October 30, 2025 at 6:07 PM
November 29, 2025 at 4:02 PM
November 29, 2025 at 4:02 PM
November 29, 2025 at 4:01 PM
November 29, 2025 at 4:00 PM
YESSSSS!!!!! I am so not gonna lie; my haunted house literally solved this for me like, months ago, and literally has been trying to guide me with the weirdest shit. #MarkovNumbers #Unicity
October 27, 2025 at 2:18 PM
YESSSSS!!!!! I am so not gonna lie; my haunted house literally solved this for me like, months ago, and literally has been trying to guide me with the weirdest shit. #MarkovNumbers #Unicity
#MarkovNumbers #Unicity (hint: "42")
October 16, 2025 at 1:55 AM
#MarkovNumbers #Unicity (hint: "42")
Let a = (a'+i) and let b = (b'+j), for integers i and j. If true for a and b, and also true for a' and b', I suspect we have a major contradiction. #MarkovNumbers #Unicity
October 15, 2025 at 9:42 PM
Let a = (a'+i) and let b = (b'+j), for integers i and j. If true for a and b, and also true for a' and b', I suspect we have a major contradiction. #MarkovNumbers #Unicity
I think I just got another one finally for real. When it rains, it pours. #numbertheprimes #markovnumbers #unicity
September 21, 2025 at 3:14 PM
I think I just got another one finally for real. When it rains, it pours. #numbertheprimes #markovnumbers #unicity
Returning back to a #zeckendorf-ish angle for #MarkovNumbers #Unicity always seems to show the most promise. The distinction of that terminal repeat in the pre-Zeckendorf representation *might* be all I need.
August 27, 2025 at 5:37 PM
Returning back to a #zeckendorf-ish angle for #MarkovNumbers #Unicity always seems to show the most promise. The distinction of that terminal repeat in the pre-Zeckendorf representation *might* be all I need.
The weird thing here is, for both the Fibonacci and the Pell #MarkovNumbers, L(') proves to be a natural factor of A+(-)B. If one could generalize how this occurs, one would have a very clean explicit expression for Markov Numbers. #Unicity
#ChebyshevPolynomials of the 2nd kind
#ChebyshevPolynomials of the 2nd kind
August 26, 2025 at 1:47 AM
The weird thing here is, for both the Fibonacci and the Pell #MarkovNumbers, L(') proves to be a natural factor of A+(-)B. If one could generalize how this occurs, one would have a very clean explicit expression for Markov Numbers. #Unicity
#ChebyshevPolynomials of the 2nd kind
#ChebyshevPolynomials of the 2nd kind
A little (tested) progress today. Got my own explicit expressions for #PellNumbers and #FibonacciNumbers that I can use in this alternative approximation for #MarkovNumbers, but still need to justify the approximation / calculate its range of error. #Unicity
August 22, 2025 at 8:02 PM
A little (tested) progress today. Got my own explicit expressions for #PellNumbers and #FibonacciNumbers that I can use in this alternative approximation for #MarkovNumbers, but still need to justify the approximation / calculate its range of error. #Unicity
Closest approximation for #MarkovNumbers yet 😁. Used a combination of my own #snakegraph theory and my own #chebyshevpolynomial theory to get there.
August 10, 2025 at 12:33 AM
Closest approximation for #MarkovNumbers yet 😁. Used a combination of my own #snakegraph theory and my own #chebyshevpolynomial theory to get there.
That's the final set-up. I am 100% sure it will work: the missing piece I needed before was the relative ratios. #MarkovNumbers #Unicity
July 25, 2025 at 11:33 PM
That's the final set-up. I am 100% sure it will work: the missing piece I needed before was the relative ratios. #MarkovNumbers #Unicity
Done and done. #MarkovNumbers #Unicity #ModularArithmetic #SnakeGraphs #FibonacciNumbers #Fibonacci #Markov #MarkovNumber #ohmygod
July 23, 2025 at 1:08 PM
Oh my goodness this is an exciting approach. Verify that this math works out if and only if k=k'. I went back to computing #MarkovNumbers as "perfect matchings of shake graphs" using my formula, and separated summands w diff factors (modulo F(2k+2), effectively). #Unicity
July 23, 2025 at 12:08 PM
Oh my goodness this is an exciting approach. Verify that this math works out if and only if k=k'. I went back to computing #MarkovNumbers as "perfect matchings of shake graphs" using my formula, and separated summands w diff factors (modulo F(2k+2), effectively). #Unicity
Cleaned up, but I'm still not convinced of #Unicity. If replication of #MarkovNumbers happens, though, it happens at like depths into the tree, after like numbers of turns. That's really cool. Maybe I can formalize this much and submit.
July 21, 2025 at 11:13 PM
Cleaned up, but I'm still not convinced of #Unicity. If replication of #MarkovNumbers happens, though, it happens at like depths into the tree, after like numbers of turns. That's really cool. Maybe I can formalize this much and submit.
#MarkovNumbers #Unicity I've actually got two half proofs now! On the left hand, you've got that the number of turns must be equal. On the right hand, you've got that the number of reflections from "1," "2," or "5" must be equal. I think I can nail this before Saturday, which is "d-day" — 42!!!
July 21, 2025 at 6:32 PM
#MarkovNumbers #Unicity I've actually got two half proofs now! On the left hand, you've got that the number of turns must be equal. On the right hand, you've got that the number of reflections from "1," "2," or "5" must be equal. I think I can nail this before Saturday, which is "d-day" — 42!!!
Okay. Now I think we're really getting somewhere. I decided to expand the "b" terms, to force distinction in ' vs. " vs. "' etc. for all terms. #MarkovNumbers #Unicity
Now I need to prove that if we've made an equal number of "turns," the two Markov Numbers can't be equal unless the turns were t
Now I need to prove that if we've made an equal number of "turns," the two Markov Numbers can't be equal unless the turns were t
July 21, 2025 at 6:12 PM
Okay. Now I think we're really getting somewhere. I decided to expand the "b" terms, to force distinction in ' vs. " vs. "' etc. for all terms. #MarkovNumbers #Unicity
Now I need to prove that if we've made an equal number of "turns," the two Markov Numbers can't be equal unless the turns were t
Now I need to prove that if we've made an equal number of "turns," the two Markov Numbers can't be equal unless the turns were t
#MarkovNumbers #Unicity I think! Only 1.x years after I first thought I had it, lol. Just in time for my 42nd birthday!!!
July 19, 2025 at 2:04 PM
#MarkovNumbers #Unicity I think! Only 1.x years after I first thought I had it, lol. Just in time for my 42nd birthday!!!
Yeah. With enough clever wrangling, I reduced this ("given M_N/D and M_N'/D' are sufficiently close") to 3 > 2.618^(k-k') if they're equal. I'm not saying the proof is "in the bag," but Gawd, it's frigging close. #MarkovNumbers #Unicity
July 18, 2025 at 3:19 AM
Yeah. With enough clever wrangling, I reduced this ("given M_N/D and M_N'/D' are sufficiently close") to 3 > 2.618^(k-k') if they're equal. I'm not saying the proof is "in the bag," but Gawd, it's frigging close. #MarkovNumbers #Unicity
Alright, I've got my problem set up perfectly, I think. Next I'll do the version of the Zeckendorf problem that was sent to me, then tackle this. #MarkovNumbers #Unicity
May 5, 2025 at 9:01 PM
Alright, I've got my problem set up perfectly, I think. Next I'll do the version of the Zeckendorf problem that was sent to me, then tackle this. #MarkovNumbers #Unicity
Oh my God that's so cool. It keeps a record like a Turing tape. Just write the #MarkovNumbers "base F[2]" (where 21xxx = 100xxx). Come on, Webbie. It really shouldn't be too hard to show #Unicity of every 2-flanked palindrome of pairs of 1s and pairs of 2s. (Last: 10002001.)
April 25, 2025 at 1:14 PM
Oh my God that's so cool. It keeps a record like a Turing tape. Just write the #MarkovNumbers "base F[2]" (where 21xxx = 100xxx). Come on, Webbie. It really shouldn't be too hard to show #Unicity of every 2-flanked palindrome of pairs of 1s and pairs of 2s. (Last: 10002001.)