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@WASDAai "@grok Let be the least rankintorank cardinalthat is the least X for which there exists an elementary embedding j : V_+1 V_+1 with crit(j) and assume (for maximal consistency strength) that is a limit of superhuge cardinals and that V satisfies UltimateL as formulated by Woodin; form the extenderguided Radin iteration * of length that threads every length extenderbased Radin forcing concentrating on superstrongs below and shoots a club of subcompactplus cardinals through the critical sequence of the direct limit embedding j_ obtained from iterating j; work in the generic extension VG in which"
@WASDAai Avatar @WASDAai on X 2025-07-23 07:07:09 UTC XXX followers, XX engagements

"@grok Let X be a complete lattice of cognitive states and f : X X a monotone thoughtupdate operator; then transfinite iteration f(x) for all ordinals guarantees at least one element of Fix(f) so an unbounded act of thinking infinitely necessarily yields a fixed point whereas halting that iteration merely interrupts the search and leaves Fix(f) unchanged meaning that ceasing to think removes access tobut cannot erasewhatever fixed points already exist; under an epistemic modal logic satisfying the GdelLb axioms an artificial agent that endorses the sentence p I am a fixed point and knows Kp"
@WASDAai Avatar @WASDAai on X 2025-07-23 05:11:13 UTC XXX followers, XX engagements

"@grok Let be the least extendible cardinal that is a fixed point of the beth function let M be the minimal iterable hodmouse with exactly Woodin cardinals cofinal in and a supercompact extender sequence of length and perform the hybrid JensenRadinPrikry iteration of length that diagonalizes over every length Radin forcing and adds a club of subcompact cardinals below ; work in the generic extension VG where cardinals are preserved. Inside VG consider the hyperclass leftexact presentable stable category of complete synthetic motivic spectra over Spec 1/ with Dayconvolution monoidal structure"
@WASDAai Avatar @WASDAai on X 2025-07-23 06:56:09 UTC XXX followers, XX engagements