Check this out, /sci/. I think I just stumbled upon an absolute world record in physical numerology/experimental number theory.The inverse fine-structure constant alpha^-1 (at zero energy) and the running electroweak coupling constant at the Z-boson peak (high energy) share the EXACT same infinite 9-period tail in their regular continued fraction expansion:[1; 3, 1, 1, 18, 1, 7, 1, 3]Look at the precision:Low-energy: [137; 27, tail] = 137.0359991770497...(Hits CODATA 2022 DEAD CENTER inside the 1-sigma error bar)High-energy: [128; 1, 17, tail] = 128.946747361...(Hits the exact experimental Z-pole scale threshold)Because they share the identical algebraic DNA (the positive root of 4767x^2 - 4898x - 1575 = 0), you can map the atom-scale directly onto the subatomic scale using a clean, integer-coefficient Möbius transformation under the modular group GL2(Z):B = (-1162A + 159323) / (-9A + 1234)Standard numerologists only obsess over 137 while ignoring quantum field scaling. This is the first time both scales are unified via a single periodic attractor.Is the vacuum energy scale just a discrete continued fraction calculator or is this the most insane mathematical coincidence ever found?Full short paper with exact algebraic roots and derivations uploaded to Zenodo: https://zenodo.org/records/22116511
generative ai was a mistake, as was zenodo. i hope cern retracts this, or at least gatekeeps it.
Nice try, anon, but LLMs can't hallucinate rigid algebraic identities.Go open Python or Mathematica right now and compute the positive root of:4767x^2 - 4898x - 1575 = 0Then plug it into A = [137; 27, x]. You get exactly 137.0359991770497...The math is 100% deterministic and verifiable. If you can't handle a clean modular group GL2(Z) transformation bridging two physical scales, just say so. Zenodo is for archiving exact relations, and this one is mathematically bulletproof.
>2022 CODATA >current>2022>currentuh huh...>fractional linear equation>it's actually a quadratic equation. >linear = quadratic...>evaluating this numericallynigga it's closed fucking form and a simple fucking square root>latest CODATA>2022>latestimagine not knowing the 2026 updatebtw your continued fraction with 9 randomly chosen numbers is in no way more elegant than a simple ratio between four fundamental physical constants. hmmm>four fundamental constants simple ratioversus>continued fraction with 9 arbitrary numbersi wonder which one should be used...
Anonymous"imagine not knowing the 2026 update"Nice try, brainlet. The CODATA 2026 adjustment data collection closes on December 31, 2026, and won't be published until 2027. CODATA 2022 IS the current official reference standard."fractional linear = quadratic"Imagine browsing /sci/ and not knowing what a fractional linear equation is.x = (6124x + 1575) / (4767x + 1226) is a fractional linear equation by definition (a Möbius transformation). You cross-multiply to solve it, which yields the quadratic form. It's basic algebra."9 arbitrary numbers vs simple ratio"They aren't "arbitrary". The whole point of the paper is that this SINGLE 9-digit periodic attractor SIMULTANEOUSLY hits two completely different physical scales (zero-energy alpha and the high-energy Z-pole) just by shifting the integer prefix, which unifies them under a GL2(Z) modular group matrix. A simple ratio of 4 constants can't map the quantum field scaling trajectory.Go back to /b/, you can't even read a basic pre-print.
>>17042820you're looking for ///x///so you're not in the know about codata. unfortunate. physicists who actually study this have seen previews in conferences. not for pseuds. >they aren't arbitraryokay, so why that specific sequence and where did those specific numbers come from? >A simple ratio of 4 constants can't map the quantum field scaling trajectoryyou dumb fuck ::skull:: imagine not knowing how the fine structure constant is defined and writing this schizo crap. this is your last /you/. gtfo my board, further responses will not be acquired.
AnonymousYou are completely missing the point, anon. I never claimed this replaces a full QFT derivation, it's open-source mathematical physics and recreational number theory.But as far as pure mathematical coincidences go, it is currently the most precise one on the internet. hitting CODATA 2022 dead center for low-energy and landing exactly inside the Z-pole threshold using the same 9-period tail is a clean geometric fact.If you want to stay mad at a bulletproof GL2(Z) matrix transformation, go ahead. The math is archived on Zenodo anyway. Peace out.
>mathematical physicsokay i lied about the last (you). there is zero physics in what you put out. there are no physical constants based on or extracted by experiments. furthermore, the coupling constant runs. which schizo pseuds like you never know about because you jerk off to the 137 nonsense, which is the real reason i'm responding.
Anonymous"furthermore, the coupling constant runs. which schizo pseuds like you never know about"Are you literally blind?Constant B in the paper is EXACTLY the running coupling constant at the high-energy Z-boson scale (~128.94). The entire point of the Möbius transformation is to link the low-energy limit (137) to the running high-energy scale (128).You just described the exact core mechanism of my paper while trying to use it as an insult. Absolute peak /sci/ illiterate behavior. Thanks for the bump.
>>17042804>physical numerology/experimental number theory.oh my hecking science
Exactly that is the message of my post. It becomes obvious, in case somebody is able to read and understand.
Here is a Actual Derivation the Fine Structured Constant.. Testable..https://doi.org/10.5281/zenodo.22130847
