Logic Realism Theory

It from Bit, Bit from Fit: Foundational Physics Logically Remastered

James (JD) Longmire
ORCID: 0009-0009-1383-7698
Published: January 09, 2026 | Updated: January 09, 2026
quantum mechanics logic realism Determinate Identity measurement problem entanglement Born rule Wheeler foundations of physics
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Abstract

This paper extends Logic Realism Theory (LRT) to quantum mechanics, arguing that quantum structure is the unique stable interface between $I_\infty$ (the space of all representable configurations) and $A_\Omega$ (the $L_3$-admissible subset that can be physically instantiated). The Position Paper establishes that the Three Fundamental Laws of Logic ($L_3$: Determinate Identity, Non-Contradiction, Excluded Middle) are ontological constraints on physical instantiation. Here we develop the implications: $A_\Omega$ requires Boolean determinacy, but $I_\infty$ contains richer structures including indeterminate states. Quantum mechanics---specifically complex Hilbert space with the Born rule---provides the interface between these domains. Vehicle-invariance under mathematically equivalent decompositions forces the Born rule via Gleason's theorem; local tomography requirements select complex Hilbert space over real alternatives. The paper dissolves foundational puzzles (measurement, entanglement, wave function reality) and grounds Wheeler's "it from bit" in logical foundations. The bit---the fundamental unit of distinction---derives from Determinate Identity. Quantum mechanics is what bit-structure looks like when interfacing with Boolean actuality. *It from bit; bit from fit.*

Revision Note (January 2026): This paper has been updated to align with the refined Logic Realism Theory framework. Key changes include: updated terminology ($I_\infty$ for representable configurations, $A_\Omega$ for the $L_3$-admissible subset, Determinate Identity as the central logical principle), integration of the Identity Continuity framework, and strengthened derivational claims based on the current 5-paper suite. For the complete framework, see the LRT Zenodo Community.

1. Introduction

1.1 The Discovery

No stable experimental record, across the history of experimental science, has ever been documented as instantiating a direct violation of the classical laws of Identity, Non-Contradiction, or Excluded Middle. No detector record is both triggered and not triggered in the same respect. No logged outcome is both P and not-P at the same time. Whatever we say about quantum superposition or pre-measurement descriptions, the level of actualized outcomes exhibits determinate, non-contradictory form.

This asymmetry—between what representation permits and what instantiation produces—is the empirical foundation of Logic Realism Theory. We can conceive of logical violations (paraconsistent logics formalize them rigorously), yet physical reality never produces them. The constraint is on reality, not cognition.

1.2 The LRT Framework

The Position Paper establishes that the Three Fundamental Laws of Logic ($L_3$: Determinate Identity, Non-Contradiction, Excluded Middle) are ontological constraints on physical instantiation. The framework distinguishes:

$I_\infty$: The space of all representable configurations—everything that can be specified, described, or formally expressed, without restriction to coherence or consistency.

$A_\Omega$: The constraint-class of configurations that satisfy $L_3$. These are the configurations that can be physically instantiated as stable records.

This paper asks: what does this framework imply for physics? Why does physical reality exhibit quantum structure rather than classical structure, or something else entirely?

1.3 The Derivational Claim

The LRT framework, developed across a 5-paper suite, establishes that quantum mechanics is not merely compatible with $L_3$ but derivable from it given minimal physical constraints:

  1. $I_\infty$ is structured by distinguishability, which presupposes Determinate Identity (Id).

  2. $A_\Omega$ requires Boolean outcomes—determinate, non-contradictory, complete—as $L_3$ demands.

  3. Vehicle-invariance (the requirement that probability assignments not depend on mathematically equivalent decompositions) forces the Born rule via Gleason’s theorem.

  4. Local tomography (composite states determined by local measurements) selects complex Hilbert space over real or quaternionic alternatives.

  5. Permutation symmetry (bosons/fermions) follows from Determinate Identity applied to indistinguishable configurations.

  6. Wheeler’s “it from bit” is thereby grounded—the bit (fundamental distinction) derives from Id; quantum mechanics is what bit-structure looks like actualized.

The derivations are conditional on Tier-2 physical axioms (continuity, local tomography, information preservation), but given these, complex quantum mechanics follows uniquely.

1.4 Companion Papers

This paper is part of a 5-paper suite:

  • Position Paper: Core framework, $I_\infty$/$A_\Omega$ ontology, Identity Continuity
  • Born Rule Paper: Derivation from vehicle-weight invariance
  • Hilbert Space Paper: Complex Hilbert space from Id via local tomography
  • QFT Statistics Paper: Symmetrization postulate from Id
  • GR Extension: Spacetime implications, identity strain, kinematic constraints

Full technical derivations appear in the companion papers. This paper provides the conceptual bridge, grounding Wheeler’s “it from bit” and dissolving foundational puzzles.

1.5 Plan of the Paper

Section 2 develops the two-domain ontology ($I_\infty$ and $A_\Omega$). Section 3 analyzes distinguishability and the bit. Sections 4-6 address the interface problem, quantum structure, and the Born rule. Section 7 dissolves foundational puzzles. Section 8 examines quantum fields. Section 9 develops the fine-tuning thesis. Section 10 grounds Wheeler. Section 11 shows how LRT completes related programs. Section 12 provides honest accounting. Section 13 concludes.

2. The Two Domains

2.1 The Representable Space ($I_\infty$)

$I_\infty$ is the space of all representable configurations—everything that can be specified, described, conceived, or formally expressed, without restriction to coherence or consistency. This includes contradictions, impossibilities, and violations of every logical principle. $I_\infty$ carries no ontological commitment; it is simply the totality of what representation permits.

Several features are essential:

$I_\infty$ is not Boolean. While $L_3$ constitute distinguishability, they do not constrain $I_\infty$ to binary structure. $I_\infty$ contains:

  • Determinate states (fully specified configurations)
  • Indeterminate states (distinguishable but not resolved to definite values)
  • Superpositions (specific indeterminate states with interference structure)
  • Classical mixtures (probabilistic combinations without interference)

$I_\infty$ is structured by distinguishability. The “metric” on $I_\infty$ is how distinguishable states are from each other. This is inherently relational—comparing two states—and therefore quadratic in character.

$I_\infty$ contains all possible mathematical structures. Classical probability theory lives in $I_\infty$. So does quantum mechanics. So do structures we have not named. $I_\infty$ is the space of what can be represented, not what is actual.

2.2 The Admissible Subset ($A_\Omega$)

$A_\Omega$ is the constraint-class of configurations that satisfy $L_3$. Any physical state of affairs—any event, measurement outcome, or determinate fact—must satisfy:

Determinate Identity (Id): The state is what it is; it has determinate properties. $\forall A: A = A$.

Non-Contradiction (NC): The state does not simultaneously have and lack the same property. $\forall A: \neg(A \land \neg A)$.

Excluded Middle (EM): For any well-defined property, the state either has it or does not. $\forall A: A \lor \neg A$.

This means $A_\Omega$ is Boolean—every proposition about an actual state has a definite truth value. The actual world is a consistent, determinate configuration.

2.3 Qualitative and Quantitative Identity

A crucial distinction emerges from Determinate Identity that bridges logical structure and physical dynamics.

Qualitative Identity (Type-Identity): Two configurations are qualitatively identical if they share all intrinsic properties—if there is no property $P$ such that one has $P$ and the other lacks $P$. This is symmetric: if $A$ is qualitatively identical to $B$, then $B$ is qualitatively identical to $A$.

Quantitative Identity (Numerical Identity): A configuration is numerically identical only to itself. This is the standard reading of $A = A$: each thing is the very thing it is, not merely similar to itself.

The Physical Significance: For physical systems, qualitative identity corresponds to indistinguishability in the quantum sense. Two electrons in the same quantum state are qualitatively identical—no measurement can distinguish them. Yet they may be numerically distinct (two electrons, not one).

This distinction has profound consequences:

Lemma (Bounded Distinguishability). If two configurations $C_1$ and $C_2$ in configuration space are connected by a continuous path, and Id holds throughout the path, then their distinguishability $D(C_1, C_2)$ is bounded by the path length in the distinguishability metric.

Significance: Continuous evolution in configuration space cannot create arbitrarily large distinguishability jumps. This constraint—derived from Id—underlies the continuity of quantum dynamics and connects to the identity strain framework developed in the GR Extension.

2.4 The Asymmetry

Here is the key insight: $L_3$ constitute $I_\infty$ but only constrain $A_\Omega$ to be Boolean.

$I_\infty$ is richer than Boolean structure. It contains states that are distinguishable from each other but not yet determinate with respect to specific properties. These are not contradictions—they are genuinely indeterminate configurations.

$A_\Omega$, by contrast, must be fully determinate. When something becomes actual—when it manifests physically as a stable record—it must satisfy $L_3$ completely.

This creates an interface problem: how do the rich structures of $I_\infty$ relate to the Boolean structure of $A_\Omega$?

3. Distinguishability and the Bit

3.1 Distinguishability Is Constituted by Determinate Identity

Determinate Identity (Id) is the foundation. Without Id, there is no basis for one state to be different from another. Distinguishability is not a primitive fact discovered in the world; it is what Id establishes.

Consider: for state A to be distinguishable from state B, we need:

  • $A = A$ and $B = B$ (each is determinately itself)
  • $A \neq B$ (non-identity, which presupposes Id)
  • It is not the case that $A = B$ and $A \neq B$ (NC follows from Id)

Id is primary. NC and EM can be understood as consequences of Id applied to propositions. If $A = A$ determinately, then $A$ cannot both have and lack property $P$ (NC), and $A$ either has $P$ or lacks $P$ (EM). The asymmetry between conceivability and instantiation traces back to Id: we can represent violations of Id, but nothing can be a violation of Id.

3.2 Distinguishability Is Pairwise

To distinguish is to compare. Distinguishability is inherently a relation between two things: how different is A from B? This relational character means distinguishability has quadratic structure—it involves pairs, not individuals.

The distinguishability metric $D(s_1, s_2)$ measures the maximum probability of correctly identifying which of two states was prepared:

\[D(s_1, s_2) = \sup_M \|P_M(s_1) - P_M(s_2)\|_{TV}\]

This metric satisfies the standard axioms (identity: $D(s,s) = 0$; symmetry; triangle inequality) and is grounded in Id: the metric presupposes that states are self-identical and that equality/inequality are determinate.

3.3 The Bit as Fundamental Unit

The bit is the minimal unit of distinguishability—one binary distinction. In LRT terms:

  • One bit = the information required to distinguish between two alternatives
  • The bit is not derived from physics; physics is derived from bits
  • The grain of $A_\Omega$ is the bit—you cannot have half a distinction

This connects to Wheeler’s “it from bit”: physical reality emerges from yes/no questions. LRT grounds this insight: the yes/no question is the fundamental logical operation, and Id constitutes what makes such questions meaningful.

The bit derives from Id. A bit is a distinction between two alternatives. For that distinction to be meaningful:

  • Each alternative must be determinately itself (Id)
  • The alternatives must be determinately different ($A \neq B$ from Id)
  • Selection of one excludes the other (NC + EM from Id)

Without Id, “0 or 1” is not a genuine distinction. The bit is not a primitive posit—it is what Id looks like when applied to a minimal binary domain.

3.4 The Bit Scale

If the bit is the fundamental unit of distinguishability, and physical action is measured in units of $\hbar$ (Planck’s constant), then $\hbar$ may be understood as the conversion factor between logical and physical structure:

\[S = \hbar \cdot C\]

Where S is action (physical) and C is complexity (informational, measured in bits).

This is conjectural but supported by independent results. The Bekenstein bound states that the maximum entropy (information content) of a region is proportional to its surface area in Planck units:

\[S_{\text{max}} = \frac{k_B c^3 A}{4 G \hbar}\]

This implies a maximum bit density per Planck area - roughly one bit per Planck area. If $\hbar$ is the bit-action conversion factor, this bound follows naturally: physical regions have finite action capacity, hence finite bit capacity.

Similarly, black hole entropy (the Bekenstein-Hawking formula) gives entropy proportional to horizon area in Planck units. In LRT terms: the horizon bounds the distinguishability capacity of the interior.

These connections suggest:

  • One bit of complexity corresponds to approximately $\hbar$ of action
  • The classical world appears continuous because specifying it exactly would require infinite bits
  • The Planck scale marks where the bit-structure of reality becomes directly relevant
  • The holographic principle reflects fundamental limits on distinguishability density

4. The Interface Problem

4.1 Many Structures Satisfy the Constraints

For any structure in $I_\infty$ to interface with $A_\Omega$, it must permit a map from its states to binary outcomes. This map must satisfy:

  1. Totality (from Excluded Middle): defined for all states
  2. Single-valuedness (from Non-Contradiction): no contradictory outputs
  3. Distinguishability-preservation (from Identity): different states can yield different outputs

Classical probability satisfies these constraints. A probability distribution over outcomes, sampled to yield a definite result, produces $A_\Omega$-admissible outcomes from a richer structure.

Quantum mechanics also satisfies these constraints. A quantum state, measured in some basis, yields a definite outcome according to the Born rule.

4.2 The Selection Problem

If multiple structures satisfy the formal interface constraints, what selects among them?

The answer is not logical necessity. Logic does not dictate that reality must be quantum rather than classical. The selection is empirical - we observe that reality is quantum.

But this raises a deeper question: why does quantum structure, rather than classical structure, produce stable physics?

4.3 The Parsimony Principle: From Constitution to Parsimony

The thesis equation from the companion paper includes a parsimony operator ($\mathfrak{P}$):

\[\mathcal{A} = \mathfrak{P}(\mathfrak{C}(\mathcal{I}))\]

Parsimony selects among the paths through $I_\infty$ that satisfy $L_3$ constraints. But what grounds parsimony itself? If parsimony is merely a methodological preference or an inference to best explanation, LRT’s foundation remains incomplete. This section establishes that parsimony is not an axiom but a consequence of more fundamental commitments: the constitutive nature of $L_3$ and the requirement that Boolean facts be grounded.

4.3.1 Constitution versus Constraint

Metaphysical principles can play two fundamentally different roles:

Role What it does Relation to structure
Constraining Rules out certain configurations Negative: eliminates possibilities
Constitutive Makes something what it is Positive: generates structure

On the constraining view, $L_3$ act as filters on a pre-existing space of configurations. Many configurations pass through; something else determines which obtains. On this view, parsimony would require independent justification.

LRT rejects this picture. The core claim of Logic Realism is that $L_3$ are constitutive: they do not filter a pre-existing reality but generate the conditions for determinate being. Without $L_3$, there is no “configuration” to filter - only undifferentiated indeterminacy. Identity, Non-Contradiction, and Excluded Middle are what make it possible for anything to be determinately itself rather than something else.

This constitutive reading was implicit in Paper 1’s central thesis and in Section 2.1 above: “$L_3$ do not filter a pre-existing space. They are what makes $I_\infty$ a space of distinguishable states.”

The constitutive reading has a crucial implication. If P constitutes D, then D’s structure is determined by what P generates - no more, no less. Consider: “being H2O” constitutes water. Water therefore has exactly the structure H2O requires (two hydrogen atoms, one oxygen atom, specific bonding geometry). Water does not have “extra” atoms that happen to tag along. The constitution relation is tight.

This yields:

Constitutive Closure Principle (CCP): If principle P constitutes domain D, then D contains exactly the structure P generates. Nothing whose existence requires an independent source lies in D.

Justification. Suppose P constitutes D but D contains element x not generated by P. Then x’s presence in D has some other source S. But if S is responsible for x being in D, then S is partly constitutive of D, contradicting the assumption that P alone constitutes D.

In LRT, actuality is constituted by the package ($L_3$ + $s_0$), where $s_0$ is the contingent initial condition. By CCP:

\[\mathcal{A} = \text{Generated}(L_3 + s_0)\]

Actuality contains exactly what this constitutive package generates.

4.3.2 The Truthmaker Requirement

Actuality is a Boolean domain: every fundamental proposition has exactly one of two truth-values, consistent with Excluded Middle and Non-Contradiction. But what distinguishes genuine Boolean assignment from mere stipulation?

Consider the difference:

  • “Snow is white” is genuinely true - its truth is grounded in the nature of snow.
  • If we stipulate that “the present king of France is bald” has a truth-value, this is mere stipulation - nothing in reality grounds it.

This distinction is central to truthmaker theory, a major research program in contemporary metaphysics. The core idea, introduced by Mulligan, Simons, and Smith (1984) and systematically developed by Armstrong (2004), is that truths require truthmakers - entities or states of affairs in virtue of which propositions are true. A proposition is not true merely because we say so; something in reality must make it true. As Rodriguez-Pereyra (2005) notes in his survey of the field, truthmaker theory provides a “way of spelling out realism about a certain subject-matter” by requiring that truths about that domain be grounded in reality.

LRT adopts a restricted version of this principle:

Truthmaker Requirement (TM): For any proposition P in the fundamental physical description of actuality, if P has a Boolean value, then some ground G in the constitutive package determines that P has that value.

Without such grounds, P does not genuinely have a truth-value; at best, we could stipulate one, but stipulation is not ontological assignment.

The grounding sources recognized within LRT’s minimal ontology are:

  1. Logical necessity (from $L_3$ directly)
  2. Logical entailment from already-grounded propositions
  3. Initial condition $s_0$
  4. Propagation through derived dynamical structure

These exhaust the grounding sources. Any proposition whose truth-value is determined by one of (1)-(4) is grounded. Any proposition whose truth-value is determined by none of them is surplus.

4.3.3 Why Surplus Structure Cannot Be Actual

The key insight is that surplus propositions cannot receive genuine Boolean assignments.

By definition, a surplus proposition P has no determining ground in (1)-(4). By (TM), propositions without grounds cannot have genuine Boolean values. But actuality is not merely a domain where $L_3$ are satisfied (i.e., logically consistent); it is the domain where $L_3$ are enforced - where every proposition has a genuine Boolean value grounded in being.

This distinction matters:

Concept Definition Surplus propositions
Satisfies $L_3$ Logically consistent Could be stipulated
Enforces $L_3$ Genuinely Boolean-assigned Cannot be included

Many structures satisfy $L_3$ (any consistent structure does). But actuality does not merely satisfy $L_3$ - it is the domain constituted by them. Constitution generates genuine Boolean structure, not stipulated structure. Surplus propositions, lacking grounds, cannot be genuinely Boolean-assigned and therefore cannot be part of the constituted domain.

Therefore:

  1. Surplus propositions have no determining ground (by definition)
  2. Propositions without grounds lack genuine Boolean values (by TM)
  3. Actuality requires genuine Boolean values (by constitution)
  4. Therefore, surplus propositions are not in actuality

4.3.4 Parsimony as Structural Consequence

The conclusion follows directly:

Global Parsimony: Actuality contains exactly the grounded propositions - those whose Boolean values are determined by ($L_3$ + $s_0$) and their consequences. No surplus structure exists.

This is not parsimony as methodological preference or inference to best explanation. It is parsimony as a structural consequence of what “actuality” means given the constitutive and grounding architecture of LRT.

The derivation:

  • $L_3$ constitute actuality (LRT’s core claim)
  • Constitution generates exactly its content (CCP)
  • Genuine Boolean assignment requires grounds (TM)
  • Surplus propositions lack grounds
  • Therefore surplus propositions cannot be genuinely Boolean-assigned
  • Therefore surplus propositions are not in the constituted domain
  • Therefore actuality is minimal

Paper 3 provides the formal statement and proof of the Global Parsimony Theorem. Parsimony is not an independent assumption requiring external justification but a consequence of commitments already internal to LRT.

4.3.5 Comparative Support

The derivation above establishes parsimony from constitution and grounding. But the result also receives comparative support from assessing alternative selection principles:

Random selection: Requires a probability measure (additional primitive). Explains nothing about the simplicity of physical laws.

Maximization: Predicts complex, high-information dynamics. We observe the opposite: physical laws have exceptionally simple mathematical form.

Teleological selection: Requires purposes as primitives. Explanatorily unparsimonious.

Brute actuality: Maximally explanatorily inert. Predicts nothing, explains nothing.

Among these, only parsimony (a) predicts the observed simplicity of physical laws, (b) makes minimal ontological commitments, and (c) achieves explanatory unification. This comparative assessment does not establish parsimony - Section 4.3.4 does that. But it provides corroborating evidence that the derived result is correct.

4.3.6 Addressing a Potential Objection

One might object: “You’ve replaced parsimony (one assumption) with constitution and truthmaker (two assumptions). How is this progress?”

The response is threefold:

  1. Constitution is not new. It is LRT’s core claim, present from Paper 1. We are not adding an assumption but making explicit what was implicit.

  2. Truthmaker is independently motivated. As noted in Section 4.3.2, truthmaker theory is a major research program in contemporary metaphysics (Mulligan et al. 1984; Armstrong 2004; Rodriguez-Pereyra 2005). It is natural for any realist theory: if truths float free of reality, realism is compromised. LRT, as a realist theory about logic, should accept something like (TM).

  3. The derivation is explanatory progress. Parsimony is explained by more fundamental principles rather than assumed. Even if those principles are themselves axiomatic, showing how parsimony follows from them deepens our understanding of the framework’s structure.

The axiom base is not inflated; it is reorganized to reveal internal connections.

5. Why Quantum Structure Survives

5.1 Classical Structure Is Compatible but Unstable

Classical probability, applied at the fundamental level, does not produce stable atoms. Without interference effects:

  • Electrons would spiral into nuclei (no stable orbitals)
  • No discrete energy levels (no chemistry)
  • No tunneling (no stellar fusion)
  • No identical particles (no periodic table)

Classical structure satisfies the Boolean interface constraint but does not produce observers capable of noticing.

5.2 Quantum Structure Produces Stability

Quantum mechanics - specifically, complex Hilbert space with unitary evolution and the Born rule - produces:

  • Stable atoms (discrete energy levels from wave interference)
  • Chemistry (electron orbitals, bonding)
  • Solid matter (Pauli exclusion, fermion statistics)
  • Stars (quantum tunneling enables fusion)
  • Observers (stable structures capable of inquiry)

5.3 This Is Fine-Tuning

The relationship between quantum structure and physical stability is not necessary - it is fine-tuned. Consider what perturbations would destroy:

Perturbation Consequence
Remove complex numbers No interference; no stable atoms
Alter unitarity Norms blow up or decay; no stable evolution
Change Born exponent from 2 No valid probability measure
Use quaternions instead Lose tomographic locality
Use reals instead Lose interference; classical behavior
Perturb linearity Superluminal signaling possible
Alter commutation relations Pathological spectra; no stable matter
Remove Hilbert completeness No well-defined dynamics

Quantum mechanics sits on a razor’s edge. The structure must be exactly as it is for physics to be stable.

5.3.1 The Anthropic Character of Stability Selection

We must be explicit about what “stability” means here. The argument is:

  1. Only quantum structure produces stable atoms, chemistry, observers
  2. We are observers
  3. Therefore we observe quantum structure

This has the form of the Weak Anthropic Principle: we necessarily find ourselves in conditions compatible with our existence. Critics may object that this is circular or tautological.

The response: we are not claiming quantum structure is logically necessary. We are claiming it is observationally necessary - necessary for there to be observations at all. This is not a derivation but a selection effect.

The selection is genuine. Consider:

  • $I_\infty$ contains many possible structures (classical, quantum, others)
  • Most do not produce stable matter
  • The ones that do are the ones that can be observed
  • We observe quantum structure

This parallels cosmic fine-tuning arguments. We do not derive the value of the fine-structure constant $\alpha$ from first principles. We note that if $\alpha$ were different, no atoms - and therefore no observers to measure $\alpha$. The “explanation” is selection, not derivation.

LRT adds something to this picture: it situates the selection at the level of mathematical structure, not just parameters. The question “why quantum mechanics?” becomes parallel to “why these constants?” - both are fine-tuning facts, with structural fine-tuning being more fundamental.

We do not claim this fully explains why quantum structure exists. We claim it explains why we observe it: because it is the unique structure compatible with observers existing to ask the question.

5.4 Evidence from Reconstruction Theorems

The uniqueness of quantum structure is not merely asserted - it is supported by rigorous results in quantum foundations.

Hardy (2001): Derived quantum theory from five “reasonable axioms” including continuous reversibility and tomographic locality. The result: only quantum mechanics satisfies all five.

Chiribella, D’Ariano, Perinotti (2011): Derived quantum theory from informational axioms. Key finding: quantum theory is the unique theory satisfying causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning.

Masanes and Muller (2011): Showed that quantum theory is the unique theory with:

  • Continuous reversible dynamics
  • Local tomography (state determined by local measurements)
  • Existence of entangled states

Dakic and Brukner (2011): Derived quantum theory from three axioms about information capacity and continuity.

These reconstruction theorems converge on the same conclusion: quantum mechanics is not one possibility among many but the unique structure satisfying certain natural constraints.

In LRT terms: the constraints these theorems identify are features required for stable interface between $I_\infty$ and $A_\Omega$. Continuous reversibility preserves information in $I_\infty$. Local tomography ensures consistency across subsystems. The theorems do not derive quantum mechanics from logic alone, but they show that quantum structure is uniquely determined once reasonable interface requirements are imposed.

5.5 Structural Fine-Tuning

This is fine-tuning at a deeper level than usually discussed:

Cosmic fine-tuning concerns constants: if the fine-structure constant $\alpha$ were slightly different, no stable atoms. If the cosmological constant $\Lambda$ were much larger, no galaxies.

Quantum fine-tuning concerns the mathematical framework itself: if the structure of quantum mechanics were slightly different, no physics at all.

Structural fine-tuning is more fundamental. The constants are parameters within the framework; the framework itself must be precisely tuned for any parameters to matter.

6. The Born Rule

6.1 The Interface Is Quadratic

Distinguishability is pairwise, therefore quadratic. The natural structure on a space of distinguishable states is an inner product—a function that takes two vectors and returns a number measuring their relation.

For complex Hilbert space, the inner product is:

\[\langle\psi|\phi\rangle\]

This is sesquilinear (linear in one argument, conjugate-linear in the other), which ensures:

\[\langle\psi|\psi\rangle \geq 0\]

The norm is automatically non-negative.

6.2 Born Rule from Vehicle-Weight Invariance

The Born Rule Paper establishes a stronger result: the Born rule is derived from vehicle-weight invariance.

The Vehicle-Weight Distinction. Any physical probability assignment involves:

  • Vehicle: The mathematical representation of a state (e.g., a density matrix decomposition)
  • Weight: The probability assigned to outcomes

Vehicle-Weight Invariance (VWI). If two mathematical decompositions represent the same physical state, they must yield the same probability assignments. The physics cannot depend on mathematically equivalent descriptions.

Theorem (Born Rule from VWI). Given a Hilbert space framework and VWI, the only consistent probability assignment is:

\[P(\text{outcome}) = |\langle\text{outcome}|\psi\rangle|^2\]

Proof Sketch: VWI forces the probability measure to respect the structure of density matrices. Combined with Gleason’s theorem (which shows the Born rule is the unique frame function on Hilbert spaces of dimension $\geq 3$), we obtain the Born rule as a derived consequence, not an independent postulate.

6.3 Complex Hilbert Space from Local Tomography

The Hilbert Space Paper establishes that complex Hilbert space itself is derived, not postulated:

Theorem (Complex Hilbert Space from Id + Local Tomography). Given:

  1. Determinate Identity (Id) structures the state space
  2. Local tomography (composite states determined by local measurements)
  3. Continuous reversible dynamics (information preservation)

Then the state space is complex Hilbert space, not real or quaternionic.

Key Result: Local tomography requires $d^2 - 1$ parameters for a $d$-dimensional system. Only complex Hilbert space satisfies this with interference structure.

6.4 The Derivational Structure

The LRT framework is now derivational, not merely compatible:

Element Status Derivation
Distinguishability metric Derived From Id (Section 3)
Inner product structure Derived From pairwise distinguishability
Complex numbers Derived From local tomography + Id
Born rule Derived From VWI + Gleason
Unitarity Derived From information preservation

The derivations are conditional on Tier-2 axioms (continuity, local tomography, information preservation)—physical constraints that are empirically established and independently motivated. But given these, complex quantum mechanics follows uniquely.

7. Dissolutions

LRT does not solve the foundational puzzles of quantum mechanics in the sense of providing new dynamics or hidden variables. It dissolves them - showing that the puzzles arise from mistaken framings.

7.1 Measurement

The puzzle: How does the smooth, deterministic evolution of the wave function produce discrete, random measurement outcomes? What constitutes a “measurement”? When does “collapse” occur?

The dissolution: There is no mysterious collapse mechanism. Measurement is the interface between $I_\infty$ and $A_\Omega$.

In $I_\infty$, the quantum state evolves unitarily. When the state interacts with a context that requires Boolean outcomes - a detector, an irreversible record, a macroscopic system - $L_3$ are enforced. The state must become determinate.

This is not a dynamical process requiring new physics. It is a category transition - from the $I_\infty$ domain (where indeterminacy is permitted) to the actuality domain (where it is not).

The “measurement problem” dissolves because collapse is not a process but an interface. The question “when does collapse occur?” is like asking “when does the map become the territory?” - it reflects a category confusion.

7.1.1 What LRT Does and Does Not Provide

We must be precise about what this dissolution accomplishes.

What LRT provides:

  • An ontological interpretation of what collapse IS (category transition, not dynamical process)
  • An explanation of why definite outcomes occur ($L_3$ enforcement)
  • A reason why no new physics is needed (it is not a physical process)

What LRT does not provide:

  • A precise physical criterion for when the transition occurs
  • A derivation of the quantum-classical boundary
  • An explanation of why THIS outcome rather than THAT outcome

The question “when exactly does Boolean actuality get enforced?” remains open. Candidate answers from the literature include:

Criterion Source
Decoherence Zurek, Zeh
Irreversible amplification Daneri-Loinger-Prosperi
Thermodynamic gradient Various
Gravitational threshold Penrose
Information transfer to environment Quantum Darwinism

LRT is compatible with any of these as the physical marker of the transition. What LRT adds is the interpretation: whatever the physical criterion, what happens is category transition, not collapse dynamics.

This is analogous to how thermodynamics relates to statistical mechanics. Thermodynamics says entropy increases; statistical mechanics says how (coarse-graining, typicality). LRT says outcomes become determinate; decoherence (or another mechanism) may specify when.

The remaining question - why THIS outcome? - may have no answer. If the selection among outcomes satisfying $L_3$ is genuinely stochastic (irreducibly random), then “why this one?” has no deeper explanation. The Born rule gives probabilities; it may not admit further grounding.

7.2 Entanglement and Non-Locality

The puzzle: Entangled particles exhibit correlations that cannot be explained by local hidden variables (Bell’s theorem). Measuring one particle seems to instantaneously affect the other, regardless of distance. How can this be, given that no signal travels faster than light?

The dissolution: There is no “spooky action at a distance” because there is no action.

In LRT, $L_3$ operate as a global constraint field. They do not propagate from place to place like a signal; they simply hold, everywhere, always. An entangled state is a single configuration in $I_\infty$ with extended properties - not two separate things mysteriously connected.

When measurement occurs, $L_3$ enforce consistency across the entire state. The correlations are not caused by one particle signaling the other; they are constraint satisfaction, not communication.

7.2.0 Constraints Are Not Hidden Variables

This framing might sound like non-local hidden variables (as in Bohmian mechanics). It is not. The distinction is crucial:

A variable has a value. Hidden variable theories posit that particles have definite properties (position, momentum) that we simply do not know. The “hidden” refers to our ignorance.

A constraint is a rule. The constraint “A + B = 0” does not assign values to A and B; it specifies a relationship they must satisfy. If we measure A = 3, we immediately know B = -3 - not because a signal traveled from A to B, but because the constraint was always in force.

In LRT:

  • The entangled state is a single $I_\infty$ configuration satisfying certain constraints
  • Measurement reveals which values satisfy the constraints
  • No signal is needed because the constraint was never “communicated” - it was constitutive of the state

This is why Bell’s theorem does not threaten LRT. Bell rules out local hidden variables - pre-existing definite values that determine outcomes. LRT does not posit such values. The $I_\infty$ state is genuinely indeterminate; constraints specify relationships between outcomes, not the outcomes themselves.

The correlations are not explained by hidden information traveling faster than light. They are explained by the unified structure of the $I_\infty$ state, which does not have spatial parts that need to coordinate. The “non-locality” is in the wholeness of the state, not in any propagation.

This explains why entanglement produces correlations but not signaling. The correlations reflect the logical structure of a unified state. No information travels because there is nothing traveling - just global consistency being enforced.

7.2.1 Relativistic Considerations

The “global constraint” picture works naturally in non-relativistic quantum mechanics, where simultaneity is well-defined. In relativistic contexts, the situation is more subtle.

The concern: General relativity has no preferred foliation of spacetime. “Simultaneous” events depend on reference frame. If $L_3$ enforcement is “global,” does it require a preferred frame, violating Lorentz invariance?

The response: The constraint is on the $I_\infty$ state, not on spacetime events. The entangled state in $I_\infty$ is a single configuration; it does not have spatial parts that need to coordinate. The “global” in “global constraint” refers to the logical completeness of constraint satisfaction, not to spatial simultaneity.

When measurement outcomes are registered at spacelike separation, each outcome is locally determinate and globally consistent. The consistency is not achieved by signaling but is a feature of the unified $I_\infty$ state. Different reference frames will describe the ordering of measurements differently, but all frames agree on the correlations - which is exactly what we observe.

The limitation: A fully relativistic formulation of LRT would need to articulate how the $I_\infty$/actuality interface respects the causal structure of spacetime. This is non-trivial and represents an open problem for the framework.

Specifically:

  • Does the $I_\infty$ state have a relativistically invariant description?
  • How does the category transition (measurement) relate to the light-cone structure?
  • Can the framework be extended to quantum field theory in curved spacetime?

These questions parallel open problems in other interpretations (e.g., the preferred foliation in Bohmian mechanics, the basis problem in Everett). LRT does not solve them, but it does not introduce new difficulties either. The framework is consistent with relativistic QFT as standardly practiced; the metaphysical interpretation requires further development.

7.3 Many-Worlds Interpretation Obviated

The puzzle: If the wave function is real and collapse is not fundamental, what happens to the other branches? MWI says they are equally real - parallel worlds splitting at every measurement.

The dissolution: LRT preserves MWI’s insights while restoring single actuality.

MWI correctly recognized that:

  • The wave function is ontologically real
  • Collapse should not be a special mechanism
  • There are no hidden variables

LRT agrees with all of this. But LRT does not conclude that all branches are equally actual. Instead:

  • Possibilities are real (they exist in $I_\infty$)
  • One actuality ($L_3$ enforce a single determinate outcome)
  • Other possibilities remain in $I_\infty$, not in parallel branches

The “branching” of MWI is reinterpreted as the structure of $I_\infty$ - all possibilities are there, but only one actualizes. This is not solipsism or hidden variables; it is the distinction between possibility ($I_\infty$) and actuality ($L_3$-compliant Boolean structure).

7.4 Wave Function Reality

The puzzle: Is the wave function real (ontological) or merely a description of our knowledge (epistemic)?

The dissolution: The wave function is $I_\infty$ structure - real but not actual.

The wave function $\psi$ describes a genuine configuration in $I_\infty$. It is not “just math” or “just our knowledge.” But it is also not a physical thing in space like a classical field.

The wave function is real in the sense that $I_\infty$ is real - it is the structure of possibility constituted by $L_3$. It becomes actual only at the interface, when measurement enforces Boolean determinacy.

7.5 Quantization

The puzzle: Why are physical quantities (energy, charge, spin) discrete rather than continuous?

The dissolution: Actuality is Boolean; the bit is the grain.

In $I_\infty$, continuous structures exist. But actuality - what physically manifests - must be determinate. The bit is the minimal unit of determinacy. You cannot have 0.7 of a distinction.

Discrete quantities reflect the Boolean structure of actuality. Energy levels are discrete because the electron either is or is not in a given state. Charge is quantized because the particle either has it or does not. Spin is quantized because the measurement outcome is either up or down.

Quantization is $L_3$ at work.

7.6 Identical Particles and Permutation Symmetry

The puzzle: Why are all electrons exactly identical? Classical objects can be arbitrarily similar but always distinguishable in principle. Quantum particles of the same type are absolutely indistinguishable. Furthermore, why do identical particles obey the symmetrization postulate—bosons in symmetric states, fermions in antisymmetric states?

The dissolution: Permutation symmetry is derived from Determinate Identity.

The QFT Statistics Paper establishes the derivation:

Theorem (Symmetrization from Id). If two configurations $|a, b\rangle$ and $|b, a\rangle$ are qualitatively identical (indistinguishable by any measurement), then Determinate Identity requires they represent the same physical state or differ only by phase:

\[|a, b\rangle = e^{i\phi} |b, a\rangle\]

Applying permutation twice returns the original: $e^{2i\phi} = 1$, so $e^{i\phi} = \pm 1$.

  • $+1$: Symmetric states (bosons)
  • $-1$: Antisymmetric states (fermions)

The Key Insight: The symmetrization postulate is not an independent axiom—it follows from Determinate Identity applied to configurations that cannot be distinguished. If there is no property $P$ such that configuration $|a,b\rangle$ has $P$ and $|b,a\rangle$ lacks $P$, then Id requires they not be treated as distinct physical states.

In LRT terms, quantum fields are not substances but structures—modes of distinguishability in $I_\infty$. All electrons are identical because they are excitations of the same mode. There is no “this electron” versus “that electron” at the fundamental level—only “electron-mode excitation here” versus “electron-mode excitation there.”

The identity of particles, and the statistics they obey, follows from Id applied to the structure of distinguishability itself.

8. Quantum Fields as Logical Excitations

8.1 The Hierarchy

We can articulate a hierarchy from logic to particles:

Level Description
0: $L_3$ Ontological foundation - constitutes distinguishability
1: $I_\infty$ Structural space - totality of distinguishable states
2: Hilbert Space Geometric structure - complex vector space with inner product
3: Quantum Fields Dynamic structure - excitation modes on Hilbert space
4: Particles Phenomenological - localized excitations of fields

This inverts the usual picture. We typically think: particles are fundamental; fields describe their interactions; Hilbert space is mathematical formalism; logic is how we reason about it all.

LRT says: logic is fundamental; Hilbert space is what logical distinguishability looks like with interference; fields are modes of excitation; particles are what we observe.

8.2 What This Does Not Explain

This hierarchy does not explain:

  • Why THESE specific fields (electron, quark, photon, etc.)
  • Why THESE gauge groups (U(1), SU(2), SU(3))
  • Why THREE generations of fermions
  • Why THESE masses and coupling constants

These are further fine-tuning questions. LRT situates quantum structure; it does not derive the Standard Model.

9. Fine-Tuning Reconsidered

9.1 Three Levels of Fine-Tuning

Level What Is Tuned Examples
Constants Parameters within QM + GR $\alpha$, G, $\Lambda$, particle masses
Structure The mathematical framework Complex Hilbert space, Born rule, unitarity
Logic $L_3$ themselves Identity, non-contradiction, excluded middle

Standard fine-tuning discussions focus on Level 1. LRT reveals Level 2: the framework itself is fine-tuned.

Level 3 is not fine-tuned in the same sense - $L_3$ are constitutive, not selected from alternatives. There is no space of “possible logics” from which classical logic was chosen. $L_3$ are the condition for any structure at all.

9.2 The Depth of Structural Fine-Tuning

Consider the chain of dependencies:

  1. Without $L_3$: no distinguishability, no structure
  2. Without quantum structure: no stable atoms, no chemistry
  3. Without fine-tuned constants: no stars, no planets, no life

Level 1 (constants) gets the attention. But Level 2 (structure) is more fundamental. You cannot tune constants if the framework does not support stable physics at all.

Quantum fine-tuning is the deepest level of contingency we can articulate - deeper than cosmic fine-tuning, because it concerns the framework within which cosmic parameters are defined.

9.3 Why This Matters

Fine-tuning is often framed as a puzzle requiring explanation (multiverse, design, etc.). LRT does not solve this puzzle. But it clarifies what the puzzle is.

The question is not just: why these constants? The question is: why this structure?

LRT shows that quantum structure is required for stable physics. It does not explain why stable physics exists. But it situates the question correctly.

10. Wheeler Grounded

10.1 “It from Bit”

John Archibald Wheeler proposed that physical reality (“it”) emerges from informational yes/no questions (“bit”). This was visionary but programmatic - Wheeler never fully grounded the proposal.

LRT provides the grounding:

What is a bit? The minimal unit of distinguishability, constituted by $L_3$.

How do bits become “its”? Through the interface between $I_\infty$ and $A_\Omega$. Possibilities in $I_\infty$ become actual when $L_3$ are enforced.

Why quantum structure? Because quantum mechanics is the unique stable interface - the only structure that produces physics capable of asking the question.

10.2 “Bit from Fit”

We extend Wheeler’s slogan: It from bit, bit from fit.

  • It from bit: Physical reality emerges from information
  • Bit from fit: The bit (fundamental distinction) emerges from the fit between $I_\infty$ and $A_\Omega$

The “fit” is the fine-tuning. Quantum structure fits - it interfaces correctly between possibility and actuality while producing stable physics. Classical structure does not fit - it satisfies the interface constraints but does not produce stability. Other structures do not fit - they fail the interface constraints entirely.

“Fit” captures:

  • The precision required (exact quantum structure)
  • The selection criterion (stability)
  • The relationship (interface between domains)

10.3 The Conversion Factor

If bits are fundamental and physics emerges from them, there must be a conversion between informational and physical quantities.

$\hbar$ (Planck’s constant) is the natural candidate:

\[\text{Action} = \hbar \times \text{Complexity}\]

$\hbar$ is the quantum of action - the minimal amount of physical change. If it is also the conversion factor from bits to action, then:

  • The Planck scale is where bit-structure becomes directly relevant
  • The classical world emerges from coarse-graining over many bits
  • The “weirdness” of QM is the friction between bit-structure and continuous appearance

This is speculative but coherent with the framework.

11. Completing the Landscape

LRT does not stand alone. It connects to, grounds, or completes several existing programs in foundations of physics.

11.1 Interpretations Grounded

Copenhagen: Copenhagen refused to say what the wave function “really is” - it is a tool for predicting outcomes. LRT provides what Copenhagen refused: the wave function is $I_\infty$ structure, real but not actual until measurement.

QBism: QBism says quantum states are agent’s beliefs. LRT grounds what those beliefs track: the structure of $I_\infty$. Beliefs are not arbitrary; they correspond to genuine features of possibility space.

Relational QM: Rovelli’s relational interpretation says properties are relative to interactions. LRT explains why: context determines which partition of $I_\infty$ interfaces with actuality. Different interactions probe different aspects of the $I_\infty$ structure.

Many-Worlds: As discussed, LRT preserves MWI’s insights (wave function realism, no collapse mechanism) while restoring single actuality.

11.2 Programs Completed

Reconstruction theorems: Hardy, Chiribella, and others have derived quantum structure from operational axioms (e.g., tomographic locality, continuous reversibility). LRT grounds these axioms: they are features required for stable interface between $I_\infty$ and $A_\Omega$.

Decoherence: The decoherence program explains how interference terms vanish through environmental interaction. LRT explains what decoherence accomplishes: the transfer of phase information to the environment, enforcing local Boolean structure.

Wheeler’s program: As discussed, LRT grounds “it from bit.”

11.3 Principles Connected

Landauer’s principle: Erasing one bit of information costs at least kT ln 2 of energy. In LRT terms: destroying a distinction has thermodynamic cost because distinctions are ontologically real.

Holographic principle: The entropy of a region is bounded by its surface area in Planck units. In LRT terms: distinguishability has a spatial density limit; there is a maximum number of bits per Planck area.

Bekenstein bound: A region of space has finite information capacity. LRT: actuality can only support finite distinguishability in finite regions.

Zeilinger’s foundational principle: An elementary system carries exactly one bit of information. LRT: the bit is the fundamental unit; elementary systems are minimal carriers.

11.4 Mathematical Universe Refined

Tegmark’s Mathematical Universe Hypothesis (MUH) claims that reality IS mathematical structure - all consistent mathematical structures exist and we inhabit one of them.

LRT refines this:

  • Not all mathematical structures in $I_\infty$ are actualized
  • $L_3$ + stability select which structures produce physics
  • The relationship is constitutive ($L_3$ -> structure) not compositional (structure = reality)

LRT is compatible with the spirit of MUH while being more specific about the selection mechanism.

12. Honest Accounting

We must be clear about what LRT establishes and what remains assumed. The framework is more derivational than earlier versions suggested.

12.1 What Is Derived (Tier 1: From Id Alone)

Claim Status Basis
$A_\Omega$ is Boolean Derived $L_3$ require determinacy
Distinguishability metric Derived From Determinate Identity (Id)
Distinguishability is pairwise/quadratic Derived Structural analysis
The bit is the fundamental unit Derived Minimal distinguishability
Inner product structure Derived From pairwise distinguishability
Permutation symmetry Derived Id applied to qualitatively identical configurations
Measurement as category transition Derived $I_\infty$/$A_\Omega$ framework
Entanglement as global constraint Derived $L_3$ as constraint field

12.2 What Is Derived (Tier 2: From Id + Physical Axioms)

Claim Status Derivation
Complex Hilbert space Derived Id + local tomography + continuous reversibility
Born rule Derived Vehicle-weight invariance + Gleason
Unitarity Derived Information preservation
Bounded distinguishability (Identity Continuity) Derived Id applied to continuous paths

The Tier-2 derivations are conditional on physical axioms (local tomography, continuous reversibility, information preservation) that are empirically established and independently motivated.

12.3 What Remains Contingent (Tier 3)

Feature Status Note
Specific quantum fields Contingent Which modes exist is not derived
Particle masses Contingent Parameter-level
Coupling constants Contingent Parameter-level
Spacetime dimension Contingent Not addressed by LRT
Initial conditions Contingent $s_0$ is given

12.4 What Is Primitive

Element Status Note
Determinate Identity (Id) Primitive Constitutive; NC and EM follow
$I_\infty$ Primitive Space of all representable configurations
Parsimony Structural consequence From constitution + grounding (Section 4.3); not a new axiom but reorganization

12.5 What LRT Does Not Explain

  • Why there is something rather than nothing
  • Why $L_3$ rather than some other logical structure
  • Why THESE specific quantum fields, masses, constants
  • The arrow of time
  • Consciousness/observation (beyond functional role in measurement)

12.6 Open Problems for Future Work

  1. The physical criterion for interface transition: When exactly does $A_\Omega$-admissibility get enforced? LRT is compatible with decoherence, gravitational threshold, or other criteria.

  2. Relativistic formulation: How does the $I_\infty$/$A_\Omega$ framework respect spacetime causal structure? The GR Extension develops identity strain as a kinematic constraint.

  3. The $\hbar$-bit connection: Is $S = \hbar C$ (action = Planck constant x complexity) a deep identity?

  4. Derivation of specific fields: Can the framework explain why THESE quantum fields rather than others?

  5. Identity strain to dynamics: The GR Extension shows identity strain has quadratic leading-order form. Can this be extended to a full variational principle?

LRT is a framework that derives quantum structure from logical foundations, not a theory of everything. It explains why quantum mechanics rather than alternatives, while leaving specific parameters contingent.

13. Conclusion

13.1 Summary

Logic Realism Theory establishes that the Three Fundamental Laws of Logic ($L_3$: Determinate Identity, Non-Contradiction, Excluded Middle) are ontological constraints on physical instantiation. This paper has extended the framework to quantum mechanics.

The core insight is that quantum mechanics is derivable from $L_3$ given physical constraints. Determinate Identity grounds the distinguishability metric; vehicle-weight invariance forces the Born rule via Gleason; local tomography selects complex Hilbert space; and permutation symmetry follows from Id applied to qualitatively identical configurations.

This framework dissolves foundational puzzles:

  • Measurement is category transition, not mysterious collapse
  • Entanglement is global constraint satisfaction, not spooky action
  • Wave function is $I_\infty$ structure - real but not actual
  • Quantization reflects Boolean grain of actuality
  • Identical particles are excitations of the same distinguishability mode

The framework grounds Wheeler’s “it from bit”: the bit (fundamental distinction) derives from Id; quantum mechanics is what bit-structure looks like interfacing with $A_\Omega$.

13.2 The Title Explained

It from bit: Physical reality emerges from information - from yes/no questions, from distinctions, from bits.

Bit from fit: Those bits - those distinctions - arise from the fit between possibility and actuality. The fit is precise. The fit is fine-tuned. The fit is quantum mechanics.

13.3 Final Reflection

We have not explained why reality exists. We have not derived specific physical constants from logic. We have not solved the mystery of existence.

What we have done is derive quantum structure from logical foundations.

The question is not: why does physics obey logic? (It must—$L_3$ are constitutive.)

The question is not: why does quantum mechanics have its specific structure? (It follows from Id + physical constraints.)

The question is: why does anything exist that requires logic to structure it at all?

LRT does not answer this question. But it shows what the question is, and that is not nothing.

Determinate Identity is not merely how we think. Quantum mechanics is not merely how physics works. Together, they are the structure of $A_\Omega$ itself—the pattern in which instantiation is possible.

It from bit. Bit from fit. The fit is derived. That is why we are here to ask.

References

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LRT Paper Suite (January 2026): Available at the LRT Zenodo Community:

Longmire, J. D. “Logic Realism Theory: Position Paper.” 2026. [Core framework, $I_\infty$/$A_\Omega$ ontology, Identity Continuity]

Longmire, J. D. “Deriving the Born Rule from Logical Foundations.” 2026. [Vehicle-weight invariance derivation]

Longmire, J. D. “Deriving Complex Hilbert Space from Determinate Identity.” 2026. [Local tomography pathway]

Longmire, J. D. “LRT Constraints on QFT: Deriving Particle Statistics.” 2026. [Symmetrization postulate from Id]

Longmire, J. D. “LRT Extension to General Relativity.” 2026. [Identity strain, kinematic constraints]

Masanes, L. and Muller, M. P. “A Derivation of Quantum Theory from Physical Requirements.” New Journal of Physics 13, 2011: 063001.

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Correspondence: James (JD) Longmire jdlongmire@outlook.com ORCID: 0009-0009-1383-7698

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