Present-Day Energy Budget and Entanglement Component Refine

Summary

This pull request updates the fiducial cosmological / entanglement setup, regenerates the background diagnostics, and wires the analysis output directly into the experimental_data tree. The new configuration emphasizes a non‑negligible entanglement component (at the few‑percent level of the critical density today), a localized deformation of the equation of state over a finite interval in e‑folds, and an explicit diagnostic of the relative Hubble‑rate modification.

Obsolete SHA256 checksum files for the old experimental data snapshot are removed, since they are no longer consistent with the regenerated background and diagnostics.

---

Physics‑Level Changes

1. Present‑Day Energy Budget and Entanglement Component

The background Friedmann cosmology remains anchored to a standard ΛCDM‑like split in radiation, pressureless matter, and vacuum energy:

• Omega{r0} = 9.2 times 10^{-5} (radiation
• Omega{m0} = 0.315 (non‑relativistic matter)
• Omega{Lambda0} = 0.684 (cosmological constant / dark energy)

What changes is the treatment of the entanglement sector:

• The present‑day entanglement density parameter is increased from a negligible value Omega_{text{ent},0} sim 10^{-5} to
  Omega_{text{ent},0} simeq 0.05,
  i.e. roughly 5% of the critical density at (z=0).

This has two immediate physical consequences:

1. The entanglement contribution is no longer a tiny perturbation on top of ΛCDM; it becomes a subdominant but observable component in the late‑time energy budget.
2. The backreaction of the entanglement sector on the Hubble rate is enhanced, making its imprint on H(N) and on the effective equation of state w_{text{ent}}(N) clearly visible in the diagnostic plots.

In other words, the example ceases to be a “toy” nearly‑ΛCDM case and becomes a genuinely entanglement‑modified FRW background with a percent‑level extra component.

---

2. Deformation of the Entanglement Equation of State

The entanglement sector is described by an effective equation of state w_{text{ent}}(N) whose deviation from a reference value is parameterized by:

• A dimensionless deformation amplitude epsilon,
• A characteristic width in e‑folds Delta N,
• An onset location N_0 (in e‑folds relative to the reference pivot).

In this PR:

• epsilonis increased from (0.01) t epsilon = 0.05, so that the entanglement equation of state is more strongly deformed from its reference value. Instead of an almost imperceptible modulation of w_{text{ent}}, we now probe a deformation large enough to have a clear dynamical effect on the background expansion.

• The deformation is localized in e‑fold time:

  • The plateau length in e‑folds is reduced from a very long interval ((Delta N sim 50), i.e. an almost constant deformation across a huge range in (a)) to a finite segment, Delta N = 4.0,

  • meaning the entanglement‑induced modification is concentrated in a narrow band of e‑folds instead of smeared over nearly the entire history.

  • The center/onset N_0 is shifted from -3 to N_0 = -4.0,

  • i.e. the entanglement deformation becomes active a few e‑folds before the reference epoch N=0. This is chosen so that the “interesting” dynamics take place in the observable window around the pivot scale, rather than far away on a long quasi‑de Sitter plateau.

Physically, the background now exhibits a localized entanglement‑driven feature: over a finite interval Delta N around N_0, the effective pressure‑to‑density ratio of the entanglement component deviates significantly from its baseline, and this leaves a noticeable imprint on both H(N) and the conservation diagnostics.

---

3. Hubble Rate Diagnostics and Conservation Residual

With the new background configuration:

• The Hubble‑rate evolution H(N) is recomputed and stored as a function of e‑folds.
• A separate diagnostic Delta H / H (or equivalent) is exported as a CSV and associated in the manifest with a dedicated figure:
  • N_delta_H.csv → Relative_Hubble_Modification.png

This diagnostic explicitly tracks the fractional modification of the Hubble parameter due to the presence and dynamics of the entanglement sector, relative to a suitable reference (e.g. baseline without deformation or without entanglement). It provides a direct measure of:
frac{Delta H}{H}(N) = frac{H_{text{with ent}}(N) - H_{text{ref}}(N)}{H_{text{ref}}(N)},
and is tailored to highlight where in e‑fold space the entanglement sector most strongly distorts the expansion history.

The conservation residual diagnostic N_{text{conservation_residual}} is also regenerated:

• This quantity encodes the residual of the background conservation law (typically derived from
  nabla_mu T^{munu}_{text{total}} = 0,
  or its e‑fold‑parameterized equivalent).
• The updated CSV reflects the new background solution with the enhanced entanglement fraction and localized equation‑of‑state deformation.
• Numerically small residuals throughout the interval confirm that the modified background remains consistent with the conservation equations for the total stress‑energy tensor.

In short, the diagnostics now correspond to a self‑consistent, entanglement‑modified FRW solution with percent‑level entanglement energy and a localized EoS deformation.

---

4. Output Routing to Experimental Data Tree

The analysis entry point now writes:

• All background and diagnostic CSVs into the experimental_data/data directory.
• All figures into the experimental_data/plots directory.

From a physics perspective, this means:

• The shipped experimental bundle under experimental_data directly corresponds to a single, well‑defined background model (the one defined by the updated Omega’s and entanglement parameters).
• Regenerating the experimental data (numerical background + plots) is as simple as re‑running the analysis with this parameter set; the directories serve as the canonical “snapshot” of this particular cosmological model.

---

5. Removal of Obsolete SHA256 Checksums

The SHA256 checksum file(s) that were previously included for the experimental data are removed.

• Those checksums were tied to an older background solution different (Omega_{text{ent},0}, different (epsilon), different Delta N, etc.).
• After updating the entanglement energy fraction, the equation‑of‑state deformation, and regenerating diagnostics like H(N), Delta H/H, and the conservation residual, the old checksums no longer correspond to the actual physical data in experimental_data.
• Keeping them would suggest a false “integrity” relation between the new numerical background and the old hashes.

From a physics / reproducibility standpoint, this PR chooses physical fidelity over stale checksums: the numerical content of the experimental bundle is now internally consistent with the stated cosmological model, even though no SHA256 registry is shipped for this snapshot.

A future PR can regenerate and reintroduce checksums for this updated background if a hash‑based provenance layer is desired.

---

Impact for Users of the Physics Framework

• The default example now corresponds to a non‑negligible entanglement sector that contributes mathcal{O}(5%) of the critical density today and has a clearly visible dynamical effect on the expansion history.
• The entanglement equation of state exhibits a finite, localized deformation in e‑folds, rather than a nearly constant, near‑zero perturbation. This makes the induced structure in H(N) and w_{text{ent}}(N) explicit in the plots.
• The new N_delta_H diagnostic and its plot provide a direct quantification of the entanglement‑induced distortion of the Hubble rate.
• The conservation residual has been recomputed for this background, confirming the consistency of the modified energy–momentum content with the FRW equations.
• All of these quantities are written into the experimental data tree, so the shipped CSVs and PNGs correspond to exactly this entanglement‑modified cosmological model, without stale checksums from previous configurations.

---

What's Changed

• Present‑Day Energy Budget and Entanglement Component Changes by @morozow in #3

Full Changelog: v4.1.1...v4.2.1