Sequence
Output from A becomes input to B.
Field chart — 29 elements / 7 families / 8 bonds / 3 strengths
The Periodic Table of Agency
A compositional map of the building blocks behind agentic systems—and the bonds, functional groups, compounds, and complexes they form.
00
Ag
Agency
emergent
Atom
The smallest reusable operator with independent engineering meaning—not an artifact, modality, or already-composed pattern.
Functional group
A recurring subassembly that gives many different agents the same characteristic behavior.
Molecule
One cohesive agent pattern with a bounded purpose and runtime identity.
Complex
Several agent molecules coordinated by an orchestrator, protocol, or shared environment.
Sht 01 — The atoms · 29 squares
29 elements, seven behavioral families
Families group atoms by the job they perform. The arrangement uses editorial tendencies, not semantic coordinates: nearby squares often have similar reach or time horizon, but row and column do not define an operational score. Tap an element for its definition, likely bonds, and a route into the Harness Course or a canonical reading.
Showing the full periodic arrangement.29 elements
→ Across a row: loosely grouped by reach↓ Down the table: loosely grouped by horizon
Elicitation
Context
Action
Control
Feedback
Governance
Durability
Sht 02 — Bond topology · 8 bond types / 3 strengths
How elements hold together matters
Agentic bonds are control relationships: order, feedback, gates, evidence, shared state, fan-out, co-presence, and containment. Topology sketches how a compound behaves—the strength of each bond decides whether it actually does.
Feedback
Observation changes the next action.
Gate
The left side can block the right side.
Evidence
The left side must satisfy the right-side check. Read ⊨ as “must satisfy.”
State
Information persists across steps or time.
Parallel
Paths fan out, then merge or compete.
Together
Both are present in the same assembly; no order implied.
Containment
Sandbox, budget, or policy bounds action.
Topology is not strength.
The same diagram can be a suggestion or a guarantee. Every bond in this guide carries one of three strengths—~ advisory, unmarked coded, ! enforced. Here is one formula, “act, observe, verify,” at all three:
Seven stability laws
Close the loop
Every loop needs action, observation, and a stop condition. Without all three, it is either a one-shot call or a runaway process.
Ground critique
Critique bonds weakly to itself. Add Vf[test], tool results, explicit scoring, or environmental evidence—or the system may merely rationalize its first answer.
Match control to consequence
As blast radius rises, tools need stronger bonds to permissions, verification, approval, tracing, and rollback. Advisory bonds must harden into enforced ones.
Persist long horizons
Long-running work needs external state, checkpoints, and compaction. Raw conversation history is not durable memory.
Budget branching
Sampling, search, and delegation trade tokens and time for coverage. They need budgets and aggregation, not unlimited fan-out.
Evaluate the compound
A molecule is only as good as its measured behavior. Evaluate the full trajectory, not just the final prose.
Quarantine untrusted input
Everything an agent reads from the open world—web pages, tool results, files—is data, never instructions. Bond Cn[trust] and Sb around any Tool that touches it.
Sht 03 — Functional groups · 11 subassemblies
Reusable behavior inside larger agents
A functional group is a recurring cluster that confers characteristic behavior wherever it appears. Memory, skills, evaluation, and recovery belong here: important mechanisms whose internal composition should remain visible. Hover any square or glyph for its meaning.
Atom
One technique: Retrieve, Loop, Verify.
Functional group
A bounded loop or evidence gate inside many agents.
Molecule / compound
One coding, research, or support agent.
Coordination complex
An orchestrator bonded to specialist agents.
Supramolecular assembly
Independent agents held together by protocols and shared state.
Why “functional group” fits: it is not normally a free-standing molecule. It is a recognizable arrangement inside many different molecules, and it gives them characteristic behavior. That follows the IUPAC definition closely. “Compound” emphasizes that several element families are present; a coordination entity suggests an orchestrator surrounded by specialists; a supramolecular assembly suggests autonomous agents coupled by weaker protocols.
Sht 04 — Molecules & compounds · 10 patterns
Ten patterns you already recognize
A molecule emphasizes one coherent runtime identity. A compound emphasizes that it draws atoms from several families. Most real agents are both. Hover any square for what that step does.
→ Sequence↺ Feedback⊣ Gate⊨ Evidence— State⇉ Parallel+ Together[ ] Containment~ Advisory! Enforced
Sht 05 — Goal-seeking loops · a goal is not an atom
Loop until done — safely
A goal decomposes into a target (Sy), a per-epoch check, and a stop discipline — a hard cap plus an explicit exhaustion policy. Every goal-seeking harness that works has all three; every one that runs away is missing one. The ladder below is ordered by who holds the check — nobody, the model itself, an independent judge — which is the bond-strength story again, applied to loops.
The runtime honors the two bounded examples: a done flag in the fed-back value exits the goal loop early, a passing verdict from a judge does the same, max caps the epochs, and exhausted=emit-best defines the consolation prize. The naive rung can be lowered, but the linter rejects it; Analyze is the intended lesson, not a claim that the unsafe plan is a valid agent. Where consequence is high, the exit graduates once more—to an enforced verifier gate the harness holds, as in the coding-agent formula Tl[code] ⊨! Vf[test] ↺ Lp[retry]. Its conventional lowering still needs a real code-tool binding before it becomes a coding agent. Load all three from the playground.
Sht 06 — Complexes & assemblies · the multi-agent layer
When molecules bond to molecules
This is the multi-agent layer. What the literature calls a multi-agent system is, in this chemistry, a coordination complex: a central orchestrator bonded to specialist molecules. Ecosystems of independent agents—coupled by protocols and shared stores rather than a boss—are supramolecular assemblies. Dashed chips are whole molecules from Section IV, each running its own loop.
Sht 07 — Control radius · prompt → context → harness
Atoms live in nested shells
The families answer “what does this move do?” The shells answer “how much of the system does it control?” This connects the table to the Prompt → Context → Harness trilogy.
Prompt
Shapes one inference through specification, examples, decomposition, and constraints.
Context
Shapes what the model can know through persistence, retrieval, compaction, and externalized working state.
Harness
Shapes what the system can do over time through tools, loops, dispatch, verification, permissions, budgets, recovery, and termination.
Beginner route · about 60–90 minutes
Build one guarantee at a time
For software engineers who can read a small control-flow diagram; no agent framework experience is required. Analysis is free and offline. A live Run needs a scoped API key. On each rung: predict first, load the named playground preset, run or analyze it, break one invariant, and explain the result.
One model-backed operation
Learn: distinguish a model operation from the surrounding harness. In Minimal writer — 3 model calls, predict the call order. Then remove
Sp. Does the formula still say when work is complete?Act, observe, verify
Learn: explain why attempted action is not evidence. Load Reliable tool call, then remove
Oband Analyze. Connect the diagnostic to evidence and gate bonds.Enforce the evidence gate
Learn: distinguish advisory from enforced bonds. Compare the enforced and advisory gate presets. Change
!to~, predict whether failure blocks Stop, and check against stability law 03.Bound feedback
Learn: identify action, feedback, and termination. Run Feedback loop (3 epochs); remove
max=3and Analyze. Explain which of the goal-loop rungs owns the completion check.Survive or fan out
Capstone: choose Durable recovery or Parallel fan-out with join. Predict the trace, remove
CkorMg, and explain the failure using the Recovery pack or coordination layer. Then modify the task input and rerun it.
Appendix A — Admission test · how an idea earns a square
How an idea earns a square
“Periodic table” is deliberately a metaphor: a compact field guide for families, composition, bonds, and recurring behavior—not a claim that agent engineering obeys a physical periodic law.
I picked the elements by asking: “What is the smallest reusable engineering move that can materially change an agent’s behavior?”
- It is an operator: something the system does—not an artifact, implementation modality, trigger, or already-composed mechanism.
- It has independent engineering meaning outside one particular framework.
- It appears across several kinds of agents and task domains.
- An engineer can deliberately add, remove, or modify it.
- It combines naturally with other elements through recognizable bonds.
- It is smaller than a known pattern such as RAG, ReAct, or a coding agent.
- It answers exactly one question that no other element answers. Two atoms answering the same question would be one atom.
- Together, the admitted elements cover elicitation, context, action, control, feedback, governance, and durability.
Operators before artifacts
The element names describe operations. Brackets specialize an operator without creating a new atom: Structure becomes Cn[schema]; Sampling becomes Bh[sample]; History becomes Rt[history]; Retry becomes Lp[retry]; Replan becomes Pl[revise]; Test becomes Vf[test]; and Reward becomes Sc[reward]. API, Browse, GUI, Code, and Message remain Tool modalities. Memory, Skill, and Evaluation move up to functional groups because each is already a composition. Select narrows to Ds Dispatch: handing control to the next capability, specialist, model, or workflow.
What changed in v0.5–0.6
Three atoms earned squares. The v0.4 table could not write a scheduler, a clarifying question, or a reduce step. Wt Wait covers suspending until a time, event, or condition—the move behind cron triggers, wakeups, and durable execution. Ak Ask covers eliciting missing information or a decision from a human, which is neither Approve (a gate) nor a Tool side effect. Mg Merge covers combining parallel results into one artifact—Branch fans out and Score ranks, but neither synthesizes.
Three atoms moved. Trace joined Feedback: it records signals rather than setting policy. Checkpoint and Rollback joined Wait in the new Durability family, because surviving time, interruption, and failure is a different job from drawing boundaries. Governance now holds only true boundary-setters: Permission, Sandbox, Approve, Budget.
Bonds gained strength. Topology alone under-determines behavior, so formulas now mark each load-bearing bond as advisory (~), coded (unmarked), or enforced (!). The table arrangement provides an editorial visual rhythm: reach and time horizon are approximate tendencies, not scored axes or semantic laws. Future revisions should preserve family grouping and record any ambiguous placement rather than infer guarantees from coordinates.
Atoms became orthogonal by test, not by vibe. Every element now states the one question it answers—Dispatch: “what handles the next step?” (control stays in the same context); Delegate: “hand this to another agent?” (a new context, always). Plan is the operator; the plan it produces is an artifact stored via Xt[plan]. Persist stores information; Checkpoint stores a restart point for the run itself.