Research Plan · Theoretical Physics · 2025–ongoing

The Informational Singularity
Intersection Hypothesis

What if every fundamental limit in physics — the speed of light, absolute zero, the Planck length — is the same phenomenon seen from different informational angles? The ISI Hypothesis proposes a single axiomatic foundation from which the measurable constants of physics emerge as necessary consequences.

Active · v3.5 published on Zenodo
The Axiom

A single foundation

A1 — The Foundational Axiom
"The number 1 is the unique topologically unreachable Möbius-dual fixpoint — the only value that cannot be constructed from below or approached from above within any complete informational system."

From this single axiom, the ISI Hypothesis derives the speed of light, absolute zero, and the Planck length as necessary informational boundaries — not arbitrary constants but inevitable consequences of the structure of information itself.

The hypothesis further proposes that abstraction force — the drive of systems toward higher-order organisation — is a fundamental cosmological driver, connecting physics to biology, to demography, and to the emergence of consciousness.

Research Structure

Five connected claims

Claim 0 — Multi-dimensional metric spaces (foundational precursor)
Every physical measurable is a separate one- or more-dimensional metric space — analogous to the way classical three-dimensional space uses distance as its metric. Within each such space, fractal singularities emerge and iterate over time. These iterating fractal singularities can merge: when they do, a higher-order version of that singularity emerges within the same space. When singularities from different metric spaces intersect, only their projection is visible and measurable within each individual space. What we observe and measure in our three-dimensional space are therefore the projections of fractal singularities from other metric spaces — not the singularities themselves. This framework preceded and motivated the ISI Hypothesis, providing its geometric intuition.
Claim 1 — Physical constants as informational boundaries
The speed of light c, absolute zero 0K, and the Planck length lP are not independent empirical facts but different expressions of a single informational limit: the boundary of what can be measured, transmitted, or structured within a finite informational system. In the language of Claim 0: they are the projections of the same singularity seen from within different metric spaces.
Claim 2 — FractAlgebra
Fractals are not merely geometric patterns but the primitive elements of a new algebraic system — FractAlgebra — in which the operations of combination, scaling, and self-reference are foundational. FractAlgebra provides the mathematical language connecting the multi-dimensional metric space framework (Claim 0) to its physical implementations. The merging of fractal singularities described in Claim 0 is the algebraic operation of FractAlgebra at its most fundamental.
Claim 3 — Abstraction force as cosmological driver
Complex systems — physical, biological, social — exhibit a directional tendency toward higher-order organisation that cannot be explained by entropy alone. ISI names this "abstraction force" and proposes it as a fundamental driver alongside gravity and electromagnetism. In the framework of Claim 0, abstraction force is the tendency of fractal singularities to merge into higher-order versions — an intrinsic property of the multi-dimensional metric space structure of reality.
Claim 4 — Standard Model fermion mass clustering
The observed mass distribution of Standard Model fermions is not random but clusters in a pattern consistent with ISI's informational boundary framework. This is the primary empirically testable prediction of the hypothesis in its current form. In the Claim 0 framework, fermion masses are projections of singularity intersections across metric spaces — their clustering reflects the discrete nature of those intersections.
Methodology

How the research proceeds

AI-augmented formal derivation
The ISI Hypothesis is developed through sustained human-AI dialogue. Every derivation step is archived with attribution ([H] human insight, [AI] synthesis, [H+AI] augmented). All claims are stress-tested across multiple AI models with consistent framing. Contradiction between models is treated as data — it marks the boundary of what is currently formalizable.
Zenodo preprint publication
Each version is published as a peer-reviewable scientific preprint on Zenodo under a citable DOI. The current version (v3.5, DOI 10.5281/zenodo.20095134) is the primary reference. Versioned publication allows transparent iteration: the scientific community can track how the hypothesis has changed and why.
Empirical test: fermion masses
The mass clustering prediction is the most tractable near-term empirical test. The methodology uses published PDG (Particle Data Group) mass values and tests whether the ISI-predicted clustering pattern is statistically distinguishable from random distribution. This analysis is in progress as of v3.5.
Connection to Floquet theory and time crystals
ISI v3.4+ explores connections between the foundational axiom and Floquet theory (periodically driven quantum systems) and time crystals. These connections are currently speculative but structurally motivated — they represent the next formal derivation target after the fermion mass analysis.
Timeline

Research roadmap

2025 Q1–Q3
ISI v1.0–v2.8. Initial formalization of the foundational axiom. First Zenodo deposit. English translation. Introduction of the operators F (fractal) and Π (projection). Connections to Penrose tiling identified.
2025 Q4–2026 Q1
ISI v3.0–v3.5. FractAlgebra formalized. Abstraction force operationalized. Fermion mass clustering prediction derived. Floquet / time crystal connections explored. Current published version.
2026 Q3–Q4
Empirical analysis. Statistical test of fermion mass clustering prediction against PDG data. Peer review submission target: journal in mathematical physics or foundations of physics.
2027+
FractAlgebra extension. Formal axiomatization of FractAlgebra as an independent mathematical system. Connections to Holographic Fractal Ledger (HFL) and EquoraVault formalized. Broader peer engagement sought.
📄 Read ISI v3.5 on Zenodo — DOI 10.5281/zenodo.20095134 →
Research Notes

Active observations & cross-domain connections

Working notes that emerged from active research — structural resonances, unexpected connections, and draft proposals that are not yet formal publications but are too significant to leave undocumented.

Working Note · 2026-06-28
Erdős & Probabilistic Existence: Connections to Fractal Ontology
The 1947 probabilistic method — proving a network exists without constructing it — maps structurally onto ISI Axiom A1, the FractAlgebra Π-operator, and HFL's Monte Carlo PoE. A proposed Probabilistic Existence Lemma bridges the traditions formally. Read note →
ISI · FractAlgebra · HFL
Method & Scope

How this page was produced

Trilith Method™ · Research Card
Programme status
Active · v3.5 published on Zenodo
Machine contributionI
Literature discovery and synthesis, candidate identification, computational modelling, and first drafts of this page. Volume and speed are the machine's contribution; none of it is treated as verified on its own.
VerificationII
Claims traced to primary sources rather than to summaries of them. Contested claims run through assert–refute–adjudicate across independent model families. Errors found after publication are corrected on this page with their date.
Human governanceIII
Problem selection, the evidentiary bar, and the decision to publish rest with Pölö (László Papp), EQUORA Institute, who holds editorial responsibility for this page.
Evidence basis
Stated in the Methodology section, per component. Where a source is a preprint, a pilot study, a single trial or a modelled estimate, the page says so at the point of use.
Version
v1.0 · 2026-06-27
Method
Trilith Method™ framework · how the method is being tested
What this page is

This is a research plan rather than a result. It sets out what the programme intends to test, on what basis, and what would count as failure. Parts of it will turn out to be wrong; where that happens, the correction is recorded here with its date instead of being quietly removed.

Work by third parties is attributed to its sources and described at the confidence its evidence supports. Nothing on this page should be read as professional advice in the programme's domain, and nothing here has been peer reviewed unless a specific publication is cited as such.

Research Lead

Principal investigator

Pölö (László Papp) — Founder, EQUORA Institute. The ISI Hypothesis is the foundational theoretical work of the Institute, connecting all other research domains through the abstraction force framework. Questions and peer engagement: lpapp@equora.institute