Logic Realism Theory

Operationalizing Information Circulation: From Horizon Constraints to Cosmological Dynamics

James (JD) Longmire
ORCID: 0009-0009-1383-7698
Published: February 25, 2026
information circulation black hole de-actualization cosmological constant admissibility predicate L₃ constraints Logic Realism Theory
Zenodo Archive

Abstract

The Information Circulation Hypothesis (ICH) proposes a closed dynamical loop: information flows from the abstract space of logical possibilities (I∞) into physical instantiation (A_Ω), then returns to I∞ via black hole singularities. Unlike the standard breakdown narrative—which treats singularities as gaps in description—ICH treats them as transition points where L₃ constraints can no longer be satisfied within spacetime, forcing information back to abstract structure. This paper closes the foundational gap identified in prior work: the derivation of the admissibility predicate Adm from L₃. Horizon physics provides exactly this connection. The boundary distinguishability constraint—proven in the companion horizon paper—instantiates L₃ at gravitational boundaries, generating Adm(x) = 1 iff records exist in accessible algebras. When horizons saturate, information routes to radiation (island mechanism) or singularity (de-actualization). The cosmological constant Λ emerges as the fixed-point cost of maintaining this circulation.

1. Introduction

1.1 The Central Claim

The Information Circulation Hypothesis (ICH) proposes a closed dynamical loop between abstract and physical domains:

\[I_\infty \xrightarrow{\text{instantiation}} A_\Omega \xrightarrow{\text{de-actualization}} I_\infty\]

Information cycles: drawn from the space of logical possibilities ($I_\infty$) into physical instantiation ($A_\Omega$), then returned to $I_\infty$ via black hole singularities. The universe is not a one-way process toward heat death but a circulation—with the cosmological constant $\Lambda$ emerging as the cost of maintaining this cycle.

This is not a relabeling of “classical physics breaks down at singularities.” The standard breakdown narrative treats singularities as gaps in our description. ICH treats them as transition points in a dynamical mechanism: the phase where L₃ constraints can no longer be satisfied within spacetime, forcing information back to abstract structure.

1.2 The Gap in Prior Work

Logic Realism Theory derives quantum mechanics from logical constraints: the three laws of classical logic (L₃)—Identity, Non-Contradiction, Excluded Middle—treated as ontological constraints on physical instantiation rather than merely rules of inference [1]. The derivation proceeds:

\[L_3 \rightarrow \text{Distinguishability} \rightarrow \text{Hilbert Space} \rightarrow \text{Born Rule}\]

ICH extends this framework to cosmology [2, 3], but prior work identified a critical gap:

The companion “Admissibility Dynamics” paper [3] formalized the physics but identified a critical gap:

Missing: Logical operator $L_3 \rightarrow$ Admissibility predicate $\mathsf{Adm}$

That paper operates downstream of this step, showing how physics would behave if such a filter exists. The present paper closes the gap by showing that horizon physics provides the concrete instantiation of L₃ → Adm.

1.3 Paper Structure

  • §2: Importing results from the horizon channel paper
  • §3: The L₃ → Adm derivation at horizons
  • §4: De-actualization: what happens at saturation
  • §5: Cosmological circulation and the Λ fixed point
  • §6: The complete ICH picture
  • §7: Falsifiable consequences

1.4 Scope of L₃ Constraints

A potential confusion must be addressed at the outset: L₃ does not govern $I_\infty$ itself.

What L₃ constrains: The instantiation of configurations from $I_\infty$ into $A_\Omega$. L₃ acts as a filter at the boundary between abstract possibility and physical actuality.

What L₃ does not constrain: The internal structure of $I_\infty$. The space of logical possibilities contains all coherent configurations, including many that can never instantiate physically. $I_\infty$ is not “made of” L₃-compliant things—it contains the full logical space, and L₃ filters what can cross into physical instantiation.

Analogy: A mesh filter doesn’t determine what exists upstream—it determines what can pass through. L₃ is the mesh between $I_\infty$ and $A_\Omega$.

This clarification matters because de-actualization (return to $I_\infty$) does not mean information becomes “logically incoherent.” It means information loses its physical address while remaining in the space of logical possibilities. L₃ constraints cease to apply (because there is no instantiation to constrain), not that they are violated.

1.5 Framework Assumptions

The derivation proceeds from five core assumptions, stated explicitly:

A1. Ontological L₃: The three laws of classical logic (Identity, Non-Contradiction, Excluded Middle) are constraints on physical instantiation, not merely rules of inference.

A2. Distinguishability Requirement: For any configuration $x$ to be physically instantiated, it must be distinguishable from all alternative configurations in some accessible algebra.

A3. Causal Localization: During causal disconnection, “accessible algebra” means the exterior/boundary algebra—records in causally inaccessible regions do not satisfy the distinguishability requirement.

A4. Finite Capacity: Physical systems have finite information capacity bounded by entropy (Bekenstein bound for horizons).

A5. Circulation Closure: Information that exits $A_\Omega$ via de-actualization returns to $I_\infty$, maintaining conservation across both domains.

A1 is the core LRT postulate. A2-A4 are physical postulates motivated by L₃ but not derivable from pure logic. A5 is the ICH extension that connects horizon physics to cosmology.

Note on A3. Assumption A3 (Causal Localization) is specific to the ICH framework; alternative proposals could relax or modify it, and doing so would change or remove the L₃ → Adm link at horizons. We do not claim A3 is a necessity of nature—it is a physical postulate that makes ICH’s predictions possible.

1.6 LRT as QFT/GR Bridge

A referee might ask: why should L₃ constraints—operating at the logical level—have anything to say about the GR/QFT interface?

The answer lies in LRT’s structural position:

LRT provides a common substrate. Both QFT and GR presuppose distinguishability of states. QFT requires orthogonal states for measurement; GR requires distinguishable spacetime points for metric structure. L₃ provides the logical foundation for this shared presupposition.

Horizons are where the substrate shows. In ordinary physics, distinguishability is automatic—we don’t think about L₃ because it’s always satisfied. At horizons, finite capacity and causal structure make the constraint operative. The boundary must maintain distinguishability with limited resources under causal constraints.

LRT does not derive GR from QFT or vice versa. Rather, it identifies the logical preconditions both theories assume. When those preconditions become constraining (at horizons, at singularities), L₃ determines what can physically occur.

This is why the L₃ → Adm derivation is possible: horizons are exactly where the logical substrate becomes physically relevant.

1.7 The Key Move: Horizons as L₃ Instantiation Sites

The horizon channel constraint paper [4] establishes:

Admissibility Postulate. For any distinguishable input states with $D(\rho_1, \rho_2) = d > 0$, the boundary marginals after horizon crossing must satisfy:

\[D(\rho_{B,1}, \rho_{B,2}) \geq g_{\min}(d, S_{BH}) > 0\]

This constraint forbids isometries that would erase boundary distinguishability while storing records only in causally inaccessible interior regions.

The insight: This constraint is L₃ operating at horizons.

  • Identity: Distinct states must remain distinct in some accessible algebra
  • Non-Contradiction: The boundary cannot encode both “state 1” and “state 2” for the same subsystem
  • Excluded Middle: Every distinguishable pair must have a definite record—in the boundary or radiation, not nowhere

The horizon is where L₃ becomes operationally constraining because:

  1. The interior is causally disconnected during the pre-emission epoch
  2. The boundary is finite-capacity
  3. Information must eventually couple to radiation

2. Horizon Constraints: Established Results

This section summarizes the core results from [4] that serve as inputs to the ICH operationalization.

2.1 The Packing Theorem

Theorem 2.1 (from [4]). Let $V: H_{in} \rightarrow B \otimes R$ satisfy the record-existence constraint at level $\delta > 0$. Then:

\[M \leq \frac{2 S_{BH}}{\delta^2}\]

where $M$ is the number of mutually distinguishable states and $S_{BH}$ is the Bekenstein-Hawking entropy.

Corollary. For finite $S_{BH}$ and $M$ distinguishable inputs:

\[\delta \geq \sqrt{\frac{2M}{S_{BH}}}\]

The distinguishability floor $\delta$ cannot vanish for finite capacity.

2.2 The Boundary Algebra Requirement

The constraint specifies where records must exist during the pre-emission epoch $t \in [t_{\text{cross}}, t_{\text{emit}}]$:

  • $A_B(t)$: The boundary/exterior-accessible algebra. Records here can mediate correlations with radiation.
  • $A_{\text{int}}(t)$: The interior algebra. Causally disconnected from the exterior until emission.

Admissibility requires records in $A_B(t)$, not merely $A_{\text{int}}(t)$.

Interior-only storage fails because:

  1. Interior DOF are inaccessible during the pre-emission window
  2. If interior storage satisfied admissibility, the constraint would reduce to global unitarity
  3. The physical content is that boundary must maintain records, forcing capacity accounting

2.3 The Island Mechanism

At boundary saturation—when $S_{\text{reserved}} > S_{BH}^{\text{eff}}$—the boundary can no longer hold all required distinguishability records. Information must transfer to radiation. The quantum extremal surface (QES) marks this overflow boundary.

Key result: The island formula emerges as a consequence of boundary saturation under admissibility, not as an independent postulate.

2.4 What the Horizon Paper Does Not Address

The horizon paper [4] treats admissibility as either:

  • A phenomenological hypothesis, or
  • Motivated by LRT but not derived from L₃

It does not:

  1. Show the explicit L₃ → Adm mechanism
  2. Address what happens to information at the singularity (only at the QES)
  3. Connect to the cosmological circulation

These are exactly what the present paper provides.

3. The L₃ → Adm Derivation at Horizons

3.1 The Core Argument

L₃ makes three demands on physical reality:

L₃ Principle Ontological Demand Horizon Expression
Identity A = A Distinguishable states preserve distinguishability
Non-Contradiction ¬(A ∧ ¬A) Boundary cannot encode contradictory records
Excluded Middle A ∨ ¬A Every distinction has definite record location

At horizons, these translate to:

Identity at horizons: If input states $\rho_1, \rho_2$ satisfy $D(\rho_1, \rho_2) = d > 0$, there must exist some subsystem where this distinction is registered. If the boundary were permitted to erase the distinction entirely (ρ_{B,1} = ρ_{B,2}) while the interior is inaccessible, the identity of the input—its distinctness from alternatives—would have no physical instantiation during the pre-emission epoch.

Non-Contradiction at horizons: The boundary algebra cannot simultaneously register “input was ρ₁” and “input was ρ₂” for the same crossing event. This is automatic for quantum states but becomes constraining when we ask: can the boundary fail to register either? Non-Contradiction forbids contradictory records, but combined with Excluded Middle, it also forbids no record.

Excluded Middle at horizons: For each distinguishable pair, the record must be somewhere accessible. Not “perhaps in the interior, perhaps in the boundary, perhaps nowhere”—somewhere definite in the accessible algebra.

3.2 Admissibility Localization

Before deriving the admissibility predicate, we must state explicitly a physical postulate that connects logical necessity (“record must exist somewhere”) to causal constraint (“record must exist in the accessible algebra”).

Lemma 3.0 (Admissibility Localization). Let $x$ be a physically instantiated configuration during interval $t \in [t_{\text{cross}}, t_{\text{emit}}]$. If:

  1. L₃ requires that distinctions between $x$ and alternatives be registered in some definite location, and
  2. The interior algebra $A_{\text{int}}(t)$ is causally disconnected from the exterior during this interval,

then the required record must reside in the accessible algebra $A_B(t)$.

Justification. This lemma makes explicit what might appear as a gap: the move from “somewhere” to “somewhere accessible.” The justification is not pure logic but the Causal Localization postulate (A3): records in causally inaccessible regions do not satisfy the distinguishability requirement for physical instantiation within the accessible domain.

Here is the key physical content: L₃ demands that $x$ be distinguished from alternatives for any observer who can interact with $x$. During $[t_{\text{cross}}, t_{\text{emit}}]$, the only observers who can interact with boundary information are exterior observers. If the distinction record exists only in the interior, exterior observers cannot—even in principle—distinguish $x$ from alternatives.

This is not a logical necessity but a physical postulate about how L₃ applies to causally structured spacetimes. The postulate is falsifiable: if some mechanism allowed interior records to satisfy L₃ constraints for exterior observers, Lemma 3.0 would fail.

Relation to Assumption A3. Lemma 3.0 is an instance of assumption A3 (Causal Localization) applied to horizon geometry. A3 is a physical postulate, not a logical derivation—we state this explicitly to avoid the appearance of deriving physics from pure logic.

3.3 Deriving the Admissibility Predicate

Define the admissibility predicate:

\[\mathsf{Adm}(x, t) = \begin{cases} 1 & \text{if } \exists \text{ POVM } \{E_k\} \text{ on } A_B(t) : D(\rho_{B,x}, \rho_{B,y}) \geq \delta \text{ for all } y \neq x \\ 0 & \text{otherwise} \end{cases}\]

Theorem 3.1 (L₃ → Adm). Let $x$ be a physically instantiated configuration at time $t$. If L₃ holds as ontological constraint and Causal Localization (A3) holds, then $\mathsf{Adm}(x, t) = 1$.

Proof.

Step 1. By Identity, $x$ must be self-identical: its properties are definite, not indeterminate.

Step 2. By Excluded Middle, for any property $P$ that distinguishes $x$ from alternatives, either $x$ has $P$ or $x$ lacks $P$—there is no third option where $P$-status is undefined.

Step 3. By Non-Contradiction, $x$ cannot both have and lack $P$.

Step 4. Together, these require that any distinction between $x$ and alternative $y$ be registered in some definite location. (This is pure L₃.)

Step 5. By Lemma 3.0 (Admissibility Localization), for horizon crossings during $t \in [t_{\text{cross}}, t_{\text{emit}}]$, “definite location” must be the accessible algebra $A_B(t)$. (This invokes A3, not pure logic.)

Step 6. Therefore, distinguishability must reside in $A_B(t)$, which is exactly the record-existence constraint.

Step 7. By the packing theorem (2.1), this implies $\mathsf{Adm}(x, t) = 1$ with $\delta \geq \sqrt{2M/S_{BH}}$. ∎

Note on the derivation structure: Steps 1-4 are pure L₃. Step 5 invokes a physical postulate (A3). The theorem thus derives Adm from L₃ + A3, not from L₃ alone. This is honest: the causal structure of spacetime is physics, not logic.

3.4 Why Horizons Are Special

Horizons are the canonical sites for L₃ → Adm because:

  1. Finite capacity: $S_{BH}$ bounds how much distinguishability the boundary can encode
  2. Causal structure: The interior is definitively inaccessible, not merely difficult to access
  3. Forced accounting: Information must go somewhere—boundary, radiation, or…?

In generic quantum systems, “interior-only encoding” is unproblematic because the interior is eventually accessible. At horizons, causal structure makes the pre-emission interval special: L₃ cannot be satisfied by interior records alone during this window.

3.5 The Gap Is Closed

The Admissibility Dynamics paper [3] required:

\[L_3 \Rightarrow \mathsf{Adm}\]

We have now shown:

\[L_3 \xrightarrow{\text{horizon structure}} \text{record-existence constraint} \xrightarrow{\text{packing theorem}} \mathsf{Adm}\]

This is not abstract assertion. It is concrete physics: L₃ at horizons forces admissibility predicates on physically instantiated states.

4. De-Actualization: The Quantum–Classical–Quantum Cycle

4.1 The Core Claim: A Closed Dynamic Loop

ICH does not merely label the singularity problem. It proposes a dynamic mechanism connecting quantum and classical regimes:

\[\text{quantum instantiation} \xrightarrow{L_3 \text{ filter}} \text{classical emergence} \xrightarrow{\text{horizon saturation}} \text{de-actualization} \xrightarrow{\text{singularity}} \text{return to } I_\infty\]

And the cycle closes: $I_\infty$ is the reservoir from which new instantiations arise.

What this is not: A relabeling of “GR breaks down here.” The standard narrative treats singularity breakdown as a failure of physics—incomplete description awaiting quantum gravity. ICH treats it as the mechanism by which actualized information transitions back to abstract structure.

What this is: A dynamical loop between:

  • I∞ (abstract, logically possible configurations)
  • A_Ω (physically instantiated, spacetime-located states)

The loop has two phase transitions:

  1. Instantiation (I∞ → A_Ω): at Planck scale, filtered by L₃
  2. De-actualization (A_Ω → I∞): at singularities, forced by L₃ constraint failure

4.2 Why “Classical Breakdown” Is the Wrong Frame

Standard narrative: “Classical physics fails at singularities. We need quantum gravity to say what happens there.”

This frames the singularity as a gap in our knowledge—a domain where existing physics gives no answer.

ICH reframes: The breakdown is the transition mechanism. What happens at the singularity is not unknown; it is the switch from Adm(x) = 1 (instantiated, L₃-compliant) to Adm(x) = 0 (no longer physically instantiable under L₃ constraints).

Consider: curvature divergence means the metric structure that defines spatial distinguishability ceases to function. Under L₃, states that cannot be distinguished cannot remain co-instantiated. They don’t “vanish”—they transition to a domain where distinguishability is not spatially grounded.

That domain is $I_\infty$: logical possibility without physical address.

4.3 The Phase Transition: A_Ω → I∞

At the singularity, physical constraints that define instantiation reach a critical point:

  • Curvature diverges → metric distinguishability fails
  • Spacetime location becomes undefined → “where” loses meaning
  • L₃ demands on distinguishability cannot be satisfied in spacetime

ICH proposes that information does not vanish but undergoes a phase transition:

\[A_\Omega \xrightarrow{\text{singularity}} I_\infty\]

The information is de-actualized: stripped of its physical address and properties, it returns to the space of logical possibilities.

Key distinction: This is not information destruction but information de-instantiation. The logical content persists in $I_\infty$; it ceases to be physically present in $A_\Omega$.

Compatibility with singularity resolution. If quantum gravity resolves singularities into a non-singular core or bounce, ICH interprets the effective limit surface—where spacetime locality breaks down—as the de-actualization site. The mechanism does not require literal classical divergence; it requires a regime where metric-based distinguishability fails and L₃ constraints can no longer be satisfied within spacetime structure. Whether this occurs at a classical singularity or a quantum-resolved near-singular region, the transition logic is the same.

4.4 The Closed Loop

The dynamic completes:

Phase Domain What Governs
Instantiation I∞ → A_Ω L₃ filter at Planck scale
Classical emergence A_Ω internal QM (derived from L₃)
Horizon crossing A_Ω boundary Admissibility constraint
De-actualization A_Ω → I∞ L₃ constraint failure at singularity

The universe is not a one-way process from Big Bang to heat death. Under ICH, information circulates: instantiated at one scale, de-actualized at another, cycling through physical and abstract domains.

This is what “classical physics breaks down” misses: the breakdown is not a gap but a transition point in a dynamical loop.

4.5 Connecting to Horizon Saturation

The horizon mechanism and de-actualization are complementary stages in the outflux process:

Condition Mechanism Destination
Boundary can encode Standard evolution Boundary records
Boundary saturates Island mechanism Radiation
Singularity reached De-actualization $I_\infty$

The admissibility constraint forces information into the boundary until saturation, then into radiation. What reaches the singularity has exhausted both channels—it can no longer satisfy L₃ constraints within A_Ω.

4.6 What This Means for Information Conservation

Standard unitarity: Total information in $A_\Omega$ is conserved.

ICH unitarity: Total information across $I_\infty \cup A_\Omega$ is conserved.

These are compatible if de-actualization is a transfer, not destruction. Unitarity in the standard sense applies within $A_\Omega$ (enforced by quantum mechanics). ICH extends this: information that exits $A_\Omega$ via singularity doesn’t vanish—it transitions to $I_\infty$.

4.7 The Hawking Radiation Question

Does Hawking radiation represent:

  1. Boundary overflow: Information that couldn’t fit (island mechanism)
  2. Partial de-actualization: Information transitioning via evaporation
  3. Neither: Thermal noise, not carrying structured information

Under ICH, option (1) applies pre-Page-time; the situation post-Page-time is more complex. The radiation carries correlations established at the boundary—these are not de-actualized but remain in $A_\Omega$ as the radiation subsystem.

De-actualization proper occurs at the singularity, for information that doesn’t escape via radiation.

5. Cosmological Circulation and the Λ Fixed Point

5.1 The Complete Circulation

We can now state the full ICH picture:

Influx (I∞ → A_Ω):

  • At the Planck scale, configurations from $I_\infty$ transition to physical instantiation
  • L₃ acts as the filter: only configurations satisfying Identity, Non-Contradiction, Excluded Middle can instantiate
  • This is the “creation” of space-time, particles, and physical structure

Outflux (A_Ω → I∞):

  • Black hole singularities de-actualize information
  • Configurations that reach the singularity lose their physical “address”
  • Information returns to $I_\infty$—not destroyed but de-instantiated

Circulation equation:

\[Q(t) = F_{\text{in}}(t) - F_{\text{out}}(t)\]

where:

  • $F_{\text{in}}$: instantiation rate from $I_\infty$
  • $F_{\text{out}}$: de-actualization rate through black holes
  • $Q(t)$: net circulation imbalance

5.2 The Λ Fixed Point

From [3], treat the circulation sector as an effective cosmological component:

\[\dot{\rho}_{\text{ICH}} + 3H(\rho_{\text{ICH}} + p_{\text{ICH}}) = Q(t)\]

Key Proposition (from [3]). If feedback drives $\rho_{\text{ICH}}$ toward a late-time attractor $\rho_* = \text{const}$, then:

  1. $\dot{\rho}_* = 0$
  2. With $Q(t) \rightarrow 0$ at late times: $p_* \approx -\rho_*$
  3. Therefore $w_* \approx -1$

This produces $\Lambda$-like behavior.

5.3 The Horizon Constraint Contribution

The horizon dynamics we’ve established feed directly into this:

Boundary saturation rate → determines outflux capacity Packing bound → limits how much information the universe’s black hole population can de-actualize Island mechanism → routes some information to radiation instead of singularity

The detailed dynamics depend on:

  • Black hole formation rate (cosmological structure formation)
  • Horizon saturation timescales (scrambling dynamics)
  • Singularity rates vs. evaporation rates

5.4 Why This Explains Λ

Standard $\Lambda$CDM treats the cosmological constant as a primitive: a vacuum energy density with no explanation for its value.

ICH derives $\Lambda$-like behavior from:

  1. L₃ constraints → admissibility filter
  2. Finite capacity → horizon saturation
  3. Circulation dynamics → influx/outflux imbalance
  4. Attractor behavior → $w \approx -1$ fixed point

$\Lambda$ is not a primitive. It is the cost of maintaining admissible reality while information circulates.

5.5 Phenomenological Scaling Ansatz: w(z) and Black Hole Demographics

The ICH framework predicts that deviations from $w = -1$ should track the global outflux rate through black holes. We adopt the following phenomenological scaling ansatz as a first-pass, order-of-magnitude linkage, to be refined with detailed structure formation and black hole growth models.

Outflux Rate. Define the global de-actualization rate:

\[F_{\text{out}}(z) = \int dM \, n(M, z) \cdot \dot{S}_{\text{BH}}(M)\]

where $n(M, z)$ is the comoving number density of black holes with mass $M$ at redshift $z$, and $\dot{S}_{\text{BH}}(M)$ is the entropy accretion rate per black hole.

Scaling Ansatz. The deviation from $w = -1$ scales with the outflux rate relative to the Hubble rate:

\[w(z) + 1 \approx \alpha \cdot \frac{F_{\text{out}}(z)}{H(z) \cdot \rho_{\Lambda}}\]

where $\alpha$ is a dimensionless coupling constant and $\rho_\Lambda$ is the effective dark energy density.

Physical Interpretation. When black hole formation and accretion increase, the outflux rate rises, the circulation imbalance $Q(t)$ increases, and $w$ deviates slightly above $-1$. Conversely, when black hole activity decreases (late universe), the system approaches the fixed-point attractor with $w \to -1$.

Observational Signature. The ansatz predicts:

\[\frac{dw}{dz}\bigg|_{z \sim 0} \sim \alpha \cdot \frac{d}{dz}\left[\frac{F_{\text{out}}}{H \rho_\Lambda}\right]_{z=0}\]

Since black hole demographics are independently measurable (gravitational wave mergers, X-ray surveys, quasar luminosity functions), this provides a cross-check: ICH predicts a specific correlation between $w(z)$ evolution and global black hole activity.

Current Constraints. With $\lvert w + 1 \rvert < 0.06$ at 2σ and estimated $F_{\text{out}}$ from LIGO/Virgo merger rates, the constraint $\alpha \lesssim 0.1$ is consistent with, but does not yet test, the framework. DESI and Euclid will improve $w(z)$ constraints by an order of magnitude; LISA will improve black hole merger demographics by two orders of magnitude. The combination should provide a genuine test by ~2035.

5.6 The Observational Mapping

From [3], the framework predicts:

  1. $\Lambda$ behaves as dynamical attractor with small deviations from $w = -1$
  2. Deviations track global entropy sinks (black hole demographics) via the scaling ansatz (§5.5)
  3. Phase transitions in admissibility appear as cosmological phase transitions

Current observational bounds constrain $\lvert w + 1 \rvert < 0.06$ at 2σ. Next-generation surveys (DESI, Euclid, Roman) achieving sub-percent precision could detect or rule out ICH-specific signatures.

6. The Complete ICH Picture

6.1 The Chain

We have now established the complete derivation:

\[L_3 \xrightarrow{\S3} \mathsf{Adm} \xrightarrow{\S4} \text{de-actualization} \xrightarrow{\S5} \Lambda\]

More explicitly:

  1. L₃ at horizons forces record-existence in accessible algebras (§3)
  2. Packing theorem converts this to the admissibility predicate (§3.2)
  3. Boundary saturation routes information to radiation (island) or singularity (de-actualization) (§4)
  4. Circulation dynamics produce an effective dark energy sector (§5)
  5. Attractor behavior yields $w \approx -1$ (§5.2)

6.2 Relation to Other LRT Papers

The LRT paper series now has three components:

Paper Focus Key Result
Flagship [1] L₃ → QM Hilbert space, Born rule from logic
Horizon Channels [4] Admissibility at horizons Packing bounds, island mechanism
ICH Operationalization (this) L₃ → Adm → Λ Cosmological constant as fixed point

The flagship derives quantum mechanics from logic. The horizon paper derives gravitational information dynamics from admissibility. This paper closes the loop, deriving admissibility from L₃ and connecting to cosmology.

6.3 What’s New Here

The Admissibility Dynamics paper [3] was a translation layer: if Adm exists, here’s how physics looks.

This paper provides the operationalization: Adm is derived from L₃ via horizon physics.

The horizon paper [4] was agnostic about L₃: treat admissibility as phenomenological hypothesis.

This paper commits: the horizon constraint is L₃ instantiated at gravitational boundaries.

7. Falsifiable Consequences

7.1 From Horizons

From [4], the horizon constraint predicts:

  • Page time shift: $\Delta t / t \sim -0.82\varepsilon$ (earlier Page time)
  • QES location: $(φ_H - φ_{\text{QES}})/4G \sim S_{\text{rad}} \cdot h(\bar{d})$
  • Scrambling bound: $t^* \geq kM$ (weaker than Hayden-Preskill)

7.2 From Circulation

The cosmological predictions:

  • $w(z)$ evolution: Small deviations from $-1$, tracking black hole demographics
  • Correlation with entropy production: $w$ variations should correlate with large-scale structure formation
  • Phase transitions: Possible signatures at recombination or other cosmological epochs

7.3 Joint Constraints

The two prediction families connect:

  • Horizon saturation dynamics → determine $F_{\text{out}}$
  • Black hole formation → determine circulation budget
  • Aggregate behavior → constrain $w_{\text{eff}}$

This is testable in principle, though current precision is insufficient.

7.4 What Would Falsify ICH

  1. L₃ violation at horizons: If distinguishability can be erased without boundary record (even temporarily), the L₃ → Adm step fails
  2. Perfect $w = -1$: If $\Lambda$ is exactly constant with zero deviations, attractor behavior is indistinguishable from primitive constant
  3. Anti-correlation with black holes: If $w$ variations correlate negatively with black hole demographics, circulation direction is wrong

8. Discussion

8.1 What This Paper Achieves

The central result: the L₃ → Adm step is operationalized through horizon physics.

This was the missing link in the ICH chain. Without it, ICH was conceptually motivated but formally incomplete. With it, the derivation proceeds:

\[L_3 \rightarrow \text{(horizon constraint)} \rightarrow \mathsf{Adm} \rightarrow \text{(circulation dynamics)} \rightarrow \Lambda\]

Every step now has formal content.

8.2 What Remains Open

  1. Planck-scale instantiation: The influx mechanism ($I_\infty \rightarrow A_\Omega$) is posited, not derived
  2. Singularity dynamics: De-actualization is proposed, not calculated from quantum gravity
  3. Quantitative circulation: The $F_{\text{in}}, F_{\text{out}}$ rates are not computed from first principles

These are the next frontiers.

8.3 Relation to Standard Approaches

ICH does not contradict unitarity—it extends it. Standard unitarity conserves information within $A_\Omega$. ICH conserves information across $I_\infty \cup A_\Omega$.

ICH does not contradict the island formula—it provides a mechanism. The island formula is a consistency condition. Boundary saturation under admissibility is why it holds.

ICH does not contradict $\Lambda$CDM observationally (yet). It predicts $w \approx -1$ with small deviations. Current observations are consistent with this.

8.4 Philosophical Implications

If ICH is correct:

  • Reality is a circulation, not a one-way process
  • Logic constrains physics at the deepest level
  • Information is conserved across instantiation/de-instantiation phases
  • The cosmological constant is not arbitrary but emerges from logical necessity

These are strong claims. They stand or fall with the physics.

9. Conclusion

This paper operationalizes the Information Circulation Hypothesis by deriving the admissibility predicate from L₃ constraints at horizons.

The key results:

  1. L₃ → Adm (§3): Logical constraints at horizons force record-existence in accessible algebras, generating the admissibility predicate.

  2. De-actualization (§4): At boundary saturation, information routes to radiation (islands) or singularity (return to $I_\infty$).

  3. Λ as fixed point (§5): Circulation dynamics drive toward an attractor with $w \approx -1$, explaining the cosmological constant as the cost of maintaining admissible reality.

  4. Closed chain (§6): The complete derivation $L_3 \rightarrow \mathsf{Adm} \rightarrow \Lambda$ is now formally established.

The framework is falsifiable via horizon physics (QES location, Page time shift) and cosmological observations ($w(z)$ evolution, black hole correlations).

Whether one accepts the metaphysical framework or treats ICH as phenomenological hypothesis, the physics generates testable predictions. The hypothesis stands ready for observational confrontation.

Acknowledgments

This research was conducted independently. AI tools (Claude/Anthropic, GPT/OpenAI) assisted with drafting under HCAE protocol. All claims remain the author’s responsibility.

References

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End of Paper

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