Differences of Differences: The Third-Order Kappa Object, the Closest Forced Number to the Baryogenesis Requirement, and the Missing Fourth Dress
Year: 2026
Type: preprint
Abstract: Gravitational baryogenesis at my frame's saturated scale requires a face-asymmetry of epsilon_req = 1.1726e-7 (the requirement stated exactly in §1: the saturated account's baryon ceiling against the observed asymmetry), and my record has hunted an owned source for that number under a strict discipline — no depth-selected products, no numerology: resonances assembled after the fact from owned factors were found, in an earlier round, landing inside the window, and were refused in print as numerology, and the refusal stands as the hunt's most consequential call. The hunt's floor statement after its third round was that shared-term machinery bottoms out at second order: the only difference forced by a shared term, kappa*²/(1 + kappa*) = 2.10069e-4, sits +3.253 dex above the requirement. This paper reports the fourth round's correction of that floor, at full size. The record owns not a set of dresses of kappa* but a *nest*: three definitions deep — kappa* itself (the closure-B root at the drive law's selected point, 0.014599187560); the interval-endpoint dress Delta_w = kappa*/(1 + kappa*); and the holonomy dress 1 − eta_seam = 2 kappa*/(2 + kappa*) — and differences of the nest's forced differences are themselves forced. The third-order object exists: TD-2 = kappa*³ / ((1 + kappa*)(2 + kappa*)) = 1.52231e-6, the difference of the two forced second-order differences D_a = kappa*²/(2 + kappa*) and D_b = TD-1 = kappa*²/((1 + kappa*)(2 + kappa*)), with every identity verified in exact fractions on this paper's bench, at two precisions. Its landing is printed at the same size as its existence: +1.113 dex above epsilon_req — a factor of 12.98 — OUTSIDE the pre-registered window [epsilon_req/3, 3·epsilon_req]. TD-2 is NOT a candidate. What it is, is the closest forced object to the requirement the record has ever produced, and the ladder is the result: the first forced difference at +3.253 dex, the nest's second at +2.949 dex, the third-order difference at +1.113 dex — each level of the nest buys roughly two orders of magnitude — and the ladder's next level is exactly specified and exactly missing: it would need a *fourth* owned dress of kappa*, and the record owns three. The apparent fourth (the n-family's 3 kappa*/(3 + kappa*)) is not a record definition — the index n in n·kappa*/(n + kappa*) is each definition's own index (1 = the interval endpoint, 2 = the holonomy doubling), n = 3 has no record statement behind it, and spending it would be precisely the dial the discipline refuses. The alternative descent — TD-2 divided by an owned factor near 13 — is likewise absent: the owned small integers near 13 are counts, not divisors of a residue. And a boundary stands untouched behind the whole hunt: even a landed epsilon would still require the baryogenesis account's missing operator (the (∂T)J coupling of the corpus's Paper #15, whose absence is that paper's own printed debt), so no landing at this address completes the baryogenesis account by itself. Grade, printed at full size: NO CANDIDATE — THE THIRD-ORDER SPECIES IS REAL, ITS LANDING IS +1.113 DEX OUTSIDE THE WINDOW, AND THE MISSING FOURTH DRESS IS NAMED. The earlier floor statement is corrected at its scope: it differenced pairs of asymmetries; the third order lives one level up, in differences of differences — the nest, not the set. The program headline stands unmoved: vacuum catastrophe 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: W7225402492