Addendum 6 — Closure-Complete Subordinate Dynamics Occur Before Biological Function
Recursive Replacement Across Biological Timescales
Abstract
Addendum 5 established recursive replacement directly at the myosin-switch ensemble.
Individual myosin switches possess distinguishable states and trajectories at their own boundaries. Yet when the enclosing ensemble state is defined, those individual identities and trajectories are no longer state coordinates of the ensemble. Distinct subordinate realizations that produce the same ensemble occupancy become one enclosing state, and their number becomes multiplicity.
The same argument does not stop at the myosin switch.
The switch itself is an enclosing state relative to faster protein dynamics. Those protein dynamics are themselves realized through still faster molecular recurrence. Molecular recurrence is realized through still faster vibrational and electronic recurrence.
Biological systems therefore expose a hierarchy:
fast subordinate recurrence → closure → recursive replacement → new enclosing state.
At every boundary, the subordinate trajectory is physically defined at its native scale.
After closure, however, that trajectory does not persist as a state coordinate of the enclosing boundary.
Thus:
\[\Gamma_n\longrightarrow\mathcal C_n\overset{\kappa_n}{\longmapsto}B_{n+1},\]
but not
\[\Gamma_n\longrightarrow\Gamma_{n+1}.\]
The completed subordinate recurrence contributes to the realization of the enclosing state. Its internal path identity is replaced.
This distinction is stronger than temporal averaging.
Conventional multiscale descriptions often assume that a slow biological variable is the average of faster trajectories that remain physically primitive beneath it.
R²D instead proposes that each enclosing biological function possesses its own state domain. Faster subordinate trajectories realize that state only after their own recurrence is complete relative to the enclosing classification.
A microsecond protein fluctuation is therefore not a millisecond switch trajectory viewed at finer temporal resolution.
A millisecond molecular switch is not a muscle-scale trajectory viewed at finer resolution.
An infrared recurrence is not a hidden microsecond protein trajectory.
Each belongs to a different boundary.
Biological function is recursively realized through them, but it is not identical to them.
This leads to a new boundary-relative definition.
A subordinate boundary is closure-complete relative to an enclosing boundary when its native recurrence has completed such that the enclosing state can be specified without retaining the subordinate path as an independent state coordinate.
Closure-complete does not necessarily mean conventional thermodynamic detailed-balance equilibrium.
Subordinate dynamics may continue indefinitely.
They may carry flux.
They may consume free energy.
They may repeatedly cycle.
What has closed is their path identity relative to the enclosing state classification.
This distinction is directly visible in active isometric muscle.
At stall,
\[A_M=0\]
and
\[P_M=R_M,\]
while myosin switching and deeper molecular dynamics remain physically active.
A stable enclosing state therefore does not require subordinate inactivity.
It requires subordinate recurrence to be closure-complete relative to the enclosing read.
The central statement is:
Biological function is not the slow trajectory obtained by averaging faster trajectories.
Hence:
Closure-complete subordinate dynamics occur before biological function.
1. Addendum 5 Established Replacement at One Boundary
Addendum 5 considered an ensemble of myosin switches.
Each switch can occupy
\[M_1\]
or
\[M_2.\]
For N switches, a labeled subordinate realization is
\[\mathbf x=(x_1,x_2,\ldots,x_N).\]
The enclosing ensemble does not retain this labeled vector as its own state.
Instead, it distinguishes the occupancy
\(i=\#\{\alpha:x_\alpha=M_2\}\).
The replacement map is
\[\pi_N:\{M_1,M_2\}^{N}\longrightarrow\{0,1,\ldots,N\}.\]
The number of subordinate realizations compatible with state i is
\[W_N(i)=\left|\pi_N^{-1}(i)\right|=\binom{N}{i}.\]
Individual switch identity has therefore been replaced by ensemble multiplicity.
Addendum 6 asks whether this replacement is unique to the switch-to-ensemble boundary.
It is not.
2. The Myosin Switch Is Itself an Enclosing Boundary
The myosin states
\[M_1\]
and
\[M_2\]
are not primitive objects.
Each is physically realized through faster molecular and protein dynamics.
A myosin molecule contains internal structural recurrence occurring on timescales faster than the switch transition itself.
Thus:
faster protein dynamics → myosin-switch realization.
But the logic of Addendum 5 now applies again.
If multiple faster subordinate realizations are compatible with the same switch state, those realizations do not remain independent state coordinates of the switch boundary.
They have been recursively replaced.
3. Recursive Replacement Repeats
Let \(B_n\) denote a subordinate boundary and \(B_{n+1}\) its enclosing boundary.
A native trajectory at \(B_n\) can be represented as
\[\Gamma_n:i_n\longrightarrow j_n\longrightarrow\cdots.\]
When the recurrence returns to its native state,
\[\mathcal C_n:i_n\longrightarrow j_n\longrightarrow\cdots\longrightarrow i_n,\]
closure has occurred at \(B_n\).
That completed recurrence can contribute to the realization of \(B_{n+1}\).
The cross-boundary operation is therefore
\[\Gamma_n\longrightarrow\mathcal C_n\overset{\kappa_n}{\longmapsto}d_{n+1},\]
where \(d_{n+1}\) is the enclosing count consequence of the completed subordinate recurrence.
The trajectory itself is not carried upward.
4. The Native Trajectory Does Not Become the Enclosing Trajectory
Recursive replacement therefore does not imply
\[\Gamma_n\longrightarrow\Gamma_{n+1}.\]
The enclosing boundary possesses its own state classification and, if recurrent, its own native trajectory.
Thus:
\[\Gamma_n\ne\Gamma_{n+1}.\]
The two trajectories are not successive temporal segments of one persistent state object.
They are native trajectories of different count domains.
5. Definition — Closure-Complete Relative to an Enclosing Boundary
A subordinate boundary \(B_n\) is closure-complete relative to \(B_{n+1}\) when its internal recurrence has completed such that the enclosing state can be specified without retaining the subordinate path as an independent coordinate.
Symbolically:
\[\Gamma_n\longrightarrow\mathcal C_n\overset{\kappa_n}{\longmapsto}B_{n+1}.\]
After replacement,
\[\Gamma_n\]
remains meaningful as a trajectory at \(B_n\),
but
\[\Gamma_n\]
is not a trajectory coordinate of \(B_{n+1}\).
6. Trajectory Existence Is Boundary Relative
The statement that a subordinate trajectory is replaced does not mean that the trajectory did not physically occur.
At \(B_n\),
\[\Gamma_n\]
is a physically distinguishable recurrence.
At \(B_{n+1}\), however, the state classification no longer contains that path as an independent distinction.
Therefore:
\(\Gamma_n\) is defined at \(B_n\)
while
\(\Gamma_n\) is not defined as a state coordinate at \(B_{n+1}\).
This is the boundary-relative meaning of trajectory replacement.
7. Replacement Is Therefore Not Concealment
The subordinate trajectory is not merely hidden beneath the enclosing state.
It is not an unobserved version of the enclosing trajectory.
Instead:
subordinate trajectory → closure → new state domain.
The state definition changes.
Thus:
recursive replacement is not a hidden trajectory.
8. The Biological Hierarchy Makes This Process Accessible
Biological systems contain experimentally distinguishable recurrences across many timescales.
Schematically:
IR-scale recurrence
↓
μs-scale protein dynamics
↓
ms-scale molecular switching
↓
s-scale biological function.
The precise boundaries must be established experimentally.
The timescale alone does not define them.
What matters is that each candidate level possesses its own distinguishable state classification and native recurrence.
9. A Microsecond Protein Fluctuation Is Not a Faster Switch Trajectory
Suppose a protein possesses a distinguishable microsecond recurrence
\[\Gamma_{\mu\mathrm{s}}.\]
A millisecond myosin switch possesses a different state classification,
\[M_1\leftrightarrow M_2.\]
The microsecond trajectory may physically realize the switch transition.
But it does not follow that
\[\Gamma_{\mu\mathrm{s}}=\Gamma_{\mathrm{switch}}.\]
Instead:
\[\Gamma_{\mu\mathrm{s}}\longrightarrow\mathcal C_{\mu\mathrm{s}}\overset{\kappa}{\longmapsto}\text{switch realization}.\]
The switch boundary owns the switch state.
The faster protein boundary owns the microsecond trajectory.
10. A Switch Trajectory Is Not Muscle Function at Finer Resolution
Likewise, the millisecond transition
\[M_1\leftrightarrow M_2\]
does not remain the trajectory of muscle-scale function.
Addendum 5 already demonstrated why.
Many distinct switch histories can realize the same ensemble occupancy.
The ensemble then participates in an enclosing muscle-scale state.
Thus:
\[\Gamma_{\mathrm{switch}}\longrightarrow\mathcal C_{\mathrm{switch}}\overset{\kappa}{\longmapsto}\text{ensemble realization},\]
and subsequently:
\[\text{ensemble closure}\overset{\kappa}{\longmapsto}\text{muscle-scale realization}.\]
At no stage is the subordinate trajectory simply extended upward.
11. Infrared Recurrence Is Likewise Boundary Owned
Molecular vibration and infrared-scale recurrence occur at still faster boundaries.
These recurrences are physically real at their native state domains.
But when larger protein states become the relevant distinctions, the IR trajectory need not remain as a coordinate of that larger state.
Thus:
\[\Gamma_{\mathrm{IR}}\longrightarrow\mathcal C_{\mathrm{IR}}\overset{\kappa}{\longmapsto}\text{larger molecular realization}.\]
The detailed spectral consequences of this replacement will be developed separately.
For the present argument, only the recursive state transition is required.
12. There Is No Single Biological Trajectory Across All Scales
The conventional mechanical picture encourages a nested trajectory:
\[\Gamma_{\mathrm{fast}}\subset\Gamma_{\mu\mathrm{s}}\subset\Gamma_{\mathrm{ms}}\subset\Gamma_{\mathrm{function}}.\]
R²D rejects this identification.
The trajectories belong to different boundaries:
\[\Gamma_{\mathrm{IR}}\ne\Gamma_{\mu\mathrm{s}}\ne\Gamma_{\mathrm{switch}}\ne\Gamma_{\mathrm{function}}.\]
Their relation is recursive realization.
Not trajectory persistence.
13. The Correct Sequence Contains Closure Between Every Boundary
The biological hierarchy is therefore better written as
\[\Gamma_{\mathrm{IR}}\longrightarrow\mathcal C_{\mathrm{IR}}\overset{\kappa_1}{\longmapsto}B_{\mu\mathrm{s}}\]
\[B_{\mu\mathrm{s}}\longrightarrow\mathcal C_{\mu\mathrm{s}}\overset{\kappa_2}{\longmapsto}B_{\mathrm{switch}}\]
\[B_{\mathrm{switch}}\longrightarrow\mathcal C_{\mathrm{switch}}\overset{\kappa_3}{\longmapsto}B_{\mathrm{ensemble}}\]
\[B_{\mathrm{ensemble}}\longrightarrow\mathcal C_{\mathrm{ensemble}}\overset{\kappa_4}{\longmapsto}B_{\mathrm{function}}.\]
Every cross-boundary step contains replacement.
14. Replacement Across Several Boundaries Is Necessarily Non-Invertible
Each replacement map is many-to-one.
Let
\[\kappa_n\]
map closure at \(B_n\) into the enclosing state domain \(B_{n+1}\).
Across several boundaries,
\[\kappa_{N-1}\circ\kappa_{N-2}\circ\cdots\circ\kappa_n\]
is therefore also many-to-one.
An enclosing biological function does not uniquely specify the detailed subordinate trajectory that realized it.
Thus:
\[B_N\not\Rightarrow\Gamma_n\]
for a unique deep subordinate trajectory.
The inverse is not defined.
15. Functional State Does Not Encode a Unique Molecular History
A muscle can occupy the same functional state after many different sequences of molecular events.
A protein can occupy the same conformational state after many different vibrational histories.
A switch can occupy \(M_1\) after many different faster structural recurrences.
Thus:
one enclosing state ⇐ many subordinate histories.
That many-to-one structure is not merely experimental ignorance.
It is recursive replacement.
16. This Is Stronger Than Averaging
The usual multiscale description is:
fast fluctuations → average → slow variable.
This retains the faster trajectories as the underlying primitive state.
The slow variable is merely their statistical summary.
R²D instead gives:
fast trajectory → closure → replacement → new state domain.
The distinction is fundamental.
17. Averages Can Still Be Useful
Recursive replacement does not invalidate averaging as a mathematical operation.
One may calculate average displacement, orientation, energy, rate, or occupancy.
Such averages can remain excellent physical projections.
But:
useful averaging is not ontological identity.
The success of an average does not prove that the enclosing boundary is merely the subordinate trajectory viewed slowly.
18. The Enclosing Boundary Possesses Native Statehood
Once replacement occurs, the new boundary possesses its own macrostates.
Its state classification is not borrowed from the faster scale.
Therefore:
\[B_{n+1}\ne\langle B_n\rangle\]
as an ontological statement.
The enclosing state may be statistically related to subordinate activity.
It is nevertheless a new boundary-defined state domain.
19. Biological Function Is Defined at the Scale of Function
This point is especially transparent in biology.
Muscle force is a muscle-scale distinction.
A myosin-switch state is a myosin-scale distinction.
A protein conformation is a protein-scale distinction.
A vibrational recurrence is a molecular-scale distinction.
Each function is physically defined at the boundary on which it is distinguishable.
Thus:
function ownership follows boundary ownership.
20. Subordinate Dynamics Realize Function Without Becoming Function
The myosin switch is required for muscle mechanics.
Protein dynamics are required for myosin switching.
Molecular vibration is required for protein realization.
But requirement for realization does not imply identity.
Thus:
subordinate dynamics → realization of function
does not imply
subordinate trajectory = functional trajectory.
This distinction is central to R²D.
21. Closure Completeness Is Not Conventional Equilibrium
The phrase “closed subordinate dynamics” might be mistaken for thermodynamic equilibrium.
That would be incorrect.
A subordinate boundary can repeatedly cycle while:
• consuming free energy;
• producing heat;
• carrying chemical flux;
• exchanging matter;
• or participating in a nonequilibrium steady state.Thus:
closure complete is not detailed-balance equilibrium.
Closure is boundary relative.
22. Boundary-Relative Equilibrium
The relevant R²D sense of equilibrium is narrower.
A subordinate boundary is equilibrium-like relative to the enclosing classification when its internal trajectory has closed and therefore no unresolved path remains as an independent enclosing state coordinate.
Thus:
closure-complete relative to \(B_{n+1}\)
means that the enclosing boundary reads only the completed consequence of the subordinate recurrence.
This can coexist with persistent local activity.
23. Active Isometric Muscle Is the Direct Example
At active isometric stall,
\[A_M=0\]
and
\[P_M=R_M.\]
Yet muscle remains metabolically active.
Myosin switching can continue.
Protein fluctuations continue.
Molecular vibration continues.
Subordinate dynamics have not disappeared.
The enclosing state remains stationary because those subordinate dynamics are closure-complete relative to the muscle-scale read.
24. Stable Function Does Not Require Static Components
A stable biological function is therefore compatible with enormous subordinate activity.
Schematically:
\[\Gamma_1,\Gamma_2,\Gamma_3,\ldots\]
may continue while
\[B_F=\text{constant}.\]
This is not paradoxical.
The subordinate trajectories are not the trajectory of \(B_F\).
They realize it.
25. “Fluctuation” Is a Boundary-Relative Description
A rapid molecular motion appears as a fluctuation when viewed from an enclosing boundary because its native trajectory closes before it becomes an enclosing state distinction.
Thus:
fluctuation at \(B_{n+1}\)
can correspond to
native recurrence at \(B_n\).
Calling it a fluctuation does not make it physically unstructured.
It states that its native trajectory has been replaced relative to the larger boundary.
26. Thermal Fluctuations Are Therefore Native Dynamics of Subordinate Boundaries
In a biological system, microsecond protein motions, faster molecular vibrations, and other thermally active recurrences need not be interpreted as featureless noise beneath function.
They possess native structure at their own boundaries.
What makes them appear thermal from above is that their trajectories have closed before the enclosing functional state is defined.
Thus:
native subordinate recurrence → enclosing thermal fluctuation.
This relation will become important when the hierarchy is extended toward spectroscopy.
27. Replacement Explains Why Fast Dynamics Need Not Predict Slow Function One-to-One
If the slow function were simply the averaged fast trajectory, one might expect sufficiently complete knowledge of the fast dynamics to determine the enclosing functional state uniquely.
Recursive replacement breaks that inference.
Because many subordinate histories map into one enclosing state,
\[\Gamma_n^{(1)},\Gamma_n^{(2)},\ldots\longrightarrow B_{n+1}.\]
The enclosing state depends on the boundary classification, not on retention of one unique subordinate path.
28. The Reverse Inference Also Fails
Observing a biological function does not uniquely recover its molecular history.
Thus:
\[B_{\mathrm{function}}\not\Rightarrow\Gamma_{\mathrm{switch}}\]
uniquely.
And still less:
\[B_{\mathrm{function}}\not\Rightarrow\Gamma_{\mu\mathrm{s}}\]
or
\[B_{\mathrm{function}}\not\Rightarrow\Gamma_{\mathrm{IR}}.\]
Every intervening replacement increases the degeneracy of the inverse problem.
29. Realization and Causal Definition Must Remain Distinct
The subordinate dynamics are causally necessary in the ordinary mechanistic sense.
Without molecular recurrence, biological function cannot be physically realized.
But Addendum 4 showed that the asymmetry of the myosin switch is defined by the enclosing relation
\[A_M=P_M-R_M.\]
Thus the subordinate trajectory does not contain the full causal definition of the enclosing state.
The distinction is:
subordinate dynamics realize the state
while
the enclosing relation defines its directional organization.
30. The Recursive Architecture Therefore Runs in Two Directions
Organization acts downward:
\[B_{n+1}\Longrightarrow A_n.\]
Subordinate recurrence realizes upward:
\[\mathcal C_n\overset{\kappa_n}{\longmapsto}B_{n+1}.\]
These are not opposite forces.
They are different aspects of recursive realization.
The enclosing relation determines compatibility.
The subordinate boundary supplies the physical closure through which that compatibility is realized.
31. Replacement Occurs Before the Next Native Recurrence
Once \(B_n\) closes relative to \(B_{n+1}\), its trajectory has been replaced.
Only then can \(B_{n+1}\) possess its own native recurrence.
Thus:
subordinate closure → recursive replacement → enclosing native recurrence.
This ordering is fundamental.
The enclosing recurrence is not simply the slowed subordinate recurrence.
32. Principle — Every Biological Boundary Owns Its Native Trajectory
For each boundary \(B_n\),
\[\Gamma_n\]
belongs to the state classification of \(B_n\).
Therefore:
\[\Gamma_n\ne\Gamma_{n+1}\]
in general.
Cross-scale realization does not imply trajectory identity.
33. Principle — Closure Precedes Replacement
A subordinate trajectory contributes to the enclosing state through completed recurrence:
\[\Gamma_n\longrightarrow\mathcal C_n\overset{\kappa_n}{\longmapsto}B_{n+1}.\]
The unresolved subordinate path is not carried upward as an enclosing trajectory.
34. Principle — Closure-Complete Does Not Mean Inactive
A subordinate boundary may remain dynamically active while being closure-complete relative to an enclosing state.
Therefore:
persistent subordinate activity does not imply persistent enclosing change.
35. Principle — Biological Function Is a Native Enclosing State
A biological function is defined on the boundary at which that function is distinguishable.
It is not merely the time average of all faster subordinate coordinates.
Thus:
function is not an averaged subordinate trajectory.
36. Principle — Subordinate Histories Are Not Recoverable Across Recursive Replacement
Because replacement is many-to-one,
\[B_{n+1}\not\Rightarrow\Gamma_n\]
uniquely.
Across several boundaries, this non-invertibility compounds.
37. Principle — Fast Biological Fluctuations Are Native Recurrences Seen After Replacement
What appears as a thermal or structural fluctuation at an enclosing boundary may be a complete native recurrence at a subordinate boundary.
Thus:
subordinate recurrence → enclosing fluctuation.
The label “fluctuation” is boundary relative.
38. Logical Status
Established in Addendum 4
The myosin-switch asymmetry obeys the experimentally grounded architecture
\[A_M=P_M-R_M.\]
The enclosing chemical-mechanical relation organizes the observed molecular distribution.
Established in Addendum 5
Individual switch identities and trajectories are replaced by the enclosing ensemble classification.
For the binary ensemble,
\[W_N(i)=\left|\pi_N^{-1}(i)\right|=\binom{N}{i}.\]
New Definition
A subordinate boundary is closure-complete relative to an enclosing boundary when its native recurrence has completed such that its internal path no longer remains an independent state coordinate of the enclosing state.
New Recursive Result
The switch-to-ensemble replacement is not structurally unique.
Every realized biological state can itself be treated as an enclosing boundary relative to faster subordinate dynamics.
Thus:
\[\Gamma_n\longrightarrow\mathcal C_n\overset{\kappa_n}{\longmapsto}B_{n+1}.\]
New Boundary-Ownership Result
The subordinate trajectory is defined at \(B_n\) but is not carried as the trajectory of \(B_{n+1}\).
Thus:
\[\Gamma_n\not\longrightarrow\Gamma_{n+1}.\]
New Biological Interpretation
Biological function is realized through a hierarchy of closure-complete subordinate dynamics rather than being the temporal average of one persistent trajectory spanning all scales.
Not Yet Claimed
This addendum does not yet establish:
• the exact spectral coordinates carried by IR or other molecular recurrences;
• whether physical frequency itself survives recursive replacement;
• the formal principle of cross-scale spectral replacement;
• why biology uniquely permits several adjacent replacement boundaries to be directly observed;
• or how the same replacement architecture appears beyond the biological window when one
primitive coordinate becomes unreadable.These are the subjects of the following addenda.
39. The Biological Replacement Hierarchy
The biological hierarchy can now be represented schematically as:
fast molecular recurrence
↓
\(\mathcal C_0\overset{\kappa_0}{\longmapsto}\) larger molecular state
↓
\(\mathcal C_1\overset{\kappa_1}{\longmapsto}\) μs-scale protein state
↓
\(\mathcal C_2\overset{\kappa_2}{\longmapsto}\) ms-scale switch state
↓
\(\mathcal C_3\overset{\kappa_3}{\longmapsto}\) ensemble state
↓
\(\mathcal C_4\overset{\kappa_4}{\longmapsto}\) biological function.
At every step:
native trajectory → closure → replacement → new native state.
No single trajectory persists through the entire sequence.
40. Conclusion
Addendum 5 directly established recursive replacement from individual myosin switches to the switch ensemble.
The individual switch identities do not survive as state variables of the ensemble.
Their distinct assignments become ensemble multiplicity.
Their completed trajectories contribute to ensemble realization without becoming the ensemble trajectory.
Addendum 6 extends this experimentally visible result recursively.
The myosin switch is not primitive.
It is itself realized through faster protein dynamics.
Those protein dynamics are realized through still faster molecular recurrence.
At every level, the same architecture applies:
\[\Gamma_n\longrightarrow\mathcal C_n\overset{\kappa_n}{\longmapsto}B_{n+1}.\]
A native subordinate trajectory is physically real at its own boundary.
After closure, however, the enclosing boundary does not retain that trajectory as one of its state coordinates.
The enclosing boundary possesses a new state classification and, where recurrent, a new native trajectory.
Therefore:
\[\Gamma_n\ne\Gamma_{n+1}.\]
This makes recursive replacement fundamentally different from ordinary temporal averaging.
Biological function is not obtained by following one microscopic trajectory and smoothing it until a slow macroscopic trajectory remains.
Instead, each scale closes into the next.
Fast molecular recurrence closes.
Its consequence is recursively replaced into a larger molecular state.
That state undergoes its own native recurrence.
It closes into a protein-scale state.
The protein-scale state closes into a molecular-switch state.
The switches close into an ensemble state.
The ensemble closes into biological function.
At every step the subordinate dynamics remain physically necessary.
But physical necessity does not imply trajectory persistence.
The subordinate dynamics realize the adjacent scale.
They do not become its trajectory.
This is directly evident in active isometric muscle.
At stall,
\[A_M=0\]
while
\[P_M=R_M.\]
Myosin switching and deeper molecular recurrence can remain active even while the enclosing muscle state remains stationary.
Calling those faster events fluctuations that merely “average out” misses the change in physical statehood.
They are native dynamics of subordinate boundaries whose trajectories have closed relative to the enclosing function.
The appropriate description is therefore not:
fast trajectories → average → slow trajectory.
It is:
native subordinate trajectory → closure → recursive replacement → new enclosing state.
Repeated across the biological hierarchy:
IR-scale recurrence → μs-scale state → ms-scale switch → ensemble → function
Each arrow represents recursive replacement.
The central result is therefore:
Biological function is not the slow trajectory obtained by averaging faster molecular trajectories.
[Editorial source note: the rest of this boxed sentence is clipped in the archived PDF after “It i…”. It is left for author review.]
Hence:
Closure-complete subordinate dynamics occur before biological function.