Four conjectures against a corpus of periodic continued-fraction families, and the measurement that frames them

A study of four conjectures proposed against the deposited summaries of a corpus of periodic continued-fraction families, each given a falsifier before it was computed and then tested by exact computation against the corpus's own ledgers. Three of the four were wrong or ill-posed as stated. All four produced a result. WHAT IS NOT CLAIMED. No deposited result is claimed to be wrong; every statement here is about what is established, not about what is true. No general claim is made about AI-proposed conjectures: n = 4, one collaborator, one corpus, one week. No claim of completeness for any tested set. Agreement at finite precision is recorded VERIFIED and never PROVEN. The measurement in the framing section is a statement about the status of the literature's surface assignments, corroborated from the literature's own text; it is not a claim that any assignment is false. THE FOUR OUTCOMES. C-1, that the Borel branch exponent is a function of the leading coefficient alone, is FALSIFIED in all three of its forms by a witness pair sharing that coefficient. What survives is an exact closed form for the exponent, derived symbolically at degrees 2 to 5, in which the exponent of the leading coefficient is the same at every degree; the conjectured exponent agrees with it only at degree 2, which is the degree the conjecture was proposed from. C-2, a coefficient filtration and a no-go at its first level, is WITHDRAWN AS POSED rather than refuted: the level-1 join induces 5 blocks and the full coefficient tuple induces 5, so they are the same partition and there is no filtration to have a no-go at. What survives is the per-invariant question, which was correctly scoped in its source throughout, and a partition lattice over 12 invariants in which 44 of 66 pairs are incomparable, 15 strictly comparable and 7 equal. One supporting result fell to its own pre-registered falsifier when a table value was checked against the primary source, and that is reported rather than repaired. C-3, that the window-law slope set is the Farey set indexed by degree, is FALSE AS STATED on two counts: the counts are each larger by 1 through an endpoint double-count, and the controlling index is the least common multiple of the root denominators rather than the degree. What survives is stronger than the conjecture -- at root denominator y the slope set is exactly the unit group of the integers mod y, so Farey structure is a restatement of the lifting law rather than a coincidence to be tested. The wrong index was unfalsifiable from the deposited data for two independent reasons, both reported. C-4, that golden-slope self-similarity transfers to the prefactor, is CONFIRMED at its proper scope, after the barrier word's recursion was ceded as classical: the identity was settled by constructing the classical object rather than by searching for it, and the construction cost the run its strongest-sounding claim. THE FRAMING MEASUREMENT. Of the degree-2 families in the primary table, 0 carry an established surface label. The three denominators at which this holds -- a 6-family roster, a 10-row catalogue and the primary's 30 -- are three different facts and are reported separately. The catalogue's own assignment document states that its labels are not proofs and that nine of its ten families are unconfirmed; the tenth was the anchor, and the anchor was later retracted into a class that excludes the label it anchored. Re-deriving the discriminant from each catalogue row's own coefficients shows that the 6 negative-discriminant families are the primary's named anomaly bin member for member, so they are a principled selection, while the 4 positive rows are a curated pick admitted as a judgment call on the record. METHOD. The claim worth making is not that the conjectures were good -- three were not -- but that a falsifier written before the computation converts a bad conjecture into a result. The study also reports a conjecture whose natural test could not have failed, and an instance in which a verdict reachable by construction was settled by construction against the run's own interest. All figures are read from 483 ledger entries across 11 source runs at entry granularity. Every numeral in the manuscript is emitted by a script from a named artifact. The 23 outcomes and counts the study was handed were checked against their source entries before being recorded, with 2 carried in corrected form.