Independent mathematical research

OMEGA NAUGHT

OMEGA NAUGHT is an independent mathematical research and computational reproducibility project by Matthew Alan Newman.

The project studies marked Euclidean geometry, scale transformations, rational floor maps, exact remainder reconstruction, and finite spherical sampling.

Author: Matthew Alan Newman · ORCID 0009-0007-5468-3125

Open the atlas Try the 399 example

New here? Start with the reading guide.

Research identity and evidence

This is a mathematical research archive, not a fiction or world-building project. Interactive tools demonstrate specified mathematical constructions and computations.

Evaluate each claim under its stated definitions, assumptions, and domain. A repository deposit, a theorem label, or a successful program run does not by itself establish mathematical correctness, novelty, peer review, or independent validation.

Mathematical statement and proof: Read the exact statement, hypotheses, and argument. Assess the proof separately from implementation results.
Computational check or certificate: A recorded result applies to its declared inputs, arithmetic, checks, and artifact version.
Formal verification: Applies only to the linked formal statements, recorded assumptions, toolchain, and build evidence.
Implementation conformance: Records agreement with a named specification or reference output; it is not a blanket verification of the mathematics.
Peer review: Claimed only for a specific work with linked publication or review evidence.
Independent reproduction: Claimed only for a named third-party reproduction with public evidence.
Conjecture or proposed application: Not an established result. Further mathematical or empirical support is required.

Publication, review, and independent-reproduction status are maintained on the Status page. No site-wide claim of novelty, peer review, or independent validation is made.

27 October 2026

A 120-signal extension on the 600-cell graph is recorded separately from the typed interface network. The reserved DOI remains unpublished.

24 October 2026

OMEGA NAUGHT studies marked geometry and recoverable information through explicit mathematical representations. The current development links self-similar scaling, rational quantization, exact geometric discrepancies, and witness-preserving reconstruction, and organizes those operators into a decodable reference language.

Six baseline marks around a one-arcsecond circular opening. The selected outer segment is G = a phi; the opposite semicircle is C = a pi. A magnified inset separates the seed marks. — Six labeled marks, a selected semicircle, and a declared readout. The inset magnifies the one-arcsecond opening without changing the model. G + C is a selected measurement, not the full outline length. Open full-size diagram: The marked construction

Drawn from the stated formulas

Unit circle with the retained major arc and six labeled baseline marks. The outer marks are the declared extensions. — The marked plan at scale one. The opening between d and b is one arcsecond, so those two marks meet at this scale.

A filled ellipse compared with the unit circle and the six baseline marks. The outer marks lie outside the ellipse. — Equal-weight moment ellipse. It is not the arc-and-feet curve, and the semiaxis R is not φ.

A nearly square rectangle around the six baseline marks, with width and height labeled. — Outer scaffold from the adopted drawing rule. Its departure from a square is the one-arcsecond chord.

Equal-scale arc and bilateral steps, with an enlarged inset of the one-arcsecond seed. — The same shape at equal axis scales. The inset is a change of scale, not a second object. Open the geometry page.

Choose a calculation

All tools

Construct the geometry

Inspect the marks, change the pose, and export the specified coordinates.

Start with radius 1 and the canonical one-arcsecond seed.

Recover an integer record

Follow the floor map and reconstruct a seed from its ordered remainder record.

Start with 399; the first quotient is 135.

Average a polynomial

Compare a spherical average with a finite weighted sample.

Try x². Its normalized sphere average is 1/3.

Reconstruct a field

Explore what the aligned boundary measurements determine in a specified field space.

Compare the twelve-sample reading with the extra cubic-mode probe.

Explore the relationships

What makes a connection admissible?

A shared symbol suggests a question. An admitted relationship needs a stated relation, a witness, and a contract naming its domain and what it preserves or loses.

Inspect the typed witness graph Browse the mathematical branches

Read the evidence in context

Exact certificates, parameter declarations, and trusted analytic schemas carry different kinds of support. Their labels and restrictions remain attached to each relationship.

Read the existing network proof dossier.