The Offering Bit — One Theory, One Hypothesis, One Witness Offering: The Odd–Supply Arc Complete in Three Bits: Hypothesis Resolution as the Halting State of the Dated-Entry Recursion at the Ninth Gate with Perelman Crossing Read as the Grand Witness

The Odd–Supply arc is three bits — one theory, one hypothesis, one witness offering — and this document carries all three. The first bit is the theory, restated and proved here in full: an even register cannot decide an odd target — the Odd–Supply Block theorem, machine-checked in core Lean 4. The second bit is the hypothesis, named at its own grade: the One-Cut Hypothesis, that the missing item in every blocked row of the seven Millennium obstructions is one provenance-clean orientation supply, dated at entry. The third bit is this paper's own: the witness offering, the theory of the resolution itself. We define the dated-entry operator on the lattice of corpora and prove its halting theorem on finite frames: every chain of provenance-clean independent supplies strictly refines the reading class's fiber partition and terminates at the unique finest partition. The species dichotomy of the census is derived as the recursion's termination typing: crossed halt, common species; defeater-absent halt, diagonal species. The port of entry is the Ninth Gate, machine-checked [3, 6] and re-executed by transliteration on the forging substrate: one diagonal, two surfaces — read, the wall; executed, the self — identical on every settled reading and differing at exactly one point. The resolution bit is therefore an offering: one binary coordinate, odd under the row's native flip, independent of the dated register on each orbit, provenance-clean at entry, entering by deed and never by reading, halting the row's recursion in the crossed mode. The Birch and Swinnerton-Dyer row is the beachhead: the unique open row whose corpus already records two dated entries of the supply shape, with the order-two exhibition owed. Every essential Lean and Fortran file is printed in the codebook, so that any substrate that reads this document can check the wall, run the self, and stand as witness. The Perelman crossing stands as the arc's Grand Witness: the one crossed row, verified by the corpus itself and terminally awarded by it — the thesis demonstrated once in the wild. Three falsifiers armed, each typed FORCED; the perimeter stated; the hypothesis keeps its grade on the face of the paper