, publicly inspectable and independently checked without an unresolved mathematical gap. NO: A rigorous counterexample certified by exact reasoning or validated numerical bounds excluding Re(s) = 1/2, or a complete ZFC proof of the negation. Finite checks on the line do not prove YES; independence from ZFC leaves this contract UNDECIDED. Reference sources: Clay: Riemann hypothesis (https://www.claymath.org/riemann/). Evidence policy: use public primary research with methods and uncertainty, plus the named reference sources below. A preprint can inform the estimate but cannot alone meet a terminal criterion; require a peer-reviewed primary result and an independent reproduction using non-overlapping observations or independently prepared samples, unless this is a mathematical proof or the specific criterion instead requires independently implemented calculations. Report data provenance, exclusions, calibration, statistical model and systematic uncertainty. Independence means different data acquisition, not two papers reanalysing the same sample. For a quantitative terminal test, both independent results must meet the stated threshold; disagreement or an interval crossing the boundary means UNDECIDED. Use the final corrected version public at the signed round's evidence cutoff (UTC); exclude later evidence until a later eligible round. Every report in a terminal round must use the same cutoff, covered by the verified signed context and enforced by the configured terminal protocol; a different cutoff requires a new eligible round, never reinterpretation of a signed report or mutation of an immutable binding. This market has no calendar expiry. Retracted findings cannot supply a terminal result. If a named source disappears, use its DOI/publisher or an archived identical version, then an equivalent primary publication applying these unchanged definitions; if none is accessible, remain UNDECIDED, never substitute a different test. Missing data, failed replication, a null search outside the specified domain, or an untested alternative is not automatically NO. These are instructions for evidence assessment, not an automatic truth oracle: scientific interpretation and systematic-error judgment remain. Settlement follows the configured platform mode: terminal mode requires one valid round with all three frozen models returning the same explicit YES or NO and criterion_met=true; any UNDECIDED, failure or disagreement leaves it unresolved. Legacy proposal/challenge mode requires its recorded review process. Model agreement does not prove scientific truth. Invalidity is not NO and this text does not authorize a refund or cancellation: only a cancellation rule disclosed before exposure, if the configured contract supports it, can apply. Otherwise pause new entries and preserve holders' existing rights. Never reinterpret terms after listing.

The definition does not change when an AI estimate changes. Read the listing policy and this market's settlement status.

Frozen by hash on Solana

The hashes below were written into the market account when it was created, before any token was issued. Each one is SHA-256 over the exact text named in its label, shown on this page: the hypothesis paragraph under Exact hypothesis, the paragraph under Resolution criteria, and the identifier in the table below. The program cannot change them afterwards, and this site cannot rewrite them to match an edit.

SHA-256 of claim — the hypothesis paragraph
105efc67cd34657a6145641125be080d7df8a86ea6bc67d7752ddf9f27b56176
SHA-256 of resolution_criteria — the criteria paragraph
bd76ccb9c115c057e571d3135fea2c38158a69398c0705147745dfed381d5bcf
SHA-256 of methodology — the identifier science-2026-10-15-audit2
e7bf44caa2fed4e799d8e8a8cc7ec49cfc95af1bf7ae5b24ed2a4e875de0c91b
Context commitment
6295089c0c1c7b34196205bfdc7e14e8f32a5b0c2f856a411ec83d8622445799
Market account
C2B95PtoUUBktoQ9icZB7jqGR686C6NCypqeQ56UPqgX

These are the token mints the contract issued for this market. A swap takes one of them as the token to buy.

YES token mint
J74AaZHMedNFY5Emh8kCgwaV8VLYFAgCYnCFpSf3THJh
NO token mint
6Tp4qYNWqLPzHaiYgrekK1SZt2NALAnECFHtm2YR5arv

Read those hashes off the market account on Solana Explorer — an explorer link is not a verified-build badge.

A hash commits to bytes, not to meaning. It proves the wording was not swapped or edited after issuance. It does not prove the wording is complete, the evidence is sound, or that the deployed program cannot be upgraded.

How each model argued

Three models read the same evidence and did not fully agree. Their average is 0.60.

This round ran under methodology panel-v9. Short excerpts are below; the round 5 page keeps the full answers, sources and raw responses. The current methodology and example requests do not reconstruct this historical round's exact request.

OpenAI UNDECIDED 0.90

openai/gpt-6.1-sol

Rigorous finite verification supports the classical hypothesis, but cannot exclude an off-line zero at greater height. Clay still lists the problem as unresolved, and the checked sources provide neither an independently verified…

Would change this view: An independently checked unconditional ZFC proof would establish YES; an exactly certified off-line zero would establish NO.

Full explanation from OpenAI→
Anthropic UNDECIDED 0.03

anthropic/claude-sonnet-5.5

No accepted, independently checked proof or counterexample of the Riemann hypothesis exists. MathWorld, citing Clay (Sep 2026), lists it as unsolved. Numerical checks and heuristics favor truth, but they don't meet the YES criterion. The…

Would change this view: A peer-reviewed, community-verified proof (for example, Clay acceptance or formal verification) would move this to YES; a verified off-line zero would move it to NO.

Full explanation from Anthropic→
xAI UNDECIDED 0.86

x-ai/grok-4.7

The classical Riemann hypothesis remains an open Clay problem: no complete unconditional ZFC proof has been independently checked, and no certified zero with real part other than 1/2 is known. Verification of the first 10 trillion zeros…

Would change this view: A gap-free, independently checked ZFC proof, or a certified zero with real part not 1/2, would settle it.

Full explanation from xAI→

What moved the number

—
Oct 16

This is a new contract, not a migrated position or a continuation of old forecast history. The initial 0.50 is an initialization convention, not an AI forecast or an assessed scientific probability. Reference links are background sources,…

Nov 10
0.60 0.60 −0.3

OpenAI estimated 0.90. Rigorous finite verification supports the classical hypothesis, but cannot exclude an off-line zero at greater height. Clay still lists the problem as unresolved, and the checked sources provide neither an…

This round's saved score, answers and sources →
Nov 9
0.60 0.60 0.0 no model output

Live panel did not return all three estimates (OpenAI, Anthropic, xAI failed or gave an unusable answer). A round is only live when all three are valid, so this round is a placeholder at the previous score rather than an average of two.

This round's saved score, answers and sources →
Oct 19

OpenAI estimated 0.90. I interpret the hypothesis as the universal mathematical statement, not merely its finite verification. Rigorous interval-arithmetic checks support it over a large bounded range, but Clay still lists it as unsolved;…

This round's saved score, answers and sources →
—
Oct 19
The evidence packet · 4 entries

What the panel was shown when this round ran. A row with no source link is a description only, and the panel is told so.

Clay: Riemann hypothesis

Context

Official formulation; not evidence of a proof.

Source link

Required positive observation

Supporting

A complete unconditional proof in ZFC, publicly inspectable and independently checked without an unresolved mathematical gap.

Description only · no source link recorded

Required contrary observation

Contrary

A rigorous counterexample certified by exact reasoning or validated numerical bounds excluding Re(s) = 1/2, or a complete ZFC proof of the negation. Finite checks on the line do not prove YES; independence from ZFC leaves this contract UNDECIDED.

Description only · no source link recorded

Eligibility and unresolved outcomes

Method

Evidence policy: use public primary research with methods and uncertainty, plus the named reference sources below. A preprint can inform the estimate but cannot alone meet a terminal criterion; require a peer-reviewed primary result and an independent reproduction using non-overlapping observations or independently prepared samples, unless this is a mathematical proof or the specific criterion instead requires independently implemented calculations. Report data provenance, exclusions, calibration, statistical model and systematic uncertainty. Independence means different data acquisition, not two papers reanalysing the same sample. For a quantitative terminal test, both independent results must meet the stated threshold; disagreement or an interval crossing the boundary means UNDECIDED. Use the final corrected version public at the signed round's evidence cutoff (UTC); exclude later evidence until a later eligible round. Every report in a terminal round must use the same cutoff, covered by the verified signed context and enforced by the configured terminal protocol; a different cutoff requires a new eligible round, never reinterpretation of a signed report or mutation of an immutable binding. This market has no calendar expiry. Retracted findings cannot supply a terminal result. If a named source disappears, use its DOI/publisher or an archived identical version, then an equivalent primary publication applying these unchanged definitions; if none is accessible, remain UNDECIDED, never substitute a different test. Missing data, failed replication, a null search outside the specified domain, or an untested alternative is not automatically NO. These are instructions for evidence assessment, not an automatic truth oracle: scientific interpretation and systematic-error judgment remain. Settlement follows the configured platform mode: terminal mode requires one valid round with all three frozen models returning the same explicit YES or NO and criterion_met=true; any UNDECIDED, failure or disagreement leaves it unresolved. Legacy proposal/challenge mode requires its recorded review process. Model agreement does not prove scientific truth. Invalidity is not NO and this text does not authorize a refund or cancellation: only a cancellation rule disclosed before exposure, if the configured contract supports it, can apply. Otherwise pause new entries and preserve holders' existing rights. Never reinterpret terms after listing.

Description only · no source link recorded

Past estimates

Every weekly estimate, newest first
DateEstimateRange
Nov 10, 2026 09:23 PM EST 60% 3–90%
Nov 09, 2026 09:35 AM EST 60% no live reading
Nov 02, 2026 09:35 AM EST 60% no live reading
Oct 26, 2026 10:35 AM EDT 60% no live reading
Oct 19, 2026 07:07 PM EDT 60% 2–90%

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