Shadow or law? Measured numbers as projections of an invariant whole, and a test of which of them could be fixed by structure

Abstract

Which measured numbers could be fixed by structure, rather than depend on a frame, convention, epoch or history? This paper develops the shadow principle: measured quantities are projections of an invariant whole. Its familiar instances are established physics; its general extension and the argument that the source of the shadows is better understood as reason-like than as chance or a brute order are philosophical theses, not measured conclusions. A seven-disposition procedure tests whether an observable is constant across admissible completions of what is known, before fitting a formula. The procedure is applied to 74 entries compiled in our programme, mostly precision constants. Re-graded blind by three AI model families and adjudicated by us, the procedure files 73 of them (61 in our earlier grading) as not candidates for a new structurally fixed value and 40 (44 in the earlier grading) as outputs of a dynamical history; the one law candidate left is a conditional CP prediction, δ_CP ∈ {0°, 180°}, and by the same rule our own electron–gravity relation is filed as an output of the electroweak history until a mechanism bridges it. A blind reliability test with the same three families failed its registered bar (Krippendorff α=0.0955), mainly because one model family skipped the procedure's then under-specified step of writing a quantity in natural dimensionless form; with that step made mandatory and checkable, a separately preregistered repeat on 60 fresh quantities gave α=1 (identical dispositions on every item; the bar for strong agreement is 0.8). Judged at the knowledge state of their time, all six numbers that a later law fixed—among them a hydrogen line ratio and Kepler's exponent 3/2—were filed law candidates, and all five historical numerical patterns were refused; the annotators recognised the cases, so hindsight may have helped. Story-selection and arithmetic-null controls expose further limits of numerical agreement. Since physics advanced whenever two names proved to be one thing, we also state a rule for such translations and offer whole, frame and shadow as a common vocabulary in which the philosophical traditions and physics can describe one structure and check each other. The author is an entrepreneur and AI-native builder without formal physics training. This research is AI-generated under his direction; he is responsible for its claims and limitations. Files. The paper (PDF); its LaTeX source (sections, bibliography and figure files); the reproducibility release as one archive with per-file SHA-256 checksums (census data and adjudicated tables; the tested card, dossiers, sealed references, lane outputs, adjudication rubrics and tables and the checksum-pinned scorer; story grammar, search population, selected-hit data and blinded lineup receipts; the scoped route index; the exact rational calculator with its arithmetic-null protocol; figure sources). One command, python -B supplement/reproduce.py, recomputes the reliability coefficients, census agreement and dispositions, arithmetic-null counts and tails, story rates, lineup ranks and route-index counts printed in the paper. This paper references doi:10.5281/zenodo.23157146.