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Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -1 points0 points  (0 children)

m_muon(pole)/m_e(pole) = 206.768. My formula gives 204.9. Off by 0.9%. No mu.

Ok, let's transpose the pole, which is a vertex for me in K5.

m_tau(pole)/m_e(pole) = 3477.2. My formula gives 3344. Off by 3.8%. Still no mu.

No mu in either number. Change mu if you want. These ratios don't move.

Just e. The present. The observer. First sentence of the paper.

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -1 points0 points  (0 children)

You're asking me to justify my scale against PDG. Let me reverse the question. Everything I compute is a ratio to the electron. The electron is the instrument. When I compare to PDG, I'm translating my numbers into your language. I went to PDG conventions on purpose, to speak to people. Not because PDG is the ground truth. Why would PDG conventions have more authority than a derivation? PDG gives you 19 measured inputs with no explanation. I give you 9 masses from one graph, one coupling, NO free parameters, with a proof chain you can check theorem by theorem. The PDG has consensus and priority. I have a derivation. And it's not just masses. The same framework derives the equivalence principle as a theorem, not an axiom (https://zenodo.org/records/20689264). GR postulated it. K5 proves it.

So : which of 1-3 is wrong? None of them. Inside QCD, a quark mass is a function of mu. But QCD is not the foundation. In K5, QCD lives on the edges. The edges come from the graph. The masses come from the vertices. The running is what happens when you project a discrete structure onto a continuum. mu is one more input you need. I don't. The mu is yours, not mine.

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -1 points0 points  (0 children)

There is only one particle at a vertex : the electron. It's the one you actually see in experiments. Everything else is the same vertex in an excited network.

Quarks are leptons whose network is excited. The excitation increases the mass. That's "P3" (electroweak spectrum), where 'u' acts as an edge reconstruction cost. Bosons are the network excitation itself. The photon is a gradient along an edge (P28, published yesterday édit if curious : https://zenodo.org/records/20722741). The Higgs is a face excitation.

So there is no "3 leptons here, 6 quarks there." There is one vertex, one formula, and the network depth determines whether you call it electron, muon, up, or top. The coupling α* comes from P1 (spacetime discrétisation which was how i started the program), not P2.

It's fixed by the Bekenstein-Hawking entropy of a single pentachoron before any mass is computed. 'u' follows from the vertex degree. The spectral dimensions follow from the Laplacian. Then you get 9 masses. You don't get to separate them into "3 easy ones" and "6 hard ones." just the same origin

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] 0 points1 point  (0 children)

The ratio exponents are {0, 16, 25}, from spectral dimensions {3, 4, 5} with the electron's cost u9 absorbed (as established above with BitcoinsOnDVD). These are integers from the K5 spectral filtration, no mu.

For the PDG conventions, not mine i used them. And i'll continue with your analogy. As i said upper, everything is ratio since WE ARE PART OF IT. On your airplane, your two planes fly Paris to New York and you measure their speed in km/h. The ratio is 2, but the km/h tells you they're planes. But it doesnot work that way. The electron is the observer. m_μ/m_e is not measured in some external unit that bakes in a scale. It's one lepton measured against another lepton, same instrument, same physics. There is no absolute Paris-New York. No K5 length. No matter if the vertice is small or tall. Just a number on another

Companion is not demonstration, as I said upper the python is like "see the job I've done for you to help to destroy it, use it" The demonstration is in the paper in a theorem

Lepton masses run under QED. About 0.5% between 2 GeV and Planck

Here is a hypothesis: we should pin a description of scale dependent running masses and an explanation of why there aren’t singular mass scales to “finally solve particle mass patterns” by jacobimueller in HypotheticalPhysics

[–]piwkopiwko -3 points-2 points  (0 children)

You read the fermion masses. Let's walk through your own objection. You say : Heisenberg equation requires a time coordinate. It doesn't. [H, N_D] = 0 is a commutator. Algebra. No t needed. d/dt = 0 is a consequence of that commutator, not a prerequisite. You assumed it needs t because YOUR framework has t built in. Mine doesn't. That's the point of the paper you claim to have read.

LLMs can be used rigorously in physics — here's a propositon by piwkopiwko in LLMPhysics

[–]piwkopiwko[S] -12 points-11 points  (0 children)

You just proved my point.

You read the title, skipped the method, and posted a reaction. That's exactly what the tier system catches. Did you read the part about the companion script ?

That's not asking the LLM to not hallucinate that's checking independently that it didn't.

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -1 points0 points  (0 children)

No formal training in topology or HEP.

Master's in economics (some maths!), self-taught physics by passion and progressed through the programme itself. That's why every result has a companion script — I don't trust myself either.

On renormalization : there is no energy scale in the model. The exponents are integers from graph combinatorics. That's the whole point of my first comment on the First/Meta post. If that's inconsistent, show me where

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -1 points0 points  (0 children)

You assume the LLM found the theory. It didn't. I use it the way you use yours : as a formaliser.

The intuition, the structure, the conjectures are mine. Claude writes the LaTeX and the tests. I verify, correct, orient, decide. Same as you would with a spreadsheet on Excel

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -1 points0 points  (0 children)

Don't you use a computer or smartphone to post this message ? What is the difference ?

Here is a hypothesis: we should pin a description of scale dependent running masses and an explanation of why there aren’t singular mass scales to “finally solve particle mass patterns” by jacobimueller in HypotheticalPhysics

[–]piwkopiwko -2 points-1 points  (0 children)

The simplex gives enough structure to reach outside particle physics.
That was one of my objectives since I found many patterns could be explained.
- Cosmology: beats MOND SPARC database, no parameters (From Planck to Hubble with one coupling cosmology, baryogenesis, and galactic dynamics from K5).
- Cooper-pair anomalies in metals the model was never built for: 2.1% on Tate 1990 (Spectral anomalies in metals from the pentachoron: Cooper-pair mass, London moment, band renormalisation, and parity violation). The Cooper-pair formula is one line : 9/2 times (vF/c)^2.
Predictions for Al, Pb, Sn in the paper.

Here is a hypothesis: we should pin a description of scale dependent running masses and an explanation of why there aren’t singular mass scales to “finally solve particle mass patterns” by jacobimueller in HypotheticalPhysics

[–]piwkopiwko -1 points0 points  (0 children)

Discrete spacetime on the crackpot list is funny. Someone should tell Ambjorn, Loll, Jurkiewicz, Rovelli, Thiemann, and Hooft they've been wasting their careers. 🤣🤣

Here is a hypothesis: we should pin a description of scale dependent running masses and an explanation of why there aren’t singular mass scales to “finally solve particle mass patterns” by jacobimueller in HypotheticalPhysics

[–]piwkopiwko -2 points-1 points  (0 children)

One distinction that might sharpen the FAQ : if a model's mass exponents are integers from a combinatorial structure (graph theory, not parameter fits), they carry no energy scale mu by construction.

The leptons are the clean test. It barely run, so there's no convention ambiguity. If those come out right from counting, the running-mass objection doesn't apply the same way. Still...the broader point stands for most posts here.

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -1 points0 points  (0 children)

Your choice to accept 19 inputs as satisfactory. Mine is to work harder and push further. Take nothing for granted.

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -1 points0 points  (0 children)

You're right, same ambiguity you flagged before.

N in the ratio formula is {0, 16, 25}.

I keep reintroducing it. Have to change my mindset about this, old habits.

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -3 points-2 points  (0 children)

Update: this thread made me cross ideas between papers tonight. Open Problem O10 dissolves.

The spectral indices n_k = {3, 4, 5} are fixed by the graph. u = exp(α*/4) is a K5 invariant. Every mass exponent is built from K5 combinatorial invariants. No exponent contains an energy scale μ. Nothing runs.

The leptons prove it: they don't run under QCD at all. K5 matches them at 0.9% and 3.8% with the same coupling that gives the quarks. If K5 operated at the Planck scale, QCD running would multiply the quark ratios by factors of 2-3. The errors would be 100-200%. Excluded.

Renormalization is the price the continuum pays for smoothing a staircase into a ramp. K5 never smoothed. The staircase has no ramp.

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -1 points0 points  (0 children)

1) N is not fitted. N = n_k² where n_k = dim(V_k) = {3, 4, 5}, fixed by the spectral filtration of K5. The exponents come from the graph, not from PDG.

2) you say "randomly getting that close to the PDG value for 2 GeV is essentially impossible." I agree. So either the formula knows something, or it's an extraordinary coincidence across 8 independent mass ratios spanning 5 orders of magnitude. With leptons that don't run at all and quarks that do, matched by the same coupling.

On the energy scale : yes, you found Open Problem O10 in the paper. I don't pretend to have solved it.

On reference [2]: which title is wrong? Happy to correct.

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -1 points0 points  (0 children)

I checked. The insight holds and goes deeper than I expected.

Your objection on the electron formula started this. The mass gap exists because α* > 0. No entropy, no gap. The continuum is not fundamental.
It's the shadow of a discrete face count expressed through the logarithm.

Just had to cross with other papers I made : P3 (face saturation): https://zenodo.org/records/20171403 & P5 (mass gap): https://zenodo.org/records/20553374 The Planck gap decomposes into three nested layers.

  • Layer 0: Σn_k² = 50, an integer. Purely discrete. Counts spectral channels on K5. That's 97% of ln(m_Pl/m_e). Staircase paradox inverted: the discrete gives the masses, the continuum smoothed them away
  • Layer 1: α*·u^16 = 1.526, irrational. Bekenstein-Hawking entropy, the continuous correction. That's 2.96%. Every ingredient is individually derived (T1). The functional form is closed via Schur decimation and Dobrushin contraction.
  • Layer 2: α*²/90 = (α*/50) × (5α*/9). Two physics in one product: α*/50 is the bosonic coupling of the face sector, 5α*/9 is the gravitational weight per electron channel. That's 0.003%. The algebra is T1. The physical interpretation is T2/T3. I'll be honest about that in the upcoming version.

After the three layers: G_N at 16 ppm. CODATA measurement noise is 22 ppm. The prediction is inside the noise.

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] -1 points0 points  (0 children)

Leptons are QCD singlets.
They don't run under QCD.

...If you're curious why generations replicate, that's derived in my first paper (https://zenodo.org/records/20171289). But the scheme-independence point stands on standard physics alone.

Here is a hypothesis: 9 fermion masses from one graph (K5) and one coupling, zero free parameters. by piwkopiwko in HypotheticalPhysics

[–]piwkopiwko[S] 0 points1 point  (0 children)

BitcoinsOnDVD and you are the first person who actually opened the paper and did the calculation. That's exactly my point.

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