Case 5 — A plausible number with an unwarranted inference

What a reader needs to know

Ball Mapper represents observations in local groups that can overlap. Counting observations in groups at two dates does not identify which named observation moved directly from one group to another. A direct movement claim requires matched observations, not only group totals. The mathematical term coupling below means an assumed link between the two sets of group memberships.

Research setting

An early AI-generated interpretation treated changes in overlapping Ball Mapper occupancy as if they identified a direct movement of the same systems from one neighbourhood to another.

A numerical quantity looked plausible and was computable.

The problem

The numerical margins were not the central error.

The inferential move was.

Products of overlapping endpoint memberships imposed a coupling that the representation did not identify as same-system direct movement.

Correction

The direct-flow claim was withdrawn before publication.

Replacement evidence relied on observable endpoint states (the recorded position of a named system at each end) and robustness across landmark orders (different construction orders for the reference neighbourhoods). In the canonical ordered chain, 36 systems could be classified at both endpoints; 21 moved downward, 14 were unchanged and 1 moved upward.

The paper therefore separated:

• changes in neighbourhood occupancy;
• observed endpoint state movement;
• robustness of the broad directional pattern.

Reason-provenance lesson

A correctly computed quantity can still support the wrong substantive inference.

Verification must therefore include the meaning attached to a number, not only its arithmetic.

Evidence status

The withdrawal is frozen in the project record and current empirical manuscript.

Public-release control: any original AI wording should be quoted only after checking it against the authoritative conversation record.

Evidence available to public readers

The endpoint counts and claim withdrawal are described from frozen internal project material. The full calculation, data, logs and original AI wording are not published here; the reported counts cannot be independently reconstructed from this page.

Boundary

The episode should not be presented as proof that AI reliably self-corrects. The correction emerged from a deliberately adversarial workflow and subsequent researcher-controlled revision.