Addendum 57 — Directional Asymmetry Occurs Before the Friedmann Branch
Source–Area Compatibility, Physical Rate, and the Missing Sign of Cosmological Evolution
Abstract
Addendum 56 established a conditional bridge between the R²D cosmological structural state and the conventional scale factor.
A cosmological structural transition,
\[i_\zeta^\ast \to k_\zeta^\ast\]
can acquire a gravitational boundary-area read,
\[A_{\zeta,i} \to A_{\zeta,k}\]
provided physical area factors through the cosmological macrostate classification.
Under an isotropic FLRW projection,
\[\frac{a_k}{a_i}=\sqrt{\frac{A_{\zeta,k}}{A_{\zeta,i}}}\]
Once a physical clock coordinate is independently supplied,
\[H=\frac{\dot a}{a}=\frac12\frac{d\ln A_\zeta}{dt}\]
The next question is therefore not what the scale factor means.
It is:
What constrains the physical rate of the projected cosmological geometry, and what / determines its direction?
Conventional cosmology answers the first question through the Friedmann equations.
For physical energy density
\[\epsilon\]
the first Friedmann equation is
\[H^2=\frac{8\pi G}{3c^2}\epsilon-\frac{kc^2}{a^2}+\frac{\Lambda c^2}{3}\]
Using the area read,
\[H=\frac12\frac{d\ln A_\zeta}{dt}\]
this becomes
\[\frac14\left(\frac{d\ln A_\zeta}{dt}\right)^2=\frac{8\pi G}{3c^2}\epsilon_\zeta-\frac{kc^2}{a^2}+\frac{\Lambda c^2}{3}\]
This equation relates a physical source read to the magnitude of a physical geometric rate.
But it does not determine the sign of that rate.
For positive right-hand side,
\[H=\pm\sqrt{\frac{8\pi G}{3c^2}\epsilon-\frac{kc^2}{a^2}+\frac{\Lambda c^2}{3}}\]
Thus the same instantaneous source–geometry values are compatible, at the level of the Friedmann constraint, with two oppositely oriented branches:
\[H>0\]
and
\[H < 0\]
The first Friedmann equation therefore does not by itself answer the primitive R²D question:
Which way is the cosmological state being realized?
R²D places that question earlier.
At a nonterminal cosmological boundary,
\[A_{\zeta,i\to k} = P_{\zeta,i\to k} - R_{\zeta,i\to k}\]
This is the directional count asymmetry that biases realization of the cosmological multiplicity landscape.
It is not identified with
\[H\]
\[H^2\]
\[\epsilon\]
\[p\]
\[\Lambda\]
or any other mature cosmological coordinate.
Instead, the proposed causal ordering is
\[A_\zeta\]
↓
biased structural realization
\[i_\zeta^\ast \to k_\zeta^\ast\]
↓
geometric projection
\[A_{\zeta,i} \to A_{\zeta,k}\]
↓
physical clock read
\[H=\frac12\frac{d\ln A_\zeta}{dt}\]
The source variables appearing in Friedmann cosmology constitute another physical read of the same cosmological organization.
They too must satisfy the macrostate factorization condition introduced in Addendum 56.
If energy density is to represent a cosmological macrostate coordinate, there must exist
\[\bar\epsilon_\zeta:\mathcal M_\zeta\to\mathbb R\]
such that
\[\epsilon\circ\Pi_G=\bar\epsilon_\zeta\circ\pi_\zeta\]
Likewise, a macrostate pressure read requires
\[p\circ\Pi_G=\bar p_\zeta\circ\pi_\zeta\]
The Friedmann equations can then be interpreted as compatibility relations among multiple physical reads of one prior cosmological state:
source read ⟷ geometric read.
They do not establish the primitive causal direction between those reads.
Define the physical Friedmann branch variable
\[\sigma_\zeta=\operatorname{sgn}H.\]
away from a turning point.
Define
\[F_\zeta=\frac{8\pi G}{3c^2}\epsilon_\zeta-\frac{kc^2}{a^2}+\frac{\Lambda c^2}{3}\]
Then
\[H=\sigma_\zeta\sqrt{F_\zeta}.\]
This separates two different pieces of physical information:
Fζ = allowed squared-rate compatibility,
whereas
σζ = orientation of the realized physical branch.
R²D proposes that the primitive origin of this directional information lies upstream in the enclosing asymmetry.
But the theory must not simply assert
\[\sigma_\zeta=\operatorname{sgn}A_\zeta\]
The physical projection can preserve or reverse orientation.
Let
\[s_A\]
denote the orientation of the macrostate-to-area map for a transition,
\[s_A=\operatorname{sgn}\left(\frac{\Delta A_\zeta}{\lambda_{\zeta,i\to k}}\right)\]
Then, if structural response follows the sustained sign of the R²D asymmetry, the area projection is monotonic, and the physical clock preserves the realized transition ordering, the candidate branch relation is
\[\sigma_\zeta\sim s_A\,\operatorname{sgn}A_\zeta\]
This is a conditional bridge to be derived, not an established identity.
The important result is more primitive:
the Friedmann constraint loses the directional sign that R²D assigns to the prior realization process
The acceleration and continuity equations provide additional physical evolution constraints.
The acceleration equation is
\[\frac{\ddot a}{a}=-\frac{4\pi G}{3c^2}(\epsilon+3p)+\frac{\Lambda c^2}{3}\]
The source continuity relation is
\[\dot\epsilon+3H(\epsilon+p)=0.\]
Using the area rate,
\[H=\frac12\frac{d\ln A_\zeta}{dt}\]
the continuity relation becomes
\[\dot\epsilon+\frac32(\epsilon+p)\frac{d\ln A_\zeta}{dt}=0\]
These equations describe the coupled evolution of projected physical source and geometric reads.
They still do not justify identifying
\[\epsilon\]
with Pζ ,
\[p\]
with Rζ ,
or
\[\Lambda\]
with Aζ .
The R²D turbine remains upstream.
The central statement is therefore:
the Friedmann equation does not determine cosmological direction. It constrains a physical geometr
And hence:
directional asymmetry occurs before the Friedmann branch.
1. Friedmann Dynamics Enter Only After Physical Projection
The primitive cosmological sequence is already defined before the Friedmann equations appear:
\[{B_{\zeta-1,\alpha} } \to \Omega_\zeta \to \mathcal M_\zeta \to i_\zeta^\ast \to k_\zeta^\ast\]
The Friedmann equations belong to the later gravitational physical description.
2. The Geometric Read Has Already Been Defined
When area satisfies the macrostate factorization condition,
\[A\circ\Pi_G=\bar A_\zeta\circ\pi_\zeta\]
the cosmological state possesses the area coordinate
\[A_{\zeta,i}\]
Under isotropic projection,
\[a\propto\sqrt{A_\zeta}\]
3. A Physical Clock Produces the Rate Read
Once physical time t is independently calibrated,
\[H=\frac{\dot a}{a}=\frac12\frac{d\ln A_\zeta}{dt}\]
The Hubble parameter is therefore downstream of both the state projection and the clock projection.
4. A Source Variable Must Pass the Same Projection Test
Physical energy density cannot simply be inserted into the primitive count architecture.
If it represents the cosmological macrostate, it must factor through the same classification.
Thus require
\[\epsilon\circ\Pi_G=\bar\epsilon_\zeta\circ\pi_\zeta\]
5. Energy Density Must Be Constant Across the Macrostate Fiber
If
\[\pi_\zeta(\mu_\alpha)=\pi_\zeta(\mu_\beta)=i\]
then a genuine macrostate energy-density read requires
\[\epsilon[\Pi_G(\mu_\alpha)]=\epsilon[\Pi_G(\mu_\beta)]\]
Only then is
\[\epsilon_{\zeta,i}\]
well defined.
6. Pressure Requires the Same Condition
Likewise, if pressure is a boundary-level physical coordinate,
\[p\circ\Pi_G=\bar p_\zeta\circ\pi_\zeta\]
Then
\[p_{\zeta,i}\]
is a well-defined source read of cosmological macrostate i.
7. Source and Geometry Can Therefore Be Parallel Reads
One cosmological state
\[i\]
may acquire both
\[A_{\zeta,i}\]
and
\[\epsilon_{\zeta,i},\quad p_{\zeta,i}\]
These are different physical coordinates of one prior R²D classification.
8. Neither Read Is Automatically Primitive Cause of the Other
The existence of a relation
\[\epsilon\longleftrightarrow A\]
does not by itself establish
\[\epsilon\to A\]
as the primitive causal ordering.
Both may descend from one enclosing count relation.
9. Introduce the First Friedmann Constraint
For an FLRW projection,
\[H^2=\frac{8\pi G}{3c^2}\epsilon-\frac{kc^2}{a^2}+\frac{\Lambda c^2}{3}\]
This is an imported mature physical relation.
10. Rewrite the Constraint in Boundary-Area Coordinates
Using
\[H=\frac12\frac{d\ln A_\zeta}{dt}\]
we obtain
\[\frac14\left(\frac{d\ln A_\zeta}{dt}\right)^2=\frac{8\pi G}{3c^2}\epsilon_\zeta-\frac{kc^2}{a^2}+\frac{\Lambda c^2}{3}\]
11. Friedmann Is Now a Source–Area Compatibility Equation
The equation relates:
source-property reads
to
geometric-rate reads.
Its physical role can therefore be written schematically as
\[{\epsilon, p, \ldots} \longleftrightarrow {A, a, H, \ldots}\]
12. This Is Not Yet the Primitive R²D Turbine
The R²D turbine is
\[A_\zeta=P_\zeta-R_\zeta.\]
The Friedmann equation contains none of these quantities explicitly.
Therefore it should not be treated as the primitive R²D causal equation.
13. The First Friedmann Equation Is Direction Blind
Because it contains
\[H^2\]
the constraint determines only the square of the physical rate.
If
\[H\]
is a solution of the instantaneous constraint, then
\[-H\]
has the same square.
14. Define the Friedmann Rate Function
Let
\[F_\zeta=\frac{8\pi G}{3c^2}\epsilon_\zeta-\frac{kc^2}{a^2}+\frac{\Lambda c^2}{3}\]
Then the constraint is
\[H^2 = F_\zeta\]
15. Positive Fζ Permits Two Instantaneous Branches
Where
\[F_\zeta > 0\]
the constraint gives
\[H=+\sqrt{F_\zeta}\]
Thus two oppositely oriented physical-rate branches satisfy the same squared-rate constraint.
16. Expansion and Contraction Are Different Branches
The branch
\[H>0\]
corresponds to increasing isotropic spatial scale.
The branch
\[H<0\]
corresponds to decreasing isotropic spatial scale.
The first Friedmann constraint alone does not select between them.
17. Define the Physical Branch Orientation
Away from
\[H = 0\]
define
\[\sigma_\zeta=\operatorname{sgn}H.\]
Then
\[H=\sigma_\zeta\sqrt{F_\zeta}.\]
18. Magnitude and Direction Are Now Explicitly Separated
The quantity
\[F_\zeta\]
controls the allowed squared rate.
The quantity
\[\sigma_\zeta\]
specifies the physical orientation of the realized branch.
Thus:
H = direction × allowed magnitude.
19. This Separation Mirrors the R²D Problem
R²D already distinguishes:
available realization structure
from
directional bias of realization.
The Friedmann branch structure exposes an analogous separation in the mature physical projection.
20. The Source Terms Do Not Alone Supply the Branch Sign
The values
\[\epsilon, a, k, \Lambda\]
determine
\[F_\zeta\]
They do not, through the first Friedmann constraint alone, determine
\[\sigma_\zeta\]
21. This Is the Missing Directional Datum
The conventional constraint therefore requires additional branch information:
\[\sigma_\zeta\]
This information is not contained in H 2 .
22. R²D Already Possesses a Primitive Directional Quantity
For a nonterminal cosmological transition,
\[A_{\zeta,i\to k} = P_{\zeta,i\to k} - R_{\zeta,i\to k}\]
This quantity biases realization before the gravitational rate is defined.
23. But Aζ Is Not H
Dimensional and causal considerations immediately give
\[A_\zeta \ne H\]
One is a primitive dimensionless count asymmetry.
The other is a physical inverse-time rate.
24. Nor Is Aζ = H 2
Likewise,
\[A_\zeta \ne H^2\]
The squared rate has already discarded orientation.
The primitive R²D asymmetry is directional.
25. R²D Direction Acts Before Physical Rate
The proposed order is
\[A_\zeta\]
↓
biased structural transition
↓
area change
↓
physical-time rate H.
26. The Area Projection Can Preserve or Reverse Orientation
A positive R²D transition coordinate
\[\lambda_{\zeta,i\to k} > 0\]
does not automatically imply
\[A_{\zeta,k} > A_{\zeta,i}\]
The physical map must be checked.
27. Define the Area-Projection Orientation
For a monotonic transition define
\[s_A=\operatorname{sgn}\left(\frac{A_{\zeta,k}-A_{\zeta,i}}{\lambda_{\zeta,i\to k}}\right)\]
Then
\[s_A = +1\]
means the physical area projection preserves the count orientation.
28. An Orientation-Reversing Projection Is Also Possible
If
\[s_A = -1\]
then a positive count distinction projects as decreasing physical area.
R²D must therefore not identify count direction and spatial direction without this bridge.
29. The Physical Clock Must Also Preserve an Ordering
The rate
\[H\]
requires a physical time orientation.
Thus a complete sign bridge also requires the clock coordinate to preserve the ordering of the structural transition.
30. A Conditional Branch Relation Can Then Be Proposed
If:
- the sign of sustained Aζ determines the realized structural branch; 2. the area projection is monotonic; 3. the physical clock preserves transition ordering;
then one expects schematically
\[\sigma_\zeta\sim s_A\,\operatorname{sgn}A_\zeta\]
This is a bridge hypothesis.
It is not yet a theorem.
31. This Is Stronger Than Writing Aζ = H
The relation separates:
• primitive direction; • structural realization; • physical projection orientation; • physical rate.
It therefore preserves the causal layers instead of collapsing them.
32. Terminal Orientation Remains Distinct
If the cosmological boundary is terminal,
\[B_\zeta = B_\star\]
then ordinary
ordinary \(A_\zeta=P_\zeta-R_\zeta\) is replaced at the terminal level by the unresolved orientation
\[\Xi_\star\]
Thus the ultimate branch orientation would have to descend from terminal nonclosure rather than another enclosing P − R relation.
33. The Friedmann Branch Does Not Identify the Terminal Boundary
An expanding universe,
\[H > 0\]
does not prove
\[B_\zeta = B_\star\]
A subordinate cosmological boundary can possess an expanding physical branch while remaining inside a larger open relation.
34. Friedmann Direction Is Therefore Boundary Relative
The sign
\[\sigma_\zeta\]
belongs to the projected cosmological boundary under consideration.
It is not automatically the absolute direction of the complete recursive hierarchy.
35. A Turning Point Has H = 0
At a physical turning point,
\[H = 0\]
Therefore,
\[F_\zeta = 0\]
The projected area rate vanishes.
36. A Turning Point Is Not Automatically R²D Stall
Primitive R²D stall is
\[A_\zeta=P_\zeta-R_\zeta=0\]
No derivation yet establishes
\[A_\zeta=0\iff H=0\]
These conditions belong to different layers.
37. R²D Stall Means No Net Primitive Directional Preference
If
\[A_\zeta = 0\]
the relevant alternatives possess no net local directional asymmetry after retention.
This does not yet determine the fate of an already realized physical rate.
38. Physical Momentum or Recurrence May Matter to the Rate Bridge
A projected system may possess a nonzero physical rate even when the instantaneous primitive bias changes.
Therefore the relation between
\[A_\zeta\]
and
\[H\]
must be dynamical, not merely algebraic.
39. The Acceleration Equation Constrains Rate Evolution
Conventional FLRW cosmology supplies
\[\frac{\ddot a}{a}=-\frac{4\pi G}{3c^2}(\epsilon+3p)+\frac{\Lambda c^2}{3}\]
This equation describes how the physical geometric rate changes.
40. The Acceleration Equation Is Still Downstream
The quantities
\[\epsilon, p, \Lambda, a\]
are already projected physical coordinates.
Therefore the acceleration equation does not directly define
\[\dot A_\zeta\]
41. Do Not Identify Negative Pressure With Possibility
It may be tempting to write
\[P_\zeta \sim -p\]
Nothing established here justifies that mapping.
Thus:
\[P_\zeta \ne -p\]
by definition.
42. Do Not Identify Matter With Retention
Likewise,
\[R_\zeta \ne \epsilon_m\]
unless a bridge is independently derived.
Matter and retention occupy different descriptive layers.
43. Do Not Identify Λ With Residual Asymmetry
The cosmological constant contributes to the projected physical acceleration.
But:
\[\Lambda\ne A_\zeta\]
and
\[\Lambda\ne \Xi_\star\]
without a separate mapping.
44. Rewrite Acceleration in Area Coordinates
Since
[Archival source layout requires author review] 1/2 / a ∝ Aζ ,
we have
\[H=\frac12\frac{d\ln A_\zeta}{dt}\]
Therefore,
\[\frac{\ddot a}{a}=\frac12\frac{d^2\ln A_\zeta}{dt^2}+\frac14\left(\frac{d\ln A_\zeta}{dt}\right)^2\]
45. The Acceleration Equation Becomes an Area-Evolution Constraint
Thus,
\[\frac12\frac{d^2\ln A_\zeta}{dt^2}+\frac14\left(\frac{d\ln A_\zeta}{dt}\right)^2=-\frac{4\pi G}{3c^2}(\epsilon+3p)+\frac{\Lambda c^2}{3}\]
Again, this is a mature physical compatibility relation.
46. Introduce Source Continuity
For a conventional homogeneous FLRW source,
\[\dot\epsilon+3H(\epsilon+p)=0.\]
This constrains how the source read changes with the geometric expansion rate.
47. Rewrite Continuity Using Boundary Area
Substituting
\[H=\frac12\frac{d\ln A_\zeta}{dt}\]
gives
\[\dot\epsilon+\frac32(\epsilon+p)\frac{d\ln A_\zeta}{dt}=0\]
48. Source Evolution and Area Evolution Are Explicitly Coupled
The equation now relates:
change in source-property read
to
change in boundary-area read.
This is exactly the physical architecture required by Addenda 55–56.
49. The Continuity Equation Does Not Establish Primitive Bottom- Up Causality
One may read the equation as expansion changing density.
One may also rearrange it as density evolution constraining expansion.
The equation itself expresses mutual physical compatibility.
R²D locates primitive causal organization earlier.
50. Friedmann Cosmology Is Therefore a Coupled Projection System
The mature physical projection consists of at least:
constraint equation,
acceleration equation,
and
source continuity.
Together they describe compatible evolution of source and geometry reads.
51. The R²D Turbine Sits Above This System
The primitive ordering remains
\[P_\zeta - R_\zeta\]
↓
biased peer organization
↓
physical source and geometry projections
↓
Friedmann-compatible evolution.
52. This Is the Correct Causal Inversion
The conventional narrative is often summarized as
\[\rho, p, \Lambda \to a(t)\]
R²D instead proposes
enclosing count asymmetry → peer realization,
after which both source and geometry are physically projected.
53. Principle — Cosmological Source-Read Factorization
A physical source variable X can represent a cosmological R²D macrostate only if
\[X\circ\Pi_G=\bar X_\zeta\circ\pi_\zeta\]
Energy density and pressure must satisfy this criterion before being treated as macrostate coordinates.
54. Principle — Friedmann Source–Area Compatibility
When source and area both factor through the cosmological macrostate classification, the Friedmann equations relate two physical reads of the same prior R²D cosmological organization.
Thus:
Friedmann dynamics = physical source–geometry compatibility.
55. Principle — Friedmann Magnitude Does Not Supply Direction
The first Friedmann constraint is
\[H^2 = F_\zeta\]
Therefore it fixes the allowed squared physical rate but not its sign.
The branch variable
\[\sigma_\zeta=\operatorname{sgn}H.\]
is additional directional information.
56. Principle — Directional Asymmetry Precedes Branch Orientation
R²D assigns directional organization before the physical rate is defined:
Aζ → structural branch → σζ .
No direct numerical identity between Aζ and σζ is asserted.
57. Principle — Physical Branch Orientation Requires a Projection Bridge
The sign of the physical rate depends on:
• the sign of the realized structural transition;
- the orientation of the macrostate-to-area projection;
- the orientation of the physical clock coordinate.
Therefore the bridge from R²D direction to Friedmann branch must be explicitly derived.
58. Logical Status
Canonical R²D
For a nonterminal transition,
\(A_\zeta=P_\zeta-R_\zeta\) is the prior directional count asymmetry.
Addendum 54
The cosmological structural transition is a reorganization of compatible peer-boundary realization.
Addendum 55
The peer relation can acquire source and gravitational geometry reads.
Addendum 56
Boundary area can provide a physical macrostate read when it factors through the cosmological classification.
Under isotropic projection,
\[a\propto\sqrt{A_\zeta}\]
New Source Factorization Requirement
Energy density and pressure are valid cosmological macrostate coordinates only when they factor through the same R²D classification.
Imported Friedmann Constraint
\[H^2=\frac{8\pi G}{3c^2}\epsilon-\frac{kc^2}{a^2}+\frac{\Lambda c^2}{3}\]
Derived Area Form
\[\frac14\left(\frac{d\ln A_\zeta}{dt}\right)^2=\frac{8\pi G}{3c^2}\epsilon_\zeta-\frac{kc^2}{a^2}+\frac{\Lambda c^2}{3}\]
New Branch Observation
The first Friedmann constraint permits
\[H=+\sqrt{F_\zeta}\]
It therefore does not by itself specify physical branch orientation.
Candidate R²D Interpretation
Primitive directional asymmetry acts upstream of the physical branch selection.
Not Established Here
This addendum does not establish:
- \(\sigma_\zeta=\operatorname{sgn}A_\zeta\);
- \(A_\zeta=H\);
- \(A_\zeta=H^2\);
- \(P_\zeta=\epsilon\);
- \(R_\zeta=\epsilon_m\);
- \(P_\zeta=-p\);
- \(\Lambda=A_\zeta\);
- \(\Lambda=\Xi_\star\);
- that \(A_\zeta=0\) implies \(H=0\);
- a physical clock derivation;
- a derivation of Friedmann dynamics from primitive R²D;
- or the physical identities of \(P_\zeta\), \(R_\zeta\), and \(\Xi_\star\).
59. The Full Causal Sequence
The terminal or enclosing relation supplies primitive direction:
\[\Xi_\star\quad\text{or}\quad A_\zeta=P_\zeta-R_\zeta\]
That direction biases realization of the peer-boundary state landscape:
\[i_\zeta^\ast \to k_\zeta^\ast\]
The gravitational projection gives an area read:
\[A_{\zeta,i} \to A_{\zeta,k}\]
Under isotropy,
\[\frac{a_k}{a_i}=\sqrt{\frac{A_{\zeta,k}}{A_{\zeta,i}}}\]
A physical clock supplies
\[H=\frac12\frac{d\ln A_\zeta}{dt}\]
The same cosmological state acquires physical source reads:
\[\epsilon_\zeta,\quad p_\zeta\]
The mature projected variables satisfy
\[H^2=\frac{8\pi G}{3c^2}\epsilon-\frac{kc^2}{a^2}+\frac{\Lambda c^2}{3}\]
The equation determines
[Archival source layout requires author review] ∣H∣,
while branch orientation is represented separately by
\[\sigma_\zeta\]
Thus:
\[H=\sigma_\zeta\sqrt{F_\zeta}.\]
The complete ordering is therefore
directional count asymmetry
↓
structural peer realization
↓
area orientation
↓
physical branch sign
together with
source–geometry compatibility
↓
[Archival source layout requires author review] ∣H∣.
The physical rate combines them:
H = branch orientation × compatible rate magnitude.
60. Conclusion
The Friedmann equations enter R²D cosmology only after the cosmological state has already acquired physical source and geometric coordinates.
A cosmological macrostate may possess an area read
\[A_{\zeta,i}\]
an energy-density read
\[\epsilon_{\zeta,i}\]
and a pressure read
\[p_{\zeta,i}\]
provided each physical observable factors through the same R²D macrostate classification.
The Friedmann equations then constrain how those physical reads can coexist and evolve.
The first Friedmann equation becomes
\[\frac14\left(\frac{d\ln A_\zeta}{dt}\right)^2=\frac{8\pi G}{3c^2}\epsilon_\zeta-\frac{kc^2}{a^2}+\frac{\Lambda c^2}{3}\]
But the square removes directional information.
The same squared-rate relation permits
\[H=+\sqrt{F_\zeta}\]
or
\[H=-\sqrt{F_\zeta}\]
Thus the conventional constraint does not, by itself, determine whether the cosmological boundary area is increasing or decreasing.
That directional question belongs earlier.
For a nonterminal R²D cosmological boundary,
\(A_\zeta=P_\zeta-R_\zeta\) is the prior directional count asymmetry.
Its first consequence is biased realization of the cosmological peer-boundary landscape.
That structural realization then acquires a physical area orientation and, after clock calibration, a Friedmann branch orientation.
R²D therefore does not identify thermodynamic asymmetry with Hubble expansion.
It separates their causal roles.
The source–geometry variables determine which physical rates are compatible.
The primitive asymmetry determines which structural realization is favored.
The projection bridge determines how that structural direction appears physically.
Only after all three are supplied does the observed rate
\[H\]
become fully specified.
The central statement is therefore:
the Friedmann equation does not determine cosmological direction. It constrains the magnitude of a
Within R²D, that upstream direction originates in
\(A_\zeta=P_\zeta-R_\zeta\) is the prior directional count asymmetry. reaches
\[B_\star\]
And hence:
directional asymmetry occurs before the Friedmann branch.