ESD — Energy–Space–Displacement

A classical unified field theory. A single covariant parent action and five φ-locked closure constants carry one D/E/S channel grammar from gravity to galaxies. Zero per-sector fit parameters once G and H₀ are fixed. Reproduction studies + theory derivations, all falsifiable.

---

About

The frameworks parent action (below) places the metric $g_{\mu\nu}$, the displacement scalar $D$, and the electromagnetic potential $A_\mu$ under one Lagrangian, fed by a fixed closure pool of five constants — all anchored on the golden ratio.

$$ \mathcal{S}_{\mathrm{ESD}}=\int d^4x\sqrt{-g}\left[\frac{R-2\Lambda_{\mathrm{eff}}}{16\pi G}-\frac{\alpha X_0}{2}\mathcal{F}(X/X_0)-V(D)-\tfrac14 Z(D)F_{\mu\nu}F^{\mu\nu}\right]+S_m[A^2(D)g_{\mu\nu},\psi_m] $$

Fixed closure pool of the five constants:

symbol	value	role
$\phi$	$(1+\sqrt5)/2$	discrete scaling, hierarchy clock
$q$	$2\ln\phi/\phi \approx 0.5950$	bridge / transition exponent
$c$	$(4\ln\phi-1)/\phi \approx 0.5716$	irreducible floor
$b$	$\phi^6-2 \approx 15.944$	rung-selected amplitude
$s$	$16\phi+1 \approx 26.889$	full-closure readout

Together they assemble the screening form

$$ R(u)=\frac{s}{u^{\phi}+b,u^{q}+c}, \qquad u=4g/a_0 $$

and three carrier channels — Displacement (anchor / drive), Energy (bridge / transfer), Space (floor / completion) — that carry the same grammar from cosmological scales down through galactic dynamics.

What the framework is not: a theory of everything, a completed quantum-gravity derivation, a replacement for observational studies/data.

This repository is the cosmology slice — the gravitational and large-scale-structure track of the full framework.

---

What's in this repo

The repo has two parallel tracks: reproduction studies and theory derivations. Each lives in a numbered folder, ships its own audit and figures, and pulls every constant from one shared esd_core/ package.

• A reproduction study (studies/NN_<name>/) takes one published observational dataset or empirical relation and checks it against ESD's locked predictions — no fitting, no tuning. The audit is a pass/fail gate: either the dataset lies inside the framework's grammar or it doesn't.
• A theory derivation (theory/NN_<name>/) applies Paper 1's axioms (A1: bound-system locality, A2: acceleration definedness, A3: closure universality) to a regime the reproduction studies don't directly cover, and ships an audit that certifies whether the screening form R(u) applies, what it predicts, and — when honest — where the framework declines to make a prediction at all.

studies/ — reproduction studies (21)

#	study	domain
01	01_linear_cosmology_disco	linear cosmology + galactic dynamics closure
02	02_btfr	baryonic Tully–Fisher relation
03	03_sparc_rotation_curves	SPARC galaxy rotation curves
04	04_a0_derivation	derivation of the MOND acceleration scale
05	05_rar	radial-acceleration relation
06	06_cmb_lss_lock_audit	CMB + LSS consistency lock
07	07_desi_y1_bao	DESI Y1 BAO
08	08_hubble_tension	H₀ tension audit
09	09_gw_propagation	GW170817 propagation speed
10	10_cluster_ratio	cluster mass ratios
11	11_lyalpha_jeans	Lyman-α / Jeans scale
12	12_a0_anchor	independent a₀ anchor cross-check
13	13_jwst_highz	JWST high-z galaxies
14	14_wide_binaries	wide-binary acceleration test
15	15_bullet_cluster	Bullet Cluster offset
16	16_udg_dmfree	DM-free ultra-diffuse galaxies
17	17_eht_shadows	EHT black-hole shadows
18	18_s8_tension	S₈ tension
19	19_growth_derivation	growth-of-structure derivation
20	20_redshift_derivation	cosmological-redshift derivation
21	21_gw_derivation	gravitational-wave sector derivation

theory/ — applicability-theorem derivations

#	track	result
01	01_bh_relational	black-hole horizons sit deep in R(u) ≪ 1; Sᴮᴴ unchanged

esd_core/ — shared locked-constant package

Every study imports the closure pool, the kernel, and the locked identities from one editable package, so no two studies can silently drift apart.

---

Suite status

64 / 64 audits passing.

• 44 reproduction gates across studies/01–18
• 12 derivation gates across studies/19–21
• 8 theory gates in theory/01_bh_relational

Honest negatives are reported in-place when the framework declines to make a prediction. See each study's scripts/outputs/*.json.

---

Quickstart

git clone https://github.com/<user>/esd-cosmology.git
cd esd-cosmology
python -m venv .venv
# Windows:  .venv\Scripts\Activate.ps1
# POSIX:    source .venv/bin/activate
pip install -e .                          # installs esd_core

# run any study
cd studies/05_rar
pip install -r requirements.txt
make all                                   # regenerates tables and figures

# run any theory derivation
cd ../../theory/01_bh_relational
pip install -r requirements.txt
make all

Docker images for bit-exact reproduction live under docker/.

---

Repository layout

esd-cosmology/
├── esd_core/              shared locked constants and identities
├── studies/NN_<name>/     one self-contained reproduction per folder
├── theory/NN_<name>/      applicability-theorem derivations
├── docker/                shared base image
├── docs/                  replication guide
└── .github/workflows/     CI smoke tests

Each studies/*/ and theory/*/ folder follows the same convention: scripts/ (audit + figures), scripts/outputs/ (JSON + CSV artifacts), paper/ (write-up), Makefile, requirements.txt.

---

Citation

See CITATION.cff for the canonical citation block. Each study's paper/README.md carries the paper-specific DOI once assigned.

---

License

See LICENSE.