Live markets · visual mathematics · open research

See the structure.
Follow the evidence.

Watch market weather. Explore the geometry of fractions. Follow a paper from its first picture to the exact rule behind it.

Finance is descriptive, not a trading signal. Research results, finite certificates and open questions are labelled separately.

Reduced fractions arranged in concentric denominator shells, coloured by denominator
A fraction, drawn. The Polar Shell Renderer places reduced k/n at radius √n and angle 2πk/n. Explore the object →

Choose your entrance

Three ways into the work.

Begin with the live object, the visual explanation or the paper. You do not have to learn the whole vocabulary first.

01

Watch the markets

Sixteen chamber-level views of public market data, with the snapshot time, coverage and limitations kept visible.

02

Find the connection

A guided Atlas of fractions, geometry, waves and the current analysis program. Read the object before exploring the relationship map.

03

Read the research

Start with the latest volume, browse 59 indexed records, or follow the earlier papers and tools that led here.

The current reading entry

From a triangle to a research frontier.

Five records since July 31 →
Cover of Triangular-n Postmaster, Reading Volume v4.2; RH status open
CURRENT READING VOLUMEv4.2RH OPEN

Triangular-n Postmaster

From the triangular primitive to the completed source frontier.

Reading Volume I · 97 pages · September 12, 2026

A familiar triangle becomes a coordinate, then a fold, then a ladder of exact identities. The new reading guide shows where the established results end and the all-order source estimate remains open.

Objects you can inspect

Move from the picture to the rule.

All interactive tools →

Polar shells & rational addresses

See denominator populations, primitive roots and the difference between an equal-area shell and a constant-density disk.

Geometry you can rotate

Explore the rational chamber, the six-cardinal construction and the reciprocal-metallic plane. Related pictures retain their own assumptions.

Waves with an evidence trail

Exact boundary scattering, finite-model claims and receipt-bound figures in the existing Finite-Observer Ledger companion.

Origins remain part of the site

Addresses, instruments, meaning.

The tools that started the project are still here, without being the first thing every visitor has to decode.

A public identity, a checkable trail

Read the claim. Keep its limits.

Papers connect to their records and tools. A finite computation does not become an all-order theorem; a market visualization does not become permission to trade.