When Transcript Supervision Cannot Locate Characters: Set-Valued Cuts and Sparse Anchors for CTC OCR

Connectionist temporal classification (CTC) learns transcripts by summing monotone alignments, but its character peaks need not identify physical separators. We formalize adjacent-character segmentation as an ordered, one-dimensional, set-valued cut task: a cut is accepted between the projected right edge of one character and the left edge of the next, including their overlap. We establish a two-world lower bound when identical observable word images and transcripts admit separated valid-cut sets, and derive an anchor-recovery relation under fixed linear features and full-rank design. A recognition-conditioned SVTRv2 system combines CTC decoding, a bounded residual cut head, interval supervision from sparse character boxes, and an optional soft interval-gated CTC objective. On 61,842 source-disjoint SynthText words of length 2–5, 1% cut supervision raises midpoint ±2-frame all-cut word accuracy from 69.52% to 90.32%; dense supervision reaches 95.17%. The corresponding strict transcription-and-all-cuts rates are 64.78%, 84.15%, and 88.76%. Controlled synthetic experiments reproduce the lower-bound and rank-transition predictions, while OCR results quantify the gain from sparse geometric anchors.