An Exploratory Application of the Structural Methodology to Physics as a Domain

1. Introduction

This paper is the most exploratory in the series. We say this up front because the subject — the foundational structure of physics — is one where the field has earned the right to skepticism toward outsiders. Many attempts have been made to “rethink physics from information”; most have been imprecise where they needed to be precise, and over-confident where they needed to be tentative. We have no wish to add to that list.

The paper applies the structural analysis methodology of A Structural Methodology for Information System Domains to physics treated as an information-substrate domain. The methodology has been useful across roughly twenty domains; physics is one such domain, and applying the methodology to it yields some structural readings that align suggestively with existing mathematical frameworks in physics and quantum gravity. Whether these alignments are deep or superficial is not something we can adjudicate; we are not physicists or mathematicians by training. What we can do is report what the methodology produces, identify which alignments seem promising to us, and pose the questions back to people qualified to answer them.

1.1. What This Paper Is Not

To preempt the natural reflex: the paper does not claim, and we do not believe, that we have unified physics, derived the Standard Model, solved quantum gravity, resolved the measurement problem, or explained why the universe has the laws it has. None of those claims is in this paper, and we ask the reader not to attribute them to us.

The paper is also not a piece of professional theoretical physics. We have read deeply in the literature we cite, but we are not active researchers in quantum gravity, mathematical physics, or formal verification. The specific mathematical structures we discuss — spectral triples, Dirac operators, cellular automata, propagator identities — are well-developed in the published literature; we use them as vocabulary for what the methodology surfaces, not as objects of our own original development.

1.2. What This Paper Is

The paper has three modest goals:

1. To record what the methodology produces when applied to physics as a domain. The methodology has structural outputs (primitive sets, filter stringencies, core triads, phase transitions) that we can compute from any sufficiently characterized domain. Physics yields six primitives, an 18.75% filter, a core triad, and pattern of phase transitions consistent with the methodology’s cross-substrate observations. We report this for what it is: a methodology output.

2. To propose the spectral-triple framework as a candidate mathematical framing that aligns with what the methodology surfaces. The spectral triple has been under development for decades (Connes 1996; Chamseddine and Connes 1997); it derives the Standard Model gauge group from mathematical structure (Chamseddine et al. 2007); and a related programme builds spectral triples over holonomy loops, connecting the construction to the canonical variables of loop quantum gravity (Aastrup and Grimstrup 2006; Aastrup and Grimstrup 2016; Aastrup and Grimstrup 2025). The methodology’s “Planck information substrate” picture and the spectral triple have similar structural shape. We treat this as a candidate alignment worth recording, not as a theory.

3. To sharpen the open questions raised in Information as Substrate about information as substrate. The structural reading suggests specific questions: Is the physical substrate fundamentally discrete? What is the relationship between the local update rule and the global state? What does the “evaluation-feedback distance” mean at the physics level, and how does the chain of higher substrates emerge from it? These are not physics questions we are positioned to answer; they are information-theory questions the methodology surfaces, and they connect to the philosophical analysis in Information as Substrate.

The paper succeeds if the reader closes it with sharper questions, not with answers. If we managed to write a useful exploratory note, the methodology’s value at the physics layer is to organize the questions, not to settle them.

1.3. Posture Throughout

Three discipline notes guide the rest of the paper.

We hedge consistently. Where the methodology suggests something, we say “the methodology suggests”; where the alignment with spectral-triple mathematics is suggestive, we say “suggestive”; where we are speculating, we say “we speculate”; where we are out of our depth, we say so. We do not claim certainty we do not have.

We defer to specialists. Where physicists disagree among themselves (e.g., about discreteness, about background independence, about the measurement problem), we report the disagreement and do not pretend to resolve it. Where mathematicians have established results we reference, we cite the results and trust them; we do not attempt to verify them ourselves.

We treat the paper as a reference, not a publication target. This paper is not intended as a leading entry in the series. We expect it to be read primarily by readers who have already worked through the substrate papers and the abiogenesis treatment in Abiogenesis as Progressive Hardening, and who are curious whether the methodology’s reach extends to the physics layer. We make it available to such readers and ask others to weight it accordingly.

The rest of the paper: the methodology applied to physics as a domain (briefly); the Planck information substrate as a candidate; the cellular-automaton reading as one of three equivalent vocabularies; the evaluation-feedback distance as the substrate-of-substrates variable; cross-substrate comparison; honest limitations; and a closing section on what information-theoretic questions this reading sharpens.

2. The Methodology Applied to Physics

The full methodology is in A Structural Methodology for Information System Domains. Briefly: information-substrate domains decompose into ~6 irreducible primitives, with partial-level decompositions, a dependency DAG, a coherent sub-lattice that filters to 12-20% of the full lattice for substrate-style domains, one or more core triads of heavy pair-relationships, and a topology of structural roles called the Situated Substrate Architecture (SSA). The methodology has been applied to twenty-plus domains; the cross-substrate patterns it surfaces are the methodology’s empirical content.

Applying the methodology to physics raises a strategy question. Physics is not a single research program; quantum gravity has six major communities (loop quantum gravity, causal dynamical triangulations, causal sets, string theory, asymptotic safety, noncommutative geometry); quantum mechanics has its own primitive structure separately. We approach physics through three nested analyses:

• Quantum gravity domain analysis. Extract primitives from landscape convergence across the six QG programs. The result is a six-primitive QG domain.
• Quantum mechanics domain analysis. Extract primitives from the standard formalism. The result is a six-primitive QM domain that maps cleanly onto the convergence domain (see A Structural Methodology for Information System Domains).
• The Planck information substrate. Take the spectral-triple framework as a candidate mathematical realization that integrates QG and QM concerns. Extract primitives. The result is a six-primitive substrate-style domain that we call the Planck information substrate.

This is one of several possible analytical paths. Other paths (e.g., starting from a different QG program, or from a different mathematical framing of physics) might produce different primitive sets. We chose the spectral-triple path because the methodology’s structural signature (substrate-like filter, encoding-evaluator-code core triad, hub primitive at the evaluator) emerged cleanly. This is an interpretive observation, not an adjudication among physics programs.

2.1. What the Reader Should Hold Loosely

The specific numeric outputs of the methodology applied to physics (the 18.75% filter; the 7/15 heavy-pair ratio; the specific six-primitive set) depend on analyst-authored choices: which primitives are extracted, how the partial levels are defined, which dependencies are enforced. We have run the methodology with a particular set of choices that align with the spectral-triple framework. Different choices, equally defensible, might yield different numbers within the same general range (~6 primitives, ~15% filter).

The cross-substrate comparison (physics vs biology vs entity system) is robust at the structural level (all three settle around six primitives, all three exhibit a core triad with encoding-evaluator-code structure, all three filter to the substrate-typical range). It is less robust at the specific-number level. We treat the structural pattern as the load-bearing claim; the specific numbers as illustrative.

3. The Planck Information Substrate as Candidate

A note on the substrate’s name. We call this the Planck information substrate because Planck units (Planck length, Planck time, Planck energy) denote the physical scale of the underlying carrier independent of any specific operator framing. The spectral-triple framework discussed below is one candidate mathematical realization, and within it the Dirac operator plays the evaluator role. If the underlying mathematical framing turns out to be displaced — by causal sets, spin foams, asymptotic safety, or any other candidate quantum-gravity program — the substrate’s name remains stable; only the specific evaluator candidate changes. The name therefore separates the substrate (Planck scale, the underlying thing) from the evaluator (Dirac operator, a specific candidate within one specific framing).

The methodology’s primitive extraction applied to the spectral-triple framework yields six primitives. We list them and what they correspond to in the standard mathematical vocabulary; the structural claims about how they compose are in the source material and we summarize only what this paper requires.

The dependency structure: Cf is the root; Ev is the hub (four heavy pairs); Gm is terminal (depends on both Sp and Et). The structural reading is that “spacetime emerges from spectral data plus entanglement” — neither alone suffices. The coherent sub-lattice filters to 12 of 64 subsets (18.75%), within the substrate-typical band. The heavy-pair ratio is 7/15 (47%), consistent with the cross-substrate pattern. The core triad $\{\text{Cf, Ev, Sp}\}$ has the same shape as the methodology produces in other substrate domains (encoding + evaluator + code).

3.1. Why “Candidate”

We mark this analysis as a candidate alignment rather than a settled framework for three reasons:

The spectral triple is one of several mathematical framings. Noncommutative geometry is mathematically rich and has produced specific physical predictions (the Standard Model gauge group; the Higgs mass before its measurement, with mixed accuracy depending on the prediction’s vintage). The Higgs prediction is the clearest illustration of the mixed record: the neutrino-mixing model put the mass near 170 GeV (Chamseddine et al. 2007), above what was later measured. But it is not the only mathematical framework for physics: loop quantum gravity uses different mathematics; string theory uses different mathematics; causal-set theory uses different mathematics. We chose the spectral triple because the methodology’s output aligned with it; we do not claim it is the right framework.

The methodology’s primitive extraction is analyst-authored. Where the spectral triple has $\mathcal{A}$, $\mathcal{H}$, and $D$, we have separated these into six primitives by adding partial-level structure for entanglement and geometry. Other separations are possible. Our six-primitive set survives the methodology’s three-test criterion (minimality, compositionality, recurrence across instances), but we acknowledge that a different decomposition could survive equally well.

Experimental confirmation is partial. The spectral triple’s predictions (gauge group from mathematical necessity; convergence with LQG; Lorentzian signature handling; spectral-action coefficients) are theoretical results. Direct experimental tests of the spectral-triple picture are limited; the framework’s empirical content overlaps substantially with established quantum field theory but does not yet have a distinctive experimental signature that distinguishes it from alternatives.

We are interested readers of this framework. We are not advocates.

4. The Cellular-Automaton Reading

The spectral triple admits a cellular-automaton (CA) reading: $D$ is the update rule (first-order differential operator $=$ depends on immediate neighbors), $\mathcal{A}$ is the configuration space, $\mathcal{H}$ is the state space. The commutator $[D, a]$ defines the neighbor structure; space emerges from $D$’s neighbor relations averaged over many cells. This is one of three equivalent vocabularies (spectral triple is mathematical; CA is computational; information substrate is structural) for the same underlying structure.

We find the CA reading useful for a specific structural reason: it suggests an analogy between the methodology’s “evaluator” role at the physics level and what an update rule does in a discrete dynamical system. In a CA, the update rule is local, deterministic, and parallel; it contains the “law” while the cell states contain the “data”; the rule does not change while the states evolve. This is structurally similar to how the methodology characterizes the evaluator role in higher substrates (the ribosome in biology, the dispatch mechanism in the entity system) — a fixed mechanism that operates over varying data.

4.1. Three Vocabularies, Same Structure

Each vocabulary highlights different features. The spectral triple is the most mathematically developed and connects to established quantum field theory through the propagator identity (the Schwinger proper-time representation makes the QFT propagator the time-integrated heat kernel, an exact identity (Schwinger 1951)). The CA vocabulary makes locality and discreteness explicit. The information-substrate vocabulary makes the cross-domain comparison with biology and the entity system possible.

We do not claim that physics “is” a cellular automaton. The CA reading is one vocabulary among three; whether the universe is “fundamentally” a CA in any deep ontological sense is a question we are not equipped to answer. What we observe is that the CA reading produces a coherent structural picture that the methodology recognizes and that the spectral-triple mathematics supports.

4.2. Caveats About the CA Reading

Three caveats are worth stating:

Discrete vs continuous is open. Whether the physical substrate is fundamentally discrete (cellular automaton, true Planck-scale grid) or fundamentally continuous with discrete approximations is an open question in physics. The CA reading commits to discreteness; the spectral-triple framework is more permissive (spectral data is discrete; underlying geometry can be either). We are not in a position to adjudicate.

Multiple CA candidates exist. Wolfram’s hypergraph framework (Wolfram 2002; Wolfram 2020), ’t Hooft’s deterministic CA program (Hooft 2016), the quantum cellular automaton (QCA) approach with proven convergence to Dirac propagators in the free-QED continuum limit (Bisio et al. 2015; Bisio et al. 2017) — these are distinct CA-style approaches with different commitments about what is fundamental. The methodology’s reading is compatible with QCA most cleanly, but we note the alternatives without picking among them.

The CA reading does not derive physics. The CA picture organizes the structural features but does not derive specific physical constants, the values of the Standard Model parameters, or the cosmological initial conditions. These remain free entries in the framework. The CA reading is consistent with the existence of such free parameters; it does not eliminate them.

5. The Evaluation-Feedback Distance

The methodology’s most interesting structural observation when applied across substrates is the evaluation-feedback distance: the spatial, temporal, and organizational separation between where evaluation happens and where feedback operates (see A Structural Methodology for Information System Domains). At the physics level this distance is effectively zero; in higher substrates the distance opens progressively.

At the physics level, $D$ applied to a state produces the next state, which is the input for the next application of $D$. The evaluator is also the selector (what persists is what $D$’s evolution produces) and the arena (the neighbor structure $D$ defines is what we call space). These three roles, which separate at higher substrates, are structurally fused at the physics level. We describe this fusion as “evaluation-feedback distance $\sim 0$” rather than calling it any of the more grandiose names tempting at this depth.

5.1. What the Distance Does

The structural observation: the evaluation-feedback distance is a continuous variable that varies monotonically along the realization chain (physics $\to$ chemistry $\to$ biology $\to$ cognition $\to$ computing). At each bridge between substrates, a specific mechanism opens the distance further. In abiogenesis (see Abiogenesis as Progressive Hardening), compartmentalization (Mem 0.5 $\to$ Mem 1, mineral micropore to lipid vesicle) is the distance-opener. In computing, protocol specification is the distance-opener. The pattern recurs.

Complexity, the methodology suggests, exists in the evaluation-feedback gap. At distance zero (physics), there is no room for organizational complexity — evaluation and its consequence are identical. As the distance opens, room appears for structures that local evaluation does not determine but global feedback does select for. Metabolic networks, regulatory circuits, evolved organisms, cultures, codes — each is content of the gap between evaluation and feedback at its own substrate level.

5.2. Information-Theoretic Connection

The evaluation-feedback distance is the load-bearing connection back to Information as Substrate’s information-theoretic analysis. That analysis develops the eternal/temporal distinction (content store as eternal, tree as temporal, emit as the crossing), the purity boundary (hash references as referentially transparent, path references as state-dependent), and the limits of self-reference (informational completeness without physical closure). The evaluation-feedback distance is, from one angle, the physical instantiation of the gap Information as Substrate describes between “computation as structure” and “computation as activity.”

At distance zero, computation-as-structure and computation-as-activity coincide — there is no separate evaluator running the structure, because the structure IS the evaluator. As distance opens, structure and activity separate; an evaluator becomes distinguishable from the encoding; the substrate becomes inspectable; reflection becomes possible. The chain of substrates can be read as the progressive opening of this gap.

This is the paper’s primary information-theoretic claim: the evaluation-feedback distance is structurally the same variable Information as Substrate analyzes philosophically, made operational by the methodology and instantiated at multiple substrate levels. The claim is not that physics determines the philosophy; the claim is that the methodology, applied across substrates, recovers a variable that has independent grounding in philosophical analysis.

6. Cross-Substrate Comparison

The methodology applied to physics, biology, and the entity system produces three substrate-level domains with comparable structural invariants. We report the comparison briefly.

The structural pattern recurs: six primitives at substrate-style filter stringency, a core triad with encoding-evaluator-code structure, a heavy-pair ratio near half, a crystallization event whose character varies by substrate kind. What varies meaningfully across substrates is the evaluator-selector relationship (fused at physics, separated at biology, designed-separate at computing) and the crystallization mode (continuous, discrete, designed). What stays roughly invariant is the structural shape: six primitives, a core triad, a code that crystallizes.

We are honest about the limits of this comparison. The biology and entity-system analyses are well-grounded (biology in established molecular biology; entity system in three reference implementations). The physics analysis is more speculative: we are not in a position to claim the same level of empirical grounding for the Planck-substrate primitive extraction as we have for the other two. The cross-substrate alignment is at least suggestive, and may be more than that, but we do not over-position it.

7. What This Sharpens in the Interpretive Companion

The most useful thing this exploration does is sharpen the open questions in Information as Substrate about information as substrate. We list the sharpened questions.

What is beneath E+I+T? Information as Substrate ends with the observation that the entity system’s three informational primitives (Entity, Identity, Tree) appear to implement something more primordial — distinction, sameness, reference. Beneath those, perhaps just relation. The physics-domain analysis, read carefully, suggests these primitives are not specific to the entity system: the methodology’s substrate-level analysis of physics surfaces analogous structures (configurations distinguishable from each other; identity-by-content under the spectral hash; reference through entanglement). The “beneath E+I+T” question may have an information-theoretic answer that physics instantiates at its level.

What does “information precedes computation” mean physically? Information as Substrate argues that information structure (E+I+T) exists before computation (M+X) in the build-up sequence. At the physics level, this distinction blurs — the evaluation-feedback distance is zero. But the substrate-level analysis of physics suggests the same primitive structure recurs (configurations, identity-by-content, connectivity), which is at least consistent with the claim that information structure is more fundamental than temporal computation, even at the physics level.

Is there a fundamental “carrier”? Information as Substrate discusses the evaluator regression and its termination at physics. The CA reading proposes that the carrier (at the physics level) is a cell — discrete, quantum, locally connected, finitely stated. We do not commit to this proposal as physics, but we note that the methodology’s structural analysis suggests some structural carrier exists at the physics level, with similar partial-level decomposition to the carriers at higher substrates.

What grounds the evaluation-feedback distance? The eternal/temporal distinction in Information as Substrate lives at the information-substrate level. The methodology’s evaluation-feedback distance lives at the cross-substrate level (varies along the realization chain). Whether these are the same variable seen from two angles, or two different variables that happen to align, is an open question. If they are the same, the methodology and the philosophy reinforce each other; if not, the relationship between them is worth understanding.

These are the questions the exploration sharpens. They are information-theoretic questions, not physics questions, and we believe they are the most useful output of the paper.

A note on the deeper open question. The “what is beneath E+I+T” question, like the broader question of what underlies physics, admits multiple coherent framings that this paper does not select among. Information, time, and space could themselves be the primordial substrate, with physics one elaborated surface of them. All three could be emergent from a deeper substrate the methodology is not equipped to analyze. The realization chain might not terminate, in which case “primordial” is a methodological floor declaration rather than a structural fact. The question might be malformed at the deepest level, if the methodology’s analytical apparatus does not extend coherently below physics. The methodology’s posture (developed in A Structural Methodology for Information System Domains’s §Methodological Discipline) is to hold these framings open rather than to force a choice. This paper’s analysis is consistent with each of them; selecting among them is beyond what the methodology can do from inside itself.

8. Honest Limitations

We are explicit about what this paper does not establish.

• No new physics. The mathematical structures we discuss (spectral triple, Dirac operator, propagator identities, cellular automata) are all well-developed in the published literature. We use them as vocabulary; we do not extend or contribute to them.
• No formal results. We do not prove theorems. We do not derive Standard Model parameters. We do not produce experimental predictions distinguishable from established quantum field theory. The Lean 4 formalization path described in the outline is a longer-term aspiration, not a contribution of this paper.
• No adjudication among physics programs. Loop quantum gravity, string theory, causal dynamical triangulations, causal sets, asymptotic safety, noncommutative geometry — we do not pick among them. We cite noncommutative geometry’s spectral-triple framework because the methodology aligns with it; the alignment is suggestive, not selective.
• No empirical claims. The methodology’s structural outputs (filter stringency, core-triad structure, primitive count) are not measurements. They are analyst-authored decompositions that the methodology produces from a particular set of choices. Different choices, equally defensible, might produce different specific numbers.
• No claim to professional standing. We are not physicists. We are not mathematicians. We have read the literature we cite carefully and we have used it carefully, but we cannot adjudicate disputes within physics or mathematics from inside the methodology. Where we describe specific mathematical or physical content, we report what the literature says and defer to specialists on its correctness.
• No commitment about the universe. We do not claim that the universe is, fundamentally, an information substrate; or that physics is, fundamentally, a cellular automaton; or that the spectral triple is, fundamentally, the right framework. These are framings that align with what the methodology produces; the methodology does not establish their fundamental status.

The paper is exploratory. Future work may sharpen any of its claims, or it may not. Future work by people qualified to do the work may discard the framing entirely. We make the exploration available as a reference and ask the reader to weight it accordingly.

• Generated under prompt-and-review. This paper, like the rest of the corpus, the supporting implementations, and the architectural specifications, is LLM-generated under direction from the author. The author provides prompts, evaluates outputs, redirects, and approves — text, code, and design refinements are generated rather than directly authored. The methodology this enables is described in The Entity Core Protocol. Given that this paper is the most speculative in the corpus, readers should weight the LLM-generation context particularly carefully here.

9. Conclusion

This paper applied the structural methodology of A Structural Methodology for Information System Domains to physics as an information-substrate domain. The methodology produces a six-primitive decomposition (the Planck information substrate, with primitives Cf, Am, Ev, Sp, Gm, Et) that aligns suggestively with the spectral-triple framework of noncommutative geometry. The decomposition has substrate-typical structural signatures: filter stringency around 18.75%, heavy-pair ratio around 47%, a core triad of encoding-evaluator-code shape. The cellular-automaton reading provides a third vocabulary, in which the Dirac operator is the update rule. At the physics level, the evaluation-feedback distance is structurally zero — evaluator, selector, and arena are fused. The realization chain to higher substrates is the progressive opening of this distance.

We are explicit that this is exploratory work. The alignments are suggestive, not proofs. The mathematical framework we lean on (the spectral triple) is one candidate among several. We are not physicists or mathematicians; we report what the methodology produces and defer to specialists on its physical and mathematical status.

The paper’s most useful contribution is information-theoretic: it sharpens the open questions of Information as Substrate about what is beneath the informational primitives, what “information precedes computation” means physically, what carrier exists at the substrate level, and what grounds the evaluation-feedback distance. These are questions the methodology surfaces; physics is a vehicle for asking them.

The paper is open to correction. Where the methodology’s primitive extraction is wrong on its own terms, where the spectral-triple alignment is shallow, where specialists in physics or mathematics see the framework misrepresenting their domain — each of these is a reading the authors would want to hear. The paper is offered as a reference for exploration, not as a settled position.

If the paper is useful, it is useful as a structural lens on physics that might — might — help organize information-theoretic questions about the substrate. If it is not useful, the failure is contained to one exploratory paper and does not affect the rest of the series. The substrate papers, the methodology paper A Structural Methodology for Information System Domains, and the abiogenesis paper Abiogenesis as Progressive Hardening stand on their own grounding; this paper is auxiliary.

The substance is in the methodology, the substrate, and the application to domains where we have firm ground. The physics application is an exploration, offered in that spirit.