DOI: [To be assigned]
John Swygert
July 29, 2026
Abstract
This paper formally develops the preliminary expressed/unexpressed-energy distinction introduced in The Expressed and Unexpressed Energy Distinction in TSTOEAO: A Preliminary Framework for Potential, Localization, Binding, and Cosmic Expansion. The earlier paper divided a total energy condition into expressed and unexpressed components,
\[
E_T=E_x+E_u,
\]
and proposed first-order relations between expressed fraction, binding burden, unexpressed fraction, and expansion freedom. It explicitly presented those relations as conceptual scaffolding rather than completed physical equations. The present paper does not retract or silently replace that framework. It preserves its distinction between committed and uncommitted potential while showing that physical expression cannot be represented adequately as a single binary transition from unexpressed energy to ordinary matter.
Expression is developed here as a multiaxial relational condition involving localization, structural commitment, coupling, pressure behavior, phase, persistence, scale, cosmological history, geometry, and observer frame. Energy may be strongly expressed along one axis while remaining weakly expressed along another. Radiation is physically expressed without being ordinary rest matter. Dark matter, if particulate, may be hidden structural expression whose observable consequences depend upon gravitational and possibly nongravitational couplings. A cosmological expansion component may be diffuse yet physically consequential through pressure, geometry, or boundary relations. An observed dark-energy signal may alternatively be influenced by source evolution, observer motion, anisotropy, inhomogeneity, calibration, and model assumptions.
The compact TSTOEAO relation,
\[
V=E\times Y,
\]
is applied at cosmological scale by distinguishing energetic content \(E\) from the relational architecture \(Y\) through which that content becomes observable. The realized cosmological result \(V\) may therefore depend jointly upon matter density, radiation, hidden sectors, coupling pathways, phase histories, source properties, geometric assumptions, and observational frame.
Three branches are maintained prospectively: a real expansion-dominant physical sector, a relationally apparent dark-energy signal, and a mixed architecture containing both. Dark matter is likewise treated through multiple branches rather than prematurely identified with one unknown particle. The paper introduces a conceptual expression-state vector, a cosmic coupling matrix, covariant exchange relations, revised definitions of binding burden and expansion freedom, observational discriminators, and explicit failure conditions. It does not claim to derive dark matter, dark energy, or cosmic acceleration. Its purpose is to convert an earlier binary ontology into a multidimensional architecture capable of being compared with relativistic cosmology and exposed to prospective observational failure.
01
Prologue: A Formal Evolution, Not a Retraction
Scientific development requires continuity without immobility.
A preliminary paper should preserve the reasoning available at the time it was written. A later paper should not silently rewrite that record merely because the underlying theory has become more precise. It should state what remains valid, identify what proved insufficient, and show how the architecture changed.
The earlier expressed/unexpressed-energy paper established several foundational propositions:
1. Energy committed to physical form acquires structure, relation, persistence, and constraint.
2. Unexpressed energy does not mean nothingness or nonexistence.
3. Expression carries cost.
4. Localized matter participates in inertia, binding, and gravitational structure.
5. Potential not committed to ordinary matter-form may possess a different degree of local obligation.
6. Cosmic expansion should not automatically be identified with an ordinary force pushing material objects outward.
7. Unexpressed energy should not be declared identical to dark energy, zero-point energy, or vacuum energy without mathematical and observational justification.
8. The framework must eventually become quantitative or remain philosophical.
Those propositions remain important.
What requires refinement is the preliminary binary picture:
\[
\text{unexpressed energy}
\longrightarrow
\text{expressed matter}.
\]
Physical expression is more diverse than matter formation alone. Energy can be expressed through radiation, fields, pressure, momentum, curvature, interaction, phase, and nonlocal organization. A component can remain diffuse while still participating in gravitational dynamics. A hidden sector can be structurally consequential without being directly luminous. An observed cosmological effect can also be produced partly by relations among source history, observer frame, geometry, and inference rather than by a single new substance.
The present development therefore preserves the original distinction while enlarging its dimensionality.
The evolved proposition is:
> Expression is not one switch between potential and matter. It is a multidimensional condition describing how energy becomes localized, coupled, structured, persistent, pressurized, observable, and relationally consequential.
02
Scope and Epistemic Status
This paper is an architectural cosmology proposal.
It is not presented as:
a replacement for general relativity;
a derivation of the Einstein field equations;
a proof that dark matter is a particular substance;
a proof that dark energy exists;
a proof that dark energy does not exist;
a completed scalar-field model;
a validated modified-gravity theory;
or a numerical fit to cosmological data.
Its present tasks are narrower:
1. Preserve the scientifically useful core of the expressed/unexpressed distinction.
2. correct its overly matter-centered definition of physical expression;
3. distinguish cosmic expansion from accelerated expansion and from the inferred entity called dark energy;
4. separate energetic content from relational and observational architecture;
5. incorporate coupling, source history, scale, geometry, and observer frame;
6. provide a mathematical scaffold compatible with covariant conservation;
7. define competing interpretive branches;
8. identify measurements capable of distinguishing those branches;
9. state what results would weaken or defeat the framework.
The architecture remains provisional wherever its terms have not yet been mapped to independently measurable quantities.
03
The Earlier Expressed/Unexpressed Distinction
The earlier framework began with:
\[
E_T=E_x+E_u,
\]
where:
\[
E_T=\text{total energy condition},
\]
\[
E_x=\text{expressed energy},
\]
and
\[
E_u=\text{unexpressed energy}.
\]
It then defined:
\[
\chi=\frac{E_x}{E_T},
\]
\[
\upsilon=\frac{E_u}{E_T},
\]
with:
\[
\chi+\upsilon=1.
\]
The first-order interpretive relations were:
\[
B\propto\chi
\]
and:
\[
F\propto\upsilon,
\]
where \(B\) represented binding burden and \(F\) represented expansion freedom.
The underlying intuition was stated in plain language:
> Matter is energy that has become committed.
> Gravity is the burden of that commitment.
> Expansion is what unexpression preserves.
The earlier paper was careful to describe this as a bookkeeping skeleton rather than a final physical model. It also warned that zero-point energy, dark energy, and unexpressed energy should not be declared identical merely because they appear conceptually adjacent.
The present paper retains:
energetic commitment;
differential constraint;
binding burden;
expansion freedom;
and the distinction between existence and physical expression.
It revises the assumption that the relevant division is exhausted by:
\[
\text{ordinary matter}
\quad\text{versus}\quad
\text{everything not expressed as ordinary matter}.
\]
04
Why a Binary Classification Is Insufficient
A binary model becomes inadequate for at least six reasons.
4.1 Radiation is expressed but not ordinary matter
Photons carry energy and momentum. Radiation participates in the stress-energy accounting of general relativity even though photons possess no rest mass and do not constitute ordinary baryonic matter.
A definition equating expression only with massive matter would therefore classify an unquestionably physical and gravitationally consequential form of energy as unexpressed.
4.2 Pressure contributes to gravitational dynamics
In relativistic cosmology, pressure is not an incidental property. The combination of energy density and pressure affects the evolution of the cosmic scale factor.
A diffuse component can therefore remain spatially smooth while having a major cosmological effect.
4.3 Localization and gravitational participation are not identical
A field can be diffuse and still contribute to stress-energy.
A localized state can have complex internal pressure.
A propagating wave can be nonstationary but fully expressed.
A hidden sector may cluster weakly, strongly, or only above particular scales.
4.4 Visibility and expression are not identical
Dark matter is inferred through gravitational and structure-formation effects, not ordinary electromagnetic emission. If it exists as a physical component, its invisibility does not make it unexpressed.
It may instead be:
> physically expressed but electromagnetically hidden.
4.5 Observed effects depend upon coupling
The same component density can produce different observations if its interactions differ.
Dark matter that interacts only gravitationally does not produce the same perturbation history as dark matter that exchanges momentum with neutrinos, baryons, radiation, or another hidden sector.
4.6 Cosmological inference depends upon source and observer relations
An observed supernova magnitude is not a direct reading of cosmic acceleration. It is processed through source luminosity, progenitor history, dust, host environment, redshift, local motion, calibration, sky sampling, and the cosmological model used to interpret the signal.
The same measured light can yield different cosmological conclusions under different relational assumptions.
Physical expression must therefore be represented as a multiaxial state rather than a binary label.
05
Cosmological Background: Expansion, Acceleration, and Dark Energy
Let \(a(t)\) represent the cosmic scale factor.
The Hubble parameter is:
\[
H(t)=\frac{\dot a}{a}.
\]
The universe is expanding when:
\[
H>0.
\]
The deceleration parameter is:
\[
q(t)=-\frac{a\ddot a}{\dot a^2}.
\]
Accelerated expansion corresponds to:
\[
q<0,
\]
while decelerated expansion corresponds to:
\[
q>0.
\]
These are not interchangeable statements.
A universe can be expanding while its rate of expansion is slowing:
\[
H>0,\qquad \ddot a<0.
\]
Therefore:
\[
\text{expansion}
\neq
\text{accelerated expansion}
\neq
\text{dark energy}.
\]
Dark energy is a proposed physical explanation for accelerated expansion. It is not another name for expansion itself.
For a homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker model, the first Friedmann equation can be written schematically as:
\[
H^2
=
\frac{8\pi G}{3}\rho
–
\frac{kc^2}{a^2}
+
\frac{\Lambda c^2}{3},
\]
where \(\rho\) is the total energy density, \(k\) represents spatial curvature, and \(\Lambda\) is a cosmological-constant term.
The acceleration equation is:
\[
\frac{\ddot a}{a}
=
-\frac{4\pi G}{3}
\left(
\rho+\frac{3p}{c^2}
\right)
+
\frac{\Lambda c^2}{3}.
\]
If a cosmological component is incorporated into \(\rho\) and \(p\) rather than placed in a separate \(\Lambda\) term, accelerated expansion requires the total effective relation:
\[
\rho+\frac{3p}{c^2}<0.
\]
For an equation-of-state parameter:
\[
w=\frac{p}{\rho c^2},
\]
a separately conserved dominant component generally drives acceleration when:
\[
w<-\frac{1}{3}.
\]
This means that “unlocalized,” “uncommitted,” or “free from matter-form” is not enough to explain acceleration. A proposed expansion-dominant sector must possess positive physical properties—such as an effective pressure, field dynamics, geometric influence, or modified coupling—that reproduce an expansion history.
The standard flat six-parameter \(\Lambda\)CDM model remains highly successful in fitting cosmic microwave-background data, although present research continues to test its assumptions and possible extensions.
06
Expression Beyond Baryonic Matter
The earlier definition of expressed energy emphasized energy localized into mass-bearing matter.
The revised definition is:
> Expressed energy is energy committed to a definite and causally consequential physical relation, state, pathway, phase, interaction, or structure.
This includes, but is not limited to:
baryonic matter;
massive particles;
radiation;
electromagnetic fields;
kinetic energy;
pressure;
momentum flow;
gravitational radiation;
coherent field configurations;
hidden-sector structures;
interaction terms;
and any physical state contributing measurably to dynamics or observation.
This does not mean every form of expression is equally localized, equally persistent, or equally constrained.
A star and a photon are both physically expressed, but their relational architectures differ profoundly.
A star is:
locally concentrated;
structurally persistent;
gravitationally bound;
internally pressurized;
and composed of many interacting degrees of freedom.
A photon is:
propagating;
nonresting;
nonbaryonic;
capable of transferring momentum;
and responsive to spacetime geometry.
Physical expression is therefore a category containing multiple dimensions rather than one material endpoint.
07
The Multiaxial Expression State
Let the physical expression state of a component or region be represented provisionally by:
\[
\boldsymbol{\xi}
=
\left(
\ell,
s,
c,
\pi,
\varphi,
\tau,
r,
h,
o
\right),
\]
where:
\[
\ell=\text{degree of localization},
\]
\[
s=\text{degree of structural commitment},
\]
\[
c=\text{coupling architecture},
\]
\[
\pi=\text{pressure or equation-of-state behavior},
\]
\[
\varphi=\text{phase condition},
\]
\[
\tau=\text{persistence or characteristic lifetime},
\]
\[
r=\text{relevant physical scale},
\]
\[
h=\text{formation and interaction history},
\]
and:
\[
o=\text{observer-frame and observational relation}.
\]
These variables are not yet assumed to be universally normalized scalar quantities. Some may require functions, tensors, spectra, probability distributions, or scale-dependent operators.
The vector is introduced to express one central correction:
> No single axis determines whether energy is physically expressed or how that expression will appear cosmologically.
A component may have:
low localization but strong pressure effects;
high localization but weak electromagnetic coupling;
low visibility but high structural influence;
strong early-universe coupling but weak late-universe coupling;
high physical expression but low direct detectability;
or observer-dependent apparent behavior.
The expression state is therefore better understood as a position in a multidimensional relational space.
08
The Earlier Expressed Fraction as a Projection
The scalar:
\[
\chi=\frac{E_x}{E_T}
\]
remains useful as a first-order bookkeeping projection.
It should not be treated as a complete physical description.
The revised form is:
\[
\chi
=
\mathcal{P}_x
\left(
\boldsymbol{\xi};
\mathbf{W},
\mathcal{D}
\right),
\]
where:
\(\mathcal{P}_x\) is a defined projection from the multiaxial expression state into a scalar expressed fraction;
\(\mathbf{W}\) contains prospectively assigned weights or physical mappings;
and \(\mathcal{D}\) identifies the domain and scale of application.
The complementary quantity is:
\[
\upsilon=1-\chi.
\]
However, \(\upsilon\) cannot simply collect every property not represented by \(\chi\). It must eventually be associated with positive physical characteristics.
Two systems can have the same projected \(\chi\) while differing in their full expression states:
\[
\chi_1=\chi_2,
\]
but:
\[
\boldsymbol{\xi}_1\neq\boldsymbol{\xi}_2.
\]
If relational architecture matters, then:
\[
V_1\neq V_2
\]
may follow even when the scalar expressed fractions are equal.
This is the cosmological equivalent of a matched-marker test:
> Equal scalar classification does not guarantee equivalent physical state.
09
Cosmic Relational Architecture
The TSTOEAO relation:
\[
V=E\times Y
\]
states that realized expression depends jointly upon energetic opportunity and relational architecture.
At cosmological scale:
\[
E_{\text{cosmic}}
\]
may include:
baryonic energy density;
radiation;
neutrinos;
hidden matter;
field energy;
vacuum-like components;
curvature-associated terms;
and possible substrate conditions.
The relational architecture:
\[
Y_{\text{cosmic}}
\]
may include:
gravitational coupling;
nongravitational coupling;
geometry;
phase;
pressure relations;
boundary conditions;
scale;
interaction history;
source evolution;
observer motion;
instrument response;
calibration;
and model assumptions.
A more explicit representation is:
\[
V_\alpha
=
E_{\text{cosmic}}
\times
Y_\alpha
\left(
\boldsymbol{\xi},
\mathcal{G},
\mathcal{C},
\mathcal{H},
\mathcal{F},
\mathcal{I}
\right),
\]
where:
\(V_\alpha\) is a particular cosmological observable;
\(\mathcal{G}\) is geometry;
\(\mathcal{C}\) is coupling architecture;
\(\mathcal{H}\) is physical and source history;
\(\mathcal{F}\) is observer frame;
and \(\mathcal{I}\) is instrument and inference architecture.
The multiplication sign remains an architectural operator until the terms are made domain-specific. It should not automatically be read as ordinary scalar multiplication.
The proposition is:
> Cosmological observables are not transparent readouts of isolated energy components. They are realized through relations among physical content, interaction, geometry, history, and observation.
10
A Cosmic Coupling Matrix
A provisional coupling architecture may be represented by:
\[
\mathbf{Y}_{\text{cosmic}}
=
\begin{bmatrix}
Y_{bb} & Y_{bd} & Y_{b\nu} & Y_{bu}\\
Y_{db} & Y_{dd} & Y_{d\nu} & Y_{du}\\
Y_{\nu b} & Y_{\nu d} & Y_{\nu\nu} & Y_{\nu u}\\
Y_{ub} & Y_{ud} & Y_{u\nu} & Y_{uu}
\end{bmatrix},
\]
where the provisional sectors are:
\(b\): baryonic and ordinarily visible matter;
\(d\): hidden structural or dark-matter-like sector;
\(\nu\): neutrino sector;
\(u\): expansion-dominant or minimally localized sector.
The diagonal terms represent internal behavior:
\[
Y_{bb},\quad
Y_{dd},\quad
Y_{\nu\nu},\quad
Y_{uu}.
\]
The off-diagonal terms represent interaction pathways:
\[
Y_{bd},\quad
Y_{d\nu},\quad
Y_{du},
\]
and their corresponding reverse or reciprocal relations.
The matrix is not offered as a completed Lagrangian or field equation. It is a discipline for preventing the cosmological model from assuming that each sector can be understood independently.
The realized structure of the universe may depend as strongly upon off-diagonal relations as upon the amount of energy assigned to each diagonal sector.
11
Observation Is Part of the Relational Architecture
A cosmological observation is produced through at least four levels:
11.1 Physical source state
What emitted, absorbed, scattered, or redirected the signal?
11.2 Propagation history
Through what geometry, matter distribution, gravitational potential, plasma, or intervening structure did the signal travel?
11.3 Observer state
From what location, velocity frame, gravitational environment, and sky coverage was it measured?
11.4 Inference architecture
What calibration, statistical model, prior assumptions, covariance structure, and cosmological geometry were used to translate the measurement into a physical conclusion?
This can be represented schematically as:
\[
D
=
\mathcal{I}
\left[
\mathcal{O}
\left(
S,
P,
F
\right)
\right],
\]
where:
\(S\) is the source state;
\(P\) is propagation;
\(F\) is observer frame;
\(\mathcal{O}\) is measurement;
and \(\mathcal{I}\) is inference.
The inferred cosmological quantity is therefore:
\[
V_{\text{inferred}}
\neq
V_{\text{source alone}}.
\]
It is the result of the complete measurement relation.
This does not imply that every observation is arbitrary or unknowable. It means that source, observer, and inference variables must be included explicitly rather than treated as transparent.
12
Localization Is Not Equivalent to Gravitational Participation
The earlier framework associated localized matter with gravitational obligation.
That insight remains valid but incomplete.
In general relativity, gravitational dynamics respond to the stress-energy distribution, not only to rest mass. Energy density, pressure, momentum density, and stress can all participate.
The revised statement is:
> Localization increases certain forms of structural and gravitational commitment, but gravitational participation is broader than localization.
A diffuse field may affect cosmic expansion.
Radiation influences the early-universe expansion rate.
Pressure affects acceleration.
A hidden sector may cluster differently at different scales.
An interaction term can modify perturbation growth without adding a large new background density.
Therefore:
\[
\text{localization}
\not\equiv
\text{all gravitational expression}.
\]
A more accurate hierarchy is:
Localized structural expression
Matter, compact objects, stars, galaxies, and persistent bound systems.
Propagating expression
Radiation, waves, and momentum-carrying fields.
Diffuse dynamical expression
Fields or sectors whose effects arise through pressure, background evolution, or weak clustering.
Hidden structural expression
Components inferred through gravitational organization but not ordinary luminosity.
Relational or geometric expression
Observable effects arising from curvature, averaging, frame, boundary, or coupling relations.
13
Revising Binding Burden
The original first-order relation was:
\[
B\propto\chi.
\]
That remains an intuitive approximation, but binding burden cannot depend upon expressed fraction alone.
The revised form is:
\[
B
=
\mathcal{B}
\left(
\rho_x,
p_x,
\ell,
s,
c,
\varphi,
r,
\mathcal{G},
\mathcal{H}
\right),
\]
where:
\(\rho_x\) is expressed energy density;
\(p_x\) is effective pressure;
\(\ell\) is localization;
\(s\) is structural commitment;
\(c\) is coupling;
\(\varphi\) is phase;
\(r\) is scale;
\(\mathcal{G}\) is geometry;
and \(\mathcal{H}\) is history.
Binding burden is redefined as:
> The degree to which a physical expression is constrained by localization, inertia, curvature, coupling, structural maintenance, and the energetic cost of preserving a particular organization.
This definition permits several distinctions.
A black hole and a diffuse gas can contain comparable total mass-energy while possessing radically different binding architectures.
A galaxy can remain gravitationally organized while its internal components move.
A structure can be locally bound while participating in global expansion only negligibly.
A hidden matter sector may contribute strongly to gravitational structure while remaining weakly coupled to light.
Binding burden is therefore relational and scale-dependent.
14
Revising Expansion Freedom
The original first-order relation was:
\[
F\propto\upsilon.
\]
The revised architecture defines expansion freedom as:
> The degree to which a physical region or component participates in, permits, or produces increasing relational separation rather than local structural consolidation.
A more developed expression is:
\[
F
=
\mathcal{F}
\left(
\rho_u,
p_u,
w_u,
c_u,
\varphi_u,
r,
\mathcal{G},
\mathcal{H}
\right),
\]
where:
\(\rho_u\) is the density assigned to the proposed expansion-dominant condition;
\(p_u\) is its effective pressure;
\(w_u\) is its equation-of-state behavior;
\(c_u\) represents couplings;
\(\varphi_u\) is phase;
\(r\) is scale;
\(\mathcal{G}\) is geometry;
and \(\mathcal{H}\) is history.
Expansion freedom cannot mean merely “absence of mass.”
An empty region within a matter-dominated decelerating universe does not by itself produce accelerated expansion.
A valid expansion-dominant component must generate measurable consequences through one or more of the following:
negative effective pressure;
scalar-field evolution;
vacuum-like stress-energy;
modified gravitational dynamics;
geometric averaging;
inhomogeneous clock or expansion relations;
interaction-dependent energy transfer;
or another explicitly defined mechanism.
The earlier statement can therefore be refined:
> Unexpression may preserve a wider range of available relational configurations, but accelerated expansion requires a specific physical or geometric mechanism, not freedom alone.
15
Dark Matter as Hidden Structural Expression
Dark matter should not be grouped automatically with an outward or expansion-dominant sector.
Its inferred cosmological roles are primarily structural:
gravitational clustering;
galaxy and cluster dynamics;
gravitational lensing;
formation of large-scale structure;
and influence upon cosmic microwave-background anisotropies.
Within the present architecture, the leading TSTOEAO interpretation is:
> Dark matter may be hidden structural expression: physically consequential organization whose underlying substrate and complete coupling architecture remain unknown.
This is not an assertion that dark matter has been identified as a particle.
Three broad branches remain open.
15.1 Particulate hidden expression
Dark matter consists of one or more particles or fields with weak ordinary-sector coupling.
15.2 Relationally modified hidden expression
A dark component exists, but its observed behavior depends significantly upon self-interaction or coupling to neutrinos, baryons, radiation, or another hidden field.
15.3 Effective structural residual
Some observations attributed to dark matter arise partly from incomplete gravitational modeling, environmental effects, emergent geometry, or another relation rather than one new substance.
These branches may also coexist.
The governing caution is:
\[
\text{observed missing gravitational effect}
\not\Rightarrow
\text{one uniquely identified substance}.
\]
16
Neutrino–Dark-Matter Coupling as a Relational Example
A 2026 Nature Astronomy analysis examined a model in which dark matter exchanges momentum with neutrinos. In the model studied, the interaction modifies density and velocity perturbations and alters the matter-power spectrum. A combined analysis using Planck, baryon acoustic oscillations, ACT, and DES Year 3 cosmic shear found a nearly \(3\sigma\) preference for a nonzero interaction parameter around:
\[
u_{\nu\mathrm{DM}}\approx10^{-4}.
\]
The authors emphasize that the result remains below discovery status, that the assumed constant cross-section is phenomenological, and that future weak-lensing surveys should be capable of confirming or excluding the preferred region.
The importance for TSTOEAO is architectural.
The relevant realized structure is not determined solely by:
\[
\rho_{\mathrm{DM}}.
\]
It also depends upon the pathway:
\[
Y_{\nu\mathrm{DM}}.
\]
Schematically:
\[
V_{\text{structure}}
=
E_{\mathrm{DM},\nu}
\times
Y_{\nu\mathrm{DM},\mathcal{G},\mathcal{H}}.
\]
The same nominal dark-matter abundance can produce a different cosmic structure if momentum transfer, redshift dependence, particle mass, or cross-section differs.
This supports—not proves—the proposition that dark-sector behavior must be analyzed relationally.
17
Dark Energy Requires a Branched Interpretation
The phrase dark energy currently compresses several logically distinct possibilities.
17.1 A cosmological constant
A constant term with:
\[
w=-1
\]
produces vacuum-like negative pressure and accelerated expansion.
17.2 A dynamical field
A scalar or other field can possess an evolving density and equation of state:
\[
w=w(z).
\]
17.3 Modified gravitational dynamics
Acceleration-like observations may indicate that the gravitational description requires modification rather than a new material component.
17.4 Inhomogeneous or anisotropic relational effects
Apparent acceleration may be affected by cosmic structure, averaging, local bulk flow, observer frame, or departure from exact homogeneity and isotropy.
17.5 Source or calibration evolution
The luminosity or standardization of the objects used to infer distance may evolve with redshift, population age, environment, or another hidden variable.
17.6 Mixed realization
A real expansion-dominant component may coexist with observational and relational distortions.
The present architecture therefore does not declare:
\[
E_u=\text{dark energy}.
\]
It proposes instead:
> A dark-energy-like observation may arise from a real expansion-dominant physical condition, a hidden relation, an observational residual, or a mixed architecture.
18
Source History and the Supernova Standardization Problem
Type Ia supernovae are central to observational cosmology because their light curves can be standardized and used to infer relative luminosity distances. Pantheon+ assembled 1,701 light curves from 1,550 distinct supernovae over a broad redshift range and, when combined with other probes under standard model assumptions, produced results consistent with a cosmological constant.
The inference nevertheless depends upon the validity of the standardization relation.
A 2026 analysis by Sah, Rameez, and Sarkar applied a redshift-dependent progenitor-age luminosity correction to Pantheon+ and reported that the monopole component of the deceleration parameter shifted toward positive values, corresponding to deceleration, while a local dipole remained.
Other researchers dispute the magnitude, implementation, or implications of the proposed age correction. A separate 2026 paper argued that the age-bias correction remains robust under different host-to-progenitor-age mappings, while another July 2026 Pantheon+ decomposition reported near-zero baseline acceleration and isotropic deceleration but challenged the specific dipole interpretation of Sah and collaborators. The disagreement remains active.
TSTOEAO should not decide this dispute by preference.
The architectural lesson is:
> A source possesses history. If that history affects intrinsic luminosity, then the relational architecture between source age and standardized brightness participates in the inferred cosmic result.
The inference can be represented as:
\[
V_{q_0}
=
E_{\mathrm{SN}}
\times
Y_{\text{progenitor, host, dust, calibration, redshift, model}}.
\]
A hidden source variable within \(Y\) can alter the inferred \(V\) without requiring the underlying cosmic expansion history to change.
19
Observer Frame, Bulk Flow, and Anisotropy
Standard cosmological analyses commonly use an FLRW framework that assumes large-scale statistical homogeneity and isotropy.
This remains an extraordinarily productive approximation. It is not immune to testing.
A 2025 analysis of Pantheon+ reported statistically significant dipolar variation in the inferred expansion rate over a specified redshift range and a redshift-dependent dipolar modulation of the deceleration parameter. The authors interpreted the signal as related to anomalous local bulk flow rather than a universal cosmological constant.
Other analyses using different methods and data partitions have reported much weaker or null evidence for cosmological anisotropy, illustrating that the result depends upon method, sample, frame, and treatment of systematics.
The observer-frame issue can be expressed schematically as:
\[
z_{\mathrm{observed}}
=
z_{\mathrm{cosmic}}
+
z_{\mathrm{peculiar}}
+
z_{\mathrm{relational}},
\]
where the terms are not necessarily additive at full relativistic precision but represent distinguishable contributions to the measured redshift.
An observer participating in a coherent bulk flow does not sample the universe from an abstract frame outside cosmic structure.
The observer belongs to the relational architecture.
This gives:
\[
V_{\text{inferred}}
=
E_{\text{signal}}
\times
Y_{\text{cosmos, source, propagation, observer}}.
\]
The observer does not create the universe arbitrarily. The observer changes the relation through which the universe is measured.
20
Three Prospective Dark-Energy Branches
The theory should preserve three competing branches until observations distinguish them.
Branch A: Substantive Expansion-Dominant Sector
A real physical component or phase contributes to accelerated expansion.
Necessary features may include:
positive energy density or another defined gravitational source;
negative effective pressure or equivalent dynamics;
a measurable equation of state;
consistent behavior across independent probes;
and a covariant relation to the rest of the cosmic system.
Possible realizations include a cosmological constant, scalar field, vacuum-like state, or another substrate condition.
Branch B: Relationally Apparent Dark Energy
No independent dark-energy substance is required.
The apparent acceleration results principally from some combination of:
source evolution;
observer motion;
local bulk flow;
anisotropy;
inhomogeneity;
averaging;
geometry;
calibration;
or an incomplete gravitational model.
Under this branch, “dark energy” is primarily an inference residual within \(Y\).
Branch C: Mixed Architecture
A real expansion-dominant component exists, but its inferred magnitude, isotropy, constancy, or time evolution is distorted by relational effects.
This may produce:
a genuine baseline acceleration;
direction-dependent residuals;
redshift-dependent source bias;
local-flow effects;
and probe-dependent estimates.
The branches must not be blended after the data are known.
Each requires prospective predictions.
21
Dark Matter and Dark Energy Are Not Symmetric Unknowns
Dark matter and dark energy are often grouped as the dark sector, but their inferred behaviors differ.
Dark matter is associated predominantly with:
clustering;
lensing;
gravitational wells;
and structural growth.
Dark energy is associated predominantly with:
background expansion;
negative effective pressure;
smoothness at relevant scales;
or the residual required to reconcile observations with a chosen cosmological model.
The evolved TSTOEAO distinction is therefore:
> Dark matter may be hidden structural expression.
> Dark energy may be hidden relation, expansion-dominant expression, observational residual, or a mixture of these.
This is not established physics.
It is a disciplined classification of possibilities.
It avoids placing both unknowns into one vague category of unexpressed energy.
22
Covariant Sector Decomposition
A physically serious development must be compatible with local covariant conservation.
A provisional sector decomposition may be written:
\[
T_{\mu\nu}^{\mathrm{total}}
=
T_{\mu\nu}^{(b)}
+
T_{\mu\nu}^{(r)}
+
T_{\mu\nu}^{(\nu)}
+
T_{\mu\nu}^{(d)}
+
T_{\mu\nu}^{(u)}
+
T_{\mu\nu}^{(\mathrm{int})},
\]
where:
\(b\) represents baryonic matter;
\(r\) represents radiation;
\(\nu\) represents neutrinos;
\(d\) represents a hidden structural sector;
\(u\) represents a proposed expansion-dominant sector;
and \(\mathrm{int}\) represents interactions not captured by independently conserved components.
The total satisfies:
\[
\nabla_\mu T_{\mathrm{total}}^{\mu\nu}=0.
\]
If two sectors exchange energy or momentum, they need not be conserved separately.
For example:
\[
\nabla_\mu T_{(d)}^{\mu\nu}=Q^\nu,
\]
\[
\nabla_\mu T_{(\nu)}^{\mu\nu}=-Q^\nu.
\]
Then:
\[
\nabla_\mu
\left(
T_{(d)}^{\mu\nu}
+
T_{(\nu)}^{\mu\nu}
\right)
=0.
\]
The exchange vector \(Q^\nu\) represents energy-momentum transfer.
This is the relativistic form of cost relocation:
> One sector’s gain is represented through another sector’s corresponding loss or redirection, while the total local accounting remains conserved.
The expression does not specify the microscopic mechanism. It establishes the form that a valid interacting model must respect.
23
The Global Energy Caution
The earlier identity:
\[
E_T=E_x+E_u
\]
should not automatically be interpreted as a globally conserved scalar energy for the entire expanding universe.
In curved and evolving spacetime, local covariant conservation is fundamental:
\[
\nabla_\mu T^{\mu\nu}=0.
\]
A unique globally conserved total energy does not exist in every spacetime in the same straightforward form familiar from isolated systems in flat spacetime.
The earlier identity should therefore be treated as:
> a domain-defined partition of the modeled energy condition, not a universal proof of globally conserved cosmic energy.
A future formalization must specify:
the hypersurface or region over which energy is evaluated;
the observer field;
the time coordinate;
the gravitational-energy convention;
and whether the partition is local, quasi-local, comoving, or global.
Without those specifications, \(E_T\) remains conceptual bookkeeping.
24
Expression Flow and Phase Transition
The theory permits the possibility that energy changes expression state.
Let:
\[
\boldsymbol{\xi}(t)
\]
represent a component’s evolving expression condition.
A transition may be written:
\[
\boldsymbol{\xi}_1
\longrightarrow
\boldsymbol{\xi}_2
\]
under boundary condition:
\[
\mathcal{B}_c.
\]
The transition rate may be represented provisionally as:
\[
\Gamma_{1\rightarrow2}
=
\Gamma
\left(
E,
Y,
\mathcal{B}_c,
T,
\rho,
p,
\varphi,
t
\right).
\]
Examples of ordinary physical expression changes include:
particle production;
annihilation;
recombination;
ionization;
condensation;
symmetry breaking;
radiation emission;
gravitational collapse;
nuclear transformation;
and phase transition.
The present paper does not claim that dark energy converts into matter or that matter converts into dark energy.
It states the testable requirement:
> If TSTOEAO proposes conversion between expressed and unexpressed conditions, it must identify a boundary condition, transition law, conservation relation, and observable signature.
No conversion should be inferred merely because two sectors are conceptually complementary.
25
Level 000, Level 100, and Level 200
Earlier TSTOEAO work used a three-level cosmological classification.
Level 200
Visible baryonic matter and directly observable structured material expression.
Level 100
Hidden gravitational structure associated provisionally with dark-matter-like behavior.
Level 000
Diffuse, equilibrium-dominant, or dark-energy-like cosmic behavior.
The present paper refines these levels.
They should not be interpreted as a simple vertical ladder from nothing to complete matter.
A better interpretation is:
Level 200: Direct structural expression
Strong localization, ordinary electromagnetic interaction, persistent matter-form, and direct material observability.
Level 100: Hidden structural expression
Gravitationally or dynamically consequential organization with incomplete direct observability or unknown coupling.
Level 000: Expansion-dominant or substrate-near condition
A region of expression-state space characterized by low ordinary localization, possible diffuse pressure or geometric behavior, and uncertain relationship to accelerated expansion.
The levels are therefore projections or families of states.
They are not necessarily unique physical substances.
Level 000 may represent:
a real diffuse sector;
a boundary condition;
an effective relation;
a geometric state;
or the observational surface nearest a deeper substrate condition.
This preserves continuity with the earlier system while preventing categorical overreach.
26
Observer-Independent Reality and Observer-Dependent Measurement
Observer relation does not imply that physical reality exists only when measured.
TSTOEAO distinguishes:
\[
\text{physical state}
\]
from:
\[
\text{observed expression of that state}.
\]
A galaxy possesses physical structure whether or not a particular observer measures it.
However, its measured redshift, luminosity, angular size, peculiar velocity, and inferred distance depend upon relational conditions.
This gives two different quantities:
\[
V_{\mathrm{physical}}
\]
and:
\[
V_{\mathrm{observed}}.
\]
Their relationship may be written:
\[
V_{\mathrm{observed}}
=
\mathcal{M}
\left(
V_{\mathrm{physical}},
Y_{\mathrm{observer}},
Y_{\mathrm{instrument}},
Y_{\mathrm{inference}}
\right).
\]
The measurement operator \(\mathcal{M}\) can preserve, distort, obscure, or incompletely sample the physical state.
A valid cosmological theory must model both.
27
The Difference Between More Variables and Relational Architecture
Modern cosmology is already mathematically multidimensional.
It would be inaccurate to claim that standard physics literally examines only one or two variables.
The distinction proposed here is more specific:
> A model may contain many parameters while still treating the relationships among its major sectors as fixed, independent, or secondary.
TSTOEAO emphasizes that:
energetic content;
coupling;
boundary;
phase;
scale;
source history;
geometry;
and observer relation
may jointly determine the realized observation.
The purpose is not to maximize the number of adjustable variables.
An unconstrained theory containing endless variables would explain everything and predict nothing.
The purpose is to identify the minimum relational architecture necessary to discriminate among physically different states.
Every additional variable must therefore satisfy four requirements:
1. It is defined independently of the outcome.
2. It has a measurable or inferable physical meaning.
3. Its inclusion changes a prospective prediction.
4. A result exists that could show the variable is irrelevant or incorrectly modeled.
Relational richness without constraint becomes post-hoc flexibility.
Relational richness with prospective exclusion becomes scientific architecture.
28
Primary Predictions
The present development generates several provisional predictions.
28.1 Equal energy density need not produce equal cosmological behavior
Two models with similar sector densities but different coupling matrices may produce different:
structure-growth rates;
matter-power spectra;
lensing signals;
CMB anisotropies;
and redshift evolution.
28.2 Equal projected expressed fraction need not imply equivalent state
If:
\[
\chi_1=\chi_2
\]
but:
\[
\boldsymbol{\xi}_1\neq\boldsymbol{\xi}_2,
\]
then independent observables should be capable of distinguishing the states.
28.3 A true universal expansion-dominant sector should survive source and frame corrections
After prospectively defined corrections for:
progenitor history;
host environment;
peculiar motion;
local flow;
sky anisotropy;
and calibration,
a real universal component should leave a coherent residual across independent probes.
28.4 A primarily relational acceleration signal should vary with architecture
If dark energy is principally an inference residual, estimates of acceleration should change systematically with:
observer frame;
source population;
direction;
redshift partition;
geometric model;
or averaging procedure.
28.5 A mixed architecture should produce separable residuals
A genuine isotropic baseline may remain after directional or source-dependent terms are removed.
The residual could be represented:
\[
q_{\mathrm{obs}}
=
q_{\mathrm{base}}
+
q_{\mathrm{source}}
+
q_{\mathrm{frame}}
+
q_{\mathrm{direction}}
+
q_{\mathrm{model}}.
\]
A mixed branch predicts:
\[
q_{\mathrm{base}}\neq0
\]
after the other terms are constrained.
28.6 Interacting hidden sectors should produce scale-dependent signatures
Coupling between dark matter and another sector should not merely shift one background parameter. It should alter perturbations in a scale-, epoch-, or energy-dependent manner.
28.7 Dark matter should not be classified through visibility alone
A hidden component can remain strongly expressed through gravitational structure even when it is electromagnetically undetected.
28.8 Expansion freedom must correlate with positive physical observables
If \(F\) is more than metaphor, it must correlate prospectively with quantities such as:
\(w(z)\);
\(\rho_u(z)\);
clustering behavior;
sound speed;
energy transfer;
geometric evolution;
or another defined signature.
29
Observational Discriminators
29.1 Cross-probe expansion reconstruction
Compare expansion histories inferred independently from:
Type Ia supernovae;
baryon acoustic oscillations;
cosmic chronometers;
standard sirens;
strong-lensing time delays;
and cosmic microwave-background-conditioned models.
A universal expansion-dominant sector should produce mutually compatible histories after known systematics are modeled.
29.2 Source-population partitioning
Partition supernova samples by:
progenitor or host age;
host mass;
metallicity;
star-formation history;
dust;
color;
and redshift.
Predeclare how each partition should affect standardized luminosity.
29.3 Directional and frame analysis
Estimate cosmological parameters in:
heliocentric frame;
Local Group frame;
CMB frame;
bulk-flow-corrected frame;
and prospectively defined sky partitions.
A directional signal should be tested against:
survey geometry;
uneven sky coverage;
calibration;
and simulated isotropic catalogues.
29.4 Growth-versus-background comparison
A real physical expansion sector affects background evolution.
Dark-sector interactions may alter perturbation growth.
Comparing:
\[
H(z)
\]
with:
\[
f\sigma_8(z)
\]
and lensing observables may distinguish background acceleration from interaction-modified structure.
29.5 Lensing and dynamical mass comparison
If dark matter is hidden structural expression, lensing, dynamics, and clustering should produce a coherent relation.
Systematic discrepancies may indicate:
baryonic modeling errors;
environmental effects;
self-interaction;
modified gravity;
or incomplete geometry.
29.6 Redshift-dependent interaction tests
A dark-matter coupling should be tested for:
constant;
energy-dependent;
temperature-dependent;
and redshift-dependent
cross-sections rather than assuming one phenomenological form is fundamental.
29.7 Model-independent reconstructions
Use minimally parametric reconstructions of:
\[
H(z),\qquad q(z),\qquad w(z)
\]
to determine how strongly conclusions depend upon a predetermined \(\Lambda\)CDM or \(w_0w_a\)CDM form.
30
A Prospective Branch Test
A future locked protocol should compare the three dark-energy branches.
Input datasets
Predeclare:
supernova catalogue and quality exclusions;
BAO dataset;
CMB likelihood;
peculiar-velocity correction;
host-age model;
sky mask;
covariance matrices;
and calibration version.
Model A
A universal expansion-dominant sector with isotropic background behavior.
Model B
No independent expansion-dominant sector; acceleration-like inference arises from source, frame, geometry, or relational terms.
Model C
A universal sector plus prospectively defined relational corrections.
Primary outcomes
Compare:
out-of-sample predictive likelihood;
information criteria;
posterior predictive checks;
directional residuals;
redshift residuals;
cross-probe consistency;
and parameter stability under justified data partitions.
Required failure rule
TSTOEAO cannot claim support merely because the most relational model fits best.
A model with more flexibility will often fit better.
The relational model must:
improve out-of-sample prediction;
use prospectively justified variables;
avoid unconstrained nuisance absorption;
and produce at least one correct prediction not used in model construction.
31
Falsification and Failure Conditions
The framework would be weakened if any of the following occurs.
31.1 Expression variables remain purely verbal
If localization, coupling, structure, pressure, history, and observer frame cannot be operationalized, the multiaxial model remains philosophy.
31.2 The scalar split adds no predictive value
If:
\[
E_T=E_x+E_u
\]
cannot be connected to measurable quantities or discriminating predictions, it remains bookkeeping rather than physics.
31.3 Unexpressed energy has no positive definition
If \(E_u\) is defined only as whatever has not yet been explained, it becomes an unfalsifiable remainder category.
31.4 Expansion freedom does not reproduce expansion dynamics
If \(F\) cannot generate or map onto a measurable \(H(z)\), \(q(z)\), or equivalent geometric relation, it does not explain cosmic expansion.
31.5 Binding burden reduces to ordinary density relabeling
If \(B\) contributes nothing beyond established mass-energy, pressure, and curvature relations, it should not be presented as a new physical variable.
31.6 Relational variables are added after every failed prediction
A variable introduced only after the outcome creates a revised model. It cannot retroactively confirm the original.
31.7 The framework cannot distinguish its branches
If substantive, relational, and mixed dark-energy branches make no differing predictions, the branch structure is scientifically empty.
31.8 The coupling matrix becomes unlimited
If every sector is allowed arbitrary coupling to every other sector without constraints, the model becomes infinitely adjustable.
31.9 Conservation is violated without an explicit mechanism
Any claimed exchange between sectors must respect an appropriate conservation relation or state clearly which established assumption is being modified.
31.10 Observational success merely reproduces ΛCDM
If the final model generates no distinct prediction and only renames \(\Lambda\), cold dark matter, and ordinary systematics, it is an interpretation rather than a new physical theory.
31.11 Observer dependence is used to dismiss all evidence
Observer-frame effects must produce calculable directional, scale-dependent, or redshift-dependent signatures. They cannot be invoked generally whenever data conflict with the theory.
32
Relation to Existing Cosmological Frameworks
The present architecture overlaps conceptually with several established areas.
General relativity
It accepts that geometry and stress-energy are relationally connected.
Interacting dark-sector models
It permits exchange and coupling between sectors.
Dynamical dark energy
It permits time-dependent expansion-dominant behavior.
Modified gravity
It leaves open the possibility that apparent missing sectors reflect incomplete gravitational dynamics.
Inhomogeneous cosmology
It recognizes that averaging, local environment, and large-scale structure may affect inference.
Observational cosmology
It treats source evolution, calibration, and frame as part of the measured relation.
Effective field theory
It allows observable behavior to be described without prematurely claiming a complete microscopic ontology.
The proposed distinction is not that existing physics ignores these subjects.
It is that TSTOEAO attempts to place them under one common architectural grammar:
\[
\text{energetic condition}
\rightarrow
\text{relational architecture}
\rightarrow
\text{realized observation}.
\]
The value of that grammar will depend upon whether it eventually produces tighter—not looser—experimental discrimination.
33
Interpretive Limits
This paper does not establish that:
dark energy is imaginary;
dark energy is a substance;
dark matter interacts with neutrinos;
dark matter is modified gravity;
observer motion explains every acceleration measurement;
supernova age bias removes all evidence for acceleration;
the FLRW framework is invalid;
Level 000 is a known physical field;
unexpressed energy is vacuum energy;
the universe possesses one globally conserved scalar energy;
or \(V=E\times Y\) is already a completed cosmological field equation.
It also does not treat every unknown relationship as evidence for TSTOEAO.
The recent dark-energy and dark-matter studies are relevant because they illustrate the scientific importance of:
source history;
observer frame;
anisotropy;
coupling;
and scale-dependent interaction.
They do not validate the theory.
Their value is that they reveal where a cosmological model may fail if it treats unknown sectors as isolated substances with fixed relationships.
34
Refined Working Definitions
Expressed Energy
Energy committed to a definite, causally consequential physical state, relation, pathway, interaction, phase, structure, or measurable dynamical role.
Unexpressed Energy
A proposed substrate or potential condition not equivalently committed to the localized, structurally persistent, or interaction-specific organizations identified with established expressed states. It requires positive physical definition before it can function as a scientific variable.
Expression State
The multiaxial condition of energy described by localization, structural commitment, coupling, pressure, phase, persistence, scale, history, and observational relation.
Hidden Structural Expression
Physical organization inferred through gravitational, dynamical, or structural effects but not directly identified through ordinary luminous matter.
Binding Burden
The relational and energetic constraint associated with maintaining localized, inertial, curved, coupled, or structurally persistent physical organization.
Expansion Freedom
The degree to which a component, geometry, or region permits or produces increasing relational separation rather than local structural consolidation.
Hidden Relation
A coupling, geometric condition, historical dependence, observer-frame effect, or inference relation not adequately represented in the model producing an observed residual.
Observational Residual
The portion of an inferred phenomenon remaining after the selected physical, source, geometric, instrumental, and observer relations have been modeled.
Cosmic Relational Architecture
The complete organization of energetic sectors, couplings, phases, boundaries, geometry, histories, scales, observers, and inference procedures through which cosmological observations are realized.
35
Plain-Language Statement
The universe may not be divided cleanly into visible matter, invisible matter, and a mysterious outward substance.
Energy can be expressed in many ways.
It can become matter.
It can move as radiation.
It can form fields.
It can generate pressure.
It can remain hidden from light while shaping structure.
It can interact weakly with another sector.
It can influence geometry.
Its observable meaning can depend upon its history, its scale, its surroundings, and the observer measuring it.
Dark matter may be energy expressed through hidden structure.
Dark energy may be a real expansion-dominant condition.
It may instead be a hidden relationship inside the way cosmic observations are produced and interpreted.
It may be both.
The task is not to choose the most appealing story.
The task is to define each possibility clearly enough that the universe can reject it.
36
Conclusion
The earlier TSTOEAO distinction between expressed and unexpressed energy established a useful conceptual foundation.
It recognized that energy committed to form acquires structure and constraint, while potential not equivalently committed to matter-form may retain different relational possibilities. It introduced:
\[
E_T=E_x+E_u,
\]
\[
\chi+\upsilon=1,
\]
\[
B\propto\chi,
\]
and:
\[
F\propto\upsilon.
\]
Those equations remain valuable as first-order bookkeeping.
They are not sufficient as a cosmological model.
Physical expression is not exhausted by ordinary matter. Radiation, pressure, fields, hidden structure, interaction, geometry, and propagation are also forms of causally consequential expression.
Expression must therefore be represented through multiple axes:
\[
\boldsymbol{\xi}
=
\left(
\ell,
s,
c,
\pi,
\varphi,
\tau,
r,
h,
o
\right).
\]
The earlier scalar expressed fraction becomes a projection from a richer state:
\[
\chi
=
\mathcal{P}_x
\left(
\boldsymbol{\xi};
\mathbf{W},
\mathcal{D}
\right).
\]
The cosmological realization is governed not only by how much energy exists, but by how it is organized:
\[
V_{\text{cosmic}}
=
E_{\text{cosmic}}
\times
Y_{\text{cosmic}}.
\]
Dark matter should not be classified simply as unexpressed energy. If it exists as a physical sector, it is more naturally interpreted as hidden structural expression whose realized effects may depend upon gravitational and nongravitational coupling.
Dark energy requires several preserved branches.
It may be:
a real expansion-dominant physical sector;
a hidden geometric or observational relation;
a residual produced by incomplete source or observer modeling;
or a mixed architecture containing more than one of these.
Cosmic expansion, accelerated expansion, and dark energy must remain distinct concepts.
Observer frame does not create arbitrary reality, but it participates in measurement.
Source history does not invalidate cosmology, but it participates in standardization.
Coupling does not eliminate energetic content, but it changes what that content expresses.
The central developed proposition is:
> Cosmic phenomena presently classified as dark matter or dark energy may not map one-to-one onto isolated hidden substances. Their observed behavior may arise from energetic content expressed through multidimensional relational architectures involving localization, pressure, coupling, phase, scale, source history, geometry, and observer frame.
The most concise resulting distinction is:
> Dark matter may be hidden structural expression. Dark energy may be hidden relation, expansion-dominant expression, observational residual, or a mixture of these.
This is not yet a solution to the dark sector.
It is a more disciplined statement of the problem.
TSTOEAO will advance scientifically only if these categories become operational, constrained, and prospectively discriminating. The architecture must produce measurable differences among its branches. It must preserve covariant accounting. It must prevent post-hoc variable addition. It must identify outcomes that would show that expression state, coupling, source history, or observer frame were incorrectly assigned.
The theory’s purpose is not to make the universe more complicated than necessary.
Its purpose is to avoid simplifying the universe by deleting relationships that determine what becomes observable.
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