Concept study / Tests & research methodsConceptual illustration. Shapes, colors, and motion are not measured data.
The framework currently combines established ideas with speculative extensions. Geometry affects many physical interactions; material systems can retain histories; scaling patterns occur in defined settings. These foundations do not yet provide a unified equation for Hill’s proposal. The open problems are therefore concrete: what exactly repeats, which state stores a trace, how does it change future behavior, and what measurable influence could a surrounding domain have? A productive contribution need not endorse the whole picture. It can supply a derivation, dataset, counterexample or test that resolves one of these questions within a clearly stated domain.
Problem 1: specify the cross-scale map
Identify a pair of systems, a mathematical representation of each and a transformation between them. State which observables should remain invariant and which parameters change. Explain why similar appearance is insufficient and specify a control that could reproduce it accidentally. The requested deliverable is a quantitative prediction for a third, withheld system or scale. A successful map may reveal a shared mathematical approximation without establishing identical physics. A failed map is also useful if it identifies a characteristic scale or interaction that blocks the proposed universality.
Problem 2: locate the memory mechanism
Define a state variable, an encoding process, a readout and a retention condition. Then ask whether the trace survives a specified transformation, such as relaxation or a controlled structural change. Distinguish persistence in correlations from persistence in a single energy value. The requested deliverable is a benchmark that predicts when the trace should disappear as well as when it should remain. Any extension to consciousness requires additional operational and theoretical work; a materials-memory result alone does not bridge that gap or establish a universal informational substrate.
Problem 3: give Alpha 1 an observable consequence
Specify a mathematical model of the proposed parent domain and its coupling to our observable universe. A center and a spiral drawn outside the observable domain are not yet measurable coordinates. The requested deliverable is a prediction that differs from an established cosmological baseline while respecting existing constraints in the relevant model family. If no observable coupling can be given, retain Alpha 1 as a conceptual hypothesis. The same standard applies to travel proposals: identify a physical mechanism, conservation accounting and measurable intermediate prediction before discussing a route to an inaccessible center.
The mathematical lens
A project criterion for contributions, not a physical equation. Negative results and counterexamples meet it when their scope is clear.
Turn it into a question.
- Question
- Which missing specification prevents the next empirical test?
- Method
- Choose one problem and submit a model, reproducible analysis or counterexample with a stated failure condition.
- What would count against it?
- A contribution that cannot distinguish alternatives leaves the empirical status unchanged.
Progress means reducing a specific uncertainty, including by ruling an idea out.
Follow the original work.
These sources support the mechanisms and limits discussed here. They do not endorse Hill’s framework. Notes distinguish research proposals, reviews, and observations.
Continue the investigation
Edition 02 · 18 October 2026 · AI-assisted synthesis. See editorial method.