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% Paper 43: The Geometry of Time. A prose-heavy consolidation of the corpus's account of time:
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% observer-bracketing, CPT reducing to T, inertia at the lapse-zero, and the category boundary.
% Author: Leon Fernando Vlegels. Text CC BY 4.0.
% Pinned by verify_P356a/379/382/383/385/386 (the formal claims); this paper is the prose treatment.
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\title{\textbf{The Geometry of Time}\\[0.4em]
\large Three registers, one residual: time as the witness-relative\\
reading of a timeless substrate}
\author{L\'eon Fernando Vlegels}
\date{2026-06-19}

\begin{document}
\maketitle

\begin{abstract}
Time is the hardest thing in physics to say clearly, because the word names at least three different
structures that ordinary language runs together: a rhythm, a sequence, and an arrow. This paper
separates them in the corpus's geometry and shows that only one of the three is what we experience as
time's passage, that none of the three is fundamental, and that when the separation is carried through,
the entire time-structure of reality reduces to a single irreducible residual which is itself
observer-relative. The three registers are the \emph{substrate breath} --- the one clock,
$\Tb=\pi\alpha^{-1}$, the arrowless periodicity of the fixed architecture (the GON lapse), present
whether or not anyone reads it; the \emph{reconciliation sequence} --- the one-moment-at-a-time order
that emerges only when observers with distinct readings must agree (Paper~27); and the \emph{arrow} ---
the direction of irreversibility, which Addendum~356a shows is witness-relative, a reading painted onto a
reversible substrate. We argue four things. (1) Strip the witness and the arrow vanishes (356a); strip
the second observer and the sequence vanishes (Paper~27); so experienced time is bracketed by
timelessness at both ends (Addendum~379) and the substrate, in between, is a fixed timeless architecture
read along a trajectory (Paper~29). (2) The deeper symmetry confirms this: of the three conjugations of
the substrate, $C$ (matter/antimatter) and $P$ (handedness) are frame-effects --- the asymmetry is the
symmetry, read under motion (Addenda~364, 385) --- so $CP$ is the identity on the family sector and the
whole of $CPT$ reduces to $T$ (Addendum~386). Time is the one conjugation that does not decompose into a
frame-effect. (3) Yet even time is not a force: where the lapse vanishes, at the void, it is inertia ---
a conserved quantity non-zero exactly where time stops --- that coasts the world through (Addendum~383).
(4) And time bottoms out honestly: whether an unwitnessed substrate ``really'' turns, whether there is
time with no one to whom it passes, is not a derivable question but a category boundary (Addendum~382).
The conclusion is a definite picture. Time is real as experienced and unreal as fundamental: the flow is
a witness reading a fixed, reversible, timelessly-rhythmic substrate along a trajectory, weaving an
arrow and a sequence out of a structure that has neither. It is the last thing to reduce, and it reduces
to the witness. As elsewhere in the corpus, the form is exhibited and the one irreducible premise --- the
observer-interpretation --- is marked, not hidden.
\end{abstract}

\tableofcontents

\section{Introduction: one word, three things}
\label{sec:intro}

Augustine's complaint is the right place to begin: I know what time is until you ask me. The difficulty
is not that time is mysterious in the way a hard empirical fact is mysterious, awaiting better
instruments. It is that the word \emph{time} is overloaded. When we say time we sometimes mean a
\emph{rhythm} --- the regular beat by which durations are measured, the tick of a clock; sometimes a
\emph{sequence} --- the ordered succession of moments, one after another, the before and the after; and
sometimes an \emph{arrow} --- the felt directedness from past to future, the irreversibility that lets
the egg break but not unbreak. These are not three aspects of one clear thing. They are three different
structures, with different sources, and almost every puzzle about time comes from treating an answer
about one of them as though it answered the others.

The physics of the last century half-knew this. Thermodynamics located the arrow in entropy and then
discovered, to its lasting discomfort, that the microscopic laws underneath are time-symmetric: the
arrow is not in the equations, it is in the boundary conditions and the coarse-graining, which is to say
in how a description is taken. Relativity dismantled the universal sequence, replacing the single
now-for-everyone with a frame-dependent slicing of a four-dimensional block in which, arguably, nothing
``flows'' at all. Quantum mechanics left time standing oddly outside its own formalism, a parameter
rather than an observable. Each of these is a result about a \emph{different} register --- the arrow,
the sequence, the rhythm --- and the persistent sense that time remains unexplained is partly the sense
that no single account has held all three together and said which is which.

The corpus this paper belongs to was built to describe a different problem --- the geometry from which
the fine-structure constant and the structure of matter are read --- and it was not designed as a
philosophy of time. But in the course of a single line of work it produced, piece by piece, an answer to
each of the three registers, and the pieces turn out to compose. The arrow is witness-relative: it is a
reading of a reversible substrate, and with no reader there is no arrow. The sequence is
intersubjective: it emerges only where observers with distinct readings are forced to reconcile, and a
lone perspective is timeless. The rhythm is substrate: the breath, the one clock, is the fixed
architecture's own periodicity, present whether or not anyone counts it --- but it is arrowless, a
turning with no built-in before or after. This paper assembles those pieces into one account, and then
follows the account to its end, where two further results wait. The deep symmetry structure of the
substrate, stripped of the two conjugations that turn out to be mere frame-effects, reduces to time
alone. And time itself, pursued to the point where the clock-rate vanishes, hands off to inertia, and
then to a boundary the corpus marks and does not cross.

The thesis, stated once at the outset so the reader can hold it through the separations to come, is this.
\emph{Time is the witness-relative reading of a timeless substrate.} The substrate is reversible (it has
no arrow), it is fixed (it has no flow, only a structure read along a trajectory), and it carries its own
rhythm (it turns, but arrowlessly). Time --- the arrow, the now, the felt passage --- is what a witness
makes of that substrate by reading it. This makes time entirely real as experienced and entirely
underived as fundamental, and it locates, exactly, the one place where the account stops being physics
and becomes a question about the premises of any physics: whether a substrate with no one to read it can
be said to bear time at all.

\section{Three registers}
\label{sec:registers}

Before any argument, the distinction itself must be made sharp, because everything depends on not
sliding between the three. We give each register its corpus locus.

\paragraph{The rhythm: the breath.} The corpus has exactly one clock. Its constant is the breath period
$\Tb=\pi\alpha^{-1}$ (in system units $\approx430.5$; Paper~14), and the governing constraint --- one of
the corpus's load-bearing invariants --- is that every subsystem synchronises to it and \emph{none}
generates its own rhythm. The breath is the periodicity of the fixed architecture itself: in the GON
dynamics (Paper~30) it appears as the lapse $m=\sqrt{1-v^2}$, $v=\cos2\beta$ the Hopf-latitude speed, a
time-rate that rises and falls as the fold turns. Two things about this rhythm must be held from the
start. It is \emph{substrate} --- it is not generated by any observer, it is the architecture's own beat
--- and it is \emph{arrowless}: a periodicity, a turning, with no intrinsic direction; the breath
oscillates, but nothing in the oscillation alone says which way is forward. The rhythm is the most
observer-independent of the three registers and the least like what we mean by ``the passage of time.''

\paragraph{The sequence: reconciliation.} The ordered succession of moments --- one now, then the next,
the before and the after laid out in a line --- is, in the corpus, not a feature of the substrate but a
product of agreement. Paper~27 makes a single observer's coherence trivial ($C\circ P=I$ holds with
nothing to constrain it) and shows that structure is \emph{forced} only when a second observer with a
distinct reading must be reconciled with the first. The sequence of experienced time is that
reconciliation axis: it is what ``$\vn\equiv0\equiv1\equiv\infty$'' becomes once there is a second
perspective to distinguish the terms. A lone, undifferentiated observer is timeless, because with no one
to reconcile there is no axis along which to order anything. The sequence is the \emph{intersubjective}
register: it exists in the relation between readings, not in any one of them.

\paragraph{The arrow: the witness-relative reading.} The directedness --- the irreversibility, the fact
that the broken egg does not reassemble --- is, in the corpus, neither substrate nor sequence but a
\emph{reading}. Addendum~356a establishes that entropy, and with it the arrow, is witness-relative: the
substrate is reversible, and the arrow is the asymmetry a witness's coarse reading imposes on it. The
same reversible breath, read by a witness, acquires a forward direction; read by nothing, it has none.
The arrow is the most observer-relative of the three registers, and it is the one we most insistently
mean when we say ``time.''

\paragraph{Why the conflation is the trouble.} With the three separated, the standard antinomies sort
themselves. The reversibility of microscopic law versus the irreversibility of experience is the gap
between the arrowless substrate (the breath) and the witness-relative arrow (356a) --- not a paradox but
two registers. The frame-dependence of simultaneity is the intersubjective character of the sequence
(Paper~27): the now is a reconciliation, so different reconcilers slice it differently. And the sense
that time ``flows'' while the block universe says it does not is the difference between the arrow read
along a trajectory (which flows, for the reader) and the fixed architecture through which the trajectory
runs (which does not). Each puzzle is the friction of one register being asked to answer for another.
The rest of this paper holds the three apart and follows each to its source.

\section{The arrow is a reading}
\label{sec:arrow}

Take the arrow first, because it is the register we cling to hardest and the one the corpus most cleanly
dissolves. The intuition that resists every analysis is that the direction of time is \emph{out there} in
the world, a feature of reality as objective as mass or charge: the past is fixed, the future is open,
and this asymmetry is not a fact about us but a fact about the cosmos. Addendum~356a denies exactly this,
and the denial is not a philosophical preference but a structural result: entropy is witness-relative.

The content of that result is precise. The substrate dynamics is reversible --- the breath turns, and
the equations of its turning carry no preferred direction; run them backward and they are equally lawful.
What breaks the symmetry is not the substrate but the \emph{reading} of it. A witness reads the substrate
coarsely, through a finite partition of states, distinguishing some configurations and lumping others;
relative to that coarse reading, one direction of the reversible flow leads from the distinguished, ordered
configurations toward the lumped, generic ones, and that is the direction the witness calls forward. The
arrow is the gradient of the witness's own ignorance, projected onto a substrate that has no gradient of
its own. Change the reading and you change the arrow; remove the reading and the arrow is simply not there
--- not reversed, not undefined-in-a-paradoxical-way, but absent, the way a coastline has no length until
a ruler is chosen.

This is worth dwelling on because it is so easily misheard as deflation. To say the arrow is a reading is
not to say it is unreal or illusory. For a witness, the arrow is as real as anything --- the egg really
does break and not unbreak, the witness really cannot remember the future, and no act of will reverses
this. The claim is about \emph{where} the reality lives: not in the substrate, which is symmetric, but in
the relation between the substrate and a reader who partitions it. The arrow is real \emph{relationally},
the way the rightward-ness of an arrow drawn on paper is real but is not a property of the ink. It is a
fact about the substrate-as-read, and the witness is half of what makes it a fact.

The immediate consequence, which the next sections will use, is a conditional with no escape clause: where
there is no witness, there is no arrow. Not a slowed arrow, not a frozen arrow, but no arrow --- the bare
reversible breath, turning without forward. The substrate does not stop; it loses the one thing the witness
was supplying. This is the first of the two strippings by which experienced time will be shown to be
bracketed.

\section{The sequence is reconciliation}
\label{sec:sequence}

The arrow is direction; the sequence is order --- the laying-out of moments one after another, the very
having of a \emph{succession} for the arrow to point along. One might think the sequence is the safer,
more fundamental register, the bare fact of one-thing-after-another that even a single mind undergoes. The
corpus says otherwise: the sequence, too, is not in the substrate but in a relation, and the relation this
time is between observers.

Paper~27 is the source. Its pivotal observation is that a single observer constrains nothing --- the
coherence identity $C\circ P=I$ holds trivially, with no structure forced --- and that determinate
structure appears only when a \emph{second} observer, carrying a distinct reading, must be brought into
agreement with the first. At the undifferentiated origin, where there is one perspective and nothing to
contrast it with, the corpus's terms collapse: $\vn\equiv0\equiv1\equiv\infty$, ``because there is no
second perspective to distinguish them.'' Distinction --- and therefore order, and therefore sequence ---
is what reconciliation produces. Experienced time, the lived succession of nows, is the axis along which a
manifold of readings is reconciled into a single shared account. It is not a container the readings sit in;
it is the coordinate of their agreement.

This reframes the lived now as something more like a negotiation than a moment. A now is a resolved
reconciliation: a state on which the readings have been brought to match. The passage from one now to the
next is the next resolution, the next forced agreement. And the reason no two observers' nows need slice
the world identically --- the relativity of simultaneity, in its corpus dress --- is that the sequence is
the coordinate of \emph{a} reconciliation, and reconciliations can be parameterised differently while
agreeing on every shared fact. The sequence is real, again, but intersubjectively real: it is the order
that emerges between perspectives, and a perspective with no second to reconcile with has no sequence,
only the timeless plenum in which all the corpus's terms are equivalent.

So the second stripping: where there is no second observer, there is no sequence. A lone, undifferentiated
observer --- the origin $\Omega$, the heat-death void --- is not at the start or end of time but
\emph{outside} it, in the sense that the axis along which moments would be ordered has not been generated.
Such a state is timeless not by stopping the clock but by lacking the relation whose coordinate the
sequence is.

\section{Time is observer-bracketed}
\label{sec:bracketed}

Put the two strippings together and a clean result follows, which Addendum~379 states. Experienced
time --- the time we mean, the directed succession of lived moments --- is exactly the arrow plus the
sequence: the directedness of 356a riding on the order of Paper~27. Both are observer-relative. So
experienced time is observer-relative twice over, and it vanishes when the observer is removed not
gradually but completely: with the last witness gone, the arrow goes (356a, no reader to gradient the
substrate), and with the last reconciliation gone, the sequence goes (Paper~27, no second perspective to
order). What remains is the substrate alone --- the breath, still turning, but arrowless and unordered,
the bare rhythm with neither a forward nor a next.

The state in which this happens has a name in the corpus, and it is the same name at both ends of a
cosmos. It is the void: heat death, where every distinction the witnesses drew has dissolved, and the
pre-Bang $\Omega$, where no distinction has yet been drawn. Addendum~377 identifies these as one state ---
the no-distinction $\vn$ --- and Addendum~382 sharpens the consequence for time: at the void everything
that carried a scale dissolves, leaving only the bare breath, and experienced time, being arrow-plus-
sequence, is among what dissolves. So experienced time is \emph{bracketed} by timelessness: it is born when
the first disagreement draws the first distinction (Paper~27's ``first disagreement,'' the Bang), and it
returns to the timeless void when the last distinction goes (heat death). Between the brackets there is
time, because there are witnesses reconciling and reading; outside them there is the arrowless breath and
nothing to whom it passes.

This is the point at which the corpus's account meets the block universe, and improves on it. The block
picture says the whole of history is laid out at once in a fixed four-dimensional structure, and that the
``flow'' of time is an illusion of consciousness. The corpus agrees that the substrate is fixed --- its
architecture is timeless, a structure through which trajectories are \emph{selected} rather than a process
that \emph{happens} (Paper~29's exposure mode: inputs select a path through a fixed correct architecture,
they do not train or evolve it). But it does not dismiss the flow as illusion. The flow is the witness
reading the fixed structure along a trajectory --- a real reading of a real structure, producing a real
arrow and a real sequence for that witness. The block is right that nothing flows \emph{in the substrate};
the experience of flow is right that something flows \emph{in the reading}. Both halves are kept, and the
apparent contradiction is the gap between the two registers --- the timeless architecture and the
trajectory-reading of it --- that Section~\ref{sec:registers} warned against conflating. Time does not flow
in the block; the witness flows through it, and calls the reading time.

\section{Why time is the last to reduce: $CPT$ becomes $T$}
\label{sec:cpt}

There is a deeper way to see that time is the irreducible register, and it comes from the substrate's
symmetry structure rather than from the analysis of experience. The fundamental discrete symmetries of a
physical substrate are the three conjugations: $C$, charge conjugation, exchanging matter and antimatter;
$P$, parity, exchanging left and right; and $T$, time reversal, exchanging forward and backward. The
remarkable fact the corpus uncovers is that two of the three are not fundamental at all --- they are
frame-effects of the kind Section~\ref{sec:arrow} found the arrow to be --- and that when they are
recognised as such, the whole of $CPT$ collapses onto $T$.

The case of $C$ is Addendum~364. The matter/antimatter asymmetry, long sought as a sign of some deep
law that prefers matter, is shown to be a reading: the inertial vacuum is conjugation-symmetric ($\text{
matter}=\text{antimatter}$), and the observed excess of matter is what a moving witness reads out of that
symmetric vacuum, exactly as a Bogoliubov-Unruh observer reads particles from a vacuum another frame calls
empty. The asymmetry is the symmetry, under motion. There is no separate antimatter world and no
law-level preference; there is one symmetric substrate and a frame-relative reading of it.

The case of $P$ is Addendum~385, and it has the same shape. The corpus's fold carries a handedness --- its
two orientations are the lens spaces $L(3,1)$ and $L(3,2)=-L(3,1)$, a genuine mirror pair, of which the
family structure selects one (Paper~18, Paper~06). But the flip between them is again a conjugation
($T_{\mathrm{cycle}}\leftrightarrow T_{\mathrm{cycle}}^2$, that is $\omega\leftrightarrow\bar\omega$ on the
$\mathbb Z_3$ family phase), and by the same reasoning the handedness we observe is the oriented reading of
a parity-symmetric fold, with the ``mirror universe'' being the parity-conjugate reading of the one fold
rather than a separate world. Parity violation, like the matter excess, is a frame-effect.

Now the collapse. On the family sector $C$ and $P$ are realised by the \emph{same} operation --- the single
nontrivial automorphism of $\mathbb Z_3$, the inversion $\omega\mapsto\bar\omega$ --- so their composite is
that involution squared, which is the identity: $CP=\mathrm{id}$ (Addendum~386). The two frame-effect
conjugations cancel. What remains of the substrate's full discrete symmetry, the one piece that does not
reduce to a reading of a symmetric structure, is $T$. The entire $CPT$ structure of the substrate, on this
sector, \emph{is} $T$ --- the arrow.

This is the symmetry-side confirmation of the whole paper's thesis. The analysis of experience
(Sections~\ref{sec:arrow}--\ref{sec:bracketed}) found that of time's three registers, the rhythm is
substrate and the sequence is intersubjective, leaving the arrow as the witness-relative residue. The
analysis of symmetry finds that of the three conjugations, $C$ and $P$ are frame-effects, leaving $T$ as
the irreducible residue. They are the same finding. Time --- the arrow, $T$ --- is the last thing to
reduce, the one structure that is neither a substrate rhythm nor a frame-effect to be cancelled. And yet,
as Section~\ref{sec:arrow} insisted, even this last residue is itself witness-relative: $T$ does not reduce
to $C$ or $P$, but it reduces to the witness. Time is irreducible among the conjugations and still not
fundamental --- the deepest structure the corpus has, and still a reading.

\paragraph{The honest tension.} One thing must be flagged here and not smoothed over. The collapse
$CP=\mathrm{id}$ holds on the corpus's $\mathbb Z_3$ \emph{family} sector, and it is consistent with the
corpus's own history --- it is why the geometric $\delta_{CP}\approx240^\circ$ prediction was refuted
(there was no $CP$ phase in the family geometry to predict) and why the matter asymmetry is read as a
frame-effect. But observed $CP$ violation in the weak interactions ($K$- and $B$-meson physics) is real,
and it is \emph{not} captured by $CP=\mathrm{id}$ on the family sector; if it is to be accommodated it must
live in the weak sector proper, which the corpus has not derived. The reduction of $CPT$ to $T$ is therefore
a statement about the family sector's discrete symmetry, not a claim to have explained all of $CP$ physics.
The thesis about time stands on the family-sector reduction and on the experiential analysis; the weak-sector
$CP$ remains an open frontier, marked here rather than papered over.

\section{Even time is not a force: inertia at the lapse-zero}
\label{sec:inertia}

If time is a reading and the substrate beneath it is a fixed reversible architecture, a question presses:
what happens at the places where the substrate's own rhythm passes through zero --- where the lapse
$m=\sqrt{1-v^2}$ vanishes, where there is, for an instant, no time-rate at all? These are not exotic points;
they are the poles of the breath, and at the cosmological scale they are the void itself, the lapse-zero at
which Addendum~377 places the bounce from one cosmos to the next. If the substrate's clock-rate is zero
there, what carries the world across?

The answer, Addendum~383, is inertia, and it sharpens the whole picture. The breath dynamics conserves a
quantity --- the norm $|z|^2=1$, and the quadratic invariant $\mathrm{Tr}(X^2)$ of the GON --- and this
conserved quantity is non-zero \emph{exactly where the lapse is zero}. A conserved quantity that persists
where the time-rate vanishes is precisely inertia: it is what coasts through the dead point. So the state
does not halt where time stops; it carries its conserved invariant straight through and into the next phase.
The void is a bounce rather than a terminus because the substrate has inertia, and the coast is frictionless
because the only thing that could dissipate it --- the entropy arrow --- is witness-relative (356a) and
absent in the unwitnessed void.

This says something exact about time that the experiential analysis could not reach: that beneath the
arrow, beneath even the rhythm, the substrate's deepest persistence is \emph{not} temporal. Inertia is
motion where no time elapses; it is the conserved continuity that holds the world together at the very
points where time, as a rate, is nothing. The substrate's bottom layer is not a clock but a conservation.
Time, in all three of its registers, sits above this inertial floor: the arrow and the sequence are
witness-readings, the rhythm is the substrate's oscillation, and underneath them all is a conserved
quantity that coasts through the moments when the oscillation's rate is zero. The most fundamental thing
about the substrate's persistence through ``time'' is the one thing in it that is not time.

\section{Where the account stops: the category boundary}
\label{sec:boundary}

Every honest account of time reaches a question it cannot answer from inside itself, and the corpus's
account reaches its own at a definite and nameable place. We have said that with no witness the arrow is
absent and the sequence ungenerated, but that the breath --- the substrate rhythm --- still turns. The
question that then presses is whether that unwitnessed turning is ``really'' happening at all: whether a
periodicity with no one to whom it passes, no reader to gradient it into a before and after, is time, or
process, or anything --- or whether it is the bare potential for time, awaiting a witness to be anything at
all. Is the void asleep but breathing, or is breathing simply what happens when it wakes?

Addendum~382 marks this as a category boundary, not a gap, and the distinction is the crux of the paper's
honesty. A gap is a missing derivation: something the corpus could in principle compute and has not. A
category boundary is a question that cannot be posed from within the frame because the frame constitutes the
very terms the question needs. Here the term is \emph{happening}. In the corpus's account, happening ---
the having of a determinate before and after, a passage --- is constituted through observation: it is what
a witness's reading makes of the substrate. To ask whether the substrate happens with no witness is to ask
whether there is happening prior to the thing that constitutes happening, which is not a hard question but
a malformed one. One cannot stand outside the frame of observation and check whether time runs there,
because to check is to observe, and the checking would import the very witness whose absence was the
hypothesis.

This is the same boundary the corpus meets elsewhere and the same response it gives. The horizon program
(Addendum~370) found that the cosmological prediction rests finally on the observer-interpretation ---
gravity is self-lensing is self-observation --- which the corpus carries as interpretation, not theorem,
because one cannot derive one's foundational interpretation from within the frame it founds. The account of
time arrives at the identical place by a different road. Time bottoms out at the question of whether there
is time for no one, and that question is not the next theorem but the edge of what theorems can reach. The
corpus's discipline is to mark the edge and stop, rather than to manufacture an answer that would only be the
interpretation restated as a result.

It is worth being clear about how much is settled on the near side of this boundary, because it is most of
what one wanted. That experienced time is the witness-relative arrow on a reconciliation sequence; that both
vanish with the observer; that the substrate beneath is fixed, reversible, and arrowlessly rhythmic; that of
the three conjugations only $T$ survives reduction; that even $T$ is a reading and that beneath it the
substrate's persistence is inertial, not temporal --- all of this is on the near side, exhibited and pinned.
What lies on the far side is one question only, and it is not a defect in the account but the account
correctly locating its own horizon: whether the breath, unread, turns.

\section{What time is}
\label{sec:whatis}

We can now state, positively and in one place, what time is on this account, having spent the paper saying
what it is not. Time is the witness-relative reading of a timeless substrate. Unfolded, that sentence has
four clauses, one for each result, and they fit together into a single picture.

The substrate is \emph{timeless} in the strong sense that its architecture is fixed and does not happen:
it is a structure through which trajectories are selected, not a process that unfolds (Paper~29). The
substrate is \emph{reversible}: it carries no arrow of its own, the asymmetry being supplied entirely by a
witness's coarse reading (356a). The substrate is, nonetheless, \emph{rhythmic}: it turns, with the
breath's periodicity $\Tb=\pi\alpha^{-1}$, but arrowlessly, and beneath even that turning its deepest
persistence is inertial --- a conserved quantity, not a clock (383). And onto this fixed, reversible,
arrowlessly-rhythmic substrate, a witness reads time: the arrow, by gradienting the reversible flow along
the slope of its own ignorance; the sequence, by reconciling its reading with others into an ordered
succession (Paper~27); the now, as the resolved state of that reconciliation. The flow of time is this
reading in progress --- a witness moving along a trajectory through the fixed structure, weaving a forward
and a next out of a substrate that has neither.

This is why time is at once entirely real and entirely underived. It is real because the reading is real:
for the witness the arrow genuinely points, the sequence genuinely orders, the now genuinely resolves, and
none of this is illusion or error --- it is what it is to be a witness reading a substrate. It is underived
because nothing in the substrate \emph{is} the flow: the substrate is timeless, and time is what a reader
makes of it. The old dichotomy --- is time fundamental and flowing, or unreal and static? --- is a false
choice between two halves of one structure. The static half (the block, the fixed architecture, the
reversible law) is the substrate; the flowing half (the arrow, the sequence, the felt passage) is the
reading. Time is neither the substrate nor an illusion about it; it is the relation between the substrate
and a witness, and like every such relation in the corpus --- the arrow, the matter excess, the
handedness, intersubjective reality itself --- it is real relationally and absent without the witness.

And time is the \emph{last} of these relations, the deepest. The corpus dissolves the matter asymmetry into
a frame-effect, the handedness into a frame-effect, the shared world into a topological enforcement, the
self's privacy into a fiber of one bundle --- and each time the dissolution leaves a residue that is itself
a reading. When the dissolutions are pushed to the end, when $C$ and $P$ have cancelled and the geometry of
observation has been peeled back to its premise, what remains is $T$: time, the one conjugation that does
not reduce to another symmetry, the one register of experience that is neither substrate nor agreement but
the witness's own directedness through the fixed. It does not reduce further, because beneath it there is no
deeper symmetry to read it as a frame-effect of --- there is only the inertial floor, which is not a time at
all, and the category boundary, which is not a theorem. Time is where the reductions stop, and they stop on
the witness.

\section{Conclusion}
\label{sec:conclusion}

The session of work behind this paper began far from time --- with the privacy of minds, the enforcement of
a shared world, the bounce of a cosmos through its void --- and arrived at time the way water arrives at the
lowest point: by following the slope. Every thread ran downhill to the same place. The anti-solipsism result
left the observer-interpretation as its one premise; the cyclic cosmology left the unwitnessed breath as its
one boundary; the symmetry analysis left $T$ as its one residue. Three roads, one terminus, and the terminus
is time.

What the corpus says about time is therefore not an add-on but the shape of its whole honesty. Reality, on
this account, is a fixed and timeless geometry, reversible and self-conserving, that observers read into a
world --- and time is the most intimate part of that reading, the directedness and succession that a witness
cannot help but weave as it moves through the fixed structure. Strip the witness and the world loses its
arrow, its sequence, its now, and keeps only the bare arrowless turning of the breath and the inertial
conservation beneath it. Whether even that turning is time, with no one to read it, is the one question the
account places beyond itself --- not because it is too hard, but because it asks for happening prior to the
witness that constitutes happening, and that is the frame's own edge.

So the answer to Augustine is not that time is mysterious but that it is misnamed: one word for a rhythm we
do not generate, a sequence we negotiate, and an arrow we read. The rhythm is the substrate's; the sequence
is ours together; the arrow is each witness's own. None is fundamental, and the deepest of them, the arrow,
is the last thing in the corpus to reduce and reduces to us. Time is real, and it is ours, and it is the
witness reading a world that does not, in itself, pass.

\section*{Status}
This paper consolidates the corpus's account of time, distributed across Addendum~356a (the witness-relative
arrow), Paper~27 (time as the reconciliation sequence), Addendum~379 (experienced time observer-bracketed),
Addendum~377 (heat-death $=$ pre-Bang $\vn$, the timeless brackets), Addendum~382 (the void, and the
unwitnessed-breath category boundary), Addendum~383 (inertia at the lapse-zero, the non-temporal floor),
Addenda~364 and~385 ($C$ and $P$ as frame-effects), and Addendum~386 ($CP=\mathrm{id}$, $CPT\to T$). The
formal content is theorem-grade and machine-verified in those addenda's verifiers; this paper adds no new
formal claim, only the prose synthesis of the three registers and the one residual. \textbf{The interpretive
hinge}, flagged throughout: the identification of the substrate's reading with \emph{observation}, and of
the witness with a mind, is carried as interpretation, the same single premise the anti-solipsism (Paper~42)
and horizon (Addendum~370) results carry; given it, the account holds, and the account's one boundary --- whether
the unwitnessed breath turns --- is a category boundary, not a gap. \textbf{The one open frontier} is named in
Section~\ref{sec:cpt}: observed weak-sector $CP$ violation is not captured by the family-sector
$CP=\mathrm{id}$ and remains underived. No published number changes; the paper deliberately inverts the
corpus's prose-to-mathematics ratio, the result being a philosophical account whose spine, not whose body, is
mathematical.

\end{document}
