Cohesion Dynamics: Foundational Postulates and the Emergent Structure of Spacetime

Author: Darrell Tunnell
Draft v1.0 — Foundations Paper

Abstract

Cohesion Dynamics is a phenomenological framework in which spacetime geometry, gravitational behavior, and horizon formation emerge from the dynamics of cohesive information. In this approach, physical regions maintain internal consistency through finite informational update cycles characterized by three fields: the cohesion-time τ(x), governing local update latency; the spatial-coherence bandwidth σ(x), regulating the propagation of spatial consistency; and a vector mismatch tolerance W(x), encoding channel-specific limits on synchronizability. Neighboring regions exchange predicted and realized updates, and divergence occurs when mismatch exceeds local tolerance. Divergence surfaces act as horizon boundaries, replacing singularities with finite informational thresholds and initiating new causal axes. Variations in τ and σ determine effective metric components, with classical General Relativity recovered in the high-coherence limit where σ approaches its maximal uniform value and mismatch channels remain unsaturated. This Foundations paper introduces the postulates, ontology, and coherence structure underlying Cohesion Dynamics; detailed field equations, emergent metric construction, dark-matter phenomenology, and strong-field behavior are developed in companion work.

1. Introduction

Over the last century, physics has increasingly revealed a deep relationship between information and geometry:

quantum theory is fundamentally informational,
black-hole mechanics obey thermodynamic relations,
entanglement entropies appear to shape spacetime in holographic dualities,
Einstein’s equations can be recovered from thermodynamic arguments.

Yet in all mainstream approaches, spacetime itself is presupposed.

Cohesion Dynamics reverses this assumption.

Spacetime is the macroscopic geometry of informational cohesion.
Gravity, horizons, and cosmology reflect the energetic cost of staying coherent.

This paper introduces the effective informational framework required to make this idea precise.

A companion paper (in preparation) develops the field equations for $\tau(x)$ and $\sigma(x)$ , derives gravitational phenomenology, and applies CD to:

dark-matter halo structure,
strong-field collapse,
horizon dynamics, and
cosmogenesis (inflation-like behaviour).

The present document defines the foundational layer to which all later work will refer.

Disclaimer: Scope of This Foundations Paper

This paper introduces the conceptual and postulate-level structure of Cohesion Dynamics. It deliberately omits:

field equations for the cohesion-time and spatial-coherence fields,
dynamical laws governing mismatch evolution,
explicit curvature relations or metric derivations,
action principles or microphysical substrate models.

These are developed in dedicated technical papers. The goal of the present work is to define the theoretical objects, ontology, and coherence mechanisms upon which later mathematical formulations will be built.

2. Motivations

2.1 Time dilation as informational throughput

Relativistic time dilation has an “update slowdown” character: clocks in strong gravitational fields run more slowly. Cohesion Dynamics interprets this literally:

A region with limited capacity to update internal information exhibits a longer cohesion-time $\tau$ .

High “informational pressure” → slow updates → gravitational redshift.

This motivates a local informational timescale $\tau(x)$ .

2.2 Atomic transitions as informational transactions

Atoms never change state gradually; they transition discretely. A hydrogen atom is never “part helium.” The transition is an atomic informational transaction.

Distributed systems in computer science behave analogously:

state updates require communication,
communication has finite bandwidth,
consistency requires synchronisation,
synchronisation has cost.

This motivates:

cohesion cycles (epoch cycles),
commit operations,
dependency networks between cohesive regions.

2.3 The general hypothesis

Combining these insights:

Physical behaviour arises because cohesive informational systems must maintain local consistency under finite update capacity.

Geometry, curvature, horizons, and cosmology follow from this requirement.

3. Primitives of Cohesion Dynamics

3.1 Cohesion-Time Field $\tau(x)$

$\tau(x)$ is the time required for a region to internally reconcile all informational constraints and commit an updated state.

Small $\tau$ : strongly bound, fast-updating regions
Large $\tau$ : weakly bound or vacuum-like regions

Quantum systems suggest a phenomenological relation for bound states:

\tau \approx \frac{\hbar}{|E|},

consistent with the idea that $\tau$ reflects fundamental informational capacity.

3.2 Spatial-Coherence Bandwidth $\sigma(x)$

$\sigma(x)$ governs how effectively spatial coherence propagates between regions.

High $\sigma: coherence spreads easily → low curvature
Low $\sigma$ : coherence spreads poorly → curvature or dark-matter–like effects

$\sigma$ controls the effective spatial metric components in the emergent description.

3.3 Mismatch-Tolerance Vector ( \mathbf{W}(x) )

Every cohesive region must maintain several independent informational constraints in order to remain embedded within the surrounding manifold. For this reason, the tolerance structure is vector-valued:

[
\mathbf{W}(x) = \left( W_\tau(x),, W_\sigma(x),, W_\theta(x) \right).
]

Each component corresponds to an independent channel of coherence:

(W_\tau) — tolerance to temporal-update mismatch
(W_\sigma) — tolerance to spatial-coherence mismatch
(W_\theta) — tolerance to orientational or rotational mismatch (phase-like or spin-like)

Note on component notation: The component labels ( $W_\tau$ , $W_\sigma$ , $W_\theta$ ) used in this phenomenological presentation are illustrative. Formal substrate mechanics (Paper A) establishes $W$ as a structural primitive; subsequent operational decomposition (M4) and clarifications (M8, A-OPS, R-W) treat components as admissibility channels rather than ontological physical dimensions. The notation here reflects the phenomenological stage of theory development and should not be interpreted as claiming direct physical encodings.

These channels are irreducible at the phenomenological level; no component can replace another.
Each plays a distinct role in determining whether a region can remain coherently adjacent to its neighbours during a cohesion cycle.

Divergence occurs when mismatch exceeds tolerance in any one of these channels.

3.3.1 Why the Tolerance Vector Has Exactly Three Components

The three-component structure of ( \mathbf{W} ) is not an arbitrary modelling choice.
It is the minimal number of independent mismatch channels required for a coherent 3D spatial manifold to emerge.

Temporal Coherence (1 degree of freedom)
A region must maintain consistency in update rate and commit order. This constraint is scalar.
Spatial Coherence Bandwidth (1 degree of freedom)
Maintaining adjacency across space requires a single bandwidth-like parameter governing how spatial consistency propagates.
Orientational / Rotational Coherence (1 degree of freedom)
A compact, cyclic mismatch channel must regulate orientation, angular information flow, and spin-like invariants.

Together, these three channels form a complete basis for maintaining local coherence across a differentiable 3D spatial manifold.
Introducing a fourth component would imply either:

an additional independent internal symmetry, or
an extra spatial dimension,

neither of which is part of the effective spacetime ontology of Cohesion Dynamics.

Thus:

The dimensionality of ( \mathbf{W} ) is determined by the structure of emergent 3D space itself, not by microphysical assumptions.

3.4 Mismatch Functional $\lVert M \rVert$

Neighbouring regions compare predicted and actual updates of their internal descriptors. The resulting discrepancy is the mismatch:

\lVert M \rVert^2 = \sum_i \alpha_i \, (\Delta \phi_i)^2,

where $\phi_i$ represent the relevant coherence fields
(e.g. $\tau, \sigma, \theta,\ldots$ )
and $\alpha_i$ are channel weightings.

Divergence occurs when $\lVert M \rVert$ exceeds the local tolerance vector $\mathbf{W}$ in at least one channel.

3.5 Epoch Commit Cycles

Every cohesive region repeatedly executes a four-step cohesion cycle:

Provisional branch generation — candidate successors of the current state are explored.
Constraint propagation — local and neighbour constraints propagate across adjacency links.
Mismatch filtering — candidate updates are rejected if mismatch exceeds $\mathbf{W}$ .
Commit — a single updated state is selected and made globally coherent for that region.

The sequence of commits forms an epoch chain, representing the effective timeline of the region.

3.6 Causal Axes

A causal axis is a maximal set of regions whose epoch commits remain mutually coherent.

The “parent” universe follows one such axis.
Divergence events generate new causal axes.

Distinct causal axes correspond to manifolds that cannot exchange coherent information.

4. Cohesive Information as Computation

A cohesive region behaves as a self-maintaining computational process.
Cohesion cycles are consistency-enforcing update steps.

Key ideas:

Finite update capacity.
A region cannot import or process arbitrary information in a single cohesion cycle; this is quantified by $\tau(x)$ and $\sigma(x)$ .
Local reconciliation.
Coherence is maintained only via local comparisons of $\tau, \sigma$ , and other fields with those of neighbouring regions.
No intermediate observable state.
Between commits, a region has only a provisional internal configuration, not an observationally definite state — analogous to pre-commit states in atomic transactions.

This picture grounds the physical meaning of ” $\tau$ , $\sigma$ , $\mathbf{W}$ ”, and mismatch as genuinely dynamical informational quantities rather than mere reparametrisations of geometric objects.

5. Mismatch, Motion, and Coherent Adjacency

5.1 Motion as Mismatch Minimisation

Regions rearrange themselves in order to minimise mismatch while remaining within their tolerance vector $\mathbf{W}$ .

In the weak-field regime, the effective acceleration of a test body is dominated by gradients in $\tau$ :

\mathbf{a} \approx -\nabla \tau.

Lower $\tau$ acts like a gravitational potential: objects tend to move toward regions of higher update capacity, reproducing the Newtonian limit and the equivalence principle. Free fall therefore appears as informational mismatch minimisation.

5.2 Coherent vs. Mismatched Adjacency

It is essential to distinguish coherence from mismatch.

Ordinary physical interactions—such as atomic bonding, molecular structure, and rigid macroscopic bodies—correspond to successfully coherent adjacency:

\lVert M \rVert < \lVert \mathbf{W} \rVert.

Atoms in a stable molecule continuously exchange information, adjust their local $\tau$ - and $\sigma$ -dependencies, and maintain a shared update cycle. This is coherence, not mismatch. The interface between them is a coherence-maintaining boundary.

Mismatch arises only when reconciliation fails: when predicted updates differ by more than the tolerance $\mathbf{W}$ , signalling an impending breakdown of coherence rather than its presence.

Thus:

Coherent adjacency → stable matter, chemistry, atomic structure
Stress boundaries → rising ” $\tau$ / $\sigma$ ” gradients, still reconcilable
Divergence surfaces → true mismatch, formation of horizons, inflationary tearing, and causal-axis branching

Mismatch surfaces are therefore boundaries of coherence, not features of ordinary interaction. Stable matter lives entirely within coherent domains; divergence marks the point beyond which coherence can no longer be maintained.

6. Foundational Postulates of Cohesion Dynamics

The following postulates define Cohesion Dynamics at the effective level. They do not specify microphysics; instead they describe how the phenomenological fields $\tau(x)$ , $\sigma(x)$ , and $\mathbf{W}(x)$ must behave for coherent spacetime structure to arise.

Postulate 1 — Cohesion

Physical systems behave as cohesive informational regions that update via commit cycles requiring a finite cohesion time $\tau(x)$ .

Postulate 2 — Local Coherence

Coherence between regions is maintained only through local comparisons of $\tau(x)$ , $\sigma(x)$ , and related coherence fields with those of neighbouring regions. No globally synchronised coordination is assumed at the effective spacetime level.

Postulate 3 — Mismatch

Neighbouring regions compute a mismatch $\lVert M \rVert$ from deviations between their predicted and actual updates, using local coherence fields as inputs.

Postulate 4 — Tolerance

Each region possesses a vector $\mathbf{W}(x)$ specifying the maximum admissible mismatch per channel. As long as $\lVert M \rVert \leq \mathbf{W}$ , the region can remain coherently embedded in the parent manifold.

Postulate 5 — Divergence

If $\lVert M \rVert > \mathbf{W}$ for any channel, the region can no longer maintain coherence with its surroundings and diverges. Divergence:

creates a horizon boundary for external observers,
initiates a new causal axis internally,
yields a new manifold interior.

Postulate 6 — Emergent Metric

The effective spacetime metric arises from $\tau(x)$ and $\sigma(x)$ through relations of the form:

g_{00}(x) = -f(\tau(x)), \qquad g_{ij}(x) = h(\sigma(x)) \delta_{ij},

where $f$ and $h$ are monotonic functions fixed by the gravitational field equations. GR corresponds to the fixed point where $\sigma(x)$ is uniform and maximal and mismatch modes vanish.

Postulate 7 — Information Preservation

Divergence is information-preserving. The information encoded in a diverging region is not destroyed; it is carried forward along the new causal axis and becomes inaccessible across the divergence surface.

7. Emergent Metric Structure

The postulates imply that proper time and spatial intervals can be expressed in terms of $\tau(x)$ and $\sigma(x)$ . A simple representative ansatz for the emergent line element is:

ds^2 = - \left(\frac{\tau(x)}{\tau_\infty}\right)^2 c^2 dt^2 + \left(\frac{\sigma_\infty}{\sigma(x)}\right)^2 d\vec{x}^2,

where $\tau_\infty$ and $\sigma_\infty$ are asymptotic values in a reference region.

Variations in $\tau$ reproduce gravitational time dilation.
Variations in $\sigma$ reproduce spatial curvature and can mimic dark-matter effects.
When $\sigma(x) = \sigma_\infty$ and mismatch is negligible, the geometry reduces to a GR-like Riemannian spacetime.

This paper does not attempt to derive the precise functional forms $f$ and $h$ ; that is the role of the companion gravity paper.

8. Divergence, Horizons, and New Manifolds

When mismatch exceeds tolerance, the region must diverge:

From outside, the region appears to freeze near a horizon where $g_{00} \to 0$ ; external observers cannot maintain coherent exchange with the interior.
From inside, commit cycles continue along a new causal axis with fresh coherence conditions and potentially new effective parameters ” $\tau_{\text{int}}$ , $\sigma_{\text{int}}$ , $\mathbf{W}_{\text{int}}”.
Geometrically, the divergence surface replaces a would-be singularity with a finite boundary across which coherence fails but information is preserved.

Divergence thus provides a mechanism for:

black-hole horizon formation without singularities,
causal segregation of manifolds,
information-preserving cosmic branching.

9. Strong-Field Structure and Black Holes

In gravitational collapse:

$\tau$ increases as internal consistency becomes harder to maintain,
$\sigma$ decreases as spatial coherence becomes more restricted,
mismatch grows as regions struggle to reconcile their updates.

Classical GR predicts singularities in such regimes.
Cohesion Dynamics instead predicts that divergence occurs before singularity formation:

a horizon forms where $\lVert M \rVert$ reaches $\mathbf{W}$ ,
the interior detaches as a new manifold,
external observers never see beyond the horizon,
internal observers experience a regular, evolving geometry.

The companion gravity paper will develop explicit models of collapse and horizon structure within this framework.

10. Cosmogenesis via Divergence (Inflation as Coherence Rebound)

Divergence has natural cosmological consequences. When a region detaches from its parent causal axis:

Accelerated Commit Propagation
Free of external coherence constraints, the interior can update more rapidly. The effective cohesion-time $\tau_{\text{int}}$ may differ significantly from the parent region’s value.
Rebound of Spatial Coherence
Prior to divergence, $\sigma$ is typically suppressed by extreme mismatch and curvature. After divergence, $\sigma_{\text{int}}$ can increase rapidly as the interior relaxes toward a high-coherence configuration.
Fresh Causal Axis with Low Inherited Mismatch
The new manifold begins with minimal inherited mismatch and high coherence potential. This naturally yields an early epoch of accelerated, smoothing expansion.

These ingredients together provide:

an inflation-like period of rapid, homogeneous expansion arising from informational rebound, without invoking an inflaton field.

A full cosmological implementation—including spectra and parameter constraints—is left to future work.

11. Dark-Matter Phenomenology (Conceptual Overview)

Cohesion Dynamics offers a natural route to dark-matter–like behaviour:

Suppressed $\sigma$ in low-density or outer-galaxy regions reduces spatial coherence bandwidth, modifying effective curvature without additional particle species.
Threshold behaviour in spatial components of $\mathbf{W}$ can produce cored, non-cuspy halo profiles.
Mismatch-induced drift with $\mathbf{a} \propto -\nabla \tau$ naturally supports nearly flat rotation curves in specific regimes of the $\tau$ -field.

A companion paper develops:

explicit $\tau$ – $\sigma$ field equations,
rotation-curve fits,
lensing predictions,
cluster-scale tests.

This foundations paper claims priority only for the mechanism and architecture by which such phenomena arise, not for the completed phenomenology.

12. Relation to Existing Approaches

Cohesion Dynamics intersects conceptually with several established strands of work in which geometric or dynamical structure is understood as emerging from informational principles.

Thermodynamic and Entropic Gravity

Approaches such as Jacobson’s thermodynamic derivation of Einstein’s equations and entropic-gravity models treat spacetime dynamics as emerging from information flow, entropy gradients, or coarse-grained microphysical degrees of freedom. CD shares the emphasis on information-theoretic origins of gravitational behaviour, but differs in providing explicit phenomenological fields—τ, σ, and W—and a mismatch-driven mechanism that determines when coherence can or cannot be maintained.

Informational Reconstructions and Operational Foundations

Operational and informational reconstructions of quantum theory and gravity (e.g., Hardy, Chiribella–D’Ariano–Perinotti) emphasize constraints on transformations, causality, and information processing. CD is aligned with these frameworks in treating physical regions as informational agents with finite update capacity, but extends the idea to a spacetime setting in which the geometry itself arises from coherence structure rather than being assumed at the outset.

Tensor-Network and Entanglement-Based Spacetime Emergence

Holographic tensor-network models, entanglement-geometry relations, and quantum error– correcting–code interpretations of AdS/CFT all associate geometric connectivity with patterns of informational linkage. CD similarly ties geometry to coherence structure, but does not rely on quantum entanglement or holography; instead it uses phenomenological fields describing local update latency and spatial coherence bandwidth.

Constructor-Theoretic Approaches

Cohesion Dynamics also shares conceptual affinities with Deutsch and Marletto’s constructor theory, which reformulates physics in terms of tasks that are possible or impossible given informational and physical constraints. In CD, the tolerance vector W(x) and mismatch functional define precisely which transitions between local informational states can be coherently executed. Divergence surfaces correspond to tasks that become impossible to complete due to exceeded tolerances, while coherence cycles represent possible transformations that maintain consistency with neighbouring regions. Unlike constructor theory, CD provides an explicit phenomenological implementation—via τ, σ, and W—and yields an emergent metric and gravitational phenomenology.

Distinctive Contributions of Cohesion Dynamics

Across these related perspectives, Cohesion Dynamics contributes several novel elements:

a cohesion-time field τ(x) tied directly to local informational update capacity,
a spatial coherence bandwidth σ(x) determining geometric stiffness and dark–matter–like deviations,
a vector-valued tolerance structure W(x) encoding multiple independent channels of coherence,
a mismatch-driven divergence mechanism that replaces singularities with finite informational thresholds and generates new causal axes,
and a unified conceptual account of gravity, dark-matter phenomenology, and cosmogenesis as emergent features of informational cohesion.

13. Limitations and Future Work

This paper is intentionally conceptual and phenomenological. It does not provide:

a microphysical substrate model for cohesion,
rigorous derivations of $\tau$ or $\sigma$ from underlying dynamics,
complete field equations or action principles,
detailed cosmological solutions,
a full quantum-amplitude or Born-rule account.

These will be addressed in forthcoming work.

The present paper should be read as a foundational proposal defining the theoretical objects and postulates of Cohesion Dynamics, upon which more technical work will build.

14. Conclusion

Cohesion Dynamics proposes a shift in perspective:

Spacetime is the large-scale geometry of informational cohesion.

The primitive fields $\tau(x)$ , $\sigma(x)$ , the tolerance vector $\mathbf{W}(x)$ , and the mismatch mechanism together define a coherent, falsifiable framework in which:

GR emerges as a high-coherence, maximal- $\sigma$ fixed point,
dark-matter–like phenomena arise from nonlinearities in $\tau$ , $\sigma$ , and $\mathbf{W}$ ,
horizons appear as divergence surfaces where coherence fails,
singularities are avoided via information-preserving manifold branching,
inflation is understood as the rebound of coherence in a newly diverged manifold.

This Foundations paper establishes the conceptual and postulate-level architecture of Cohesion Dynamics. The accompanying gravity and phenomenology papers will develop the mathematical structure and confront the theory with observational data.

Acknowledgments

This work represents an initial articulation of a broader research programme. Several mathematical and empirical components are intentionally deferred to future papers; their absence here reflects the staged development of the theory rather than an assumption that they are trivial. Feedback on conceptual clarity and testable predictions is welcomed.