Riemann Console dot org

An open research record on the Riemann Hypothesis.

NAV READY · TYPE SHORTCUT · ENTER EXECUTES

RC://SEARCH · PUBLIC CORPUS

SEARCH

Query public material: search concepts, mathematics, objects, evidence and provenance.

● INDEX ONLINE

TRY A QUERY

OBJECTS186
FRAGMENTS5209
EQUATIONS0
RELATIONS575
SCOPEPUBLIC ONLY

Enter a query to search released public material.

RC://SEARCH · HELP

SEARCH HELP

You can use Search like an ordinary search box, then add precision only when you want it. This drawer lists every Search operator and every public-object command currently supported.

Quick Start

Start with the words you are interested in. Search looks across public titles, summaries, sections, equations, notes, citations, figures and passages, then tells you why each result matched.

CONCEPTpositive definiteness

If a released Glossary entry exactly matches the concept, its definition is prioritised; otherwise Search finds the idea wherever it appears.

EXACT PHRASE"critical line"

Quotes ask Search to keep those words together as a phrase.

NARROW ITkind:milestone positivity

Search for “positivity”, but only inside public milestone records.

Focus an empty Search field to see public examples and completions.

(Clicking an example closes Help and prefills the Search box. It does not run the search until you press Enter or EXECUTE.)

Search Operators

Operators are optional filters typed into the same Search box. There are 10 operators. The list below is complete.

kind:
Choose a type of public record.

Complete value list: page, article, research, dsp, milestone, author, event, release, correction, lab.

EXAMPLE kind:milestone positivity

section:
Look only in one public section.

Type section: and autocomplete shows the complete set of section names in the current public index.

EXAMPLE section:research xi

id:
Find a public object by its identifier.

Exact IDs and safe public-ID prefixes can match.

EXAMPLE id:MIL-RH-0004

has:
Require a particular kind of material or relationship.

Complete value list: equation, section, citation, note, figure, relation, correction, release.

EXAMPLE has:equation xi

status:
Match a status already recorded on a public object.

Type status: and autocomplete shows the complete set of status values currently present in the public index.

EXAMPLE status:validated

cites:
Find public material that cites a bibliography entry.

You can start from a citation key or words in its public reference metadata; autocomplete resolves that to the public citation key.

EXAMPLE cites:riemann-1859

related:
Find public objects directly connected to another public object.

Use a public object ID; autocomplete can supply available public IDs.

EXAMPLE related:MIL-RH-0004

since:
Keep records dated on or after a date.

Use YYYY-MM-DD.

EXAMPLE since:2026-09-01

before:
Keep records dated before a date.

The date itself is not included. Use YYYY-MM-DD.

EXAMPLE before:2026-10-01

corrected:
Include or exclude objects with a published correction relationship.

Complete value list: true, false.

EXAMPLE corrected:true

COMBINING FILTERS

You can use several operators and ordinary words together. Every part must match: kind:milestone has:equation positivity means “milestones that contain an equation and also match positivity”.

Mathematical Search

You do not need to guess whether the site used a mathematical symbol, a TeX command or an English spelling. Search deliberately recognises a small, explicit set of equivalent spellings.

COMPARISONS · COMPLETE LIST

≥ / >= / \ge / \geq · ≤ / <= / \le / \leq · ≠ / != / \neq

GREEK ALIASES · COMPLETE CURRENT LIST

α alpha · β beta · γ gamma · δ delta · ε/ϵ epsilon · ζ zeta · θ theta · λ lambda · μ mu · ν nu · ξ xi · π pi · ρ rho · σ sigma · τ tau · φ phi · ψ psi · ω omega. The matching lowercase TeX names are also recognised.

CURATED PHRASES · COMPLETE LIST

non-negative / nonnegative · positive definite / positive definiteness · K-Bessel / Bessel K.

FIND ξ ANYWHERExi

Can match ξ whether it was written as a symbol, TeX or plain text.

EQUATIONS ONLYhas:equation xi

Return only public objects with an equation fragment that also matches xi.

Search does not infer theorem-level equivalence. It will not decide that two different formulae “mean the same thing”. If an alias rather than literal text produced the match, the result can say WHY · NOTATION ALIAS.

TRACE

TRACE answers a simple question: “What is this public item explicitly connected to?” It is a map of recorded links, not an AI guess about what might be related.

trace:<public-id>
Show the explicit public connections around an object.

You can see incoming and outgoing relationships, public bibliography citations, and—where available—short object-to-object paths up to three steps deep.

EXAMPLE trace:MIL-RH-0004

depends:<public-id>
Show only explicit dependency relationships.

Use this when you want the narrower “what does this record say it depends on?” view.

EXAMPLE depends:MIL-RH-0004

Public IDs appear on Search result cards. You can also type trace: or depends: and let autocomplete offer public IDs that are actually available.

Important: a TRACE line labelled “dependency”, “related object” or “citation” means exactly that. It does not mean “proved by”, “supports”, “confirms” or “mathematically validates”.

Provenance

Provenance answers “What does the public record say about where this item came from and how it was published?” It is about the record and its publication trail, not a verdict on whether the mathematics is correct.

cite:<public-id>
Make a ready-to-copy citation.

Search uses explicit public metadata: title, record kind, public ID, date, canonical URL, and an author only when public authorship metadata explicitly supplies one.

RESULT a citation you can copy.

verify:<public-id>
Open the recorded public verification view.

It can show public status fields, related releases, published corrections and links to the site’s general verification resources.

RESULT the evidence and publication metadata currently recorded for that public item.

What a hash, signature or timestamp can tell you: it can support a statement about the identity, integrity or timing of a particular record. By itself it does not establish mathematical correctness, novelty or authorship beyond what the public evidence actually records.

TRACE + PROVENANCE contain all four public-object commands: trace:, depends:, cite: and verify:. That list is complete.

Keyboard

↑ / ↓
Move through Search suggestions.
Tab
Accept the highlighted suggestion without running it.
Enter
Run the query.
Esc
Close suggestions or Help first; then leave Search mode.

Public Scope

Everything described here—Search, autocomplete, TRACE, citations and verification views—works from the validated public corpus only. Unpublished and review material is not part of Search.

If an identifier is unavailable, Search deliberately gives the same generic public response rather than revealing whether it is private, draft, rejected, withheld or simply does not exist.

Open the full Search manual