Named after Kepler, who went from Tycho Brahe’s observational data to the laws of planetary motion (as mentioned in the article). But one really inspiring thing about Kepler is not mentioned there is that he started with a different theory and then changed his mind when the observational data showed he was wrong. We have the laws of planetary motion because of a feat of tremendous intellectual humility where a really smart person was prepared to admit that the theory they had invested a huge amount of time and effort into formulating didn’t match the observational data, _so they changed their mind_.
Kepler’s original theory was that the orbits in the solar system were defined by polygons and their inscribed/circumscribed spheres. This seemed very attractive because at that time they knew of 6 planetary bodies and this fitted in somehow (I don’t remember exactly) into this model with nested platonic solids and the spheres around them. Then Kepler realised that the predictions of this very elegant model were worse than the heliocentric model.
So when Brahe’s observations became available he basically threw all that out and started again, to develop his wonderfully elegant laws of planetary motion based around elliptical orbits which also have the significant benefits of predicting planetary motion beautifully and were later found to be entirely derivable from Newton’s laws of motion using calculus (there is a wonderful presentation of this derivation in Spivak for anyone who is interested).
I have a faster solution for N-body gravity with orbital resonance that predicts the perihelion of Mercury than gravity from QED scattering, with Gr_C(2,4) in Lean 4 and Rust/WASM that I haven't yet published.
I noticed "Kepler" in the title and cool story about Kepler so now I'm mentioning it;
"Grassmannian Gravity from QED & Gauge Scattering Amplitudes: Complex Gr_C(2,4) Orbital Precession, Mercury's Perihelion, N-Body Dynamics, and Dilatant Dark Fluid (DDF) Unification in Lean 4" (2026)
westurner/sustainablefactory/docs/grassmannian-gravity-from-qed-scattering-paper.md at main · westurner/sustainablefactory https://github.com/westurner/sustainablefactory/blob/main/do... :
> An arXiv-ready formal verification paper deriving planetary orbits, Mercury's 42.98 arcsec/century perihelion precession, and N-body gravitational dynamics from flat-space QED/gauge scattering amplitudes, BCJ double copy on Gr_C(2,4), and Dilatant Dark Fluid (DDF) hydrodynamics in Lean
There's already gravity that fits the Perihelion of Mercury from QED scattering (Partanen, M., and Tulkki, J. (2025). "Gravity Generated by Four One-Dimensional Unitary Gauge Symmetries and the Standard Model" / "Perihelion Precession of Planetary Orbits Solved from Quantum Field Theory"). FWIU, I've here contributed the use of Grassmanian Plückers and a Complex Grassmannian - GrC(2,4) both with and without connections to DDF Dilatant Dark Fluid (Fedi).
I had created a simple particle wave visualization tool with 3js and then on a whim AI-added a double slit and a detector screen, and I asked for Huygens-Steiner Parallel-Axis Intensity as the model to simulate superposition because of [Qian and Izadi] and then I had to keep working on that instead. First the model differencing in the simulator in JS to compare the difference in model predictions in the double-slit experiment against Pilot Wave Theory and Wigner function and then with Fraunhofer and Lean 4 and Rust and a crisp symbolic error term for each model of photonic and electronic superposition. It looks like GrC(2,4) is the most efficient model for photonic and electronic superposition, too.
"Huygens–Steiner Barycentric Coherence, Complex Gr_C(2,4) Plücker Channels, and Multi-Model Double-Slit & OAM Relative Predictive Error in Lean 4" (2026)
> An arXiv-ready formal verification paper uniting Qian–Izadi Huygens–Steiner parallel-axis coherence, complex Gr_C(2,4) Plücker double-slit interference, de Broglie–Bohm pilot-wave hydrodynamics, Wigner phase-space marginals, and Orbital Angular Momentum (OAM) relative predictive error in Lean
Useful to create a devcontainer with lean4 and rust. Still working through verifying the URLs of each citation to publish some of this paper series per the latest terms for AI articles.
The first line was intriguing but the rest of it is a mishmash of buzzwords and handwaving. It looks like you are bidding for consideration of a grand unified theory, and that's great, I am one of the people that enjoys considering new proposals that unify or align previously disconnected areas of physics or mathematics.
But even though I understood (most of) the individual assertions you are trying to cram into your abstract-of-an-abstract, showing which things you are combining, how you are combining them,and how you are keeping reproducibility and provability as your top priorities, the effect of trying to communicate so many data points at once comes off as earnest but incoherent, like a bus-stop conversation with a schizophrenic.
Ideas are not self-propagating. If you just want to feed your thoughts back into other AIs in a way that lets provide useful input toward an intellectual singularity, publish it on your own blog. If you are publishing it in a social space, take some time to articulate in plain language what you think you've found, why it's important, and why other people might find it worthwhile to invest some time in wrapping their heads around it. If that seems too vague go read some Quanta articles and ponder why they read a wider audience than hyper-technical abstracts in math journals.
It's justified to mention GrC(2,4) for modeling orbital gravity here because the OP's (and Kepler's) methods will not ever derive the scattering amplitude basis for gravity or the Grassmannian geometric manifold for calculating the 1-loop scattering because of algorithmic insufficiency at the universal function approximation problem.
What I took the time to share here saves many years of false starts at modeling gravity; which - ironically - Kepler's doesn't sufficiently model either.
A question to research:
What's wrong with Keplerian gravity?
GrC(2,4) is probably more efficient than for example how NASA SPICE toolkit models gravity rivers.
I'm not finding this feedback to be helpful. I wish you luck with your own approach.
> incoherent, like a bus-stop conversation with a schizophrenic.
This is impolite and disrespectful. Do you have code or math to contribute? What tools could you use to interpret for example this the first sentence of my post?
> I have a faster solution for N-body gravity with orbital resonance that predicts the perihelion of Mercury than gravity from QED scattering, with Gr_C(2,4) in Lean 4 and Rust/WASM that I haven't yet published
I also found your post lacked coherence, but I agree GP’s feedback is delivered a bit harshly
- the way you jump right in is kind of off topic with tons of details, your connecting sentence about Kepler would have been better framing context to lead with (but it also needs revision because it reads like you’re elbowing into the conversation)
- HN is a general (technical) audience, your opening statement and the rest of your post assumes a lot of specialized knowledge. It needs some scaffolding and some distillation for a broad audience to understand what’s important about what you did
- that opening sentence isn’t grammatical? Your solution is faster than some quantum theory of gravity? Or maybe you missed a word and mean it’s more accurate than QED? And it’s a theory of gravity that predicts orbital resonance?
- you’re mixing conceptual and implementation details with the effect of information overload. Is the interesting part the theory of gravitation or the fact that you used Rust and WASM? I would lead with the scientific part, then add a separate sentence on the computational tools you used so they both get the focus they deserve
- the rest of your post is long and kind of alternates between what looks like pasted autogenerated link summaries, jargon-filled descriptions of the research, and some descriptions of visualization tools that don’t clearly connect (to someone without expertise in this field) to the rest of the post
- there’s a flood of crap science being cranked out with agents. Maybe your project is not one of these, but you’re fighting an uphill battle against everyone’s heuristics to filter out the noise. If you want to be engaging you have to distill, clarify, and adapt to your audience
I think (looking also at his website) that he is trying to make some sort of honeypot for agents. The lean code is completely nonsensical- tons of broken latex, dense references in the docstrings and the proofs are all very long names to obscure the fact that there’s nothing there. All they do is instantiate structures with lots of arguments and then assert one of the arguments.
I don't hate AI preprints, I hate slop grenades, which is what this is. Either you did that on purpose (which was what I thought looking at your website - that you created a honeypot to trap agents) or you don't realise that's what you're doing, in which case this makes me very sad.
It's tragic that you spend time harassing and diminishing about your subjective aesthetic response instead of learning to check the machine-checkable proofs using the tools.
Test coverage in Lean might be a good feature to contribute.
Yup, I checked it out, some cool ideas in there. Owl and I were talking about our deterministic algos for SR under another recent HN post on SR, which seems to be having a small moment.
Named after Kepler, who went from Tycho Brahe’s observational data to the laws of planetary motion (as mentioned in the article). But one really inspiring thing about Kepler is not mentioned there is that he started with a different theory and then changed his mind when the observational data showed he was wrong. We have the laws of planetary motion because of a feat of tremendous intellectual humility where a really smart person was prepared to admit that the theory they had invested a huge amount of time and effort into formulating didn’t match the observational data, _so they changed their mind_.
Kepler’s original theory was that the orbits in the solar system were defined by polygons and their inscribed/circumscribed spheres. This seemed very attractive because at that time they knew of 6 planetary bodies and this fitted in somehow (I don’t remember exactly) into this model with nested platonic solids and the spheres around them. Then Kepler realised that the predictions of this very elegant model were worse than the heliocentric model.
So when Brahe’s observations became available he basically threw all that out and started again, to develop his wonderfully elegant laws of planetary motion based around elliptical orbits which also have the significant benefits of predicting planetary motion beautifully and were later found to be entirely derivable from Newton’s laws of motion using calculus (there is a wonderful presentation of this derivation in Spivak for anyone who is interested).
This is Kepler's original theory, which is apparently the origin of the phrase "music of the spheres" btw. https://en.wikipedia.org/wiki/Mysterium_Cosmographicum
He didn't even had a pocket calculator, and had to figure out the geometry without a concept of Cartesian representation.
I have a faster solution for N-body gravity with orbital resonance that predicts the perihelion of Mercury than gravity from QED scattering, with Gr_C(2,4) in Lean 4 and Rust/WASM that I haven't yet published.
I noticed "Kepler" in the title and cool story about Kepler so now I'm mentioning it;
"Grassmannian Gravity from QED & Gauge Scattering Amplitudes: Complex Gr_C(2,4) Orbital Precession, Mercury's Perihelion, N-Body Dynamics, and Dilatant Dark Fluid (DDF) Unification in Lean 4" (2026) westurner/sustainablefactory/docs/grassmannian-gravity-from-qed-scattering-paper.md at main · westurner/sustainablefactory https://github.com/westurner/sustainablefactory/blob/main/do... :
> An arXiv-ready formal verification paper deriving planetary orbits, Mercury's 42.98 arcsec/century perihelion precession, and N-body gravitational dynamics from flat-space QED/gauge scattering amplitudes, BCJ double copy on Gr_C(2,4), and Dilatant Dark Fluid (DDF) hydrodynamics in Lean
There's already gravity that fits the Perihelion of Mercury from QED scattering (Partanen, M., and Tulkki, J. (2025). "Gravity Generated by Four One-Dimensional Unitary Gauge Symmetries and the Standard Model" / "Perihelion Precession of Planetary Orbits Solved from Quantum Field Theory"). FWIU, I've here contributed the use of Grassmanian Plückers and a Complex Grassmannian - GrC(2,4) both with and without connections to DDF Dilatant Dark Fluid (Fedi).
I had created a simple particle wave visualization tool with 3js and then on a whim AI-added a double slit and a detector screen, and I asked for Huygens-Steiner Parallel-Axis Intensity as the model to simulate superposition because of [Qian and Izadi] and then I had to keep working on that instead. First the model differencing in the simulator in JS to compare the difference in model predictions in the double-slit experiment against Pilot Wave Theory and Wigner function and then with Fraunhofer and Lean 4 and Rust and a crisp symbolic error term for each model of photonic and electronic superposition. It looks like GrC(2,4) is the most efficient model for photonic and electronic superposition, too.
"Huygens–Steiner Barycentric Coherence, Complex Gr_C(2,4) Plücker Channels, and Multi-Model Double-Slit & OAM Relative Predictive Error in Lean 4" (2026)
sustainablefactory/docs/grassmannian-huygens-double-slit-oam-paper.md at main · westurner/sustainablefactory https://github.com/westurner/sustainablefactory/blob/main/do... :
> An arXiv-ready formal verification paper uniting Qian–Izadi Huygens–Steiner parallel-axis coherence, complex Gr_C(2,4) Plücker double-slit interference, de Broglie–Bohm pilot-wave hydrodynamics, Wigner phase-space marginals, and Orbital Angular Momentum (OAM) relative predictive error in Lean
Useful to create a devcontainer with lean4 and rust. Still working through verifying the URLs of each citation to publish some of this paper series per the latest terms for AI articles.
Can you not?
The first line was intriguing but the rest of it is a mishmash of buzzwords and handwaving. It looks like you are bidding for consideration of a grand unified theory, and that's great, I am one of the people that enjoys considering new proposals that unify or align previously disconnected areas of physics or mathematics.
But even though I understood (most of) the individual assertions you are trying to cram into your abstract-of-an-abstract, showing which things you are combining, how you are combining them,and how you are keeping reproducibility and provability as your top priorities, the effect of trying to communicate so many data points at once comes off as earnest but incoherent, like a bus-stop conversation with a schizophrenic.
Ideas are not self-propagating. If you just want to feed your thoughts back into other AIs in a way that lets provide useful input toward an intellectual singularity, publish it on your own blog. If you are publishing it in a social space, take some time to articulate in plain language what you think you've found, why it's important, and why other people might find it worthwhile to invest some time in wrapping their heads around it. If that seems too vague go read some Quanta articles and ponder why they read a wider audience than hyper-technical abstracts in math journals.
> Can you not?
It's justified to mention GrC(2,4) for modeling orbital gravity here because the OP's (and Kepler's) methods will not ever derive the scattering amplitude basis for gravity or the Grassmannian geometric manifold for calculating the 1-loop scattering because of algorithmic insufficiency at the universal function approximation problem.
What I took the time to share here saves many years of false starts at modeling gravity; which - ironically - Kepler's doesn't sufficiently model either.
A question to research: What's wrong with Keplerian gravity?
GrC(2,4) is probably more efficient than for example how NASA SPICE toolkit models gravity rivers.
Yeah, it reminds me of Timecube.
I'm not finding this feedback to be helpful. I wish you luck with your own approach.
> incoherent, like a bus-stop conversation with a schizophrenic.
This is impolite and disrespectful. Do you have code or math to contribute? What tools could you use to interpret for example this the first sentence of my post?
> I have a faster solution for N-body gravity with orbital resonance that predicts the perihelion of Mercury than gravity from QED scattering, with Gr_C(2,4) in Lean 4 and Rust/WASM that I haven't yet published
I also found your post lacked coherence, but I agree GP’s feedback is delivered a bit harshly
- the way you jump right in is kind of off topic with tons of details, your connecting sentence about Kepler would have been better framing context to lead with (but it also needs revision because it reads like you’re elbowing into the conversation)
- HN is a general (technical) audience, your opening statement and the rest of your post assumes a lot of specialized knowledge. It needs some scaffolding and some distillation for a broad audience to understand what’s important about what you did
- that opening sentence isn’t grammatical? Your solution is faster than some quantum theory of gravity? Or maybe you missed a word and mean it’s more accurate than QED? And it’s a theory of gravity that predicts orbital resonance?
- you’re mixing conceptual and implementation details with the effect of information overload. Is the interesting part the theory of gravitation or the fact that you used Rust and WASM? I would lead with the scientific part, then add a separate sentence on the computational tools you used so they both get the focus they deserve
- the rest of your post is long and kind of alternates between what looks like pasted autogenerated link summaries, jargon-filled descriptions of the research, and some descriptions of visualization tools that don’t clearly connect (to someone without expertise in this field) to the rest of the post
- there’s a flood of crap science being cranked out with agents. Maybe your project is not one of these, but you’re fighting an uphill battle against everyone’s heuristics to filter out the noise. If you want to be engaging you have to distill, clarify, and adapt to your audience
I think (looking also at his website) that he is trying to make some sort of honeypot for agents. The lean code is completely nonsensical- tons of broken latex, dense references in the docstrings and the proofs are all very long names to obscure the fact that there’s nothing there. All they do is instantiate structures with lots of arguments and then assert one of the arguments.
Wow!
Well, it's already better than Kepler.
Have you checked the table of check figures?
Do you understand that it is correct?
Have you shown any counterexamples, or have you offered subjective aesthetic diminishment?
What a mistake it was to mention it here.
Do you have specific feedback? Or just "I hait AI preprints, ugh!"
I would accept a PR if you have specific feedback regarding the code.
I don't hate AI preprints, I hate slop grenades, which is what this is. Either you did that on purpose (which was what I thought looking at your website - that you created a honeypot to trap agents) or you don't realise that's what you're doing, in which case this makes me very sad.
It's tragic that you spend time harassing and diminishing about your subjective aesthetic response instead of learning to check the machine-checkable proofs using the tools.
Test coverage in Lean might be a good feature to contribute.
How does TabPFN perform on the same data?
From "Show HN: TabPFN v2 – A SOTA foundation model for small tabular data" https://news.ycombinator.com/item?id=42650792 :
> Benchmark of tabpfn<2 compared to xgboost, lightgbm, and catboost
Looks like it was written by human. Crazy
Yup, I checked it out, some cool ideas in there. Owl and I were talking about our deterministic algos for SR under another recent HN post on SR, which seems to be having a small moment.
https://news.ycombinator.com/item?id=50171936
Is this a bot account? The unicode everywhere and comments indicates this was 100% vibe-coded...
I bet this was fun to think about and build. Thank you for sharing!