The Redefinition Ledger: A Procedure for Any Construction That Redefines Its Quantities Mid-Calculation
Year: 2026
Type: preprint
Abstract: Some founding constructions do not merely approximate their quantities or replace their systems; they redefine their quantities in the middle of the calculation — a divergent or uncomputed piece is declared to belong to a redefined parameter, the bare parameter takes whatever value the declaration requires, and the calculation proceeds with the measured value as though nothing had happened. This paper defines a bookkeeping instrument, the redefinition ledger, fifth in the ledger series after the closure, import, constant, and restoration ledgers, and states its procedure: every such construction is entered with the quantity exactly as laid down and its provenance; its redefinition map itemized reassignment by reassignment, each with its size as a function of the regulator; the residue the map cannot absorb — the finite remainders and the conditions fixing the redefined parameters — computed and carried as the entry's state; and for each reassignment a warrant test or a cross-entry naming the address where its warrant lives. The procedure is exhibited end-to-end on a worked corpus already computed in this program — the 1946–48 renormalization papers of Tomonaga, Schwinger, and Feynman (census attack CC-150) — where the map's two reassignments grow as \ln(\Lambda/m) without bound (\delta m/m = 0.179535 already at the Planck cutoff), the residue stands computed at full size (a_e = \alpha/2\pi = 0.001161410 against the measured 0.001159652), and the warrant for the whole map stands cross-entered to its successor address, Dyson 1949 — so the entry stands partially evaluated, printing its own structure as its headline state. With this paper the ledger series' named queue — closure, import, constant, restoration, redefinition — is complete. The ledger evaluates redefinition maps; it derives none and repairs none. Grade: procedure, exhibited on a complete worked corpus. Program headline, unchanged: NOT SOLVED / PARTIAL · producing-count 0.
Author: Aldred, William Alexander
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225462547