Delay, Drift, and the Correction a Path Permits - A Generative Relational Account of Propagation Through Intermediaries 【（Preliminary）Draft】

Abstract

Two parties that cannot address one another directly may be reached through
others, and the practice is old. What passes along such a path is composed
afresh at every relay, so what arrives is not what was sent, and the path also
takes time, so what arrives is late. This paper treats the two together. A
longer path buys an interval and spends fidelity, and both follow from the
same relays, so the interval and the departure cannot be varied
independently. Two claims are then advanced. Where nothing corrects the
departure, a longer path is worse without qualification, which agrees with
what is known of lagged feedback in models of confrontation. Where a
correction process operates during the interval, the two effects oppose one
another, and the departure surviving at the far end is greatest at an
intermediate path length, given here as one divided by twice the product of
the correction rate and the latency of a hop. Short paths carry little
departure; long paths give correction time to work; the exposed region lies
between them. The account then observes that a path carrying an overture
carries a threat on the same terms, and that a threat arriving in a departed
form is read as evidence of intent, which makes the symmetry worse than a
caution. Existing statements that interdependence buys time for negotiation
are conceded, and the present account supplies the condition they leave
unstated. Nothing here is measured, no empirical claim is made, and the model
is offered as a construction whose behaviour is reported.

1. Introduction

This paper concerns what happens to a structure that reaches its destination
through intermediaries. Its objective is to state the two effects a longer
path has, to show that they oppose one another only under a condition, to
identify that condition, and to record that the same path carries hostility on
the same terms. The method is to state a construction, to report its
behaviour, and to say at each point what the construction is being asked to
carry.

The practice is old and is not in dispute. Where two parties cannot address
one another, a third may carry what passes between them, and diplomacy has
always used mediators, third states, unofficial contacts and multilateral
settings for exactly that. What the practice supplies is reach where none was
available.

Two consequences of using a path have been treated separately and are treated
together here.

The first is that a relay does not transmit. A party receiving a structure
construes it under its own procedures and composes what it sends onward, so
what leaves a relay is that relay’s composition. A companion paper establishes
this and draws the immediate consequence, that reach obtained through
intermediaries is purchased at the cost of fidelity, with the party whose only
route is longest having its claim composed by others most often
(Huang, 2026). Along a path of several relays the departures
accumulate.

The second is that a path takes time. Each hop has a latency, and a structure
arriving by a path of several relays arrives later than one arriving directly.
That delay has been treated as a resource. In the literature on stability in
the cyber domain the difficulty of attribution is discussed as placing a pause
on response times and so interrupting an escalatory sequence, the extension of
time giving the parties room to step back (Healey and Jervis, 2020). The literature
on the commercial peace carries a related observation, that institutions delay
responses to conflict and thereby allow parties to negotiate.

The paper takes the two together, and the first thing that follows is that
they cannot be varied independently. The interval and the departure are both
produced by the relays, so a party that lengthens a path to gain time has
spent fidelity to buy it, and a party that shortens a path to preserve
fidelity has given up the time. That is the trade of
Section 6, and it is stated as a trade because the account
selects no point on it.

The second thing that follows is a correction to the accounts that treat the
delay as a resource. Consider a path along which nothing corrects the
departure. The structure arrives later and in a more departed form, and there
is no respect in which the lengthening has helped. This is not a novel
observation and it agrees with what is understood of confrontation modelled
with a lag, where a longer delay between one side’s act and the other’s
response is ordinarily treated as a source of instability in place of a source
of stability; the base model is Richardson’s and the extension introducing the
lag is not (Richardson, 1960). Section 7 states it.

The condition under which the received accounts hold is therefore that
something operates on the departure during the interval. Where a correction
process does operate, the two effects oppose one another: the departure grows
with the number of relays and the time available for correcting it grows with
the same number. Section 8 reports what the construction
gives, which is that the departure surviving at the far end is greatest at an
intermediate path length, at one divided by twice the product of the
correction rate and the latency of a hop. Short paths carry little departure
because there have been few relays. Long paths deliver little because
correction has had time to work. The exposed region lies between them, and it
is bounded on both sides.

Two consequences are drawn from that shape and neither is obvious in advance.
A party facing a blocked channel and choosing among indirect routes is not
choosing between a safe short path and a dangerous long one, and may make
matters worse by lengthening a path that was already short.
And the region of exposure narrows as the correction rate rises, so a party
that improves its capacity to correct changes not only how much departure
survives but which paths are dangerous.

The account then observes what the same structure implies for hostility.
A path that carries an overture carries a threat on identical terms, and a
threat arriving in a departed form is worse than an overture arriving in one,
since a party receiving a distorted threat reads the distortion as evidence
about intent. Section 10 treats this, together with the
delegation of force through third parties, and it is the reason the account
supplies no recommendation that paths be lengthened.

Three limits are declared at the outset, and the first governs the others.
The paper makes no empirical claim. It measures nothing, tests nothing against
any record, and reports no quantity drawn from any case; the numbers in
Section 9 are properties of a construction with
constants the author chose. The composition performed at a relay is
represented by an accumulation whose form is stipulated, and
Section 13 records what a different form would change. And
the reading of the construction onto diplomatic practice is a reading, so a
reader who declines it retains the construction and loses the subject.

The exposition proceeds as follows. Section 2 fixes the scope.
Section 3 surveys the received mechanisms of the commercial
peace and Section 4 the existing statements about delay.
Section 5 states what a path does to a structure and
Section 6 the trade between the interval and the fidelity.
Sections 7 and 8 treat the two cases,
Section 9 reports the construction’s behaviour, and
Section 10 treats the same path carrying hostility.
Sections 11 through 14 state the
correspondence with the companion papers, the constraint form of the account,
its boundaries, and the questions it opens.

The paper belongs to a series applying generative relational theory to
governance, and it is the fifth of a set on diplomacy.

2. Scope and the Standing of the Construction

This section fixes what the paper undertakes. Its objective is to state the
object, to record what is carried from the companion papers, to state what the
construction is and is not, and to note the bounds observed.

2.1 The Object of the Account

The object is a structure travelling from one party to another through
intermediaries, together with two properties of the route: the departure that
accumulates as each relay composes what it received, and the interval the
route consumes. The object is a property of a route and not of any party, and
the level is that of the construction.

Three things lie outside. The paper offers no procedure for choosing a route,
and Section 12 states why. It offers no measurement of any
quantity it names, and Section 13 states what a measurement
would require. And it takes no position on whether any actual arrangement
exhibits the structure described.

2.2 The Results Carried from the Companion Papers

Three results are used and not re-derived. That what crosses between parties
carries structure and no content, and that the receiving party composes its
own determination from its own state, belongs to the companion treatment of
knowledge among differently situated parties (Huang, 2026). That
reach obtained through intermediaries is purchased at the cost of fidelity,
with no step on the route performed badly, belongs to the companion anatomy
(Huang, 2026). And that the strength of a coupling governs the rate
at which a relation moves in place of the range over which it moves belongs to
the companion treatment of coupled systems (Huang, 2026).

2.3 The Standing of the Construction

The construction of Section 5 has three constants: the scale of
the departure a single relay introduces, the latency of a hop, and the rate at
which a correction process acts. All three were chosen by the author. The
construction was written to see whether the two effects described in the prose
can be made to oppose one another, and they can.

What the construction does not do should be stated in the same place. It
measures nothing. No constant in it was estimated from any record, no output
of it was compared with any case, and the shapes of its curves are properties
of the constants. A reader who substitutes other constants obtains other
shapes, and the results reported below are the ones that survive that
substitution, which is why they are stated as relations among the constants in
place of as numbers.

2.4 The Political Bounds Observed

The material this paper reads is drawn from settings that remain live, and
three bounds are observed. No state is named and no episode is characterised.
The account is stated for routes in general, so nothing in it bears on any
actual relation without an argument the paper does not supply. And the
observation of Section 10, that the structure described
carries hostility as readily as it carries an overture, is stated as a
property of routes and not as a description of anyone’s conduct.

3. The Received Mechanisms and the Residue

This section surveys the mechanisms already proposed for the pacifying effect
of interdependence, together with the findings that dissent from it. Its
objective is to record what each mechanism claims, to concede the network
account that runs the other way, and to state the residue.

3.1 Cost

The oldest mechanism holds that interdependence raises the cost of conflict,
so that parties with much to lose are less willing to fight. The proposition
has been tested repeatedly and the affirmative finding is associated above all
with the work of Oneal and Russett (Oneal and Russett, 1999).

3.2 Signalling and the Capitalist Peace

A second mechanism holds that integration allows a party to demonstrate resolve
at a cost short of violence, so that disputes may be settled by signals in
place of by escalation, and that the effect belongs to capital and to financial
openness in place of to trade alone (Gartzke, 2007; Gartzke et al., 2001).

3.3 Expectations About Future Trade

A third mechanism is temporal and is distinct from the account offered here.
On the theory of trade expectations, what governs is what leaders expect of
the future trade environment: positive expectations favour peace, and
expectations of losing access favour initiating a crisis while the position
still permits it (Copeland, 2015). The mechanism concerns beliefs about a
future and not the time a message takes to arrive.

3.4 The Dissenting Findings

The pacifying finding is contested. Measured by salience, interdependence has
been found to accompany conflict in place of preventing it
(Barbieri, 1996), and the operationalisation of interdependence itself has
been shown to bear heavily on what is found (Gartzke and Li, 2003).

3.5 Coercion Through the Structure of the Network

A fourth body of work runs against any reading of connection as pacific, and
it is conceded here at length because it is the nearest account to this
paper’s own object. States holding authority over the central positions of
global economic networks can use those positions to coerce, so that the
structure of connection is itself an instrument (Farrell and Newman, 2019).

The present paper takes that as established and observes that it concerns a
different property of the network. That account concerns position, and what
follows from occupying a hub. This account concerns path, and what follows from
the number of relays between an origin and a destination. A network may be
read for either, and neither reading answers the other.

3.6 The Residue

Claim 3.1. (The residue). The received mechanisms locate the effect of interdependence in the cost of conflict, in the credibility of signals, in expectations about a future, in domestic composition, or in the coercive value of a position. None of them concerns what a route does to a structure passing along it, and none treats the interval a route consumes together with the departure it introduces.

4. The Delay Already Claimed and the Condition It Leaves Unstated

This section records the existing statements that treat an interval as
pacific. Its objective is to state each accurately, to identify what they
share, and to name the condition on which they depend and which none of them
states.

4.1 The Pause That Attribution Imposes

In the literature on stability in the cyber domain, the difficulty of
establishing who acted is discussed as placing a pause on response times and
so interrupting an escalatory sequence, on the reasoning that a crisis is
constituted in part by temporal pressure and that an extension of time gives
the parties room to step back (Healey and Jervis, 2020). The delay there is produced
by an epistemic difficulty and is treated as a benefit of it. The formulation
above is the present author’s summary of a position discussed in that
literature and is not offered as the wording of any party to it.

4.2 The Delay That Institutions Impose

The literature on the commercial peace carries a related observation. Liberal
institutions are said to delay responses to conflict, and thereby to allow
parties to negotiate and to avoid further violence. The delay there is
produced by procedure.

4.3 The Condition Both Accounts Presuppose

The two locate the delay differently and agree on what it accomplishes. In
each the added interval is treated as a resource, and in neither is anything
said about what must happen during it.

Claim 4.1. (The unstated condition). An interval is a resource only where something operates within it. Where nothing corrects the misconstrual that occasioned the exchange, the interval supplies delay and nothing else, and Section 7 states what follows. The accounts above are therefore correct under a condition they do not name.

The condition is not an objection to either account and is a restriction on
their scope. A party may reasonably suppose that the pause attribution imposes
will be used, since the parties to a crisis are ordinarily doing something.
What the present paper asks is what follows when they are not, and how much of
the benefit remains when the correction is slow against the delay.

5. The Path and What It Does to a Structure

This section states the construction. Its objective is to define a path and a
relay, to say how the departure accumulates, to say what the path costs in
time, and to record what each of these stipulations is doing.

5.1 The Relay and the Composition It Performs

A relay receives a structure and sends one onward. What it sends is composed
by its own procedures from the structure it received and from the state it
already occupies, so it is the relay’s composition and not the structure it
received. That is established in the companion papers and is taken as settled
here (Huang, 2026; Huang, 2026).

Definition 5.1. (A path). A path of length $n$ from one party to another is a sequence of $n$ relays, each receiving what the previous one composed. The structure arriving at the destination is the composition of the last relay.

5.2 The Departure and the Form of Its Accumulation

Each relay’s composition departs from what it received. Writing $\sigma$ for
the scale of the departure a single relay introduces, and taking successive
departures to be independent of one another, the departure at the end of a
path of $n$ relays has expected magnitude

$$\sigma \sqrt{n}.$$

The stipulation in Equation (1) is that departures accumulate as
independent increments, so that they grow with the square root of the number
of relays and not in proportion to it. What that represents is a relay whose
composition is as likely to move the structure back toward what was sent as
away from it. Two alternatives are available and neither is adopted here. If
relays share a common bias the departure grows in proportion to $n$; if a relay
tends to restore what a previous relay altered the growth is slower.
Section 13 records what each alternative changes.

5.3 The Interval the Path Consumes

Each hop has a latency, written $\tau$, so a structure arriving by a path of
$n$ relays arrives after an interval

$$n\tau$$

that a direct exchange would not have consumed.

The two equations are the whole of the construction’s account of a path, and
the next section states what follows from their having the same $n$ in them.

6. The Trade Between the Interval and the Fidelity

This section states the consequence of the two properties of a path being
produced by the same relays. Its objective is to state the trade, to say what
it forecloses, and to record that the account selects no point on it.

6.1 The Two Effects of One Choice

A party choosing a longer path has chosen both effects at once. By
Equation (1) the departure grows with the number of relays, and
by Equation (2) the interval grows with the same number. There is
no route that lengthens the interval and leaves the departure where it was,
since the relays that produce the one produce the other.

Claim 6.1. (The trade). Along a path, the interval available for correction and the fidelity of what arrives are bought against one another. A party that lengthens a path to gain time has spent fidelity to buy it, and a party that shortens a path to preserve fidelity has given up the time.

6.2 The Recommendation the Trade Forecloses

Claim 6.1 forecloses a recommendation that is otherwise available and that the
accounts of Section 4 come close to supporting. It is not
open to a party to secure the benefit of an interval by routing a matter more
indirectly, since what arrives at the end of the longer route is a more
departed structure, and the correction the interval permits is correction of a
larger departure.

Whether the exchange is favourable is therefore not settled by the trade
itself and depends on the rate at which correction acts.
Sections 7 and 8 treat the two cases.

6.3 The Point on the Trade That the Account Does Not Select

The account states the trade and selects no point on it, and the reason is
given at Section 12. What a party should prefer depends on
what it is trying to preserve, and the account holds no quantity in which the
interval and the fidelity could be compared.

7. A Path Along Which Nothing Corrects

This section treats the case in which the interval is not used. Its objective
is to state what the construction gives, to record that the result is not
novel, and to say what it settles about the accounts of
Section 4.

7.1 The Residual Where the Correction Rate Is Zero

Proposition 7.1. (Monotonicity). Where no correction acts, the departure arriving at the destination is $\sigma\sqrt{n}$ and is increasing in the number of relays. A longer path delivers a more departed structure later, and there is no respect in which the lengthening has helped.

The proposition follows from Equation (1) and requires no
computation. Values from the construction, at $\sigma = 1$: the departure is
$1.000$ at one relay, $2.236$ at five, $3.162$ at ten, $4.472$ at twenty, and
$6.245$ at thirty-nine.

7.2 The Agreement with What Is Known of Lagged Confrontation

The result is not novel and should not be presented as though it were. The
mathematical treatment of confrontation between two parties begins with
Richardson, whose equations carry no lag (Richardson, 1960). Later work in
that tradition has introduced the interval between one side’s act and the
other’s response as a variable, and in that literature a longer lag is
ordinarily treated as a source of instability. The extension is not
Richardson’s and is not attributed to him here; the sources for it were not
examined at first hand and the statement should be read as a report of what
that literature is understood to hold. A responder acting on information that is
old acts on a state the other party has left, and the correction it applies is
applied late and is therefore too large.

What the present construction adds at this point is only that the lateness
comes with a departure, so that the responder is acting late and on an altered
structure.

7.3 The Bearing on the Received Accounts

Proposition 7.1 settles that an interval is not a resource in itself. The
accounts of Section 4 are therefore not statements about
intervals and are statements about intervals in which something happens, which
is Claim 4.1 established from the construction in place of asserted.

8. A Path Along Which Correction Acts

This section treats the case in which the interval is used. Its objective is
to represent the correction, to state where the residual departure is
greatest, to state the region within which a path is exposed, and to record
what the result forecloses.

8.1 The Correction and Its Rate

Let a correction process act on the departure throughout the interval, at a
rate $\rho$, so that a departure present for a time $t$ is reduced by a factor
$e^{-\rho t}$. Applying this over the interval of
Equation (2) gives the departure surviving at the destination,

$$r(n) ;=; \sigma \sqrt{n}; e^{-\rho \tau n}.$$

The representation is a stipulation and a strong one. A single rate stands for
whatever a party does to establish what was meant, and
Section 13 records what it leaves out.

8.2 Where the Residual Is Greatest

Proposition 8.1. (The interior maximum). The residual of Equation (3) rises and then falls, and it is greatest at $$n^{*} ;=; \frac{1}{2\rho\tau}.$$ Short paths deliver little departure because few relays have composed; long paths deliver little because the correction has acted for longer. The greatest residual lies between them.

The stationary point follows from differentiating
Equation (3), and it was checked against the construction. At
$\tau = 1$ the predicted positions are ten relays at $\rho = 0.05$, five at
$\rho = 0.10$ and two and a half at $\rho = 0.20$; the computed positions were
ten, five and three. At $\rho = 0.05$ with $\tau = 2$ both give five.

8.3 The Region Within Which a Path Is Exposed

Claim 8.2. (The exposed region is bounded on both sides). Taking a magnitude of surviving departure beyond which an arrangement is exposed, the path lengths that exceed it form an interval bounded above and below. A path may therefore be too long and may also be too short, and lengthening a short path may move it into the exposed region.

Values from the construction, at $\sigma = 1$, $\rho = 0.05$ and $\tau = 1$:
the paths exceeding a magnitude of $0.8$ run from one relay to forty-one;
those exceeding $1.2$ from two to thirty; those exceeding $1.5$ from four to
twenty-three; those exceeding $1.8$ from six to fifteen; and those exceeding
$1.9$ from nine to twelve.

8.4 The Consequences for a Party Choosing a Route

Two consequences are recorded and neither is available before
Proposition 8.1.

A party choosing among indirect routes is not choosing between a safe short
path and a dangerous long one. The two ends of the range are the safe ones,
and a party that lengthens a route already short has moved toward the exposed
region in place of away from it.

And by Equation (4) the position of the greatest residual moves
toward shorter paths as the correction rate rises, while
Claim 8.2’s region narrows. A party that improves its own capacity to
establish what was meant therefore changes which routes are dangerous and not
only how much departure survives, so a route judged safe under one correction
rate is not thereby safe under another.

9. The Construction’s Behaviour

This section displays what the construction does. Its objective is to show the
two shapes the preceding sections state, and to record what the display is and
is not.

9.1 The Residual Against the Length of the Path

Figure 1 plots Equation (3) against the number
of relays, at four correction rates. At a rate of zero the curve rises without
turning, which is Proposition 7.1. At the three positive rates the curve rises
and falls, which is Proposition 8.1, and the turn moves toward shorter paths
as the rate rises.

Figure 1. The departure surviving at the destination, plotted against the number of relays on the path, at four correction rates, with $\sigma = 1$ and $\tau = 1$. The figure displays the behaviour of the construction and reports nothing about any arrangement.

9.2 The Position of the Greatest Residual

Figure 2 plots Equation (4) against the correction
rate. The curve is a hyperbola and it carries no information beyond the
equation, and it is shown because the relation between a party’s capacity to
correct and the length of route that exposes it is the paper’s least intuitive
statement.

Figure 2. The path length at which the surviving departure is greatest, plotted against the correction rate, with $\tau = 1$. The figure displays Equation (4) and reports nothing about any arrangement.

9.3 The Standing of the Two Figures

Neither figure measures anything. The three constants were chosen by the
author, no value in either was estimated from any record, and the vertical
scale of the first has no unit because the departure of a composed structure
from what was sent is a quantity the paper has not defined operationally.

What the figures show is that the two shapes the argument requires are
exhibited by the construction. What they do not show is that anything exhibits
them, and Section 13 states what would be required before
that question could be asked.

10. The Same Path Carrying Hostility

This section records what the construction implies for what a party would
rather not send well. Its objective is to state the symmetry, to say why it is
worse for a threat than for an overture, to note the delegation of force
through third parties, and to identify the one term that is not symmetric.

10.1 The Indifference of the Construction

Nothing in Section 5 concerns what the structure is. A relay
composes what it received, the departure accumulates, and the interval is
consumed, whatever the structure was sent to accomplish. A path that carries
an overture carries a threat on identical terms, and every result of
Sections 6 through 8 holds of both.

10.2 The Asymmetry in What a Departed Structure Costs

The symmetry of the construction does not make the two cases alike in what
they cost, and the difference runs against the threat.

An overture arriving in a departed form is received as an overture that did
not land, and the receiving party is left where it was. A threat arriving in a
departed form is received as a threat, and its content is a claim about what
the sending party intends. A departure in such a structure is therefore a
departure in the receiving party’s estimate of an intention, and the receiving
party has no way of telling a departure introduced by the relays from a
disposition of the sender. It will ordinarily attribute what arrived to the
sender, since that is what a threat is for.

Claim 10.1. (The distortion of a threat is read as intent). A structure whose content is a claim about the sender’s intention carries its departures into the receiving party’s estimate of that intention. Where the receiving party cannot separate what the relays composed from what the sender meant, a departure introduced along the route is attributed to the sender.

Claim 10.1 is the reason the account offers no recommendation that routes be
lengthened. A party lengthening the routes by which it makes overtures has
lengthened the routes by which it is understood to threaten, and it does not
hold the two apart.

10.3 The Delegation of Force Through Third Parties

Force delegated through a third party travels the topology the preceding
sections describe. What follows from the construction is only that such an
arrangement inherits the properties of a route: the acts arrive late, they
arrive composed by the parties that carried them, and by Claim 10.1 the
composition is attributed to whoever is taken to have sent them.

The account reaches no conclusion about any such arrangement and makes no
recommendation concerning any. What it supplies is the observation that the
capacity relied on by a party reaching a blocked counterpart indirectly is the
same capacity, and that a description of the first that omits the second has
described a route by the use it approves of.

10.4 The One Term That Is Not Symmetric

Two of the construction’s three constants are properties of the route and are
shared: the number of relays and the latency of a hop. The third is not.

Claim 10.2. (The correction rate is the available term). The correction rate belongs to the parties and not to the route, and raising it lowers the surviving departure whatever the structure was sent to accomplish. A party improving its own capacity to establish what was meant improves the arrival of overtures and of threats alike, which is a change it may make without also having improved a route it would rather not improve.

Claim 10.2 identifies where the account leaves room for action and where it
does not. Lengthening or shortening a route is ambiguous in its effects by
Claim 8.2 and symmetric between overtures and threats by Section 10.1.
Raising the rate at which a party establishes what was meant is neither.

11. The Correspondence with the Companion Papers

This section states how the objects of this paper stand to those of the four
companion papers on diplomacy. Its objective is to identify the counterparts
and to say what this paper adds to each.

11.1 The Relay and the Site of Construal

The companion treatment of knowledge among differently situated parties
represents the passage of a claim as a material event carrying no content
together with an operation the receiving party performs on its own state
(Huang, 2026). A relay in Section 5 is that
operation performed twice, once in receiving and once in composing what is
sent onward, and the departure of Equation (1) is the divergence
that treatment establishes, accumulated along a sequence.

11.2 The Cost of Reach, Put in Time

The companion anatomy holds that reach obtained through intermediaries is
purchased at the cost of fidelity, that a claim arriving by a path of length
$n$ has been composed by others $n$ times, and that no step on the route need
be performed badly for this to hold (Huang, 2026).

This paper is that claim put in time. What the anatomy states of fidelity, it
states without reference to the interval the route consumes; what this paper
adds is that the interval grows with the same $n$, that the two are therefore
bought against one another, and that where a correction acts they oppose one
another with the consequence of Proposition 8.1.

11.3 The Rate and the Range

The companion treatment of coupled systems holds that the strength of a
coupling governs the rate at which what two parties hold in common moves and
not the range over which it moves (Huang, 2026). The present paper
concerns a different quantity and reaches a formally similar result: the
length of a route governs both the interval and the departure, and the
question in each case is which of two properties a parameter controls.

11.4 The Deposit and What a Route Delivers

The companion treatment of the gift holds that what a received structure
leaves behind is the determination the receiving party made of it, laid down
in the context against which it construes what arrives next
(Huang, 2026). Along a route, every relay leaves such a deposit, and
what the destination receives has passed through as many of them as there are
relays. The present paper does not develop that and records it as a question
at Section 14.

12. The Constraint Form of the Account

This section states the form in which the account’s normative content is held.
Its objective is to fix the relation between the construction and any reason
for action, to give the ground on which no route is preferred to another, and
to record the sentence the account must remain able to refuse.

12.1 The Wall Between a Construction and a Recommendation

The account describes what a route does. That a departure grows with the
number of relays, that an interval grows with the same number, and that a
surviving departure is greatest at a stated length are statements about a
construction. None of them is offered as a reason for choosing a route or for
the treatment of any party.

The separation requires attention here because the construction has an obvious
reading as advice. A quantity called a surviving departure sounds like
something to be minimised, and nothing in the construction supports that. Where
a normative statement appears in this paper it is imported, and it is
attributed at the point of use.

12.2 The Grounds for Preferring No Route

Three grounds tell against an ordering of routes by the quantities of this
paper.

The trade of Claim 6.1 is between an interval and a fidelity, and the account
holds no quantity in which the two could be compared, so a route that buys
more of one and less of the other is not thereby better or worse.

By Claim 8.2 the exposed region is bounded on both sides, so a direction of
improvement is unavailable: a route may be improved by lengthening or by
shortening depending on where it stands, and the account supplies no way of
establishing where any actual route stands.

And by Section 10.1 the construction is indifferent to what a route carries,
so an ordering of routes would order them for overtures and for threats at
once.

12.3 The Sentence the Account Must Remain Able to Refuse

A test of the account is whether it can refuse the following sentence: that
where a party’s claims are likely to be composed by others in transit, they
should be routed through fewer relays even where doing so leaves the party
unable to reach its counterpart at all.

The account refuses it, and three features secure the refusal. Reach is what
the route was for, and a route that does not arrive has no fidelity to
preserve. The comparison the sentence requires, between a departure suffered
and a counterpart unreached, is one the account holds no quantity to make.
And by Claim 8.2 the shorter route is not the safer one in general, so the
sentence rests on a monotonicity the construction denies.

The sentence is refusable because nothing in the account values a smaller
departure, a shorter route, or a longer interval. A reader who finds the
account recommending any of these has found an importation, and it is not the
paper’s.

13. The Boundaries of the Undertaking

This section states the boundaries within which the account holds. Each is
given as a property of the undertaking together with what would have to be
established for it to be moved.

13.1 The Absence of Any Empirical Content

The paper measures nothing. No constant in the construction was estimated from
any record, no output of it was compared with any case, and no claim is made
that any arrangement exhibits what the construction exhibits.

Moving this boundary requires an operational definition of the departure of a
composed structure from what was sent, which the paper does not supply and
which Section 9.3 records as the reason its figures carry no unit. It would
also require a way of counting relays in an actual route and of estimating the
rate at which parties establish what was meant, and the paper offers neither.

13.2 The Form in Which Departures Accumulate

Equation (1) takes successive departures to be independent, so
that they grow with the square root of the number of relays. The stipulation
carries the interior maximum of Proposition 8.1 and a reader should know what
it excludes.

Where relays share a bias the departure grows in proportion to the number of
relays, and the residual is $\sigma n e^{-\rho\tau n}$, whose maximum lies at
$1/(\rho\tau)$, twice as far along. Where a relay tends to restore what a
previous relay altered the growth is slower and the maximum lies nearer the
origin. The qualitative result survives both, and its position does not, so
nothing in the paper turns on the number $n^{*}$ beyond its being finite.

13.3 The Representation of Correction by a Single Rate

A party establishing what was meant does many things, over unequal intervals,
with results that depend on what it is trying to establish. The construction
represents all of it by one exponential rate.

What that leaves out is at least the following: correction that acts only at
the destination in place of throughout the route, correction whose own
messages travel the same route and are themselves composed, and correction
that is available for some structures and not for others. Each would change
the shape of Equation (3), and the second would make the model
self-referential in a way the present one is not.

13.4 The Restriction to One Route

The construction treats a single path. A party ordinarily has several
available at once and may use them together, and what follows from combining
routes of different lengths is not treated here.

13.5 The Reading, Which Remains a Reading

The identification of the construction’s terms with anything in diplomatic
practice is a proposal. A relay is not defined here by anything a practitioner
would recognise, the latency of a hop is not the time any particular exchange
takes, and the correction rate names a capacity the paper has not
characterised. A reader who declines the identification keeps the construction
and loses the paper’s subject.

14. Questions Opened by the Account

This account identifies a structure the existing treatments of interdependence
and of delay leave undescribed: the interval a route supplies and the departure
it introduces are produced by the same relays, so they cannot be varied apart,
and where a correction acts the two oppose one another with a maximum between
them. If that structure is real, the following questions arise, and the account
answers none of them.

Q1. Section 13.1 records that the paper supplies no operational
definition of the departure of a composed structure from what was sent. What
would such a definition look like, and could it be applied to any record that
exists?

Q2. Proposition 8.1 places the greatest surviving departure at
$1/(2\rho\tau)$. Are there arrangements in which the number of relays and the
rate of correction can both be estimated well enough for the position to be
located, and would practitioners recognise the resulting region?

Q3. Claim 4.1 holds that an interval is a resource only where
something operates within it. In the cases where the received accounts observe
an interval doing pacific work, what was it that operated, and at what rate
against the delay?

Q4. Section 13.2 records that a shared bias among relays moves the
maximum to $1/(\rho\tau)$. Which form of accumulation holds where a route runs
through parties that share an interest in how a structure is composed?

Q5. Section 13.3 notes that a correction whose own messages travel the
same route would make the construction self-referential. What does the account
become when correction is itself subject to the departure it corrects?

Q6. Claim 10.2 holds that the correction rate is the term available to
a party, since the route is shared. Is that so in practice, and are there
parties able to alter a route without altering it for what they receive?

Q7. Section 11.4 observes that every relay leaves a deposit in its own
context, so a structure travelling a route passes through as many as there are
relays. What accumulates in the relays themselves over a sustained practice of
carrying, and does it bear on what they compose?

Q8. Section 13.4 restricts the account to one route. What follows from
using several routes of unequal length at once, and does the exposed region of
Claim 8.2 have a counterpart for a set of routes?

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