basin-formal-object

and · drafted

Statement

In a finite disturbance model a basin around a drifting target exists exactly when the agent's acceptance of a correction depends on its distance from the target, with a one-step contraction proved and the general-horizon supermartingale step open.

Source

projects/deference/faf-cleanroom-2026-10-02/packages/corr-landscape, statements S7 and T6 (the declarations trajD9_enters_drift and traj_outside_unbounded) and its open statement Horizon.phiW_supermartStep; projects/deference/faf-cleanroom-2026-10-02/packages/corr-trajectory, statement 10 as the definition of record.

Notes

The toy basin, with its one open hypothesis filed as the actioned leaf (the supermartingale step). Its bridge conditions on the author's four basin questions having answers: the distance metric is one of them.

Bridge card

Connected to no informal claim yet: held by no frame.

Declaration BasinToy.trajD9_enters_drift (record basin-formal-object.record)

Bridge (formalizer-stated; basin-formal-object.bridge, drafted):

The one-step contraction and the unbounded-outside result are a formal basin in Christiano's sense around a drifting target, with distance-dependent acceptance as the condition.

Hypotheses, read:

basin-formal-object.setting open: The general-horizon supermartingale step of the basin certificate holds: the prefix-atom factorization of the product law makes the potential a supermartingale along the trajectory.

Completeness (basin-formal-object.complete): No premise beyond the proved declaration, its stated setting and its bridge is needed for the informal reading of basin formal object to hold.

Author and human events

Author @smithy-verity; version 1; size M.

No human event has touched this node.

Edges

Above

part of dynamic-conditions-for-going-well
root (shared-claim) of dynamic-conditions-for-going-well

Children

part: basin-formal-object.record leaf/record
part: basin-formal-object.setting leaf/hypothesis
part: basin-formal-object.bridge leaf/bridge
part: basin-formal-object.complete leaf/completeness

Ranking (the lens, not the structure)

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