Both leftover threads closed with zero sorrys: omega is bridged to ArithmeticFunction.cardDistinctFactors by rfl, and the pointwise log log n form is proved from the density form by splitting (0,N] at the square root of N, consuming variance 275 and Mertens band 16 unchanged.
hunts/r_233abe (Record 29 of 98 in chronological sequence)
Guiding Question
Can omega be bridged to ArithmeticFunction.cardDistinctFactors, and can the density-form Hardy-Ramanujan theorem be upgraded to the pointwise log log n form, both kernel-checked with zero sorrys against pinned Mathlib v4.33.0-rc2?
Method & Verification
The bridge is rfl between n.primeFactors.card and n.primeFactorsList.dedup.length, carried through to a Mathlib-vocabulary restatement, and the pointwise form splits (0,N] at sqrt(N) with delta fixed at 1/2 so no extra parameter is carried.
Lineage & Relationships
Primary Sources (at pin 8fa46e134)
Editorial Notes
Case-log status is settled. Disposition maps settled to completed. The bridge is a restated definition pinned by a theorem; the pointwise form is the classical statement, including that n below e^e sit in the exceptional set where log log n is negative.
Date Provenance
commit e87dc9239bfec4bab05e97c6493c991f85f1717b, hunts/r_233abe/RESULTS.md, author 2026-08-17T22:37:47Z