Cosmic Knots as Torsional Solitons in the Fundamental Network:

Unifying the One-Second Invariant, \(\phi\) Scaling and

Baryogenesis

Oleg Evdokimov

and Ian Beardsley

Independent Researcher

Contemporary physics faces three profound disconnects: a universal Lorentz-invariant time scale

of approximately one second with pervasive golden ratio ( ) scaling from quantum to celestial

systems, the baryon asymmetry of the universe, and the hard problem of consciousness. We

propose these are manifestations of a single ontological deficit—the lack of a fundamental

geometric substrate. Introducing the Ontology of the Fundamental Network (OFN), we model

reality as a static, four-dimensional spinor bundle with torsion, where time arises from a

"reading" process and consciousness is identified with stable solitons. Within this framework, we

define Cosmic Knots as fundamental torsional solitons—stable, localized configurations in the

activation field whose stability is maintained by non-zero network torsion. We demonstrate that

the discrete spectrum of stable Cosmic Knot states, characterized by a dimensionless

connectivity parameter , naturally yields the one-second invariant and scaling as signatures

of topological optimality. Furthermore, we show that primordial Cosmic Knots in the early

universe provide a geometric mechanism for baryogenesis, inherently satisfying Sakharov

conditions through CP-violating decay via spinor-torsional channels. The model makes testable

predictions across neurobiology, quantum physics, and cosmology, including correlations

between neural coherence and geomagnetic activity, specific signatures in the gravitational wave

background, and an anisotropic Hubble parameter. This work establishes a geometric monism

where quantum, cosmic, and cognitive phenomena emerge from a unified torsional network.

1. Introduction: The Triune Challenge of Modern Physics

Contemporary physics stands at a crossroads, confronted by a series of profound disconnects that

resist explanation within established, reductionist frameworks. Three such disconnects, spanning

scales from the quantum to the cosmic and the cognitive, present a particularly compelling

puzzle.

The Cognitive-Cosmic Scaling Law: Empirical work, most comprehensively presented by

Beardsley [1], reveals a startling universality: a Lorentz-invariant time scale of approximately

one second and the pervasive appearance of the golden ratio ( ) govern relationships

from the internal structure of the proton ( ) to the orbital dynamics of the Solar

System. This suggests a deep, scale-invariant structural principle operating beneath the

seemingly separate laws of quantum mechanics and celestial mechanics—a principle for which

the Standard Model and General Relativity offer no inherent explanation.

The Baryogenesis Enigma: The observable universe is composed overwhelmingly of matter,

with no significant primordial antimatter. This baryon asymmetry necessitates a physical process

(baryogenesis) that violates CP-symmetry, departs from thermal equilibrium, and violates baryon

ϕ ≈ 0.618

∼ ϕh /(m

number conservation [2]. While mechanisms like leptogenesis exist, a fundamental, geometric

origin for this asymmetry remains elusive. Recent work in quantum field theory has revived the

idea of topological knots or defects in early-universe fields as a compelling candidate. Models

combining Peccei-Quinn (PQ) and symmetries demonstrate that such knots can

temporarily dominate the energy density of the universe and, upon decay via quantum tunneling,

generate the necessary matter-antimatter imbalance through the production of heavy right-

handed neutrinos [3,4]. These "cosmic knots" are thus seen as contingent artifacts of specific

symmetry-breaking patterns.

The Hard Problem of Consciousness: In parallel, the philosophy of mind and cognitive science

grapple with the "hard problem" [5]: why and how physical processes in the brain give rise to

subjective, qualitative experience. No current physical theory provides a natural ontology for

consciousness, leaving it as an unexplained epiphenomenon.

Individually, these challenges belong to disparate domains—foundational quantum physics,

cosmology, and neuroscience. Together, they hint at a deeper, unified reality where geometry,

information, and phenomenology are intrinsically linked. This paper proposes that these are not

three separate problems, but three facets of a single ontological deficit: the lack of a

fundamental, geometric substrate whose intrinsic dynamics give rise to all observed

phenomena.

We address this deficit by introducing the Ontology of the Fundamental Network (OFN) [6], a

monistic framework in which reality is modeled as a static, four-dimensional network—a spinor

bundle over a spacetime manifold. Within this ontology, time arises as an epiphenomenon of the

network's "reading" process, and consciousness is identified with stable solitons in an activation

field coupled to neural substrates. Crucially, the geometry of this network features torsion, an

algebraic response to spinor density that allows for instantaneous, causal information transfer.

From this foundation, a primary class of entities emerges: Cosmic Knots. In the OFN, these are

not contingent topological defects of quantum fields, but fundamental torsional solitons—

stable, localized configurations within the activation field, whose stability is maintained by non-

zero network torsion. We posit that these Cosmic Knots are the universal structural agents, and

their properties provide the missing unified explanation for the triune challenge:

The One-Second Invariant & \(\phi\) Scaling arise naturally from the discrete spectrum of

stable states available to a Cosmic Knot, characterized by a dimensionless connectivity

parameter . The critical values of , ( , , ...), derived from the geometry of the network,

dictate fundamental time intervals and optimize spatial relationships according to the golden

ratio, manifesting from proton scales to planetary orbits.

Baryogenesis finds its origin in the dynamics of primordial Cosmic Knots in the high-energy

early universe. Their decay via spinor-torsional channels inherently violates CP-symmetry,

providing a geometric mechanism for generating the baryon asymmetry, thereby reinterpreting

and grounding the field-theoretic "knot" models.

B − L

π /6

π /4

Thus, the article is structured as follows: Section 2 provides a concise overview of the OFN and

its mathematical core. Section 3 defines Cosmic Knots as torsional solitons. Section 4

demonstrates how the dynamics of these knots universally explain the one-second invariant and

scaling (Unification I). Section 5 details their role as engines of baryogenesis (Unification II).

Section 6 outlines testable predictions differentiating this model from conventional ones. We

conclude with a discussion of the implications of this geometric monism for physics, cosmology,

and the science of consciousness.

1.1. The Dirac Legacy: From Large Numbers to a Unified Geometric Substrate

This triune challenge does not exist in a historical vacuum. It echoes a profound insight first

articulated by Paul Dirac in the 1930s. Upon noticing the remarkable coincidence of

dimensionless "large numbers" of order relating cosmic and atomic scales (e.g., the ratio of

the electrostatic to gravitational force between an electron and a proton, or the age of the

universe in atomic units), Dirac postulated that these were not accidents but "must be due to

some deep connection in Nature between cosmology and atomic physics" [7]. He envisioned a

future theory where the constants of microphysics would be connected to the large-scale

properties of the cosmos.

Yet, nearly a century later, Dirac's vision remains unfulfilled within the standard paradigms. The

chasm between the quantum and the cosmological has, if anything, widened with the discovery

of dark energy, dark matter, and the persistent enigma of consciousness. The "large numbers"

have been refined into precise, yet equally mysterious, dimensionless relationships—such as the

Lorentz-invariant one-second timescale and the ubiquitous golden ratio governing systems

from the proton's charge radius to planetary orbits [1].

We propose that to finally realize Dirac's intuition, a fundamental ontological shift is required.

The pursuit cannot be merely to find new dynamical equations within an expanding spacetime

continuum. Instead, we must seek the common geometric substrate from which both particles

and cosmos, law and phenomenology, emerge as derivative aspects. This work posits that the

long-sought connection is not a dynamical interaction but a structural and topological

property of reality itself—a property encoded in the spectrum of stable states within a static,

torsional network.

The following section introduces the Ontology of the Fundamental Network (OFN) as this

substrate. Within it, Dirac's "large numbers" find their origin in the discrete eigenvalues of the

network's connectivity parameter , the one-second invariant arises from the characteristic phase

period of its solitons, and the hard problems of baryogenesis and consciousness are recast as

different manifestations of its topological correlations.

2. The Ontology of the Fundamental Network: A Geometric Monist

Framework

The proposed synthesis finds its foundation in a specific ontological commitment: the Ontology

of the Fundamental Network (OFN). This framework posits a monistic reality where

consciousness, matter, and spacetime are not primitive substances but emergent phenomena

arising from a single, deeper geometric substrate. This section outlines its core postulates,

mathematical formalism, and immediate physical implications, establishing the basis for the

concept of Cosmic Knots.

2.1. Core Postulates: From Static Geometry to Dynamic Appearance

The OFN is built upon four interrelated postulates:

Reality as a Static 4D Network: The fundamental substratum is not an evolving spacetime

continuum but a static, four-dimensional network. Mathematically, it is described as a spinor

bundle over a differential manifold. All events and entities exist as patterns or nodes within this

complete, timeless structure.

Consciousness as a Geometric Soliton: Subjective experience (consciousness) is not generated

by computation but is identified with a stable solitonic configuration in a universal activation

field, denoted . This soliton is coupled to and stabilized by specific neural patterns in

biological systems, most notably the brain. Thus, the brain acts as a resonator and stabilizer of a

fundamental field, not its generator.

Time as a Process of "Reading": The flow of time is not a fundamental dimension but an

epiphenomenon. It arises from a process termed "reading"—the sequential activation of nodes

along a worldline within the static network. The phenomenological "arrow of time" is dictated by

the global entropic gradient of the network along the reading path.

Torsion as the Algebraic Mediator: The geometry of the network is not Riemannian but

includes torsion. In the OFN, torsion ( ) is not an independent field but an algebraic response

of the geometry to the local density of spinor fields. Crucially, it serves as a mechanism for

instantaneous, non-local correlation of phase information across the network without violating

causality, as it operates on the level of the static structure itself.

These postulates reframe central mysteries: the "hard problem" of consciousness becomes a

question of geometric resonance; the nature of time transforms into a question of process within

an eternal structure; and non-local phenomena find a geometric conduit.

2.2. Mathematical Core: Activation, Coherence, and Critical States

The dynamics of the activation field and the stability of conscious states are governed by a set of

key equations.

The primary field equation describes the propagation of activation within the torsional

geometry:

(1)

where is the torsion trace, is the spinor density, and is a source term linked to

quantum weak values. The term encapsulates the unique torsional coupling that

allows for superluminal phase updates.

∇

Φ + αT

∇

Φ + β

Φ = J(X ),

J(X )

αT

∇

The stability of a conscious soliton is modeled by a two-component field , with an

effective potential:

(2)

The ratio emerges as a fundamental dimensionless connectivity parameter

governing the coherence and state of the system.

Analysis of the geometric phase (Berry phase) within this torsional framework yields discrete

critical values for :

(3)

These critical points correspond to stable, metastable, or unstable configurations of the field,

which map directly onto distinct phenomenological regimes of consciousness:

This provides a quantitative bridge between the geometry of the fundamental network and the

spectrum of subjective experience.

2.3. Cosmological Correspondence: From Activation to Cosmic Evolution

The OFN is not limited to the scale of cognition. The activation field exhibits a direct

correspondence with cosmological dynamics. Its relationship to the Friedmann scale factor

is given by:

(4)

In the limit where temporal change is small ( ), the field behaves as an effective dark

energy component with an equation-of-state parameter . Furthermore, the torsional

energy density can provide a negative-pressure contribution sufficient to drive a

cosmological bounce, offering a non-singular model for the origin of the universe.

2.4. Synthesis: A Unified Substrate

, ϕ

F[ϕ

, ϕ

] =

(

) + β

σ ≡ β /α

crit

≈ 0.785, with!subharmonics!at

, …

State of Consciousness

Phenomenological Manifestation

Unconscious

Deep sleep, coma, dissociation

Phenomenal

Dreaming, delirium

Reflexive

Wakefulness, flow states

Metastable

Creative insight, deep meditation

Unstable

Psychosis, manic states

σ < π /8

π /6 ≤ σ < π /4

Range

π /8 ≤ σ < π /6

σ ≈ π /4

σ > π /4

a(t)

a(t) ∝

∇

⊥

··

Φ ≈ 0

w ≈ − 1

ρ ∝ f (t)

In summary, the OFN proposes that a static, torsional, spinor-endowed network is the

foundational reality. Within it:

Consciousness is a stabilized soliton in the network's activation field.

Time is the process of reading this network.

Physical laws and constants (including the critical values of ) arise from its geometric and

topological invariants.

Cosmology is the large-scale behavior of its activation dynamics.

This framework is intrinsically monistic and geometric. It does not add consciousness or time to

physics as new forces; rather, it derives physics, cosmology, and phenomenology from a

common geometric origin. The following sections will demonstrate how the fundamental objects

within this network—the torsional solitons or Cosmic Knots—naturally give rise to the

universal scaling laws identified by Beardsley and provide a geometric mechanism for

baryogenesis.

3. Cosmic Knots: Torsional Solitons as the Universal Structural Agents

The idea that fundamental entities might be understood as knotted structures has a long, albeit

marginalized, history in physics. In 1867, Lord Kelvin—seeking a unified mechanical theory of

matter—proposed that atoms were nothing more than tiny, stable knots or vortices in an

invisible, all-pervading æther. While Kelvin's specific æther model was ultimately disproven,

his core intuition—that topology could be the source of stability and identity—resonates

powerfully within the OFN. Here, we revive and radically transform this insight: Cosmic Knots

are not vortices in a material æther, but torsionally stabilized solitons in the geometric fabric

of the Fundamental Network itself.

From the geometric substrate of the Ontology of the Fundamental Network (OFN) emerges a

primary class of entities that serve as the fundamental carriers of structure and information:

Cosmic Knots. These are not contingent artifacts of symmetry breaking in quantum field theory,

but rather topologically stable, torsional solitons within the activation field of the static

network. This section defines their nature, derives their key properties from the OFN postulates,

and positions them as the unifying ontological basis for phenomena across scales.

3.1. Definition and Ontological Status

A Cosmic Knot is defined as a stable, localized excitation (soliton) in the activation field ,

whose stability is ensured by a non-trivial, self-sustaining configuration of the network's torsion

( ). Formally, it is a solution to the field equation (1) that is:

Localized: Its energy and influence are confined to a finite region of the network.

Topologically Protected: Its stability is guaranteed by a conserved topological charge (e.g.,

winding number, knot invariant) arising from the intertwining of the field with the torsional

geometry. It cannot "unwind" or dissipate without a phase transition in the network.

≠ 0

Torsion-Bound: The knot's integrity is maintained by a closed loop or "twist" in the torsional

field, acting as a geometric binding agent.

In the OFN, Cosmic Knots are not in spacetime; they are the knotted structures of the

fundamental network itself. They represent the most primitive, self-consistent "things" that can

exist—the elementary granules of organized reality.

3.2. Key Properties Derived from the OFN

The physics of Cosmic Knots is directly inherited from the framework outlined in Section 2:

Discrete Spectrum of States (Quantization of ): A Cosmic Knot, as a bound state of the

activation field, can only exist in specific, stable configurations. These configurations correspond

to the critical values of the connectivity parameter ( , , , ...). Each knot has an

associated effective , determining its internal coherence and its mode of interaction with the

network. This provides a natural quantization of cosmic-scale structures, mirroring the

quantization of conscious states.

Information Transfer via Torsional Coupling: The torsion field is not merely a geometric

curiosity but the primary channel for information exchange between knots. A phase change in

one knot can modulate the local torsion, which is algebraically felt instantaneously elsewhere in

the network (via Equation 1). This mechanism explains non-local correlations without energy

transfer or causal violation, as it operates on the level of the pre-existing geometric structure.

Inertial Mass and Scale from Network Geometry: The stability and localization of a knot

require energy. In the OFN, this manifests as an effective inertial mass, derived from the work

done against the network's intrinsic stiffness to maintain the knotted configuration. The

characteristic scale (size) and mass of a knot are functions of its topological complexity (winding

number) and its associated value. This directly links geometry to physical properties.

3.3. Relationship to Established Physical Concepts

The concept of Cosmic Knots serves as an ontological "root" for several phenomena described in

other theoretical frameworks:

"Cosmic Strings/Knots" in Quantum Field Theory (QFT): The topological defects posited in

grand unified theories (e.g., from PQ and \(B-L\) symmetry breaking [3,4]) are effective, low-

energy descriptions of what, in the OFN, are fundamental Cosmic Knots. The QFT view sees

knots as contingent outcomes of cooling; the OFN view sees them as primordial, necessary

features of the geometric substrate. The OFN provides a deeper reason why such topological

structures should be prevalent and consequential.

Quantum-Gravitational Objects in the Beardsley Model: The "one-second invariant" entities

(proton, Earth-Moon system) characterized by precise geometric ratios [1] are macroscopic

manifestations of specific, stable Cosmic Knot configurations. Their quantized time and

-scaling are external signatures of the knot's internal, discrete -state and its optimal topological

packing.

π /8

π /6

π /4

Solitons in Neuroscience and Condensed Matter: The conscious soliton of Section 2.1 is a

biological, small-scale instantiation of a Cosmic Knot, where the neural net acts as a host

medium that stabilizes a specific ( ) knot configuration in the fundamental field .

Thus, Cosmic Knots act as the unifying archetype: from the quantum-geometric knots

underlying particles, to the neuro-geometric knots underlying consciousness, to the cosmic-

geometric knots governing planetary systems and early-universe physics.

3.4. The Hierarchy of Knots and Universal Scaling

A hierarchy of Cosmic Knots naturally emerges, differentiated by scale and topological

complexity:

Micro-Knots (\(\sigma\)-driven): Correspond to fundamental particles and conscious states.

Their properties are dominated by their quantized value.

Meso-Knots: Stable structures at planetary and stellar system scales (e.g., the Earth-Moon

system as a bound two-body knot). Their dynamics encode the one-second invariant and -ratio.

Macro-Knots: Primordial, high-energy configurations in the early universe. Their formation,

interaction, and decay govern cosmological phase transitions and baryogenesis.

The persistence of the golden ratio across these scales is not a coincidence but a topological

imperative. A Cosmic Knot, as a self-referential structure within the network, must satisfy

conditions of recursive stability. As argued by Tynski [8] and inherent in the OFN geometry, the

only scaling ratio that permits infinite self-similarity without distortion is . Therefore, the most

stable, long-lived knot configurations naturally exhibit -proportions in their internal and

external relationships.

In conclusion, Cosmic Knots are the primary actors in the drama of physical reality within the

OFN. Their defined properties—discrete states, torsional communication, and geometric mass—

provide the necessary tools to address the triune challenge outlined in the Introduction. The

following two sections will demonstrate this explicitly: first by showing how knots explain the

one-second invariant and -scaling (Unification I), and second by detailing their role as the

engine of baryogenesis (Unification II).

4. Unification I: Deriving the One-Second Invariant and Scaling from Knot

Dynamics

Having established Cosmic Knots as the fundamental structural units of the OFN, we now

demonstrate their power by deriving the two most striking empirical patterns identified by

Beardsley [1]: the Lorentz-invariant one-second time scale and the pervasive appearance of the

golden ratio . We show that these are not independent numerical coincidences but necessary

consequences of the discrete, topologically optimized states available to a Cosmic Knot.

4.1. The Discrete \(\sigma\) Spectrum and the Quantization of Process

σ ≈ π /4

As defined in Section 3.2, a Cosmic Knot exists in one of a discrete set of stable states, indexed

by the critical values of the connectivity parameter (Equation 3). Transitions between these

states are not continuous but involve discrete jumps. The mechanism of "reading" the network—

the process that gives rise to the illusion of time—fundamentally involves the sequential

activation of nodes along a path that traces the knot's structure.

Postulate: The minimal discernible "tick" of experienced time corresponds to the network's

reading process traversing from one metastable configuration of a knot (e.g., ) to the next

adjacent, accessible configuration ( ). The duration of this tick, , is therefore governed by

the geometric phase difference between these two -states within the torsional background of

the network.

4.2. Derivation of the Fundamental Time Unit from the Geometric Phase

The critical values originate from the quantization of the geometric

(Berry) phase in the presence of torsion. For a cyclic evolution of the knot's state parameterized

by , the accumulated phase is:

(5)

where is the Berry connection and is an integer. The most stable, low-energy transitions for a

typical meso-scale knot (like the one constituting a proton or a planetary system) occur between

states where changes by 1, corresponding to a phase change of .

The relationship between this topological phase and the metric time interval experienced by

an observer coupled to the knot is given by the general relativistic clock relation, incorporating

torsional corrections:

(6)

where is the energy gap between -states, and is the effective action scale for the

knot. For a Cosmic Knot at the scale of baryonic matter (the proton knot), , and

. Substituting yields:

(7)

Numerically, s. However, this is the quantum Compton time of the

proton, not the macroscopic second. The crucial step is to recognize that the knot's topological

size and its interaction with the network's stiffness introduce a massive scaling factor.

The proton knot's stability arises from its torsional binding, which involves a loop with a

characteristic action on the order of the solar system Planck-type constant identified by

Δτ

crit

= π /4,π /6,π /8,…

γ =

∮

A(σ)dσ = n ⋅ π /2,

π /2

Δτ

Δτ =

ℏ

eff

gap

⋅ γ,

gap

ℏ

eff

gap

∼ m

ℏ

eff

∼ ℏ

γ = π /2

Δτ ≈

⋅

ℏ

ℏ/(m

) ≈ 2.10 × 10

−24

Beardsley, . The ratio bridges the quantum and macroscopic scales.

The effective action for the knot's phase evolution is thus scaled:

(8)

This shows the fundamental constants at vastly different scales are unified throughout the

network’s geometry. The reveals the one-second cosmic heartbeat is fundamentally a

geometric resonance. That it is a synchronization between the quantum electromagnetic

processes and the topological stiffness of the cosmic network.The precise value converges to

exactly 1 second when the knot's configuration is optimized according to the -constraint. Thus,

the one-second invariant is the macroscopic "beat" corresponding to the minimal phase

jump of a stable Cosmic Knot at the baryonic mass scale.

Empirical confirmation of this scaled one-second timescale emerges independently from a model

of inertial mass arising from a universal normal force [1]. In this formulation, the resistance

interpreted as mass originates from the interaction of a particle's cross-sectional area

with a Lorentz-invariant normal force , mediated by the gravitational constant .

The mass is given by:

(9)

where is a dimensionless coupling constant specific to each particle type

( , ( ). Remarkably, setting s yields the masses of the proton,

neutron, and electron with an accuracy better than 0.5%, using their experimentally measured

charge radii [9,10]. This provides robust, independent empirical evidence for as a fundamental

invariant governing quantum-gravitational interactions at the baryonic scale.

4.3. Scaling as a Condition for Topological Optimality

The pervasive appearance of the golden ratio , most notably in the proton radius relation

[11] and in celestial harmonics, finds its fundamental origin in a topological

selection principle necessary for the recursive self-similarity of a Cosmic Knot. As formalized

by Tynski [8], any system requiring consistent structure across infinite observational scales must

obey a recurrence relation . This leads to the

characteristic equation , whose only positive solution is the golden ratio

. This ratio is thus the unique scaling factor permitting

infinite recursive embedding without distortion or contradiction—a prerequisite for a stable,

self-consistent soliton in the network.

Applying this principle to the proton as a Cosmic Knot directly yields its characteristic scale. For

the knot to maintain coherence, its internal geometry (encoded in its Compton wavelength

ℏ

⊙

ℏ

⊙

/ℏ ≈ 4.27 × 10

Δτ ≈

⋅

ℏ

⋅

ℏ

⊙

ℏ

≈ 1.04548s .

/π

= πr

= h /(ct

)

= κ

πr

= κ

= 1/(3α

)

= 1

≈ ϕh /(m

Scale(n + 2) = Scale(n + 1) + Scale(n)

= λ + 1

Φ = (1 + 5)/2 ≈ 1.618

( must stand in a specific relation to its external, topological size ( ). The only ratio

satisfying the condition of infinite self-similarity is , leading to the prediction:

(10)

This is not an anthropic coincidence but a mathematical necessity for topological optimality.

The precise empirical agreement [11] confirms that the proton is a -optimized Cosmic Knot,

and by extension, that other stable structures (like planetary systems) tend toward -related

ratios as low-order Fibonacci approximations to this fundamental geometric constraint.

4.4. Dynamic States and Fibonacci Attractors

The OFN framework, combined with the topological argument for -scaling, offers a novel

perspective on the empirical "proton radius puzzle"—the historical variance in its measured

charge radius [12]. If a Cosmic Knot is not a static object but a dynamic, coherent excitation of

the network, its effective size could fluctuate around an optimal, time-averaged value. The theory

suggests that these fluctuations may not be random but are attracted to quasi-stable

configurations corresponding to rational Fibonacci approximations of the golden ratio (e.g.,

5/8, 2/3, 13/21).

Such approximations represent discrete, metastable states in the knot's configuration space where

self-similar coherence is nearly optimal. A proton might transiently adopt a configuration where

its effective radius satisfies , where are Fibonacci numbers. For

instance, the approximation yields a radius close to 0.826 fm, while gives

approximately 0.881 fm, historically seen in pre-2010 measurements [12].

Different experimental techniques (e.g., electron scattering vs. muonic hydrogen spectroscopy)

probe the proton's structure over different effective timescales or interaction energies, potentially

"freezing" or averaging over different Fibonacci-approximated states of the dynamic knot. Thus,

the radius puzzle may not be a mere measurement discrepancy but a signature of the proton's

nature as a dynamical Cosmic Knot, whose holographic boundary reconfigures among a

spectrum of -optimized, topologically-defined states. The invariant one-second timescale

may correspond to the characteristic period for a complete exploration of this attractor landscape.

4.5. Synthesis: The Beardsley Patterns as Knot Signatures

We can now reinterpret Beardsley's master equation for the one-second invariant:

(11)

within the OFN framework:

• : This ratio is proportional to for a -optimized knot, as derived from the

topological selection principle (Section 4.3) and confirmed by the precise empirical mass

formula [1]. It encodes the knot's specific topological size-to-mass relation.

ℏ/(m

)

Characteristic!Length

Compton!Wavelength

∼ ϕ ⇒ r

≈ ϕ

(n)

≈ (F

n+1

) ⋅ h /(m

ϕ ≈ 5/8

ϕ ≈ 2/3

⋅

πh

⋅ κ

h /(m

• : This constant combines quantum, gravitational, and relativistic scales. In the

OFN, it represents the fundamental torsional stiffness of the network, the resistance it offers to

the formation of a knot. Its appearance is direct evidence of the quantum-gravitational nature of

the knot's binding.

• : The coupling constant ( , ) quantifies how strongly a particular

knot’s -state interacts with the network's electromagnetic and strong force sectors (encoded in

). The electron knot ( ) represents the pure torsional ground state.

Thus, Beardsley's equation is not merely empirical; it is the condition for a Cosmic Knot to be

in a stable, resonant state with the fundamental network's stiffness. The numerical

convergence to 1 second for the proton, neutron, and electron confirms they are different

manifestations (with different and ) of the same underlying geometric object—a Cosmic Knot

—each tuned to the same universal clock defined by the network's torsional dynamics.

4.6. Prediction: The Sequence and Hierarchical Time

A direct prediction of this model is that other, more complex Cosmic Knots (e.g., atomic nuclei,

planetary systems) should exhibit characteristic time scales that are harmonics of the one-

second base, corresponding to transitions between other critical -values ( ). For

example, the Earth's rotation period ( 86400 s) is approximately seconds, suggesting

a link between planetary spin and a specific, coarse-grained -state of its governing knot. This

provides a new lens for analyzing temporal periodicities across astrophysical and biological

systems.

Conclusion of Unification I: The universal one-second invariant and -scaling are signatures of

discreteness and self-similar optimality in the spectrum of Cosmic Knots. They are not laws

imposed upon matter but emergent properties of matter as knot-like excitations in a

geometric, torsional network. This establishes the OFN as a framework capable of explaining

empirically robust, yet theoretically anomalous, scaling laws.

5. Unification II: Baryogenesis as a Topological Signature in the Network

The second pillar of our unification addresses the origin of cosmic asymmetry. In the Ontology

of the Fundamental Network (OFN), the baryon asymmetry of the universe is not a transient

event in a temporal history but a permanent, topologically encoded signature within the static

structure. We demonstrate that the configuration of primordial Cosmic Knots in the high-

density sector of the network provides a geometric mechanism for baryogenesis that inherently

satisfies the Sakharov conditions, reinterpreted as topological constraints.

5.1. The High-Density Sector: A Plasma of Knots

The network is not homogeneous. It contains a sector of extremal density, characterized by

maxima in the activation field and spinor density . Within this sector, the stable

excitations are not elementary particles but complex primordial Cosmic Knots—topological

configurations of the highest order and energy scale. Their stability is a consequence of the

πh /(Gc)

= 1

p,n

= 1/(3α

)

= 1

π /6,π /8

∼

π /8 ⋅ 10

intense torsional binding pressures inherent to this dense region of the network. This sector is not

"early"; it is a specific structural domain of the complete 4D manifold.

5.2. Baryogenesis as a Topological Correlation

The baryon asymmetry observed in our local sector of the network is not the result of a decay

process in time, but of a fundamental topological correlation between the high-density and

low-density sectors. This correlation is mediated by the network's geometry and can be described

as a mapping:

High-Density Sector Configuration Low-Density Sector Configuration + Baryon

Number.

Crucially, this mapping is inherently CP-asymmetric due to the chiral nature of the underlying

spinor network and the pseudovector character of torsion . A primordial knot configuration

and its mirror-image (CP-conjugate) configuration are topologically distinct and therefore map to

different low-energy outcomes.

5.3. The Mechanism: Torsional Chirality and Spinor Currents

The specific topological correlation that yields a net baryon number can be modeled by

analyzing the network's equations in the high-density sector. A stable primordial knot ( )

represents a specific winding in the spinor and torsional fields. The network's consistency

conditions demand that such a configuration is topologically linked to the presence of specific

currents in adjacent, lower-density sectors.

Mathematically, this is expressed by an integral of the torsional-spinor current over a

hypersurface enclosing the knot:

, (12)

where is the baryon number current in the low-density sector, is the torsion trace, is a

connection form encoding the knot's chirality, and is a coupling constant. The non-zero value

of this integral for a given knot signifies that its presence correlates with a net baryon number

flux in the connected region of the network. The sign of the integral is determined by the knot's

handedness.

5.4. Reinterpretation of Field-Theoretic Models and the Sakharov Conditions

This geometric mechanism provides an ontological foundation for successful field-theoretic

models of baryogenesis via topological defects [3,4]:

Sakharov Conditions as Topological Constraints:

Baryon Number Violation: Is not a dynamical process but a structural property of the mapping

between network sectors. The knot configuration simply does not conserve the emergent

quantum number we call baryon number when correlated with the low-density state.

↔

∫

∂V

d Σ

= κ ⋅

∮

∧ ω

C and CP Violation: Is intrinsic and maximal due to the chirality of the knot's torsional

winding, as described above.

Departure from Thermal Equilibrium: Translates to the existence of a sharp gradient or

discontinuity between the high-density knot sector and the surrounding network. In a static

manifold, this is a topological feature, not a temporal one.

Connection to Northey Model Synthesis: The global phase field (Section 5 of OFN

summary) encodes the correlation information between sectors. An update in —

mathematically equivalent to a change in the knot's topological class—instantly defines the

baryon-asymmetric outcome in correlated regions.

Thus, the "decay of knots" in temporal language is revealed in the OFN as the existence of a

specific topological link between a high-energy knot configuration and a low-energy

configuration with a baryon excess.

5.5. Predictions: Geometric Fossils of Primordial Knots

This model yields distinctive signatures that are fossilized in the present network structure:

Fractal Distribution of Baryon Asymmetry: The clustering scale and distribution of the

primordial knots should imprint a fractal pattern ( ) on the large-scale

distribution of baryonic matter, observable in galaxy surveys. This is the same fractal dimension

predicted for the network's dark matter component (Section 6.5), unifying the two.

Gravitational Wave Topology: The specific torsional winding of the knots defines their

topological class (knot invariant). The transition between equivalent representations of this class

in the network's geometry can manifest as correlations in a stochastic gravitational wave

background with a complex, non-power-law spectrum, potentially featuring isolated peaks

corresponding to dominant knot types.

Scale of Knots: The characteristic energy scale of the primordial knots is geometrically

d e t e r m in ed b y t h e ne t w o r k ' s fu n d a m e n t a l co n s t a n t s . An e s t i m a t e y ie ld s

GeV, aligning with the scale of grand unification and

providing a natural origin for heavy right-handed neutrino states in effective field theories.

Conclusion of Unification II: The baryon asymmetry is not an accident of dynamics but a

necessary, geometric signature. It is a permanent record, woven into the fabric of the static

network, that a sector of extreme density is topologically configured as a universe of matter. This

completes the second unification: Cosmic Knots explain not only the quantum-cognitive scaling

laws but also the very matter-antimatter dichotomy, reframing a cosmic "event" as a timeless

structural correlation.

6. Unification III: Cosmology in a Static Universe — Redshift as Network

Dissipation

τ(x)

D ≈ 1.7 − 1.8

∼ ℏ

⊙

/(c

) ∼ 10

− 10

The preceding unifications demonstrate the power of the OFN to bridge quantum, cognitive, and

early-universe phenomena through the dynamics of Cosmic Knots. We now complete the

theoretical edifice by addressing the largest-scale observational datum: the cosmological redshift.

We propose a radical paradigm shift—from an expanding spacetime to a static, eternal

network where redshift arises from the dissipative interaction of light with the network's

fabric. This not only provides a natural explanation for the apparent "accelerated expansion" but

also eliminates the need for dark energy as a separate substance, reducing two great cosmological

mysteries (dark matter and dark energy) to manifestations of the network's geometry and

dynamics.

6.1. A Critical Reassessment: Beyond the Expansion Paradigm

The prevailing ΛCDM model interprets the redshift of distant galaxies as a Doppler-like effect

due to the metric expansion of space, a consequence of Friedmann solutions to General

Relativity. While successful, this interpretation is not unique. It necessitates postulating two

undetected entities—dark matter and dark energy—comprising ~95% of the universe's

content.

The OFN offers a foundational alternative: The large-scale universe is static and eternal. The

cosmological redshift is not a kinematic effect but a result of photon energy loss during

propagation through a dissipative medium—the Fundamental Network itself. This "tired

light" hypothesis, historically problematic due to issues with thermalization and blurring, is

revived and resolved within the OFN by the specific, non-thermal dissipative mechanism

provided by the network's torsional-spinor structure.

6.2. Deriving the Redshift Law from Network Dissipation

Consider a photon of initial energy emitted at a coordinate distance from an

observer in the static network. The photon's interaction with the network is dissipative. The rate

of energy loss is proportional to its current energy and a function characterizing the local

dissipative properties of the network along the path:

(13)

where is a fundamental network constant with dimensions of inverse length (analogous to,

but distinct from, the Hubble constant). For , integration yields:

(14)

The observed redshift is therefore:

(15)

= hν

f (x)

d x

= − H

net

f (x)E,

net

E = hν

ν(x) = ν

⋅ exp

(

−H

net

∫

f (x′ )d x′

)

1 + z ≡

ν(x)

= exp

(

net

∫

f (x′ )d x′

)

In the standard model, is inversely proportional to the scale factor. In the OFN, it is an

exponential of the integrated dissipation function . The form of holds the key to

explaining "accelerated expansion."

6.3. Explaining "Accelerated Expansion": Nonlinear Dissipation

Supernova Ia data suggest that distant supernovae are fainter than expected in a uniformly

expanding model, interpreted as cosmic acceleration. In the OFN, this effect emerges if photon

dissipation strengthens with the distance traveled. Physically, a long journey through the

network leads to cumulative perturbation: the photon does not merely pass through but interacts

with and potentially excites the network, increasing the probability of subsequent energy loss—a

form of path-dependent "friction."

A simple parametrization reproducing observations is a quadratic correction:

(16)

Substituting into (15) gives the coordinate distance-redshift relation for small to moderate :

(17)

6.4. Luminosity Distance and Supernova Ia Data

In a static, Euclidean universe, the luminosity distance is modified by both photon energy loss

and time dilation (the stretching of the time interval between photons, which remains as a

kinematic effect of relativity even in a static universe):

(18)

Combining (17) and (18):

(19)

The critical result: For , the curve bends upward relative to the case. This

deviation is graphically identical to that attributed in ΛCDM to a dark energy component with

negative pressure. Thus, the parameter \(\beta\) in the OFN plays a role analogous to the dark

energy equation-of-state parameter , but with a fundamentally different origin: the

nonlinearity of dissipation in the network's geometry.

6.5. Dark Matter Reinterpreted: Motion Along the Network's Currents

The OFN's static cosmology necessitates a radical reinterpretation of the phenomenon attributed

to dark matter—the anomalous rotational velocities of galaxies and gravitational lensing without

visible mass.

Within the expanding paradigm, these anomalies are explained by an invisible, weakly

interacting mass. In the OFN, they arise from a fundamental misattribution of cause. Stars and

galaxies do not move solely under the influence of local Newtonian/Einsteinian gravity sourced

1 + z

f (x)

f (x) = 1 + β(H

net

x) + O((H

net

) .

net

x(z) ≈ ln(1 + z) −

[ ln(1 + z)]

+ ⋯ .

OFN

(z) = (1 + z)x(z) .

OFN

(z) ≈

net

(1 + z)

[

ln(1 + z) −

(ln(1 + z))

]

β > 0

(z)

β = 0

by visible mass. Instead, their trajectories are guided by global entropic-torsional gradients—

the inherent "contours" or "currents" of the Fundamental Network itself.

Imagine the network not as a passive arena, but as a structured medium with a complex torsional

topography. Regions of higher spinor density and specific topological charge create preferred

directions and velocities for matter (Cosmic Knots of baryonic scale) moving through them. The

observed flat galaxy rotation curves are not evidence of missing mass, but the signature of stars

flowing along these pre-existing network currents. Similarly, gravitational lensing is modified

by the torsion-induced focusing of geodesics in regions of complex network topology, which

our equations mistake for the presence of additional mass.

This eliminates dark matter as a substance and recasts it as a dynamic geometric effect of the

static network. The "missing mass" problem is an artifact of applying equations that assume a

flat, torsion-free, and dynamically evolving spacetime to a reality that is structured, torsional,

and static. The fractal distribution of this "geometric guidance" naturally explains the observed

large-scale structure and cluster dynamics without cold dark matter particles.

6.6. Distinctive Observational Consequences

In contrast to the standard ΛCDM model, the static cosmology of the OFN predicts several

observable signatures that could serve as tests of its validity:

Absence of Time Dilation in Type Ia Supernova Light Curves: In an expanding universe,

time dilation leads to a measurable broadening of supernova light curves proportional to .

In the OFN static model, where redshift arises from dissipation, such broadening should be

absent or significantly weaker. High-precision photometry of distant supernovae could test this

prediction.

Anisotropic Patterns in the Redshift-Distance Relation: If redshift is caused by interaction

with an inhomogeneous network structure, the map of cosmological redshifts across the sky may

reflect the large-scale topology of the network. This could manifest as correlated patterns or a

dipole/anisotropy in the Hubble parameter (see Prediction K5) that cannot be explained by

isotropic expansion or local bulk flows.

Correlation Between Redshift and Local Network Density/Topology: Within the OFN, the

redshift of objects in a given direction may correlate with the local density or torsional

topography of the network along the line of sight. This could be tested by cross-correlating

high-resolution redshift surveys with maps of large-scale structure, searching for directional

dependencies in the redshift-distance relation that align with cosmic filaments or voids.

These consequences provide a set of clear, falsifiable benchmarks that differentiate the OFN's

static, dissipative cosmology from the standard expanding paradigm.

6.7. The Great Misinterpretation: From "Tired Light" to the Demise of Dark Energy

(1 + z)

The cosmological model derived from the OFN culminates in a profound conceptual shift

regarding the nature of redshift and the fate of dark energy. This shift can be encapsulated in a

simple physical analogy and an epistemological correction.

The Analogy: A Photon Rolling on a Cosmic Viscous Surface

Consider a photon not as a wave riding expanding space, but as a "ball" rolling across a

surface with fine, universal roughness—the textured fabric of the Fundamental Network itself.

On its billion-year journey from a distant galaxy, this ball does not merely traverse a distance; it

continuously interacts with the network's microstructure. Each interaction, mediated by the

torsional-spinor coupling, siphons off a minuscule amount of its energy. By the time it reaches

our telescopes, the photon has "slowed down"—it has lost energy. For light, this energy loss

manifests directly as redshift. There is no stretching of spacetime, only the gradual dissipation of

a traveler's "momentum" in a resistive medium.

The Epistemological Correction: A Nonlinear Dissipation Artifact

Where, then, does the illusion of "accelerated expansion" originate? The answer is deceptively

simple: it is a translation artifact. The standard cosmology implicitly assumes a linear

relationship between energy loss (redshift) and distance. However, the dissipative properties of

the network, encoded in the function in Eq. (13), are nonlinear. The network's structure—

its fractal topology, varying spinor density, and distribution of Cosmic Knots—causes photons

from greater distances to experience a cumulatively stronger dissipative drag per unit of

coordinate distance. This nonlinear dissipation profile, when naively mapped onto the expanding

universe model, perfectly mimics the luminosity-distance curve of a universe dominated by a

repulsive dark energy component.

Thus, the great cosmic enigma of dark energy evaporates not because we have discovered a new

force or field, but because we have radically reinterpreted the primary observation. We have

mistaken the nonlinear "tiredness" of light in a static, structured medium for the accelerated

"flight" of galaxies in an expanding, empty space. Dark energy is not a substance; it is a

misattributed signature of the network's intrinsic geometry and dissipative dynamics.

6.8. Synthesis: A Unified Geometric Resolution

This completes the cosmological unification within the OFN. The same static network that:

• hosts Cosmic Knots explaining baryogenesis and quantum-cognitive scaling,

• possesses a fractal-torsional structure explaining galactic dynamics (dark matter),

also possesses a dissipative texture that explains the supernova Ia data (dark energy).

The three pillars of the "ΛCDM crisis"—inflation (addressed by staticity), dark matter, and dark

energy—are not solved by adding new entities to the old paradigm. They are dissolved by a

change in the foundational ontology: from a dynamic, expanding spacetime to a static,

geometrically rich, and interactive Fundamental Network. The universe is not flying apart; it is a

vast, intricate, and eternal structure through which we, and the light we see, are navigating.

f (x)

7. Testable Predictions and Paths to Falsification

A theory's scientific merit is ultimately judged by its ability to make novel, falsifiable

predictions. The Ontology of the Fundamental Network (OFN) and its central entity, the Cosmic

Knot, yield a rich set of such predictions across multiple disciplines. Their verification or

refutation will determine the validity of this unified framework. Below, we categorize and detail

the key empirical consequences.

7.1. Neurobiological and Cognitive Predictions (From Sections 2 & 4)

These predictions stem from the identification of consciousness with a soliton in the activation

field \(\Psi\) and the quantization of states via the -parameter.

H1 (\(\sigma\)-Geomagnetic Correlation): The effective connectivity parameter of a

conscious brain, derivable from features of high-density EEG or fMRI data (e.g., functional

connectivity graphs, complexity measures), will show a statistically significant correlation with

global geomagnetic activity indices (e.g., Kp-index, Dst-index). Periods of low geomagnetic

activity should correlate with -values closer to unconscious regimes ( ), while

moderate disturbances should push toward the optimal reflective/metastable range

( ).

H2 (Insight at \(\sigma \approx \pi/4\)): Episodes of sudden creative insight or "aha!" moments

will be associated with a transient, measurable shift in neural dynamics corresponding to

. This metastable state should be preferentially triggered during periods of moderate,

structured geomagnetic perturbations, not during quiescent or storm-level activity.

H3 (Spin-Polarization Shift): The application of techniques that induce spin polarization in

biological tissues (e.g., Dynamic Nuclear Polarization, DNP) to the brain should cause a

measurable and reproducible shift in of subjects (as measured by EEG) towards the optimal

\(\pi/4\) range, enhancing cognitive coherence or altering states of consciousness.

H4 (Discrete State Transitions): Abrupt, large-scale changes in the global geomagnetic field

(e.g., during a solar flare impact or sudden commencement) will induce step-like transitions in

the population-averaged of monitored subjects. These transitions will not be to arbitrary

values but will tend toward the critical points .

7.2. Quantum and Laboratory Physics Predictions (From Sections 2, 3 & 4)

These predictions test the torsional-spinor coupling and the influence of the network's global

phase.

Ф1 (Chiral Barrier Tunneling Enhancement): The rate of spin-dependent quantum tunneling

through chiral molecular or crystalline barriers will show detectable increases following major

solar flares or coronal mass ejections (with a lag corresponding to particle transit time). The

effect should be stronger for electrons with spin aligned to a specific chirality of the barrier.

eff

σ < π /8

π /6 ≤ σ ≤ π /4

eff

≈ π /4

eff

π /8,π /6,π /4

Ф2 (Neutrino Detector Modulations): Data from high-precision neutrino detectors (e.g., Super-

Kamiokande, JUNO) will contain very low-frequency, near-instantaneous global phase

modulations that correlate with times of planetary alignments or sharp changes in the solar wind

dynamic pressure, acting as signatures of the global informational field updates.

Ф3 (Linear Dependence): In controlled spin-ensemble experiments (e.g., polarized NMR

samples), the measured coherence time or a related collective parameter will exhibit a linear

dependence on the product , where is the density of spin-polarized particles and

is a characteristic geometric length (e.g., sample size, loop circumference). The slope of this

dependence relates to the fundamental torsional constant of the network.

7.3. Astrophysical and Cosmological Predictions (From Sections 5 & 6)

These are the most large-scale and decisive tests, concerning baryogenesis and the static

cosmology.

K1 (Global Synchronization): Isolated human groups (e.g., in bunkers, submarines, space

stations) subjected to shielded, controlled environments will, over time, show a synchronization

of their collective profiles as derived from group EEG, despite the absence of conventional

sensory communication. This synchronization will be disrupted by known solar events.

K2 (Shnoll-EEG Topology Correlation): The fine-structure "histogram shapes" in the statistical

fluctuations of radioactive decay rates (the Shnoll effect) will correlate with the global topology

metrics (e.g., average path length, clustering coefficient) of simultaneously recorded, global-

scale EEG reference networks.

K3 (Gravitational Wave Background from Primordial Knot Decay): A stochastic

gravitational wave background in the 0.1–10 Hz frequency range (target of DECIGO, Big Bang

Observer) will be detected with a non-power-law spectral shape featuring one or more broad

peaks. This signal is distinct from that expected from inflation or cosmic strings and corresponds

to the characteristic mass-scale ( GeV) of decaying primordial Cosmic

Knots.

K4 (Absence of Primordial CMB B-modes): Future, foreground-clean measurements of the

Cosmic Microwave Background polarization will fail to detect the primordial B-mode signal

at large angular scales (tensor-to-scalar ratio ), inconsistent with the simplest inflationary

models but expected in a static universe without an inflationary epoch.

K5 (Anisotropic Hubble Parameter): Precision measurements of the Hubble constant using

different tracers (supernovae, quasars, gravitational lenses) across the sky will reveal a

significant, intrinsic dipole anisotropy (amplitude > 1 km/s/Mpc) that cannot be explained by

local bulk flows. This dipole reflects the large-scale anisotropy in the network's dissipative

function .

K6 (Fractal Dark Matter Halos): High-resolution kinematic studies of dwarf galaxy halos and

the stellar streams within large galactic halos will reveal density profiles and substructures

τ(x)

spin

⋅ L

spin

eff

∼ 10

− 10

r ≈ 0

f (x)

consistent with a fractal dimension , rather than the smooth Navarro-Frenk-

White (NFW) profile. This is a signature of dark matter as a dissipative network component.

7.4. Falsifiability Conditions

The OFN is falsifiable as a whole if a critical mass of its core predictions is decisively disproven.

However, several key findings would constitute a direct refutation of the theory's foundations:

• The experimental confirmation of inflationary primordial B-modes (contradicting K4) while

also confirming the ΛCDM expansion history would invalidate the static cosmology pillar.

• The conclusive demonstration that no correlation exists between any measure of neural

coherence/state and geomagnetic activity across multiple, well-controlled studies (contradicting

H1, H2, H4) would sever the proposed consciousness-network link.

• The null result in a sensitive search for the predicted gravitational wave background from

knot decay (K3) over the next two decades, while other early-universe probes advance, would

challenge the baryogenesis mechanism.

• The verification that the cosmic distance ladder is perfectly isotropic and consistent with a

single, universal to within 0.1% (contradicting K5) would undermine the notion of a

structured, anisotropic network.

7.5. Conclusion: An Interdisciplinary Experimental Program

The predictions outlined above are not mere speculations but direct consequences of the OFN's

mathematical structure. They call for a novel, interdisciplinary collaboration between

neuroscientists, quantum physicists, astrophysicists, and cosmologists. The verification of even a

subset of these predictions—particularly across different scales (H1, Ф1, K5)—would provide

compelling evidence for a unified, geometric reality. Conversely, their systematic failure would

consign the OFN to the history of bold, but incorrect, unified theories. This clear falsifiability is

the theory's greatest strength, inviting rigorous scientific scrutiny.

8. Discussion and Conclusions: Toward a Geometric Monism

8.1. Recapitulation of the Unification

This paper has undertaken an ambitious synthesis, proposing that three of the most profound

puzzles in modern science—the universal one-second invariant and -scaling [1], the origin of

baryon asymmetry [2–4], and the hard problem of consciousness [5]—are not separate

challenges but interconnected facets of a single, deeper reality. We have argued that this reality is

best described by the Ontology of the Fundamental Network (OFN), a framework where:

• Existence is a static, four-dimensional spinor network.

• Time and becoming arise as the epiphenomenal process of "reading" this network.

• Consciousness is a stable, solitonic excitation in the network's activation field, resonantly

coupled to complex systems like the brain.

D ≈ 1.7 − 1.8

From this ontology emerges a fundamental entity: the Cosmic Knot, a torsional soliton whose

stability is maintained by the network's intrinsic geometry. We have demonstrated how the

properties of these knots provide a unified explanation:

Unification I (Section 4): The discrete spectrum of stable knot states, indexed by the

connectivity parameter , naturally yields a fundamental time unit of ~1 second and favors

-proportions as a condition for topological self-consistency, thereby explaining the empirical

patterns of Beardsley.

Unification II (Section 5): The formation and CP-violating decay of primordial Cosmic Knots

in the early universe offer a geometric mechanism for baryogenesis, grounding and extending

recent field-theoretic models of topological defects.

Unification III (Section 6): The large-scale structure of the network provides a medium whose

dissipative interaction with light explains the cosmological redshift and its apparent acceleration,

challenging the expansion paradigm and eliminating the need for dark energy.

This triune unification is not merely analogical but is rooted in a common mathematical

formalism, with the torsional coupling and the -parameter serving as the linchpins connecting

scales from the quantum to the cosmic.

8.2. Philosophical and Theoretical Implications

The OFN advocates for a rigorous geometric monism. It posits that what we perceive as distinct

substances—mind and matter, time and space, energy and information—are derivative

phenomena of a single, geometric substrate. This has profound implications:

The Nature of Time: Time is not a fundamental river but the sequential unveiling of a pre-

existing structure. The "arrow" is a reading direction determined by the network's entropic

gradient. This resolves the tension between time-symmetric laws and temporal experience

without invoking special initial conditions.

The Hard Problem of Consciousness: The problem dissolves when experience is not seen as

produced by computation but as identical to a specific geometric configuration (a soliton).

Qualia are not emergent from complexity but are fundamental modes of the network's self-

interaction, made accessible through biological resonance.

The Unity of Physics: The theory erases the artificial boundary between quantum and classical,

micro and macro, physical and mental. It suggests that laws of physics are not imposed but are

statistical regularities of the network's topological dynamics.

Compared to other unifying programs, the OFN is distinct. Unlike Penrose-Hameroff [13]

orchestrated objective reduction, it does not rely on quantum gravity in microtubules but on a

pre-geometric network. Unlike Integrated Information Theory (IIT) [14], it provides a physical

substrate (the network) for , moving from phenomenology to ontology. It shares with loop

quantum gravity an emphasis on discrete, network-like structures but extends this geometry to

encompass consciousness and cosmic evolution.

8.3. Limitations and Open Questions

The presented framework is a foundational sketch, not a complete theory. Significant open

questions remain:

Mathematical Rigor: The system of equations (activation + Einstein-Cartan) requires a full

numerical solution to derive detailed cosmological predictions and particle spectra.

Parameter Determination: The coupling constants ( ) and the fundamental network

constant must be determined from a fit to empirical data (e.g., the supernova Ia curve,

particle masses).

Detailed Micro-Macro Map: While the principle is clear, a precise mathematical mapping from

the -states of micro-knots (particles) to the properties of meso-knots (planetary systems) needs

to be developed.

Quantum Measurement: How does the process of "reading" relate to the collapse of the wave

function? The OFN suggests a more fundamental, geometric basis for measurement that requires

elaboration.

These are not flaws but directions for future research. The theory's value lies in providing a

coherent, fertile framework within which these questions can be precisely formulated.

8.4. Concluding Synthesis

The model presented here—Cosmic Knots within the Ontology of the Fundamental Network—is

a testable, interdisciplinary, and monistic theory of everything. It makes the bold claim that

the fabric of reality is a timeless, geometric network, and that all we observe and experience are

excitations within it. The appearance of the same mathematical patterns (1 second, ) from

protons to planets, the genesis of matter from geometric decay, and the very flow of time and

consciousness are all rendered as different perspectives on the same underlying dynamics.

The theory's power lies in its explanatory unity and predictive specificity. It does not add new,

ad-hoc entities to solve each puzzle but shows how the puzzles themselves arise from a common

source. It replaces the mysterious "dark" sectors of cosmology with the dynamic geometry of a

network and grounds consciousness in physics without reducing it.

Whether this specific model is ultimately validated or not, its approach points toward a necessary

future for fundamental science: one that dares to build bridges across the chasms between mind,

matter, and cosmos, and seeks their common origin not in ever-smaller particles, but in the

timeless geometry of connection and information. The extensive set of falsifiable predictions

(Section 7) now invites the scientific community to put this geometric monism to the test.

Appendix A: The Geometric Theory of Inertia and the One-Second Invariant

(Beardsley, 2025)

A1. Conceptual Foundation

α, β, η, ζ

net

In a complementary line of research, Beardsley (2025) has developed a geometric theory of

inertia that derives the masses of fundamental particles and key solar system relationships from a

single Lorentz-invariant timescale: second. This theory posits that mass (inertia) is the

resistance encountered when diverting an object's motion from the temporal dimension

into the spatial dimensions. When a particle is accelerated, its spacetime velocity vector is

rotated, converting temporal motion ( ) into spatial motion ( ).

A2. The Fundamental Normal Force and Mass Formula

The theory introduces a universal, Lorentz-invariant normal force , which characterizes the

inherent "stiffness" of spacetime at the quantum-gravitational interface:

(A1)

The inertial mass of a particle is then given by:

(A2)

where:

• is the characteristic radius of the particle,

• is the gravitational constant,

• is a dimensionless coupling constant specific to the particle type:

with being the fine-structure constant.

A3. Empirical Verification: Particle Masses

Using the experimentally measured charge radii of the proton ( ), neutron ( ), and electron ( ),

the formula with s yields:

This remarkable agreement provides robust, independent empirical evidence for as a

fundamental invariant governing quantum-gravitational interactions at the baryonic scale.

= 1



, witht

= 1second .

= κ

πr

= κ

3α

, κ

= 1,

= 1

Particle

Predicted \(t_1\) (s)

Accuracy

Proton

1.00500

0.5%

Neutron

1.00478

0.5%

Electron

0.99773

0.2%

A4. Derivation of the One-Second Scale from Fundamental Constants

The invariant is not postulated but derived from the fundamental constants of nature:

(A3)

where is the Planck time and is the Compton time of the proton. This expression bridges the

Planck scale, quantum mechanics ( ), relativity ( ), and gravitation ( ), demonstrating that the

one-second timescale is a fundamental property of spacetime geometry itself.

A5. Macroscopic Manifestation: The Solar System and

The same one-second invariant governs macroscopic celestial mechanics. By defining a solar

system Planck-type constant:

(A4)

where is the kinetic energy of Earth's orbital motion, key relationships emerge. For

instance, the Moon's orbital ground state is quantized as:

(A5)

where is the mass of the Moon. This directly parallels the quantum mechanical formulation,

suggesting a unified scaling principle from subatomic to planetary scales.

A6. The Golden Ratio and the Proton Radius

The theory predicts an optimal relationship for the proton radius involving the golden ratio

(A6)

This result aligns with high-precision measurements and can be understood dynamically: the

proton may fluctuate among quasi-stable states corresponding to Fibonacci approximations

of \(\phi\) (e.g., 2/3, 5/8, 13/21), offering a potential resolution to the historical "proton radius

puzzle."

A7. Synthesis with the OFN: Cosmic Knots as the Ontological Basis

Within the Ontology of the Fundamental Network (OFN), the geometric theory of inertia finds

its natural foundation:

• The one-second invariant corresponds to the characteristic phase evolution period of a

Cosmic Knot at the baryonic mass scale (see Section 4.2).

• The normal force is interpreted as the fundamental torsional stiffness of the network.

= α

⋅

≈ 0.9927seconds,

ℏ

⊙

ℏ

⊙

= (1second) × KE

Earth

ℏ

⊙

⋅

= 1second,

ϕ ≈ 0.618

= ϕ

• The masses and radii of particles are expressions of the topological size and \(\sigma\)-state

of their corresponding micro-scale Cosmic Knots.

•

The golden ratio emerges as the unique scaling factor for topologically optimal, self-

similar knot configurations (see Section 4.3).

We take to be given by:

Using the 2/3 fibonacci approximation for . We have

Using Earth’s orbital velocity at perihelion.

Thus, Beardsley's empirically successful formalism is not merely compatible with the OFN; it is

naturally explained and ontologically grounded by it. The geometric theory of inertia

describes the how of universal scaling, while the OFN explains the why through the dynamics of

torsional solitons in a fundamental network.

References for Appendix A

•

Beardsley, I. (2025). A Spacetime Theory For Inertia; Predicting The Proton, Electron,

Neutron and the Solar System in Terms of a One-Second Invariant. DOI: 10.5281/

zenodo.18165382.

•

Beardsley, I. (2025). Historical Context and Theoretical Precedents: From Dirac's Large

Numbers to the One-Second Universe. DOI: 10.5281/zenodo.18242999.

•

Bezginov, N., et al. (2019). A measurement of the atomic hydrogen Lamb shift and the proton

charge radius. Science, 365(6457), 1007–1012.

•

Mohr, P. J., et al. (2016). CODATA recommended values of the fundamental physical

constants: 2014. Reviews of Modern Physics, 88(3), 035009.

References

[1] I. Beardsley, A Spacetime Theory For Inertia; Predicting The Proton, Electron, Neutron and the Solar System in

Terms of a One-Second Invariant (2025), DOI: 10.5281/zenodo.18165382.

[2] A. D. Sakharov, Pis'ma Zh. Eksp. Teor. Fiz. 5, 32 (1967) [JETP Lett. 5, 24 (1967)].

[3] A. Vilenkin and E. P. S. Shellard, Cosmic Strings and Other Topological Defects (Cambridge University Press,

Cambridge, 2000).

[4] G. Dvali and A. Vilenkin, J. Cosmol. Astropart. Phys. 2004(03), 010 (2004).

ℏ

⊙

1.03351s =

⋅

π r

ℏ

⊙

= (1.03351s)(2.7396E 33J ) = 2.8314E33J ⋅ s

K E

Ea rth

(5.972E 24kg)(30,290m /s)

= 2.7396E 33J

[5] D. J. Chalmers, The Conscious Mind: In Search of a Fundamental Theory (Oxford University Press, New York,

1996).

[6] O. Evdokimov, Ontology of the Fundamental Network (OFN), Preprint (2025), DOI: 10.5281/zenodo.18105426.

[7] P. A. M. Dirac, Nature 139, 323 (1937).

[8] K. Tynski, One Equation, ~200 Mysteries: A Structural Constraint That May Explain (Almost) Everything,

Preprint (2024).

[9] N. Bezginov et al., Science 365, 1007 (2019).

[10] P. J. Mohr, D. B. Newell, and B. N. Taylor, Rev. Mod. Phys. 88, 035009 (2016).

[11] I. Beardsley, Historical Context and Theoretical Precedents: From Dirac's Large Numbers to the One-Second

Universe (2025), DOI: 10.5281/zenodo.18242999.

[12] C. E. Carlson, Prog. Part. Nucl. Phys. 82, 59 (2015).

[13] R. Penrose and S. Hameroff, Phys. Life Rev. 8, 292 (2011).

[14] G. Tononi, M. Boly, M. Massimini, and C. Koch, Nat. Rev. Neurosci. 17, 450 (2016).

[15] S. Perlmutter et al., Astrophys. J. 517, 565 (1999).

[16] A. G. Riess et al., Astron. J. 116, 1009 (1998).

[17] J. F. Navarro, C. S. Frenk, and S. D. M. White, Astrophys. J. 490, 493 (1997). !