A corrected census of polynomial continued fractions with quadratic partial quotients and coefficients bounded by four

This paper revisits a census of the 531,441 polynomial continued fractions K = b(0) + Kn>=1 a(n)/b(n), where a and b are polynomials of degree at most two with integer coefficients in {-4,...,4}. Under a stated numerical rule (an integer relation with pi, found at 150 digits and confirmed at 300 digits), 56 families are classified Trans; they form 28 classes under the sign change b -> -b. The count depends on a staged rule: 1,060 families are counted as not Trans because a limit vouched to at least 160 digits showed no relation at 150 digits, without a confirmation at 300 digits. Without that step the upper bound is 1,116; a stricter reading that also keeps the families with no finite limit gives 64. The relations are numerical; they are not proofs of transcendence. The paper also gives exact counts of the stored heuristic bins and of the terminating families, sample estimates (not counts) for the other strata, the proof status of a boundary family, and a list of statements of an earlier manuscript that it replaces. The value 6/(3*pi - 8) of one Trans class is a known value (Campbell and Chen, eq. (7), as stated in the paper), and the paper makes no novelty claim for any individual value. Status of the claims (fixed; not to be read more strongly):- The count 56 (28 classes) holds under the stated rule only; the basis is stated beside it in the paper.- Relations for the Trans families: numerical, not proved exact; no transcendence is claimed.- Statements T0, T1, T2 of the boundary family are proved in Lean 4 (pinned toolchain and Mathlib versions) and checked by the Lean kernel; not human-refereed. They are restated from deposit 23581163, not re-checked here. The other statements of that section are proof candidates only.- Sample figures are sample estimates for a pool and are not multiplied into counts.- The review of earlier records was incomplete (13 of 71 in-scope records were not swept); the list of records is not claimed to be complete.- The scripts in the zip are re-implementations written for this paper. Every number of the paper is regenerated from the shipped data by `scripts/gen_numbers.py`; the audit scripts are consistency checks written by the same AI model, not an independent method.- No human mathematician has read any proof in this paper or in the cited deposit. AI use: this paper, its scripts and its data products were produced by AI models (Claude Sonnet 5.5 through GitHub Copilot CLI as author and preparer; claude-haiku-5.5 and Claude Sonnet 5 as second readers of parts of the cited proofs), under the direction of a human operator who publishes as Papanokechi, set the research questions and the rules of the project, authorized changes, and decides what is deposited. A further AI model (Claude Opus 5.5) assisted the operator in reviewing results. The operator has not refereed the mathematics. References that were opened are cited in the paper; the works that were not consulted are named there too. Files: f24-census-corrected.pdf (the paper, 18 pages, CC BY 4.0) and artifact.zip (frozen census data, recorded outputs, the generator and audit scripts, the paper's sources, MANIFEST.sha256 of every member; MIT licence). To regenerate the numbers, run "python -B scripts/gen_numbers.py data outputs" from the unpacked archive root; see README.md in the zip. Contact: ppapanokechi@gmail.com. Author listed under the pseudonym Papanokechi.