Behind every
claim,
foundations.
Research is also judged by how it presents its sources, dates and limitations.
Here is what this showcase lets you examine.
NOT ACCESS TO PRIVATE FILES
The sources
are identified.
This presentation rephrases the overviews from the HORIZON V1 showcase and its V2 dossier. It adds neither access to private work nor independent scientific validation.
V1 / RESEARCHGoal and research frontier
Exact, self-contained and compact representation. Research frontier dated 18 October 2026.
Predictive state growth
Research Z. Internal acceptance on 1 October 2026.
Goals, model and limitations
Detailed presentation. Access subject to V2 permissions.
V1 cites, among other sources, the project README, the research frontier of 18 October 2026 and a Research Z artifact dated 1 October 2026. The full proof and internal reports remain in the private dossier.
Every word
has a scope.
- Hypothesis
- A proposal to examine, which may be refuted.
- Finite verification
- An exact computation over a bounded, declared domain.
- Partial argument
- A line of reasoning with a step still to be established.
- Internally accepted result
- Acceptance through HORIZON’s review, within a specified scope.
- Counterexample
- A case that invalidates the proposal as stated.
- External validation
- An assessment outside the project, to be documented separately.
The meaning of the scenes.
The limits of the images.
The number map +
The integers from 1 to 1,681 are arranged in an Ulam spiral, a classical construction. Their primality is computed by a sieve. The 263 primes are highlighted. Tilt and depth are artistic projection choices; the planar arrangement preserves the spiral’s positions.
The five futures and four states +
Five distinct binary sequences illustrate five distinguishable futures. In an encoding with four states, at least two share a state. The example illustrates the counting principle, not the Research Z arithmetic family or its full proof.
The calculations and coordinates +
The HORIZON vision scene illustrates a goal: build an exact, autonomous and compact representation from n alone, preserve useful distinctions and prove its costs. Its particles, paths and groupings are artistic; they depict neither a discovered algorithm nor measurements. The polynomial n² + n + 41 and the 4ᵏ counting argument are classical teaching examples.
The luminous field and the collective +
The luminous opening and observatory landscapes are generative. The constellations and their flows illustrate responsibilities. No visual represents a measurement of laboratory activity, a new mathematical law or a proof.
Your visit.
Your pace.
Publisher
HORIZON, an independent program led by Geoffrey Muller, France. Contact: contact@horizonorigines.xyz.
What the site’s code does
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Hosting and links
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Reading comfort
The “Motion” button pauses animations. The system’s reduced-motion preference is respected. Explanations remain available without animation, and navigation works with a keyboard.
Scope of the content
An informative presentation of ongoing research, dated 29 October 2026. No general solution or external academic validation is claimed. To cite a scientific result, request the supporting proof and full scope.