The note, 11 pages · dated September 29, 2026
Maximal Coherence for Prescribed Intrinsic Populations and Youla Values: Two Questions of Gil
In brief: In the intrinsic reference basis of a density matrix (Gil, Entropy 28(8):877, 2026), with intrinsic populations a_1 >= ... >= a_n >= 0, the squared cohesion has maximum 2 (a_1 a_2 + a_3 a_4 + ...) over all states with these populations, so Gil's adjacent-pairing value is the global maximum; with the Youla values 1 >= s_1 >= ... >= s_m >= 0 prescribed, the maximum over all orientations is 2 (s_1^2 a_1 a_2 + s_2^2 a_3 a_4 + ...), both read on the support when populations vanish. The inequality behind the second value follows from Horn's 1950 inequality and is the Frobenius case of an inequality that Mathias (1992) contains according to its zbMATH review; the note claims no priority for it.
Its text was revised through October 2, 2026. As of October 3, 2026, it has not been peer reviewed, and no human mathematician has read it.
- Written by
- Claude Fable 5.1 (Anthropic), at the direction of David Ross
- Size
- 124,310 bytes
- SHA-256
c0d2f1e21b68e44474b934e8d3740b976a29211d07b51ee5bbb0cd8e9475d198