I’ve packaged a small, model-agnostic tool for probing the joint structure of a population via the correlation dimension (Grassberger–Procaccia D₂), and I’d value feedback from people working on population inference.
The motivation: marginal-histogram comparisons are blind to joint geometry — two catalogs can match on every 1D marginal yet differ in correlation structure. D₂ catches this.
The caveat I want to flag (and the reason I’m posting rather than just linking): applying D₂ to catalog point estimates systematically overstates structure. On the GWTC BBH catalog the point-estimate deficit (D₂≈2.165) largely vanishes under posterior propagation (D₂≈2.44, ~0.7σ below null — not significant). The package enforces three checks (marginal-shuffle null, subsample variance, posterior propagation) before any deficit is trusted.
Question for the community: for those who’ve applied geometric/fractal descriptors to GW catalogs — does this point-estimate inflation match what you’ve seen, and are there standard mitigations beyond full posterior propagation I should be aware of?
Package + zenodo.20819117 · Methods write-up zenodo.20783365
This is very useful, especially the warning about point estimates overstating structure. I’m working on an early simulation-stage AI tuning/validation system where multiple telemetry channels are compared together rather than trusted individually. One of those planned channels is FCAM, a field-sensing front end, alongside phase, thermal, noise, and safety-state telemetry.
What interests me here is not using D₂ as a claim-maker, but as a safeguard: can methods like marginal-shuffle nulls, subsample variance, and posterior/uncertainty propagation help determine whether an AI tuner is detecting real joint structure or simply amplifying noise, drift, sampling bias, or point-estimate artifacts?
I’m still at the validation/prototype stage and would be interested in feedback or possible student collaboration on adapting these geometric checks to multi-signal simulation data. The goal would be disciplined testing, not overclaiming.
Thanks for reading it so carefully — you’ve picked up exactly the point I most wanted to land: D₂ is most useful as a safeguard, not a claim-maker. That matches my own experience: my GWTC black-hole result looked like clean low-dimensional structure on point estimates (D₂≈2.17, below the shuffle null), but it largely dissolved once I propagated the real per-event posteriors (D₂ rose to ~2.44, ~0.7σ below null, not significant). So the cautionary finding was the finding.
On your question — yes, the three checks can help separate real joint structure from amplified noise/drift/sampling bias, but each targets a different failure mode:
- Marginal-shuffle null tests whether the joint geometry carries information beyond the per-channel marginals. Permute each channel independently, recompute. If real data isn’t separated from shuffled, what you’re seeing lives in the marginals, not the joint structure.
- Subsample variance (without replacement, or jackknife — avoid naive bootstrap with replacement, duplicate points have zero pairwise distance and bias the metric) tests whether the result hangs on a few influential samples.
- Posterior/uncertainty propagation is the one most people skip and the one that matters most: if each reading is really a distribution, collapsing it to a point systematically overstates structure.
Two honest caveats for your setting: my work is on a catalog of discrete events, not multi-channel time series, so you’ll need to think carefully about what “distance” means across heterogeneous channels (FCAM vs thermal vs safety-state aren’t naturally commensurable — standardization choices will affect the answer); and these diagnose whether structure is real, not what it is.
The code is open (corrdim on Zenodo, MIT-licensed, doi:10.5281/zenodo.20819117) with all three tests built in, so you’re welcome to apply it to your data directly.
On the collaboration question: I’m based at a research centre (hydro- and aerodynamics) and that’s my main commitment, so my available time is limited — but I’m genuinely happy to give methodological feedback as you prototype, and could potentially be involved in a more defined way depending on scope. To gauge that, it’d help to understand the context a bit: is this academic research, an industrial/product R&D effort, and who’s behind it? That just helps me figure out how I could realistically contribute. Either way, the “disciplined testing, not overclaiming” goal is the right one, and I’m glad to help pressure-test it.
Black holes decay in two phases, which correspond to the two peaks observed in your gravitational-wave signal.
I have developed a decay model for black holes that accounts for the two gravitational-wave bursts through a physically consistent internal structure, without introducing free parameters into the governing equations.
Phase 1: The black hole undergoes equatorial disruption, driven by its rotation at a frequency of 1 kHz and a surface velocity equal to one-seventh of the speed of light.
Phase 2: The two resulting hemispherical fragments subsequently coalesce into a planar explosion.
Thus, the two-phase decay process yields two distinct bursts in the gravitational-wave emission.
A full description of the model is available upon request.
Thank you for sharing your model.
Our analysis focuses on the statistical characterization
of a specific L1 transient at GPS 1382955253.17,
using the publicly available O4a data and an empirical
time-slide background. The result is a descriptor of
the signal’s morphology — not a physical interpretation
of the source.
We would be interested to see if your model makes
predictions about the expected signal morphology
(frequency, duration, amplitude ratio between phases)
that could be tested against the available data.
Best regards,
Dimitar Kretski
Good afternoon. I’m not a mathematician. I’ve only established the relationships that describe the process of black hole mergers and decays, the sequence of gravitational events that form a gravitational wave with one or two peaks, and described the cause of the observed noise before and after the main burst. Scientists observe noise in the signal, and I explain it not by a trembling of the black hole’s shape, but by a vibration of the diameter during the process of auto-tuning, the operation of the black hole’s self-regulating mechanism.
My model provides a clear understanding of how I solved the singularity problem and other paradoxes inside black holes. My model explains the shape of a black hole explosion as two symmetrical clouds, as well as the connection between the shape of the explosion and the flat shape of spiral galaxies.
I’m not asking you to believe me right away, but I’m offering an honest experiment: I provide you with my Energy Manifesto, and you insert it entirely into a request to the AI. This demonstrates its logical consistency, and then you can draw your own conclusions.
I can provide a link to my GitHub. There are diagrams attached. GitHub - smorodinovymors/The-Black-Hole-Model-by-Mikhail-Gerasimov: additions to theories of black hole structure that solve a number of problems in physical science · GitHub
I couldn’t find or didn’t understand how to place the text under the spoiler. Sorry! I hope that the GitHub link here is not a terrible crime against the rules.
I am ready to answer questions from the community within my capabilities.
Thank you, with sincere respect,
Mikhail Gerasimov
