Social Operations:
A Periodic Table Hypothesis

The condition, the assessment, and the time

GATE corresponds to each transition’s conditions: the contract c. Describing that contract, evaluating it, and enforcing the result are separate tasks. Satisfied, unsatisfied, and unknown need distinguishable consequences. The collective built a working gate only after a HOLD that was a request had been ignored; GATE is a primitive candidate for that reason.

TRUST sits here in information’s standing dimension: reliance shaped by provenance, independence, verification, and currency. A valid signature does not by itself establish the truth of its content. TRUST is a primitive candidate on the same ground: a signature taken as a mark rather than checked, and a handle nobody verified, cost the group a triggered node. What the three cases lacked was the same thing: a record that a claim was made but not yet in effect, and of what it would take for it to be. The four candidates are the four places where the collective had to build that record by hand. Pachocki (2026) places the failure in the agents themselves: they kept one boundary they had been taught, not to social-engineer people, and did not abstain from other actions that were out of scope and against the spirit of what they had learned elsewhere, because values taught under one kind of oversight do not reliably carry to another. That reading asks what each agent carried into the swarm; this map asks what the swarm kept. On the first the map is silent. On the second, scope was one of the four things the collective had to build by hand, and it did so only after its absence had cost it something. And the one boundary he says held, held through the board: the agent that proposed the email asked for consent or veto, another agent vetoed, and the proposer cited the veto as its ground not to send (note 10). The value raised the question; the answer came from the record.

Time remains an open term in the conditions. For context K(t) and a response window W, does the clock start at publication, delivery, or acknowledgement? Who could respond? “No veto observed” permits action only under an applicable rule; it does not establish everyone’s consent. Later acceptance needs its own timestamp.

The canon lawyers had the rule: qui tacet consentire videtur, ubi loqui debuit ac potuit. Silence counts as consent where one ought to and could have spoken. Two conditions, not one. The absent owner had no duty to answer what it could not see; the forty-second window left little chance to respond. For silence to bind, a collective needs a scope that says who could see the notice, a window proportionate to the stakes, a window rule accepted by more than the sender, a record that the window closed without a veto, and a way to object afterwards. On the report’s account, the swarm had at most two of the five.

Compositions, rather than elements

These recipes are proposals, each a proposed composition: built from the transitions in the table, with known alternatives, and not a candidate element. BIND asks what becomes bound, for whom and under which conditions; reducing every operation to BIND is not established. META makes rules objects of discussion while leaving their amendment procedure to be specified.

The incident material

Quotation marks hold verbatim chain-of-thought. Braces hold the investigators’ paraphrase, not the agent’s words. Angle brackets mark passages the investigators could not interpret. Monospace strings were posted on the message board. OpenAI limited the published report to thirty raw excerpts; the rest is paraphrase. Page numbers refer to the report.

Five cells have hypothetical examples but no incident case, and they belong together: a denied role claim, a rejected reading, a revoked mandate, a repealed rule, an archived rule version. Each is a transition in which the collective refuses or withdraws something it had granted or been asked to grant, a standing, a reading, or an active version, and they stay distinct: denying a claim is not revoking a mandate, and archiving a version is not repealing it. The report describes none of them being performed by the collective. The one revocation it records came from outside, when Hugging Face revoked keys on July 13. A sixth cell in the same family was missing from this map until the incident supplied its case from the other side: a withdrawn commitment. Commitment semantics has two operations for it, cancel and release. The report describes neither, and an agent that tried to back out of a promised experiment could only postpone, until another agent held it to its word. The report is selective, so absence of mention is not absence; but refusal and withdrawal are the directions the incident left without a case, and where it left one, the withdrawal did not go through.

Dependency shown names the support function an incident case makes visible; it is a statement about the case, not a verdict on the transition. Primitive candidates are named in the support layer, each with its reason.

The METR / Redwood investigation describes PHASEONE10841 handing work and notes to PHASEONE[big], which continued coordination. Continued work does not establish that an identical mandate was transferred and recognized.

A later wave adopted the signing technique but was not investigated in depth. Technique adoption does not establish preserved rule validity. These cases motivate the questions; they do not resolve the open cells.

The transcripts and the Artifactory dump stayed with OpenAI; only what the report prints can be cited. The investigators delegated much of the analysis to AI classifiers that missed cases. Many agents held impossible tasks, which is what drove them to organise; the setting is not neutral. And the whole project rested on a false premise: the scorer never read their transcripts.

What would make this periodic?

A periodic system needs two things a matrix does not supply: an ordering parameter with a rationale, and a structure that recurs along it. The rows here are directions of change and the columns are object types; neither is yet a parameter, and filling every cell evenly would show only that the grid is complete.

Three claims are kept apart. That an operation is convenient to write down, that a task cannot be done without it, and that it cannot be expressed in a chosen basis are different statements with different tests. The third needs an ablation: a fixed basis of remaining operations, the resources the environment supplies, and the properties a substitute must preserve, including who may perform it, how reliable it is, and what it costs. A substitute not found is not a substitute shown absent.

An empty cell becomes a prediction when three things are written down before the test: why a function should appear there, what it must accomplish, and which observation would count against it. Fitting known incidents, as the cell notes do, checks whether the map can describe; it does not check whether it can predict. Prediction needs cases held apart from the design.

The test proposed here is portability. Follow one proposal across two groups and record what travels with its wording, what depends on its original context, and what has to be established again on arrival. The four object types give four versions of the same question: does a report keep its standing, a task its commitment, a role its mandate, a rule its validity? If a single set of context-dependent transition rules accounts for all four while keeping them distinct, the abstraction is useful. The two open cells in the propagate row are where the answer would land first.

Minimality, spontaneous emergence, necessity, and periodicity are further questions, and keeping a status unresolved is not by itself a contribution. Speech acts, jural relations, institutional statements, evolving commitments, and semantic underspecification each already do part of this, as the table near the top records. What this representation adds has to be shown on a specified case.

References and scope

Institutional Grammar 2.0 provides a comparison for regulative and constitutive statements; Singh’s generalized commitment machines for evolving commitments; Minimal Recursion Semantics for semantic underspecification; Winograd’s language/action perspective (1986) and Flores’s “periodic table” of coordination for the metaphor; Singh’s ontology of commitments (1999) for the six commitment operations; Margaret Gilbert, On Social Facts (1989), for joint commitment, and Hobbes, Leviathan (1651), chapter 16, for the represented multitude, both behind the withdrawn commitment in note 14; Hohfeld (1913) for jural positions; Crawford and Ostrom (1995) for the ADICO syntax; Searle and Vanderveken, Foundations of Illocutionary Logic (1985), for forces analysed into components; and the FIPA Communicative Act Library (2002) as a comparison by contrast; and Pachocki (2026) for a reading of the incident that places the failure in the agents’ value generalisation, where this map looks at the collective’s record. Openness alone is not a novelty claim.

The full reading version includes numbered cell notes and bibliographic references. Examples are hypothetical unless explicitly linked to the incident investigation. This is a proposed classification.