The Baseline: A Proximity Instrument for Constant-Matching Claims

Claims that a measured value matches a mathematical constant are common and rarely accompanied by a baseline. The Baseline is a single-file browser tool that supplies one. Given a value and a candidate constant — φ, √2, the silver ratio, 2+√3, π, e, or a user-supplied value — it returns the nearest whole power, the fractional distance δ from that power, and P, the probability that an arbitrary value would fall at least that close by chance. P is computed exactly in log space as [ln(1+δ) − ln(1−δ)]/ln c rather than by the small-δ approximation, and a log-lattice ruler renders the pass bands visually, showing directly what fraction of the number line qualifies as a match at a given threshold. Two sources of inflation are flagged automatically. The first is framing: because φ = 1 + φ⁻¹ exactly, testing x against φ and testing x−1 against φ⁻¹ are the same claim but return δ values differing by a factor of φ² ≈ 2.618. The tool reports both and applies the larger. The second is search size: where m candidate values were examined rather than one, it reports 1 − (1−P)^m together with the expected count of spurious matches. As a worked example, the Kolmogorov 5/3 exponent tested against φ gives δ = 0.0303 and P = 12.5%, or about 1 in 8. At a 5% threshold, 20.8% of the number line lies inside a φ-power pass band, so roughly one arbitrary value in five will appear to match. A second module generates a pre-registration record with the computed baseline embedded, including a field for registering an outcome as inconclusive before data collection. Known limitation: the framing check currently fires only for φ at power 1; analogous identities for other constants are not detected. The tool runs entirely client-side, stores nothing, and transmits nothing. Its baseline arithmetic and failure classes derive from FCLT Protocol V3.2 (10.5281/zenodo.21522770) and LatticeNull v2 (10.5281/zenodo.21538505).