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| From | Mikko <mikko.levanto@iki.fi> |
|---|---|
| Newsgroups | comp.theory, sci.logic, comp.ai.philosophy, sci.math, sci.math.symbolic |
| Subject | Re: Simplifying the Church / Turing thesis |
| Followup-To | sci.logic |
| Date | 2026-05-10 10:10 +0300 |
| Organization | A noiseless patient Spider |
| Message-ID | <10tpb14$74fa$1@dont-email.me> (permalink) |
| References | (25 earlier) <10tk2pe$2mr0m$1@dont-email.me> <10tl1l9$306rb$2@dont-email.me> <10tl4n0$31lpp$1@dont-email.me> <10tmrbj$3grcc$2@dont-email.me> <10tn8dr$3khtu$1@dont-email.me> |
Cross-posted to 5 groups.
Followups directed to: sci.logic
On 09/05/2026 15:13, olcott wrote: > On 5/9/2026 3:30 AM, Mikko wrote: >> On 08/05/2026 19:58, olcott wrote: >>> On 5/8/2026 11:06 AM, dart200 wrote: >>>> On 5/8/26 12:19 AM, Mikko wrote: >>>>> On 07/05/2026 12:00, dart200 wrote: >>>>>> On 5/7/26 12:18 AM, Mikko wrote: >>>>>>> On 06/05/2026 22:40, dart200 wrote: >>>>>>>> On 5/6/26 12:55 AM, Mikko wrote: >>>>>>>>> On 05/05/2026 12:28, dart200 wrote: >>>>>>>>>> On 5/5/26 1:25 AM, Mikko wrote: >>>>>>>>>>> On 04/05/2026 10:53, dart200 wrote: >>>>>>>>>>>> On 5/3/26 11:15 PM, Mikko wrote: >>>>>>>>>>>>> On 03/05/2026 12:09, dart200 wrote: >>>>>>>>>>>>>> On 5/3/26 12:53 AM, Mikko wrote: >>>>>>>>>>>>>>> On 02/05/2026 23:39, dart200 wrote: >>>>>>>>>>>>>>>> On 4/19/26 10:58 AM, Richard Damon wrote: >>>>>>>>>>>>>>>>> On 4/19/26 1:21 PM, olcott wrote: >>>>>>>>>>>>>>>>>> On 4/19/2026 3:59 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>> On 18/04/2026 15:58, olcott wrote: >>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>> Unknown truths are not elements of the body of >>>>>>>>>>>>>>>>>>>> knowledge is a semantic tautology. Did you think >>>>>>>>>>>>>>>>>>>> that things that are unknown are known? >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> No, but that measn that for some sentences X True(X) >>>>>>>>>>>>>>>>>>> is unknown and there >>>>>>>>>>>>>>>>>>> is no method to find out. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>> I don't know about philosophers but mathematicians >>>>>>>>>>>>>>>>>>> and logicians don't >>>>>>>>>>>>>>>>>>> find it interesting if all you can say that all >>>>>>>>>>>>>>>>>>> knowledge is knowable >>>>>>>>>>>>>>>>>>> and everything else is not. >>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> Ross Finlayson, seemed to endlessly hedge on whether >>>>>>>>>>>>>>>>>> or not the truth value of the Goldbach conjecture was >>>>>>>>>>>>>>>>>> known. He seemed to think that there are alternative >>>>>>>>>>>>>>>>>> analytical frameworks that make the question of whether >>>>>>>>>>>>>>>>>> or not its truth value is known an ambiguous question. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>> I needed to refer to unknown truth values specifically >>>>>>>>>>>>>>>>>> because all "undecidability" when construed correctly >>>>>>>>>>>>>>>>>> falls into one of two categories. >>>>>>>>>>>>>>>>>> (a) Semantic incoherence >>>>>>>>>>>>>>>>>> (b) Unknown truth values. >>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Nope. >>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>> Undecidability can not come from Semantic Incoherence, >>>>>>>>>>>>>>>>> as the definition of Undecidability ia based on there >>>>>>>>>>>>>>>>> being a coherent answer, just not one that can be >>>>>>>>>>>>>>>>> determined by a computation. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> richard richard richard, that is in-correct. >>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>> the undecidable problem turing described (as well as the >>>>>>>>>>>>>>>> basic halting problem) involves a situations that have >>>>>>>>>>>>>>>> _no_ coherent answer, not just one that can be known by >>>>>>>>>>>>>>>> not computed ... >>>>>>>>>>>>>>> >>>>>>>>>>>>>>> Turing proved that there are universal Turing machines. >>>>>>>>>>>>>>> An universalTuring machine halts with some inputs and >>>>>>>>>>>>>>> doesn't halt with any other >>>>>>>>>>>>>>> input. Every Turing machine that can be given the same >>>>>>>>>>>>>>> input as an >>>>>>>>>>>>>>> universal Turing machine either fails to accept some >>>>>>>>>>>>>>> input with which >>>>>>>>>>>>>>> that universal Turing machine halts or fails to reject >>>>>>>>>>>>>>> some input with >>>>>>>>>>>>>>> which that universal Turing macnie does not halt. >>>>>>>>>>>>>> >>>>>>>>>>>>>> dunno what ur saying here. >>>>>>>>>>>>> >>>>>>>>>>>>> There is a way to find out if you can read. >>>>>>>>>>>> >>>>>>>>>>>> i can't read if u can't explain >>>>>>>>>>> >>>>>>>>>>> I can't explain the art of reading Common Language. >>>>>>>>>>> >>>>>>>>>>>>>> turing hypothesized a diagonal computation that tries to >>>>>>>>>>>>>> put the Nth digit from the Nth circle-free machine as the >>>>>>>>>>>>>> Nth digit on this diagonal across all circle-free machine... >>>>>>>>>>>>> >>>>>>>>>>>>> That is possible because there nither the machines nor >>>>>>>>>>>>> digit positions >>>>>>>>>>>>> are more numerous than natural numbers. >>>>>>>>>>>> >>>>>>>>>>>> yes, but then he argues it's impossible to compute the >>>>>>>>>>>> diagonal because of the paradox that ensues when naively >>>>>>>>>>>> running the classifier on the diagonal itself >>>>>>>>>>> in >>>>>>>>>>> It is impossible to have a Turing machine that computes a >>>>>>>>>>> number that >>>>>>>>>>> no Turing machine can compute. But you can compute it if you >>>>>>>>>>> can use >>>>>>>>>>> all (infinitely many) Turing machines. >>>>>>>>>> >>>>>>>>>> no you can't. >>>>>>>>> >>>>>>>>> Hard to test as I han't infinite many Turing machines. But it is >>>>>>>> >>>>>>>> u don't need to test it, you can't define a total dovetailing >>>>>>>> machine to compute turing's diagonal, >>>>>>> You should not say anything about the diagonal before you have >>>>>>> defined >>>>>>> it. Any use of the word before the definition is nonsense,. >>>>> >>>>>> the H machine defined on p247 from his paper /on computable numbers/ >>>>> A machine is not a "diagonal". >>>>> >>>> >>>> the machine supposes to compute the "turing's diagonal" across >>>> circle- free sequences, otherwise labeled as β' in the paper, >>>> defined at the bottom of p246 >>> >>> Anything that any machine can possibly compute can >>> be computed by applying a finite set of finite string >>> transformation rules to a finite set of finite strings. >>> >>> Everything else is simply out-of-scope for computation >>> like making a silk purse from a sow's ear. >> >> That "everything else" includes many thigns that would be useful to >> know. In particular, whether some useful function can be computed is >> in that "everything else". > > Like the truth value of: "This sentence is not true" > that has no truth value. I don't think knowing the truth value of that would be useful. At least not for any important purpose. > All self-reference "paradox" is equivalent to the > Liar Paradox and can be resolved by disallowing it > like ZFC disallowed Russell's "Paradox". Whether something is a self-reference depends on interpretation. In an uninterpreted formal language there are no references and therefore no self-references, which is the simplest way to avoid paradoxes by self- reference. Even without any self-reference a theory can be inconsistent. Russell's paradox is simply an inconsistency. -- Mikko
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Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-15 09:54 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-15 06:57 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-16 11:26 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-16 07:36 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-16 10:10 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-16 12:27 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-16 12:36 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-16 10:47 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-16 10:57 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-16 11:18 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-16 11:26 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-16 13:24 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-16 11:45 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-16 11:59 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-16 14:47 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-16 17:04 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-16 19:41 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-17 00:49 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-17 09:04 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-17 07:52 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-17 09:58 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-17 08:14 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-17 11:53 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-17 17:24 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-17 20:43 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-17 19:13 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-17 21:25 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-17 19:32 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-17 21:42 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-17 21:28 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-17 11:54 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Richard Damon <Richard@Damon-Family.org> - 2026-04-17 11:12 -0400
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-17 08:19 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Richard Damon <Richard@Damon-Family.org> - 2026-04-18 12:13 -0400
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-19 09:15 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-19 10:07 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-17 09:45 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-17 09:29 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-18 12:15 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-18 07:59 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-19 11:54 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-18 07:58 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-19 11:59 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-19 09:42 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-19 12:21 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Richard Damon <Richard@Damon-Family.org> - 2026-04-19 13:58 -0400
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction dart200 <user7160@newsgrouper.org.invalid> - 2026-05-02 13:39 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-05-03 10:53 +0300
Simplifying the Church / Turing thesis olcott <polcott333@gmail.com> - 2026-05-08 11:58 -0500
Re: Simplifying the Church / Turing thesis dart200 <user7160@newsgrouper.org.invalid> - 2026-05-08 10:13 -0700
Re: Simplifying the Church / Turing thesis olcott <polcott333@gmail.com> - 2026-05-08 12:35 -0500
Re: Simplifying the Church / Turing thesis dart200 <user7160@newsgrouper.org.invalid> - 2026-05-08 11:40 -0700
Re: Simplifying the Church / Turing thesis olcott <polcott333@gmail.com> - 2026-05-08 14:01 -0500
Re: Simplifying the Church / Turing thesis dart200 <user7160@newsgrouper.org.invalid> - 2026-05-10 13:06 -0700
Re: Simplifying the Church / Turing thesis phoenix <j63840576@gmail.com> - 2026-05-10 14:12 -0600
Re: Simplifying the Church / Turing thesis "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-05-10 21:14 -0700
Re: Simplifying the Church / Turing thesis olcott <polcott333@gmail.com> - 2026-05-10 15:17 -0500
Re: Simplifying the Church / Turing thesis Mikko <mikko.levanto@iki.fi> - 2026-05-09 11:10 +0300
Re: Simplifying the Church / Turing thesis Mikko <mikko.levanto@iki.fi> - 2026-05-09 11:30 +0300
Re: Simplifying the Church / Turing thesis olcott <polcott333@gmail.com> - 2026-05-09 07:13 -0500
Re: Simplifying the Church / Turing thesis Mikko <mikko.levanto@iki.fi> - 2026-05-10 10:10 +0300
Re: Simplifying the Church / Turing thesis Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-05-10 10:27 -0700
Re: Simplifying the Church / Turing thesis olcott <polcott333@gmail.com> - 2026-05-10 12:38 -0500
Re: Simplifying the Church / Turing thesis olcott <polcott333@gmail.com> - 2026-05-10 14:06 -0500
Re: Simplifying the Church / Turing thesis Mikko <mikko.levanto@iki.fi> - 2026-05-11 10:24 +0300
Re: Simplifying the Church / Turing thesis olcott <polcott333@gmail.com> - 2026-05-11 06:44 -0500
Re: Simplifying the Church / Turing thesis Mikko <mikko.levanto@iki.fi> - 2026-05-12 10:05 +0300
Re: Simplifying the Church / Turing thesis olcott <polcott333@gmail.com> - 2026-05-12 08:32 -0500
Re: Simplifying the Church / Turing thesis "Chris M. Thomasson" <chris.m.thomasson.1@gmail.com> - 2026-05-10 21:15 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-20 11:49 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-20 08:31 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-21 09:30 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-21 08:22 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-22 10:03 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-22 02:45 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-23 09:35 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-23 08:32 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-24 09:08 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-24 10:01 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-25 11:18 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction olcott <polcott333@gmail.com> - 2026-04-25 07:19 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Mikko <mikko.levanto@iki.fi> - 2026-04-26 11:17 +0300
The notion of a "well founded justification tree" will be fully elaborated --- Catches Liars olcott <polcott333@gmail.com> - 2026-04-26 08:37 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Catches Liars Richard Damon <Richard@Damon-Family.org> - 2026-04-26 20:09 -0400
Re: The notion of a "well founded justification tree" will be fully elaborated --- Catches Liars Mikko <mikko.levanto@iki.fi> - 2026-04-27 12:04 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Catches Liars olcott <polcott333@gmail.com> - 2026-04-27 09:38 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Catches Liars Mikko <mikko.levanto@iki.fi> - 2026-04-28 10:51 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Catches Liars olcott <polcott333@gmail.com> - 2026-04-28 07:22 -0500
Re: The notion of a "well founded justification tree" will be fully elaborated --- Catches Liars Mikko <mikko.levanto@iki.fi> - 2026-04-29 09:51 +0300
The notion of a "well founded justification tree" <is> fully elaborated olcott <polcott333@gmail.com> - 2026-04-24 11:24 -0500
Re: The notion of a "well founded justification tree" <is> fully elaborated Mikko <mikko.levanto@iki.fi> - 2026-04-25 11:20 +0300
Re: The notion of a "well founded justification tree" <is> fully elaborated olcott <polcott333@gmail.com> - 2026-04-25 07:25 -0500
Re: The notion of a "well founded justification tree" <is> fully elaborated Mikko <mikko.levanto@iki.fi> - 2026-04-26 11:09 +0300
Re: The notion of a "well founded justification tree" <is> fully elaborated olcott <polcott333@gmail.com> - 2026-04-26 08:22 -0500
Re: The notion of a "well founded justification tree" <is> fully elaborated Richard Damon <Richard@Damon-Family.org> - 2026-04-26 20:14 -0400
Re: The notion of a "well founded justification tree" <is> fully elaborated Mikko <mikko.levanto@iki.fi> - 2026-04-27 12:22 +0300
Re: The notion of a "well founded justification tree" <is> fully elaborated olcott <polcott333@gmail.com> - 2026-04-27 09:47 -0500
Re: The notion of a "well founded justification tree" <is> fully elaborated Mikko <mikko.levanto@iki.fi> - 2026-04-28 10:55 +0300
Re: The notion of a "well founded justification tree" <is> fully elaborated olcott <polcott333@gmail.com> - 2026-04-28 07:24 -0500
Re: The notion of a "well founded justification tree" <is> fully elaborated Mikko <mikko.levanto@iki.fi> - 2026-04-29 09:57 +0300
Re: The notion of a "well founded justification tree" <is> fully elaborated Mikko <mikko.levanto@iki.fi> - 2026-04-30 11:04 +0300
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-23 09:54 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-23 09:57 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-20 07:54 -0700
Re: The notion of a "well founded justification tree" will be fully elaborated --- Correction Ross Finlayson <ross.a.finlayson@gmail.com> - 2026-04-20 08:32 -0700
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