Advancing research in theoretical physics.
thomas connelly "I like Turtles"
Advancing research in theoretical physics.
Why Work With ME?
Physics by Tom offers personalized physics tutoring for high school, college, and graduate students. Whether you need help building strong fundamentals, succeeding in a demanding course, working through advanced mathematics, or developing a deeper conceptual understanding, sessions are adapted to your goals and learning style. Led by a PhD candidate in Natural Sciences specializing in theoretical physics, tutoring is available in mechanics, electromagnetism, relativity, quantum physics, cosmology, and related mathematics. Online sessions welcome students seeking anything from patient academic support to serious, research-level conversation.
Beyond Curved Spacetime: A Modal Foundation for Physics (Book, Pending Publication)
Beyond Curved Spacetime is the foundational book-length presentation of the Execution–Interaction–Memory framework. It develops the domain declaration of the programme: instead of treating spacetime as the primitive container of physics, it asks what minimal structure must exist for distinction, relation, and persistence to be possible.
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Beyond Curved Spacetime is the foundational book-length presentation of the Execution–Interaction–Memory framework. It develops the domain declaration of the programme: instead of treating spacetime as the primitive container of physics, it asks what minimal structure must exist for distinction, relation, and persistence to be possible.
The book introduces the EIM triad, the coordination-depth picture, and the idea that quantum behavior, classical spacetime, and horizon phenomena may be different regime expressions of one underlying coordination process. It is written as a structural argument rather than as a completed replacement for standard physics. Some quantitative identifications in the book are presented as candidate empirical bridges and are tracked in later technical audits. The book should be read as the broad conceptual foundation from which the dissertation, Codex, simulations, and specialized papers develop more targeted claims.
The Black Hole as Dynamical Bridge: A Coordination-First Account of Memory, Projection, and Saturation
This dissertation develops the black-hole sector of the Execution–Interaction–Memory framework. Its central proposal is that black holes should be understood not as exceptional breakdowns of physics, but as high-Memory coordination horizons: regimes where accumulated constraint approaches a saturation limit and ordinary spacetime descript
This dissertation develops the black-hole sector of the Execution–Interaction–Memory framework. Its central proposal is that black holes should be understood not as exceptional breakdowns of physics, but as high-Memory coordination horizons: regimes where accumulated constraint approaches a saturation limit and ordinary spacetime description must be interpreted through boundary dynamics. The work studies black holes as regulators of Memory, horizon structure, evaporation, merger behavior, and projection failure. It reframes familiar problems, including the information paradox, area-law behavior, and interior singularity, as different expressions of one saturation-boundary problem. The dissertation is a focused application of the broader EIM architecture. Its claims are presented as a developing theoretical program: some results are structural, some are candidate derivations, and some remain open problems requiring further mathematical closure.
EIM Codex
The EIM Codex is the technical reference and audit ledger for the Execution–Interaction–Memory framework. Where Beyond Curved Spacetime presents the broad structural vision, the Codex organizes the machinery behind it: primitive distinction, admissibility, Memory, the enforced EIM triad, dependency chains, formal entries, open problems,
The EIM Codex is the technical reference and audit ledger for the Execution–Interaction–Memory framework. Where Beyond Curved Spacetime presents the broad structural vision, the Codex organizes the machinery behind it: primitive distinction, admissibility, Memory, the enforced EIM triad, dependency chains, formal entries, open problems, and candidate empirical targets. Its purpose is to make the framework inspectable rather than merely persuasive, separating foundational commitments from derived results, provisional bridges, historical residues, and unresolved projection questions. The document moves from the core forcing chain into an encyclopedia-style catalogue of atomic claims and guided topic threads, allowing readers to trace how spacetime, quantum behavior, black-hole horizons, and cosmological regimes are treated as regime-dependent readouts of deeper coordination constraints. It is not a popular exposition and not a claims brochure; it is a research-grade working reference: part formal atlas, part versioned audit record, and part launchpad for papers on horizons, neutrino-sector structure, percolation thresholds, projection/readout, and the mathematical conditions under which physical law becomes observable.
EIM Simulation HUB
I’ve been experimenting with a small graph-local simulation for my EIM framework, using the dodecahedral graph as a toy substrate for “open-cylinder” readout dynamics.
The core idea is simple:
The graph is closed. The readout is open. Closure is coherence, not death.
In this notebook, I compare several regimes on Γ_dodec: ordinary isotropic
I’ve been experimenting with a small graph-local simulation for my EIM framework, using the dodecahedral graph as a toy substrate for “open-cylinder” readout dynamics.
The core idea is simple:
The graph is closed. The readout is open. Closure is coherence, not death.
In this notebook, I compare several regimes on Γ_dodec: ordinary isotropic diffusion, defect-driven internal readout, exterior-channel sink behavior, and black-hole-like compression/recycling as a Memory-architecture toy. The most useful distinction so far is this:
Black holes are terminal for the local exterior path, but not terminal for the global graph.
This is not a proof, not a derivation, and not evidence for the framework. It is a scratch diagnostic: a way to test whether the conceptual architecture can be made operational without immediately contradicting itself.
What excites me is that the visual contrast is beginning to look like a real dynamical question rather than just a metaphor. If closure is modeled as terminal absorption, active dynamics die. If closure is modeled as global coherence with internal readout and Memory compression, the system can sustain structured asymmetry while remaining globally integrated.
Still very much Appendix W territory. Cool antlers, not load-bearing antlers yet. But this feels like a promising little physics-shaped sandbox.
#theoreticalphysics #complexsystems #graphmodels #cosmology #simulation #foundations
Arithmetic from Modal Closure: Unique Factorization as the Closure Object of a Triadic Pre-Algebraic Substrate
This paper develops Modal Algebra as a proposed reconstruction of arithmetic from the Execution–Interaction–Memory triad. Its central claim is that arithmetic should not be treated as an unexplained primitive, but as a structure that becomes available only when three irreducible conditions are present: irreversible activity, composable re
This paper develops Modal Algebra as a proposed reconstruction of arithmetic from the Execution–Interaction–Memory triad. Its central claim is that arithmetic should not be treated as an unexplained primitive, but as a structure that becomes available only when three irreducible conditions are present: irreversible activity, composable relation, and retained order. From these conditions, the work reconstructs the natural numbers as the projection of accumulated Execution, then develops addition, multiplication, Euclid’s Lemma, and unique factorization as consequences of closure rather than as imported assumptions. The argument also runs in reverse: any system capable of supporting arithmetic must already contain the functional equivalents of Execution, Interaction, and Memory. In this sense, arithmetic is treated not merely as a formal construction, but as a constraint on what any reality capable of counting, combining, and preserving distinctions must already be. The paper connects this mathematical reconstruction to the broader EIM framework, where the same triadic structure appears in entropy, temporal direction, persistence, and physical structure formation. Its goal is not to replace standard foundations by assertion, but to show that arithmetic may be the visible shadow of a deeper substrate: a closure-driven process in which ordered distinction, irreversible accumulation, and composable interaction are already at work.
The Closed Kernel of EIM
This working paper isolates the closed mathematical core of the Execution–Interaction–Memory framework: a finite dodecahedral graph substrate whose spectral and representation-theoretic structure can be stated independently of the still-open projection and readout layer. Its central result is an exact identity linking three kernel feature
This working paper isolates the closed mathematical core of the Execution–Interaction–Memory framework: a finite dodecahedral graph substrate whose spectral and representation-theoretic structure can be stated independently of the still-open projection and readout layer. Its central result is an exact identity linking three kernel features defined without empirical fitting: the first cycle-counting invariant, the spectral coordination deficit, and the golden-ratio structure native to the dodecahedral graph. In plain terms, the paper shows that the EIM kernel is not merely a visual metaphor. It is a precise finite object with auditable structure and exact dimensionless relationships. The paper then separates this closed kernel mathematics from possible physical correspondences. Several suggestive bridges appear, including scalar spectral tilt, candidate neutrino-sector structure, and other links to observed physics, but these are treated as phenomenological identifications or open projection questions rather than completed derivations. The point is careful and specific: EIM now has a closed, inspectable kernel whose finite structure produces nontrivial invariants, while the map from that kernel to physical observables remains an explicit research program. This draft belongs to the broader EIM effort to develop a coordination-first foundation for physics, where spacetime and measured quantities are investigated as projection-layer readouts over a deeper Execution–Interaction–Memory substrate.
The Projection Boundary of EIM
The Projection Boundary of EIM
This working paper draws a precise boundary inside the Execution–Interaction–Memory framework: between the closed mathematical kernel, which the companion paper establishes, and the projection layer by which that kernel would register as observable readout. The question is narrow and structural — does the closed kernel contain, within its
This working paper draws a precise boundary inside the Execution–Interaction–Memory framework: between the closed mathematical kernel, which the companion paper establishes, and the projection layer by which that kernel would register as observable readout. The question is narrow and structural — does the closed kernel contain, within itself, a canonical operation that turns its structure into a registered value? — and the paper's answer is a disciplined negative.
The central result is not a derivation but a classification. The paper maps the routes by which a kernel-internal projection selector could exist and shows, one by one, which are closed and why: the canonical-scalar route is closed (the invariant scalars are Galois-fixed), the gradient and self-map route is closed (the relevant equivariant cubic is blind to the target sector), and the grading-coupling route is blocked. A single route survives as the right shape — the reduction to the tetrahedral subgroup A₄, which opens a controlled sector-crossing channel while keeping the target intact — but the kernel supplies no object that instantiates it. There is no carrier for the five-frame datum the route requires, and computational tests confirm the absence at three independent levels: no state carrier, no spontaneous operator carrier, no readout-driven frame selection.
The paper is careful about what this is and is not. It is not a projection closure; no selector is constructed, and the open problem is not solved. Nor is it a failure of search. It is a finite, typed boundary: the projection problem is shown to be neither solved nor vague but classified — the kind of object a future closure would have to supply is named precisely, and the moves that would only appear to close the gap (naming an observer, invoking consciousness, promoting a hand-built generator by fiat) are excluded in advance.
The point is not that EIM is incomplete; the point is that the incompleteness is now located rather than hidden. The closed kernel does not observe itself. The kernel constrains structure; readout requires an indexed operation — and whether such an operation can be built without smuggling in the selector the kernel was shown to lack is the open problem this paper hands, sharply, to its successors.
This draft is part of the broader EIM project to develop a coordination-first foundation for physics, where spacetime and observable quantities arise as projection-layer structures over a deeper Execution–Interaction–Memory substrate.
EIM Cosmic Collider (Colab)
The Projection Boundary of EIM
This notebook is a working sandbox for the EIM tri-lobe rule. It assembles a lattice from five copies of the dodecahedral backbone, sparsely stitched at the seams, and lets the Execution–Interaction–Memory coordination play out step by step: an explicit-memory lobe (the ρ₃⊕ρ₃′ sector), an interaction lobe (ρ₅), and an observer-commit lob
This notebook is a working sandbox for the EIM tri-lobe rule. It assembles a lattice from five copies of the dodecahedral backbone, sparsely stitched at the seams, and lets the Execution–Interaction–Memory coordination play out step by step: an explicit-memory lobe (the ρ₃⊕ρ₃′ sector), an interaction lobe (ρ₅), and an observer-commit lobe that turns accumulated interaction pressure into actualization events. Rather than the rigorous homological projectors, it uses transparent numerical proxies for each sector and projects onto the dodecahedron's own eigenvectors to read off seam occupancy, branch ratios, and commit signals over time. A gravitational-wave injection — a neutron-star-collision analogue — spikes topological debt at one node so you can watch the ripple propagate, scars spread, and the commit rate respond. Parameter sweeps over the diffusion rate and observer focus, plus an observer-trajectory analysis, round it out. The aim is exploratory: probing the dynamical side of the W.43 (OP-K1) admissibility question rather than claiming to settle it.
A Projection-First Case Study of Bell Correlations on the Dodecahedral Non-Backtracking Sector
A Projection-First Case Study of Bell Correlations on the Dodecahedral Non-Backtracking Sector
It is already known that the Platonic solids host maximal Bell violations (Tavakoli & Gisin 2020; Bolonek-Lasoń & Kosiński 2021), and that a complex structure — the “imaginary unit” of quantum theory — can emerge, unique up to sign, from the symmetry or dynamics of an underlying real structure (Moretti & Oppio 2017; Aste 2019; and, in d
It is already known that the Platonic solids host maximal Bell violations (Tavakoli & Gisin 2020; Bolonek-Lasoń & Kosiński 2021), and that a complex structure — the “imaginary unit” of quantum theory — can emerge, unique up to sign, from the symmetry or dynamics of an underlying real structure (Moretti & Oppio 2017; Aste 2019; and, in discrete form, from the unitarity of graph quantum walks). This paper does not claim to derive the Tsirelson bound, nor to discover a new prediction. Its contribution is interpretive and structural, anchored to one fully explicit finite model: the golden sector of the non-backtracking (Hashimoto) operator of the regular dodecahedron, on which a genuine A₅×ℤ₂-equivariant qubit and a CHSH value of 2√2 are realized. Against that worked example we make three claims. (1) A projection-first reading, in which spatial separation and the causal limit are outputs of a substrate projection rather than primitives, can here be stated as a mathematically defined operation rather than a metaphor — at the cost, openly admitted, of dissolving a non-paradox rather than a paradox. (2) A triadic closure classification (two local bisections plus one comparison closure) maps cleanly onto the Bell scenario and separates, in representation-theoretic terms, the parts of the correlation the substrate symmetry fixes from the part it does not. (3) The model permits a precise relocation of the open quantitative question: the cosine law and the value 2√2 are not symmetry-derivable (they live in a multiplicity space on which A₅ acts trivially); a dynamical operator and a unitarity (quantum-walk) metric premise select the complex structure canonically up to a single chirality bit; what remains genuinely unforced is exactly the measurement-circle freedom of any Bell test, plus the metric premise. The residual freedom is thereby reduced to a named one-bit object tied to the Galois structure of the golden field ℚ(√5).