DOI: 10.5281/zenodo.16868562
title: Data & Repro Pack (REALDATA) for "A testable brane-world unification: one parameter links a GW spectral break and ΔNₑff"

description: Machine-readable files sufficient to regenerate the figures and core checks in Maldonado (2025).

• PTA spectra (CSV): freq_Hz, log10rho_median, log10rho_p16, log10rho_p84• LISA sensitivity (ESA format CSV): f_Hz, Sn_1_per_Hz, label• CMB/BBN prior (JSON): Planck-2018 ΔN_eff = 2.99 ± 0.17• Best-fit parameters with 68% intervals (JSON)• Two-page Results PDF (figures + equations)• Tiny script to reproduce the plots from the CSVs• MANIFEST + CHECKSUMS + column schema and READMEs

Purpose. Enable independent inspection and reproduction of:  (1) the broken-power-law SGWB with break frequency f_br(λ) ∝ λ^{1/4}, and  (2) the mapping of the dark-radiation constant C to early-time radiation,      C/ρ_{γ,0} = (7/8) (4/11)^{4/3} ΔN_eff.

Falsifiability rule (single parameter). One and the same λ must (i) place f_br where PTA→LISA allows and (ii) yield ΔN_eff consistent with CMB/BBN. If not, the model is wrong.

Canonical files in this pack• exported_pta_spectrum_HD_30f.csv  (anchor spectrum)  • exported_pta_spectrum_CP_30f.csv  (cross-check)  • exported_pta_spectrum_HD_30f_100fDMGP.csv (denser grid variant)  • ESA_RCL2019_10yr_instrument_PLUS_confusion.csv  (LISA sensitivity)  • CMB_Planck2018_DeltaNeff_prior.json  • BestFit_with_uncertainties_20250814_200657.json  • Results_TwoPager_REFRESH_20250814_200726.pdf  (canonical two-pager)  • reproduce_posteriors.py, MANIFEST.txt, CHECKSUMS.txt, README_* and columns_and_units.txt  • Preview PNGs for Zenodo gallery
description: Files:

- exported_pta_spectrum_HD_30f.csv, exported_pta_spectrum_CP_30f.csv, exported_pta_spectrum_HD_30f_100fDMGP.csv

  Columns: freq_Hz, log10rho_median, log10rho_p16, log10rho_p84

- ESA_RCL2019_10yr_instrument_PLUS_confusion.csv

  Columns: f_Hz, Sn_1_per_Hz, label   (one-sided strain noise PSD)

- CMB_Planck2018_DeltaNeff_prior.json  (μ, σ for ΔN_eff)

- BestFit_with_uncertainties_20250814_200657.json  (demo best fit + 68% ranges)

- Results_TwoPager_REFRESH_20250814_200726.pdf  (summary figures)

- MANIFEST.txt, columns_and_units.txt, README_arXiv.txt, README_Data_and_Repro.txt

- reproduce_posteriors.py   # minimal script to remake quick-look plots

 

How to run:

python reproduce_posteriors.py \

  --pta exported_pta_spectrum_HD_30f_100fDMGP.csv \

  --lisa ESA_RCL2019_10yr_instrument_PLUS_confusion.csv \

  --cmb  CMB_Planck2018_DeltaNeff_prior.json \

  --out results/

Outputs: PTA fit preview with LISA overlay, corner/marginals (toy), and a best-fit JSON.

---------------------------------------------------

How to reproduce (quick):

1) python reproduce_posteriors.py --pta exported_pta_spectrum_HD_30f.csv \   --lisa ESA_RCL2019_10yr_instrument_PLUS_confusion.csv \   --cmb CMB_Planck2018_DeltaNeff_prior.json \   --out out/2) Compare generated plots to Results_TwoPager_REFRESH_20250814_200726.pdf.3) Optionally swap the PTA CSV for *_CP_30f.csv or *_HD_30f_100fDMGP.csv to cross-check.

Notes• “200726” two-pager is the canonical figure set. The “203614” file is a lightweight refresh and may be omitted in citations.  • LISA CSV follows Robson–Cornish–Liu (2019) style scaling; column units are in columns_and_units.txt.
description: Over the past several days I developed a compact, testable framework that ties early-universe cosmology to gravitational-wave data in a single, falsifiable way. In brief, we model our universe as a 4-D brane embedded in a higher-D bulk, yielding the standard Shiromizu–Maeda–Sasaki effective field equation on the brane and, in FRW, a modified expansion law:

 





Modified Friedmann (flat, k=0):

H^2 = (8πG/3) * ρ * (1 + ρ/(2λ)) + Λ4/3 + C/a^4



 

 

Here λ is the brane tension; the ρ^2 term is the high-energy correction, and C/a^4 is the “dark-radiation” piece from the projected bulk Weyl tensor. Two clean, near-term tests follow:

 





GW spectral break: a broken-power-law SGWB with break frequency

f_br(λ) ∝ λ^(1/4) (transition from the ρ^2 era to standard 4-D expansion), testable with PTAs now and LISA next.




Radiation excess: dark-radiation constant mapped to the early-time parameter

C / ρ_γ,0 = (7/8) * (4/11)^(4/3) * ΔN_eff, constrained by CMB/BBN.



 

 

Falsifiability (single-parameter rule): one and the same λ must jointly (i) place f_br where the PTA→LISA bands allow, and (ii) yield ΔN_eff consistent with CMB/BBN. If the required λ fails either sector, the model is wrong.

 

Status and materials. I’m attaching:

 





a short Two-Pager with the equations, the PTA fit preview, and LISA sensitivity overlays;




a compact All-in-One explainer for context;




a minimal Repro Pack (CSV + script) that regenerates the figures with public PTA spectra and Planck-style ΔN_eff priors.

(If you prefer, I can supply a Zenodo DOI for the exact CSVs/figures.)



 

 

Conceptual note (singularity): the initial “Big-Bang singularity” is replaced by a higher-D energy event (brane blast/collision), which regularizes the initial condition while leaving late-time GR intact (ρ << λ → standard GR limits). This same geometry offers avenues for dark radiation and potential dark-sector effects; black-hole signatures (e.g., modified ringdown via bulk Weyl memory) are noted as follow-ups.

 

What would confirm it? A SGWB break at the predicted range (given the λ that also satisfies CMB/BBN ΔN_eff) and a consistent joint fit. What would falsify it? No break where required, or a λ incompatible with early-radiation bounds.
description: Primary two-pager:- Results_TwoPager_REFRESH_20250814_200726.pdf

PTA CSVs (choose one when reproducing; all share the same schema):- exported_pta_spectrum_HD_30f.csv- exported_pta_spectrum_CP_30f.csv- exported_pta_spectrum_HD_30f_100fDMGP.csvColumns: freq_Hz, log10rho_median, log10rho_p16, log10rho_p84

LISA (ESA-style curve):- ESA_RCL2019_10yr_instrument_PLUS_confusion.csvColumns: f_Hz, Sn_1_per_Hz, label   (one-sided strain PSD)

Priors and results:- CMB_Planck2018_DeltaNeff_prior.json   # μ, σ for ΔN_eff- BestFit_with_uncertainties_20250814_200657.json

Docs & helpers:- MANIFEST.txt- README_arXiv.txt- README_Data_and_Repro.txt- columns_and_units.txt- reproduce_posteriors.py- CHECKSUMS.txt- Preview images: PTA_*_preview*.png, LISA_preview_20250814_203901.png, PTA_fit_with_LISA_overlay_20250814_200657.png

Reproduce (quick-look):python reproduce_posteriors.py \  --pta exported_pta_spectrum_HD_30f_100fDMGP.csv \  --lisa ESA_RCL2019_10yr_instrument_PLUS_confusion.csv \  --cmb  CMB_Planck2018_DeltaNeff_prior.json \  --out results/
description: # Data & Repro Pack — Maldonado (2025)# Version: v1.1.0 (REALDATA)# DOI (this version): (filled by Zenodo on publish)

PRIMARY_PDF  Results_TwoPager_REFRESH_20250814_200726.pdf

PTA_CSV  exported_pta_spectrum_HD_30f.csv  exported_pta_spectrum_CP_30f.csv  exported_pta_spectrum_HD_30f_100fDMGP.csv

LISA_CSV  ESA_RCL2019_10yr_instrument_PLUS_confusion.csv

PRIORS_AND_RESULTS  CMB_Planck2018_DeltaNeff_prior.json  BestFit_with_uncertainties_20250814_200657.json

DOCS  README_arXiv.txt  README_Data_and_Repro.txt  columns_and_units.txt  MANIFEST.txt  CHECKSUMS.txt

SCRIPT  reproduce_posteriors.py

PREVIEWS  PTA_HD_30f_preview.png  PTA_CP_30f_preview.png  PTA_HD_30f_preview_fromOfficial.png  PTA_CP_30f_preview_fromOfficial.png  LISA_preview_20250814_203901.png  PTA_fit_with_LISA_overlay_20250814_200657.png
description: Title: Data & Repro Pack (REALDATA) — Maldonado (2025)Use: Minimal materials to recreate the figures in the two-pager and inspect the λ ↔ {f_br, ΔN_eff} mapping.

Key files- Results_TwoPager_REFRESH_20250814_200726.pdf- exported_pta_spectrum_HD_30f_100fDMGP.csv  (alt: *_HD_30f.csv, *_CP_30f.csv)- ESA_RCL2019_10yr_instrument_PLUS_confusion.csv- CMB_Planck2018_DeltaNeff_prior.json- BestFit_with_uncertainties_20250814_200657.json- reproduce_posteriors.py

Quick runpython reproduce_posteriors.py --pta exported_pta_spectrum_HD_30f_100fDMGP.csv \  --lisa ESA_RCL2019_10yr_instrument_PLUS_confusion.csv \  --cmb CMB_Planck2018_DeltaNeff_prior.json --out results/

License: CC BY 4.0. Please cite the Zenodo DOI.
description: This pack provides (i) PTA spectral points (log10ρ vs frequency), (ii) an ESA-format LISA sensitivity curve, (iii) a ΔN_eff prior, (iv) a best-fit JSON with 68% intervals, and (v) a two-page summary PDF.

Column schemaPTA CSV: freq_Hz, log10rho_median, log10rho_p16, log10rho_p84LISA CSV: f_Hz, Sn_1_per_Hz, label   # one-sided strain PSD

Commandpython reproduce_posteriors.py --pta exported_pta_spectrum_HD_30f_100fDMGP.csv \  --lisa ESA_RCL2019_10yr_instrument_PLUS_confusion.csv \  --cmb CMB_Planck2018_DeltaNeff_prior.json --out results/

Outputs- PTA fit with LISA overlay- Corner/marginals (toy) and BestFit_with_uncertainties.json (or use the provided JSON)- Figures suitable for inclusion in a two-page brief

Notes- The two-pager filename used here is Results_TwoPager_REFRESH_20250814_200726.pdf.- Replace the PTA CSV with an official export of your choice to regenerate plots.- For LISA variants (4-yr/10-yr; instrument-only vs +confusion), use a CSV with the same f_Hz/Sn_1_per_Hz/label columns.