Parametric Decollapse of Hertault Condensates

A speculative cosmological cascade from a supermassive parent black hole to ΛCDM through Dark Geometry.

Hugo Hertault — Independent researcher, Tahiti — June 2026.

This repository contains the paper, the figure-generating code, and the numerical verification scripts for the Decollapse article, part of the Dark Geometry series.

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What this is

This article proposes a candidate mechanism — parametric decollapse — for the parent-to-daughter transition of the Dark Geometry cosmological-inheritance doctrine: how a black-hole interior saturated at ℐ = 1 becomes a daughter universe that inflates into a ΛCDM cosmology.

It is written in an explicitly speculative and self-critical register. Rather than present only a polished result, it documents the reasoning, including the candidate mechanisms that are examined and rejected, and classifies every quantitative claim by evidential tier:

• Tier A — algebraic identities (exact)
• Tier B — derivations with stated approximations
• Tier C — conjectures and order-of-magnitude estimates

The central trigger mechanism contains Tier-C elements. They are stated clearly rather than hidden.

Key results

1. Parent mass fixed by Λ. The parent mass is not a free input: it follows from the cosmological constant via the inheritance law Λ ∝ S_parent^(−p) with the conformal-weight exponent p = (d+1)/d = 4/3, giving a supermassive parent M ≈ 1.7×10⁷ M☉ whose echo lies in the LISA band (~1.9 mHz). The competing readings p = 1 and p = 3/2 are excluded in the paper (Section 2).

2. A thermal trigger is impossible. Heating the condensate to T_c requires an energy exceeding the parent's own Mc² by ~10²⁵. Shown explicitly; a deconfinement picture is developed instead.

3. Deconfinement picture. The saturated condensate is metastable, frozen by the gravitational red-shift of the horizon. The freezing factor equals the interferometric attenuation of the conformal mode through the 256 layers of the Hertault beam-splitter, √β·(sin θ_H)²⁵⁶ = √(Λ/M_Pl⁴). The trigger is the universal trace coupling, with a naturally selective threshold h_crit ~ α_*·√(sin²θ_H) ≈ 4%, crossed only by close SMBH–SMBH mergers.

4. Inflationary predictions from the DG-fixed exponent α = √(2/3): n_s = 0.9654 (Planck 0.9649 ± 0.0042), r = 3.3×10⁻³, Ω_Λ = 2/3, Ω_m = 1/3.

Repository layout

decollapse/
├── paper/
│   └── decollapse.tex          # the article (LaTeX source)
├── code/
│   ├── verify_decollapse.py    # reproduces every numerical claim
│   └── make_figures.py         # generates the four figures
├── figures/                    # generated PNGs (also committed)
├── requirements.txt
├── LICENSE
└── README.md

Reproducing the results

pip install -r requirements.txt
cd code
python3 verify_decollapse.py     # prints every claim vs reference value
python3 make_figures.py          # regenerates ../figures/*.png
cd ../paper
pdflatex decollapse.tex && pdflatex decollapse.tex && pdflatex decollapse.tex

verify_decollapse.py is self-contained: the only input is the spatial dimension d = 3, and every printed value carries its reference (Planck, BICEP/Keck, or the canonical DG constant). No fitted parameters enter the algebraic structure.

Open problems (stated in the paper)

1. Derive the surface-layer thickness δ fixing the exact coefficient of h_crit (order of magnitude ~α_* is established).
2. Quantify the decollapse rate per comoving volume from the SMBH-merger rate (falsifiable LISA prediction).
3. Compute the R² coefficient (hence A_s) by heat-kernel expansion on the fibration — the O(6) factor.
4. Derive the freezing depth 256 from first principles rather than from S_cosmo.

Status

Decollapse is offered not as an established result but as an open proposal: a mathematically continuous cascade whose surviving predictions are robust, and whose trigger mechanism is a well-posed open problem. Critical feedback is welcome via Issues.

Citation

@misc{hertault_decollapse_2026,
  author = {Hertault, Hugo},
  title  = {Parametric Decollapse of Hertault Condensates: a speculative cosmological
            cascade from a supermassive parent black hole to LambdaCDM},
  year   = {2026},
  note   = {Dark Geometry series},
  url    = {https://github.com/hugohertault/decollapse}
}

License

Code released under the MIT License (see LICENSE). The text of the paper is © Hugo Hertault 2026, released under CC BY 4.0.