A quick correction on The Only Clause Available, published Friday. I wrote there that the US–Iran ceasefire expires Monday. It expires Wednesday, the 22nd — the two-week truce began April 8, and I miscounted by two days. (Ed.: A formal theorist, miscounting.) The prediction itself stands for Wednesday: a renegotiated form of ambiguity rather than either a settled deal or a clean resumption of hostilities. The weekend has moved things, though, and in the direction of the resumption branch more than the framework-talks branch. Iran pulled out of the second Islamabad round; the United States seized an Iranian-flagged vessel on Sunday; Tehran re-declared closure of the Strait of Hormuz; the president said “maybe I won’t extend it.” That is not a clean resumption, but it is not quite what the model predicted either. I will revisit on Wednesday or Thursday. On to the rest of the world.
The Department of Government Efficiency has been visualized three times in the past ten months, and each time the picture looked different. In January, Elon Musk sat at the center, with teams radiating out to Treasury, OPM, CFPB, Labor, and Education. In May, after Musk’s departure, Russell Vought occupied what looked like the new hub, and the spokes rearranged around him. In November, with OPM director Scott Kupor announcing that DOGE had “ceased to exist” as a distinct entity and ending the government-wide hiring freeze, the picture shifted again.
None of the three pictures is wrong. None of them describes an organization whose personnel, authorities, or formal arrangements have meaningfully changed between one picture and the next.
The staff did not mostly leave when Musk did. ProPublica has tracked the persistence of roughly one hundred Musk-affiliated personnel embedded across federal agencies since its DOGE 100 roster was published in June, and the composition of that list has been largely the same people, working in largely the same agencies, on largely the same portfolios, throughout the intervening six months.1 The executive order establishing the U.S. DOGE Service inside the Office of Management and Budget’s United States Digital Service has not been rescinded. The four-employees-per-agency architecture specified in that order has not been disbanded. Access arrangements to the Treasury Department’s payment systems, the subject of federal litigation whose disposition the Supreme Court halted pending further review, remain in place. The Appointments Clause question a federal judge raised about Musk’s authority never reached a ruling on the merits, because Musk was reassigned before the ruling had to come down.2 When Kupor announced in November that DOGE had “ceased to exist,” he was announcing the re-label of a service, not the dissolution of its arrangements.
None of this is concealed information. It is in the ProPublica tracker, in the Revolving Door Project’s interactive map of Musk-affiliated agency placements, in federal court filings, in the executive order itself. Anyone who wants to know what DOGE is doing can find it. But that is not quite the same question as what DOGE looks like, and in the three pictures I described at the top of this piece, what it looks like has been changing even when what it is has not.
A picture
The widget below renders a stylized version of the DOGE institutional structure across the three moments — January, May, and November. Seventeen nodes: four named principals (Musk, Vought, Kupor, Gleason), three institutional anchors (White House, OMB, USDS), five agency teams, and five anonymous embedded staff. Twenty edges in the first view and sixteen in the other two, after Musk’s four edges drop out when he departs. A small bar chart beneath the graph tracks degree centrality across the three views for each of the four principals.
Three things are worth trying before reading on. First, click among the three views and watch the entire graph fly apart and re-form. Second, click the same view twice in a row, and watch it produce two different arrangements of the same nodes and the same edges. Third, tick the “Lock positions” checkbox and click among the three views again: now they look almost identical. The rest of the post is an argument about what each of those three observations is an observation of.
Narrative equilibrium
I argued a few weeks ago that force-directed layout algorithms — the standard tools for drawing networks, implemented in Gephi and igraph and in any of the force-simulation calls that power browser-based network visualizations — fail a condition I called Network Embedding Independence of Irrelevant Alternatives.3 The position of any node in a force-directed layout depends on the entire graph. Move one node, and every node's coordinates recompute. This makes coordinates inferentially empty: the apparent spatial relationship between two nodes in a network diagram cannot be read as telling you anything local about those two nodes, because it was produced by a global optimization over all of them.
The widget above is, strictly speaking, an illustration of that. The edge set among the thirteen non-Musk nodes is identical in all three views. Kupor's edges to OPM and to Vought do not change. The five agency teams remain connected to the same USDS node by the same five edges. And yet when the algorithm reruns, every non-Musk node, including Kupor, lands somewhere different every time. The bar chart at the bottom of the widget shows what actually remained invariant: Kupor's degree is flat across all three views; Vought and Gleason each lose exactly the one edge they had to Musk; Musk's crashes to zero. The layout above the bar chart does not respect any of this.
What I did not argue in April, and should have, is that the same pathology operates on the narrative pictures that readers assemble from journalism as it does on the algorithmic pictures that statnet produces. DOGE is the case. For roughly six months, the public image of DOGE was hub-anchored to Musk. Musk was on the covers, in the bylines, in the headlines. When a cabinet secretary talked about DOGE she talked about "Elon's people." When a federal judge ruled that Musk was the de facto leader for purposes of the Appointments Clause question, the ruling named Musk personally. The picture of the institution most people carried around with them had Musk at the center and everything else arranged with respect to him.
Then Musk left. And the picture reoptimized.
Vought, who had been director of OMB for the entire period — not a new arrival, not a post-Musk replacement, but the person to whom DOGE had always formally reported through OMB's USDS — became visible. Reporting in June and July routinely described Vought as having taken on DOGE coordination, as if he had assumed a new role. He had not. His edge to OMB was unchanged; his edge to USDS through his directorship of the parent agency was unchanged; his coordination with Kupor on overlapping workforce-reduction efforts was unchanged. What changed was that the narrative layout had lost its hub and needed a new one. Vought had been there, structurally central, the entire time. He only became legible to the public image of DOGE when the algorithm reran.
Then Kupor became visible too. When he announced in November that DOGE had "ceased to exist" — a phrase that generated roughly one news cycle of DOGE is dead coverage before being absorbed into the next week's agenda — he emerged in the picture with a clarity that did not correspond to any change in his position. His edge to OPM's DOGE team was identical in January and November. His coordination with Vought was identical. His direct line to the White House as OPM director was identical. The only thing that changed, at the November announcement, was that the picture needed an authoritative narrator of what DOGE was ceasing to be, and Kupor — already there, already central by degree, already flat on the bar chart — was the only principal in a position to deliver that narration.
The three pictures differ not because the organization reorganized three times. They differ because the narrative layout algorithm rerandomized three times, and each time it converged to a different-looking equilibrium over a structurally very similar graph.
What the picture cannot see
None of this would matter very much if the cost of a bad picture were merely aesthetic — if the worst thing that happened when a reader formed a hub-anchored mental model of an organization were that the model was slightly inaccurate. The cost of a bad picture of DOGE is larger than that, and it is paid in governance terms.
The arrangement the January executive order established is, by any reasonable classification, an unusually aggressive experiment in delegation. It took a small statutory office — the U.S. Digital Service, whose ambit under prior administrations had involved fixing broken government websites — and hung onto its legal hook an entirely different program: embedded per-agency teams with access to the payment, personnel, and regulatory-enforcement systems of most of the cabinet. Whatever one thinks of that program on the merits, the formal question delegation doctrine poses is whether the chain of authority from principal to agent is legible, bounded, reviewable, and accountable. That question has not been answered. It has been, in a literal sense, unanswerable: the federal judge who came closest to ruling on the Appointments Clause challenge to Musk's role had the question mooted by Musk's reassignment before the ruling came down.2 The subsequent renaming of the service does not revive the question; it retires it.
This is not a thing a bad picture of DOGE merely misreads. It is a thing a bad picture of DOGE obscures. Look at January DOGE and you see Musk, and you ask about the authority of Musk. Look at May DOGE and you see Vought, and you ask about the authority of Vought. Look at November DOGE and you ask whether DOGE still exists. What you do not ask, at any point, is whether the four-employees-per-agency architecture of the original order is a constitutionally tenable chain of delegation, because in no picture is that architecture the feature the hub is drawing your eye to. Every picture draws the eye to a principal; the architecture is not a principal; the architecture, which is the thing the formal literature on delegation and bureaucratic governance would need to interrogate to evaluate the arrangement, is therefore not what gets interrogated.
This is the real cost of reading networks through their layouts. The hub is legible; the hub is news; the hub is, in every force-directed sense of the word, central. But the thing the arrangement is doing, the thing delegation doctrine would need to look at to evaluate it, lives in the edges — and the edges are how the architecture is implemented. Kupor's bar is flat on the chart because Kupor has a stable, specific, legally consequential relationship to the OPM team that runs his piece of the workforce-reduction program; that relationship outlived Musk's departure and outlived the November announcement, because it is not load-bearing on any of the labels that changed. Vought's bar moves by exactly the count of his edge to Musk, no more and no less, because that is the actual change in Vought's local network. The bar chart is honest about what has changed. The picture above it is not.
Labels
One more thing, because this post is also the second installment in a series and the series has a theme. I argued over the past week, in a different set of pieces, that institutional ambiguity does not disappear when you refuse to classify it; it gets relocated.4 A junk drawer is not an absence of classification. It is a deliberate acknowledgment of a class of objects that cannot be classified anywhere else, kept visible and labeled, rather than distributed invisibly into other spaces. What the November DOGE announcement did was the opposite of a junk drawer move. The name was removed. The label was taken off the drawer. The contents were redistributed into the surrounding bureaucracy and declared, by virtue of no longer being gathered under a label, not to exist as a coherent category.
This is why the physics-of-networks critique and the delegation critique, which look at first as though they are critiques of different things, end up at the same place. In the force-directed view of the organization, the hub was Musk, and when the hub left, the organization appeared to dissolve. In the narrative view, the institution was DOGE, and when the institution was declared to have ceased to exist, its arrangements appeared to dissolve. Neither dissolution was real. The arrangements persist; the authorities persist; the embedded staff persist; the access to Treasury's payment systems persists. What was relocated, both visually and nominally, was the label.
Conservation of impossibility is, among other things, a theorem about labels.
With that, I leave you with this.
1 ProPublica, "The DOGE 100: Musk Is Out, but More Than 100 of His Followers Remain to Implement Trump's Blueprint," June 10, 2025. The tracker has been updated through the year and remains the most comprehensive public accounting of which Musk-affiliated personnel are embedded in which federal agencies. See also Revolving Door Project's interactive map, which overlays agency placements with prior private-sector employment.
2 The mootness of the Appointments Clause question is not a neutral procedural fact. A merits ruling would have produced a precedent about whether a "special government employee" arrangement can house the de facto leader of a government-wide program with broad authority over the administrative state without Senate confirmation. Musk's reassignment in May 2025 vacated the question without answering it, leaving the structure that gave rise to the question in place. This is a pattern with a name in the constitutional literature and a different name in the formal-theory literature; in both, it is a variety of what Maggie Penn and I have elsewhere called conservation of impossibility.
3 "The Physics of Political Networks," April 1, 2026. The formal definition of NEIIA is given there, along with a three-tier hierarchy in which node positions are the least-invariant object (failing NEIIA), betweenness centrality is intermediately invariant (satisfying NEIIA but not IIE, the Independence of Irrelevant Edges condition from Patty and Penn 2015), and degree centrality is the most invariant (satisfying both, and being, by the van den Brink and Gilles 2003 axiomatization, the unique centrality index that does so). The bar chart in this post tracks the most-invariant of these three objects on purpose.
4 See The Junk Drawer and Quasi, and the third installment from April 16. The payoff line of that series — if you don't have a junk drawer, eventually you'll only have junk drawers — is not quite the point being made here, but it is adjacent. The DOGE announcement is the failure mode the junk drawer is designed to prevent: unclassified contents redistributed invisibly rather than gathered under an acknowledged label.
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