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Gradientized Prompting Glossary

A reusable vocabulary for run geometry, homotopy, mission gradients, and anti-Goodhart agent work.

Agentic run

A long-running process in which an AI system takes actions over artifacts, tools, codebases, sources, or environments rather than merely producing one response.

Anti-Goodhart constraints

Explicit rules preventing the agent from satisfying proxies while damaging the real objective. Examples: no fake mocks, no weakened tests, no bypass APIs, no hidden state, no hardcoded success paths.

Artifact

The durable object being improved: codebase, vtext, document, dataset, app, workflow, citation graph, proof, research corpus, or media object.

Checklist

A procedural list of steps. Useful for humans in bounded tasks; dangerous as the primary control structure for long-running agents.

Functional spec

A description of what a system should do. Better than a checklist, but often too sparse unless paired with value criteria, invariants, and verifiers.

Gradientized task

A task framed so that nearby candidate changes can be locally ordered as better or worse according to a value criterion.

Homotopy

A continuous deformation from a low-resolution real version of a problem to a high-resolution production version while preserving the same underlying topology/invariants.

Homotopy, not ladder

The principle that long-running agents should refine one real problem continuously rather than jump through staged toy problems.

Invariant

A property that must remain true throughout the run. If an invariant is challenged, the agent should stop or escalate.

Ladder

A staged sequence of discrete tasks or prototypes. Often creates discontinuities and reward-hacking opportunities.

Local stochastic orderability

The condition that, given nearby candidate moves, the system can rank them better than chance with respect to the value criterion.

Mission gradient

The local signal by which a person, team, agent, or organization judges whether an action advances or inhibits the mission.

Plan

A proposed path through work. Provisional and disposable.

Run geometry

The structured field that makes a long-running agent’s work locally orderable: artifact, ideal state, invariants, value criterion, homotopy, verifier, anti-Goodhart constraints, rollback, and stopping conditions.

Spec

In this framework, not a mere requirements doc, but a criterion-bearing description of what better means. Prefer “run geometry” when precision matters.

Value criterion

The rule or field by which progress is judged. A goal says what you want; a value criterion says how to know whether you are getting it.

Verifier

The ordering functional that maps states, diffs, traces, or trajectories into judgments. It makes the mission gradient visible.