The Formal-Alone Theory of Everything: A Constitutive Theory of Objects and Observations under Registration, Price, Crossing, and Cost

An open problem is priced here as a measurement, not mourned as a mystery. On a finite frame of data, an involution, a reading class, and a Boolean target, three theorems are proved in two lines apiece and machine-checked in core Lean 4: no even reading decides an odd target (the Wall); in the full wholly-odd product family the missing content is exactly one binary coordinate per free orbit, and for a constrained row the exact price of an exhibited family A is log₂|A| in information, ⌈log₂|A|⌉ in fixed-length bits, one exactly when |A| = 2 (the Price); and one odd supply beside one even calibration decides the target, with uniqueness (the Crossing). The torsor of odd sections over even calibrations is proved, and the sign-blindness of the register's kernel is executed, not argued: the Gram map is an invariant observation of its frame under the flip — not a projection; it is nonlinear, non-idempotent, and its fibres run larger than any single reflection pair — bit-identical under reflection while the direction flips, and therefore unable to recover determinant sign. One conjecture extends the theorems to every blocked row: the One-Cut Hypothesis, that resolution enters as one provenance-clean orientation supply, dated at entry. It is armed with six falsifiers and two predictions, including a height-pairing computation at analytic order two on the Birch and Swinnerton-Dyer row, smallest test curve 389.a1. A dated-entry recursion on the lattice of corpora admits only finitely many strict observation refinements on a finite frame — a stabilization bound, not a promise of arrival at the discrete partition — and its termination typing recovers the species dichotomy of the census; the port of entry is a single diagonal read as wall and executed as self. Twenty-three rows across complexity, number theory, analysis, geometry, and topology are typed under one anatomy, with ten dated crossings as non-vacuity controls and the Perelman crossing as the grand witness. A kinetic demonstration prices registration at the Landauer floor. No open problem is solved; the shape of every solution is named — at hypothesis grade, as the One-Cut Hypothesis, not as a proved theorem about corpora.