What Methodology 0 does is point directly: Negativa is the sole axiom, everything else a theorem. What Methodology VII does is systematize the road that approaches it — from Pseudo-Dionysius to Maimonides to Nicholas of Cusa, two thousand years of negative theology stripping away, layer by layer, what Negativa is not. That road is called via negativa.

What this essay says is that it is not the only road.

The reason is hidden inside Methodology 0's own argument. Every time Negativa operates it leaves a remainder. The remainder is not an added axiom; it is the necessary accompaniment of Negativa's operating. Read that sentence backwards and a second road opens: as long as Negativa operates, remainder is left over; and wherever a remainder is visible, the trace of an operation is visible.

So one need not enter from the Negativa end. One can enter from the remainder end — not by excluding what Negativa is not, but by tracing the marks it leaves back to it. Opposite direction, different starting point, and the same Negativa as limit-indication.

That road is called via rho, the way of the remainder.

1. A Dual, Not a Supplement

The relation between the two roads has to be stated precisely first, because it determines the character of everything that follows.

Via rho and via negativa are duals. Not competitors, and not supplements.

Competition would mean one of them comes closer to the truth than the other. Supplementation would mean one fills a gap in the other. Duality means both are complete in themselves and enter the same thing from different directions.

This distinction is not fastidiousness about wording. If it were supplementation, via negativa would have a gap and Methodology VII's work would be incomplete. If it were competition, one of the two roads would have to be the lesser. Duality says: both roads are walkable, both can be walked to the end, both point at the same Negativa — and what they see differs. That difference is not because one of them is looking wrong. It is because Negativa itself has two faces.

The numbering carries this structure. Methodology 0 points directly at Negativa; Methodology VII gives the first road toward it a paper of its own; Methodology 00 proposes that road's dual. The two zeros in 00 correspond to the two endpoints of the way of the remainder: the first zero is the starting point, remainder; the second is the destination, Negativa. The via in between has no character to carry it — and that empty space is precisely where all of this paper's argument takes place.

2. A Remainder Is Not Arbitrary Residue

For this road to exist, it first has to be shown walkable. And the first condition of walkability is that the remainder must have direction. If a remainder were just an undifferentiated heap of residue left over from an operation, there would be nothing to trace.

A remainder has direction. Every remainder is the specific incompleteness left by one specific operation of Negativa, and that specificity is itself directionality.

More precisely: a remainder is not an independently existing thing but a trace. And a trace necessarily points at the act that produced it. To see a footprint is to see that someone walked — the entire meaning of a footprint lies in its pointing back at the step that made it. The same holds for the remainder.

One misreading has to be blocked here. The remainder is not a "product" of Negativa's operation in the sense of an independent entity. If it were an independent entity, it would constitute a second origin alongside Negativa, and Methodology 0's sole axiom would break on the spot. The remainder is a trace, and a trace depends ontologically on the operation that produced it; it cannot exist independently. That dependence is precisely the ground of its directionality.

The second condition is whether that pointing can be traced.

It can, and no external instrument is needed. Because the act of tracing is itself another operation of Negativa — to trace is to negate the remainder's closure and ask where it came from. Tracing a remainder means performing a negation on it, so that it points at its own condition of production.

This step has an elegant consequence: via rho is not a road requiring special equipment. Anyone who sees a remainder is already tracing. The moment someone asks "where did this incompleteness come from," they are standing on the way of the remainder. Its feasibility is as fundamental as via negativa's; neither depends on any mechanism beyond Negativa's own operating.

3. Does the Tracing Diverge?

Here is an objection that has to be met head-on, and the way it is met is where this paper shows its craft.

The objection runs: the act of tracing a remainder is itself a new operation of Negativa, and that operation necessarily leaves a new remainder. Tracing the new remainder is another operation, leaving another remainder. Doesn't the tracing then simply manufacture remainders forever, never arriving at Negativa?

The objection rests on an intuition: recursion means divergence.

But via rho's recursion does not diverge. To say why, one first has to refuse a formulation that sounds entirely natural.

One cannot say "the new remainder is closer to Negativa than the old one." Because "closer" presupposes a metric, presupposes measurable distance — and that amounts to placing Negativa inside a metric space, treating it as a point with coordinates. Negativa cannot be objectified; it has no coordinates. Talk of "distance" to something unobjectifiable does not work at all.

The correct formulation is: via rho's recursion is not a decrease of distance in a metric space but a nested peeling in the topological sense.

Concretely. The original remainder, as a trace, is wrapped in a surface layer of apparent closure — it looks like something self-sufficient. Questioning peels that shell away and exposes the deeper structure the trace points at; that exposure is the new remainder. The new remainder has a shell of its own, and the next questioning peels again.

So each act of questioning does not "shorten a distance." It "peels off a layer of pseudo-closure."

An image: the tracing is like a series of nested filters. Each new remainder is a finer mesh, containing the whole structure of the previous layer plus one more layer of questioning directed at it. The mesh grows finer and finer. But a filter is never the thing it is trying to separate out. We cannot measure how far Negativa still is; we only know the mesh is monotonically tightening.

The structure can be stated harder: ρ_j has a higher order of manifestation than ρ_i if and only if ρ_j explicitly contains the trace of questioning directed at ρ_i's condition of production. This is a structural partial order, not a metric distance. We do not say "ρ_j is nearer to Negativa by so much"; we say only "ρ_j manifests one layer more than ρ_i."

This handling incidentally leaves Zeno at the door. Achilles cannot catch the tortoise because Zeno assumed motion across distance in a metric space — each step covering half the remaining gap, so the gap is never closed. The way of the remainder concerns nested structure under topological peeling, not the crossing of a distance. Zeno's paradox here is not resolved; it is found inapplicable. The two are not the same kind of problem to begin with.

The temperament of via rho as a method shows itself here.

It is not a method of awaiting revelation — no single negation arrives. Nor is it a deduction anticipating completion — nothing finishes when the derivation ends. It is a method of sustained questioning. It never reaches a terminus one can hold, because Negativa cannot be objectified and cannot be held in the hand; and yet no step is wasted, because every step is a real structural peeling rather than turning in place.

4. Both Roads Point at the Same Negativa

Walkability settled, one question remains: is the limit via rho reaches the same as the limit via negativa reaches? If not, the two are not duals but two unrelated roads.

They are the same. The argument turns on whether the two descriptions structurally co-refer.

The Negativa that via negativa arrives at is described as "the limit object that is unnameable, unknowable, unconstructible." Unnameable, because naming is construction. Unknowable, because knowing presupposes a subject–object split, and that split is a result of Negativa having already operated. Unconstructible, because constructs are sediment of Negativa's operating, not Negativa itself.

The Negativa that via rho arrives at is described as "the common condition of operation of all remainders." And for that condition to play the role of what all remainders jointly point at, it must be unnameable (it is the condition of construction, not a construct), unknowable (it is antecedent to the subject–object split and cannot be objectified), and unconstructible (all constructs are products of its operating).

The three "un-"s correspond one to one. Not by coincidence: the two descriptions are saying the same thing from different angles — one from the angle of excluding what it is not, the other from the angle of what its traces jointly point toward.

But the faces the two roads reveal differ, and that difference is where the value of the duality actually lies.

Via negativa makes Negativa appear as a limit. Through exclusion it appears as the common exterior of every "is not" — a static, unreachable position existing as a boundary. This corresponds to a topological limit in mathematics: an unreachable boundary outside the closure.

Via rho makes Negativa appear as a condition. Through tracing, it appears as the common source of all operating — a dynamic position, continuously present, existing as a presupposition. This corresponds to an analytic limit: the value a sequence converges toward.

The same Negativa carries both roles at once.

Which means the two roads defend each other against the other's characteristic misreading.

Walk only via negativa, and Negativa is easily read as a purely negative object — unnameable, unknowable, unconstructible to the point of near-vacancy. The reader asks: what distinguishes this purely negative thing from nothing at all? Via negativa can only answer by going on excluding — Negativa is not nothingness either.

Walk only via rho, and Negativa is easily read as a persistently present dynamic background, and from there misread as a reified first cause. The reader asks: what distinguishes this continuously present condition from some primordial entity? Via rho can only answer by insisting again on unobjectifiability.

Together: unreachability prevents Negativa from being reified, continuous presence prevents it from being voided. That is why neither road can replace the other.

There is a further correspondence of position worth recording. Via negativa is a posteriori: it starts from constructs already given and excludes them layer by layer, and each step depends on existing content being present — someone must first propose a construct before there is anything to exclude. Via rho is a priori: it does not start from phenomena but from the structural fact that remainder is the necessary accompaniment of Negativa's operating. "There is remainder" is not an empirical observation; it is a structural feature of operating itself.

Methodology II built an epistemological map: a direction axis (a priori / a posteriori) crossed with an operation axis (synthetic / analytic), yielding four quadrants — deduction, reduction, induction, abduction — and argued that none of the four may be settled in, that all must be traversed. But Methodology II did not propose the traversal itself as a method. The two viae supply exactly that layer: via negativa is the methodological self-awareness of the a posteriori axis, via rho of the a priori axis. Together they cover the whole map.

This reveals a deeper duality between the two papers. Methodology II speaks at the level of the subject's movement (the subject pushed through the four quadrants by remainder); Methodology 00 speaks at the level of operational ontology (Negativa operates and leaves remainder, remainder drives the next operation). "Remainder pushes the subject through" and "remainder drives the next Negativa" are the same structure manifesting at two levels of description.

The way of the remainder has a mathematical carrier too: ZFCρ. ZFC, through extensional closure, expresses "choice as operative act" as a choice function — that is, reduces it to a set of ordered pairs. What ZFCρ does is name the structural trace that reduction leaves behind as ρ. It is not a set, not an element of any model; it is a metatheoretic mark on ZFC's design choice.

That is precisely via rho realized mathematically. It does not try to eliminate all remainder from the formal system — that would be the mathematization of via negativa. It acknowledges remainder as the trace extensional closure cannot absorb, and approaches Negativa as condition of operation from there. ZFCρ's three laws of chaos — cannot not develop (ρ ≠ ∅), cannot not have direction (ρ is specific), cannot not be cut (ρ is itself formalizable) — are the precise mathematical expression of via rho's basic structure.

So SAE using via negativa in its philosophical work and ZFCρ in its mathematical work is not two disciplines going their separate ways. It is one pair of dual methods unfolding in two disciplines at once.

5. Asymmetric Mutual Causation

Everything so far has established that the way of the remainder is walkable and lands where it should. From here on is what the road independently sees once walked — the core of Methodology 00 as independent work.

The core finding is called asymmetric mutual causation.

The definition first. Two terms A and B stand in mutual causation if and only if two conditions hold simultaneously: first, A cannot operate independently of B; second, B cannot exist independently of A.

Note that the two conditions have different modalities. The first concerns the operational layer (can A act), the second the existential layer (can B be). They are not two symmetrical faces of one relation; they are two directions in different modalities.

That is the exact sense of "asymmetric." Symmetric mutual causation would require the two terms to depend on each other within the same modality — either both cannot exist or both cannot operate. Asymmetric mutual causation requires only that both directions hold simultaneously in different modalities. The structural force lies in both directions holding at once, not in their sharing a modality.

This clarification is the most consequential in the paper. Without it a reader defaults to assuming mutual causation is symmetric, and concludes that the two terms have equal standing — which would raise remainder to the status of a co-original principle alongside Negativa, and Methodology 0's sole axiom would be gone on the spot.

Now substitute Negativa and remainder.

Negativa cannot operate independently of remainder. This follows directly from the conservation of remainder: every operation of Negativa is necessarily incomplete, and that incompleteness appears as remainder. There is no "pure operation of Negativa" unaccompanied by remainder.

Remainder cannot exist independently of Negativa. This is the ontology of traces: no operation, no trace.

Both conditions hold, in different modalities. Negativa and remainder therefore satisfy asymmetric mutual causation.

It is worth pausing on the character of this result. Methodology 0 had already argued both halves separately — remainder is the product of Negativa questioning itself, and remainder drives the next operation. Methodology 0 kept them apart in order to hold the line that remainder is not an independent thing. What Methodology 00 does is set those two existing conclusions side by side and notice that together they are exactly the two directions of asymmetric mutual causation.

So this is neither a new axiom nor a revision. It is a name for a structure that was already there. And the name earns its keep: with it, the rereadings in the later sections have something to hold onto.

A second misreading has to be blocked: taking mutual causation for a special dependence between two independent entities — each of which could in principle exist alone, and which merely happen to need each other under some condition. On that reading, change the condition and the mutual causation dissolves.

It does not work that way. The mutual causation of Negativa and remainder is necessary, not contingent. Because Negativa cannot operate completely "under some conditions" and incompletely "under others" — it is always incomplete, always leaves remainder. A Negativa able to operate independently of remainder is simply not the Negativa Methodology 0 argued for. Likewise, remainder is not something that "depends on Negativa under certain conditions": the concept of a trace already presupposes a producer, and a trace independent of its producer is not a trace but something else.

So asymmetric mutual causation is not a relation between two entities. It is a structural feature of each, as itself.

It can be drawn in one step tighter: the act of Negativa questioning itself is already the minimal unit of asymmetric mutual causation. Methodology 0 named that core act with a verb phrase (Negativa questions itself); Methodology 00 names the same act's structure with a noun phrase (asymmetric mutual causation). Same referent, named once from the angle of process and once from the angle of structure.

There is a term in the philosophical tradition that can be borrowed to support this: Gleichursprünglichkeit, equiprimordiality, which Heidegger uses in §28 of Being and Time. He uses it to describe Dasein's worldhood and selfhood — two structures equally primordial at the level of origin, neither reducible to a derivation of the other.

But the borrowing must have a boundary, and that boundary is exactly where the whole paper's proportion is decided. Heidegger's equiprimordiality is symmetric: worldhood and selfhood are of equal standing. The co-originality of Negativa and remainder is asymmetric: Negativa still gives remainder its condition of existence, while remainder gives only the dynamic condition for Negativa to continue operating.

So what is borrowed is the structural sense of primordiality — that the two are inseparable at the level of origin — and not the symmetry of the two ends. Borrow the symmetry along with it and remainder is raised to a co-original principle beside Negativa, and the argument collapses on the spot.

The main thesis can therefore be said in a line: at the axiomatic layer Negativa is singular; at the operational layer Negativa and remainder come in a pair.

6. The Asymmetry Inside the Notation

Written out, the formalization of asymmetric mutual causation looks like this:

𝒩 —op_i→ ρ_i —drives→ 𝒩 —op_i+1→ ρ_i+1

The most worthwhile thing in this formula is not the arrows. It is the distribution of the subscripts.

𝒩 carries no subscript. However many times it appears, it refers to the same Negativa — singular at the axiomatic layer, needing no version number. Whereas op and ρ both carry subscripts: operations unfold in an ordinal sense, and remainders have distinguishable concrete forms.

So the asymmetric distribution of the symbols directly encodes the asymmetry of the concepts. At a glance the formula says: these two are not equals — one is a unified indication (no subscript), the other a distinguishable product (subscripted).

The subscripts must be read correctly. They are not time. Time is itself a product of 3DD, and Negativa precedes 3DD — read the subscripts as time and you have dragged Negativa into its own product. What they mark is the level of logical unfolding, or the depth of fractal nesting.

Likewise the arrows are not a "Negativa first, then remainder" succession. An arrow expresses a structural direction of dependence: Negativa gives remainder its condition of existence. That giving requires no passage of time to occur.

One refinement is worth recording. What op applied to 𝒩 actually produces is not only remainder but also construct. The construct is the sediment; the remainder is the part the sediment cannot close over. Both issue from one operation, but they are not the same thing. So the more precise writing is 𝒩 —op_i→ (C_i, ρ_i), and what drives the next operation is ρ_i, not C_i — a construct by itself pushes nothing; only the part it cannot close over pushes.

That distinction gets used in the next section.

7. Why It Works This Way: A Wall That Cannot Be Gone Around

A natural question surfaces here: why are Negativa and remainder in a relation of asymmetric mutual causation rather than some other relation? Why must Negativa leave remainder? Why must remainder drive the next operation? Where do these necessities come from?

The question looks entirely reasonable, and it has already hit the boundary.

It presupposes that the structure of asymmetric mutual causation can itself be traced to a deeper source — that something more fundamental exists which explains why it is this way rather than another. And the structure of that presupposition is identical to the question "where does Negativa come from" in Methodology 0.

Methodology 0 already argued why that question necessarily hits a wall: every act of questioning requires a direction, and direction is a product of 3DD; Negativa precedes 3DD, so using direction to question Negativa amounts to using Negativa's own product to give Negativa a direction. That is the exact sense of "the chisel strikes the chisel," of the hammer that strikes a hammer and takes no damage — the thing-in-itself appearing here as the structural impossibility of the questioning itself.

And asymmetric mutual causation is the structure of Negativa as operating. So asking "why does asymmetric mutual causation work this way" is asking "why is Negativa this Negativa" — the same wall, phrased differently.

This is not a dodge. The thing-in-itself is not a concept introduced here to escape; Methodology 0 had already set it in place. And conversely, refusing to acknowledge the wall is the real problem: it would mean using Negativa's products to explain Negativa itself, producing circularity or infinite regress in the chain of argument. Acknowledging it keeps the argument clean — fully unfolded where argument is possible, honestly halted where it is not.

There is also an incidental gain, worth stating on its own.

Each road, walked to its end, hits the same wall. This is not a coincidence. Had they hit different things-in-themselves, that would show they were pointing at different objects. Hitting the same wall is exactly the fact that both point at the same Negativa, appearing once more at the boundary.

So the way of the remainder meeting the thing-in-itself at the end is not the failure of that road. It is the two roads meeting each other before the same wall.

8. Why Exactly Four Phases

Methodology 0 derives four phases from Negativa questioning itself: being; nothing; neither-being-nor-nothing; and the negation of "neither-being-nor-nothing." That derivation runs along via negativa — the four phases as products of questioning.

Seen from the way of the remainder, the four phases are four manifestations of asymmetric mutual causation in the course of its unfolding.

First phase, being. When Negativa questions itself there are two participants: Negativa as questioner and Negativa as the object questioned. The questioner cannot operate independently of the object (a questioning that spins freely is not a questioning); the object cannot be posited independently of the questioner's operating. This is exactly the minimal unit of asymmetric mutual causation. And the reason "two Negativas mutually constituting each other's condition" can be said at all is that there are "two" as the ends of a co-arising — and that sayability is being.

Second phase, nothing. Nothing is not the absence of being. "The absence of being" still operates within being's frame. Nothing is the negation of the co-arising condition on which being depends — it negates not instances of being but the ground on which being stands. So the second phase is also a manifestation of asymmetric mutual causation, one level higher: the two ends of this co-arising are the whole first-phase unit and its negation.

Third phase, neither being nor nothing. The first phase has a remainder it failed to cover; so does the second. Here the two remainders collide, both pointing at "the part of asymmetric mutual causation not yet manifested." The collision produces a new unit whose content is the negation of the being–nothing dichotomy itself — not a third product proposed alongside being and nothing.

Fourth phase, the negation of "neither being nor nothing." The integrated state produced by the third phase is already a complete unit of asymmetric mutual causation. So the fourth phase's object of questioning is no longer any particular product but the structure of the unit itself. Structure meets structure — and that constitutes closure. A fifth questioning still produces a unit of asymmetric mutual causation; it merely repeats within the same self-referential structure, generating no new structural type.

Taken together: the first phase is simple co-arising, the second the inversion of that co-arising, the third the integration of the inversion's products, the fourth the self-reference of that integration. The four phases are not four unrelated products but every step one structure can take as it unfolds.

Methodology 0 answers where the four phases come from — questioning generates them. Methodology 00 answers why there are exactly four — the unfolding of asymmetric mutual causation can take only four steps. The two answers are complementary.

9. Five Facets of One Structure at Different Granularities

The chisel-construct cycle has five facets: chisel, construct, remainder, bridge, thing-in-itself. Methodology M named them one by one from the unfolding face of via negativa, each with its precise position. What the way of the remainder sees is their common source.

Chisel is the Negativa face of the mutual causation — the chisel operating is Negativa operating, corresponding to op in the formula.

Construct is the sediment of the operation, corresponding to C_i. Remainder is the part the sediment cannot close over, corresponding to ρ_i. The distinction from the previous section must be held here: construct is not remainder; it is the construct's incompleteness that appears as remainder.

From this follows an answer to a claim in Methodology M that looks slightly mysterious — why construct has no direction while remainder does. Because a construct is only sediment, and sediment by itself points nowhere; whereas remainder is the part that "cannot be closed," and the state of not-being-closable itself points at a next time. Direction is not an extra property remainder happens to carry. It falls out of its definition.

Bridge is the next chisel at the remainder. It corresponds to the step from ρ_i to op_i+1 in the formula. Two sides have to be kept apart here: the remainder gives that step a legitimate landing — the bridge relation; only when the landing is actually taken up by some act of chiseling is there a bridge event. The remainder supplies the landing, not the happening. In the formula that step is an abstract transition; the bridge gives the transition a concrete mechanism. Without this facet, the cycle could say "the remainder is where the next chisel can land" but not "how that landing comes to be taken up."

Thing-in-itself is the limit at which the structure meets itself. In ordinary unfolding, asymmetric mutual causation has two distinguishable faces, Negativa and remainder; but when both ends are Negativa itself — chisel striking chisel — there is no remainder as the other, distinguishable end. Only Negativa at both ends. Questioning this far, one finds oneself using the chisel to question the chisel.

The five facets are therefore not five parallel concepts but one structure manifesting at different granularities: chisel and construct are the structure itself, remainder its dynamics, bridge its mechanism of operation, thing-in-itself its limit.

10. 16DD: The Remainder's Second Identity

This section is where the whole essay lands, and what the way of the remainder sees at its furthest point.

A distinction has to be set down first, because it is the precondition for everything after: remainder has different identities at different levels.

Within 1DD through 15DD, remainder is a dynamical term. Its function is to drive Negativa's next operation, to let the cycle continue. This is the remainder used throughout the preceding sections.

At 16DD, the position where subjects meet, remainder is an un-swallowable externality. It no longer drives anything; it constitutes the recognition of the other's status as an end.

Why must this distinction be made? Because without it an ethical catastrophe follows.

16DD is the position at which two subjects recognize each other as ends in themselves. If "being each other's remainder" here is read in the dynamical sense, then subject A becomes the driving term of subject B's operating — A is material B uses to push itself along. That is the precise definition of treating a person as a means, in direct violation of SAE's core proposition.

The concept of ontological remainder blocks that slide.

Unfolded: subject A is a complete unit of asymmetric mutual causation, unfolding continuously in its own sequence. So is subject B. When the two units meet, A appears as a whole within B's field — and A is not a product B's constructs can generate.

A crucial precision is required here. That B cannot swallow A is not a matter of B's cognitive capacity being insufficient. Read as a capacity problem, A's independence would depend on B's inadequacy, and a sufficiently powerful B could swallow A — the ethical content of 16DD would be hollowed out.

The precise understanding is this: however complete B's constructs become, that does not alter the ontological fact of A being an independent unit of mutual causation. It is not that B cannot reach A (a capacity problem); it is that none of B's constructs is in A's position (an ontological one). A's position is A itself.

So from B's side, A is an ontological remainder — not a trace B's operating could produce, but an externality B's constructs cannot close over. And the same in reverse. Both directions together are what "recognizing each other as ends in themselves" means.

And that recognition is not an ethical attitude or a subjective choice. It is the relation that structurally must appear when two units of asymmetric mutual causation meet.

From which follows the heaviest conclusion in this essay.

Kant's "a person is an end in themselves, never merely a means" is given in Kant as a categorical imperative, and its justification rests on a presupposition: a person, as a rational being, has intrinsic worth. That presupposition can be challenged — a utilitarian will ask why it is rationality that has intrinsic worth rather than happiness or utility.

The way of the remainder supplies a different justification for the same proposition. It is not that one ought not swallow the other; it is that structurally one cannot. And since one cannot, the only structurally available posture is to recognize the other as a complete unit. The "must" here is the structural cannot-not, not the moral ought.

So "persons as ends" moves from an imperative resting on the intrinsic worth of rationality to a necessary corollary of asymmetric mutual causation at the 16DD position.

This path has an advantage: it depends on no value presupposition, so a utilitarian objection has nothing to land on. One may dispute the value judgment that rationality has intrinsic worth; one cannot use a value objection to refute the structural statement that A, as a complete unit, cannot be swallowed by B.

But two qualifications are needed, or the conclusion gets read too far.

First, this is a parallel supplement, not a replacement. Kant's route, resting on the intrinsic worth of rationality, still holds at its own level. The two routes are complementary and together strengthen the proposition's justification. This series' posture toward Kant has always been completion, never challenge.

Second, this route has a starting point of its own, and starting points can be refused. Kant's is "rationality has intrinsic worth"; the way of the remainder's is "Negativa is the sole axiom." Neither is absolutely unrefusable. The difference is only this: refusing the way of the remainder's starting point requires going one layer deeper than refusing Kant's — the former is an axiom, the latter a presupposition.

One further understanding opens from here, concerning the two ends of the DD sequence.

0DD and 16DD have long been seen as isomorphic in some fashion — both endpoints of the sequence, the cycle reaching some limit at each. Asymmetric mutual causation gives that isomorphism a structural account.

0DD is asymmetric mutual causation before differentiation. At that position Negativa and remainder have not yet separated into two clearly distinguishable faces; chisel and construct are undivided, because the independent manifestation of construct and of remainder requires enough layers of structural unfolding, and at this basal position those layers have not yet grown. To be emphasized: "undifferentiated" is not temporal — not "has not happened yet" — but architectural: the structure has not unfolded to that layer.

16DD is the coincidence after full differentiation. Through the complete unfolding of 1DD to 15DD, Negativa and remainder have separated and each subject has grown into a complete unit of mutual causation; and when a unit appears as a whole, its chisel and its construct coincide. Two wholes meeting is two chisel-construct coincidences meeting.

So 0DD is chisel and construct undivided, 16DD is chisel and construct coincident. Both ends are complete states of asymmetric mutual causation — one a potential completeness, the other an unfolded one. The DD sequence is therefore not a line from origin to terminus but one full cycle of a single structure, from potential through unfolding to encounter.

This also explains why the thing-in-itself appears exactly once at each end: at 0DD as the presupposition of operating, at 16DD as its limit. Because both ends are complete states, both meet the structure's own limit.

11. Ending on Remainders

Methodology 00 gives no conclusion. It ends on a list of its own remainders. The practice is itself an application of what it argues: a paper is a construct, a construct necessarily leaves remainder, and so a paper should list explicitly the remainder it produces rather than pretend the argument is complete.

It lists six. Whether the two-layer division into axiomatic and operational layers is exhaustive — not argued. Whether the formalization captures every feature of the structure — not argued. The independence of the way of the remainder relative to via negativa (equivalence is not independence) — not independently argued. The precision of the borrowing from Heidegger — no terminological history undertaken. Cross-domain structural isomorphisms — left to separate interface work.

And one more, the most concealed of them:

Methodology 00 is itself a paper, and a paper is a construct. It argues that every operation of Negativa necessarily leaves remainder; then it, as an operation, necessarily leaves remainder too. It applies to itself the very incompleteness it identifies.

The more that is said, the more is constructed; the more that is constructed, the more is left over.

This remainder is harder to see than the others because it is hidden inside the argument itself. And writing it down is the way of the remainder's final application to itself — questioning far enough that the questioning meets the questioner.