Einstein Audit for Faster‑Than‑Light Hidden Sectors (MIN): Causality, Cosmology, and Multi‑Band Gravitational‑Wave Consistency

One-sentence summary
We turn “FTL is science fiction” into a **quantitative, testable audit** that links **causality**, **cosmology**, and **gravitational-wave observations**, producing explicit inequality-style bounds on how much faster-than-light “excess” could hide in nature.

### What this deposit is
This repository is an *analysis toolkit* (“Einstein Audit”) for exploring **hypothetical faster-than-light (FTL) hidden sectors** while keeping contact with real observational constraints.

It compresses three domains into one scalar diagnostic:
- **Local causality risk** (from special relativity’s antitelephone paradox)
- **Early-universe energy budget** (via extra radiation / \(\Delta N_{\rm eff}\))
- **Multi-band gravitational-wave consistency** (PTA consistency + black-hole ringdown GR tests)

The core quantity is the **Einstein distance**
\[
D_E = \sqrt{(\varepsilon_{\rm energy}\,\varepsilon_{\rm FTL}^2)^2 + (1-\mathrm{PCI})^2 + (\varepsilon/\sigma_\varepsilon)^2},
\]
where:
- \(\varepsilon_{\rm FTL}^2 = \langle (W-1)^2\rangle\) is the (small) FTL “excess” parameter,
- \(\varepsilon_{\rm energy}=\Delta N_{\rm eff}/0.3\) is the fraction of the allowed cosmological radiation budget,
- \(\mathrm{PCI}\) is a PTA Probability of Consistency Index,
- \(\varepsilon/\sigma_\varepsilon\) is a pooled ringdown GR-deviation statistic.

Imposing **Einstein-allowed** behavior (\(D_E\le 1\)) yields the “no-free-FTL-lunch” inequality:
\[
\varepsilon_{\rm FTL}^2
\le
\frac{\sqrt{1-(1-\mathrm{PCI})^2-(\varepsilon/\sigma_\varepsilon)^2}}{\varepsilon_{\rm energy}}.
\]

### What’s new in v1.1.0 (this version)
- **Executed demo outputs** for non-tiny cosmology cases: rescaled \(\Delta N_{\rm eff}\) examples at **0.1** and **0.3** (saturating the guardrail).
- **Energy-grid scans** showing how \(D_E\) changes across \((\varepsilon_{\rm energy},\varepsilon_{\rm FTL}^2)\), including contour plots.
- **Einstein budget fractions** (FTL vs PTA vs ringdown share of \(D_E^2\)) and visualization.
- **Covariance-weighted “Einstein tension”** appendix: upgrade from Euclidean norm to a \(\chi^2\)-like global statistic \(\mathcal{T}_E=X^T C^{-1}X\).
- **Toy flavor–FTL coupling bound** (\(\kappa\)) and **toy information-capacity bound** pipeline.
- A **public-facing explainer PDF** for non-technical readers.

### Important note (honesty / scope)
This release **does not claim experimental evidence** that FTL physics exists.
It provides a consistent framework for *testing and constraining* FTL-like hidden sectors as cosmology, PTA, and ringdown data improve.

## Keywords (suggested)
Faster-than-light, FTL, superluminal, causality, tachyon antitelephone, time loops, Einstein distance, Delta N eff, cosmology, gravitational waves, pulsar timing arrays, PTA, ringdown, general relativity tests, information theory, channel capacity

## Related identifiers (optional)
- “Is a new version of”: the previous Zenodo version (Zenodo will auto-link versions).
- “IsSupplementTo” (optional): your concept DOI (Zenodo will also auto-generate the concept DOI).

## References (optional)
- Einstein (1905) special relativity
- Tolman / antitelephone paradox literature
- PTA collaborations (NANOGrav / EPTA / PPTA / IPTA)
- LIGO/Virgo/KAGRA ringdown GR tests
- \(\Delta N_{\rm eff}\) cosmological constraints (CMB/BBN literature)

## Files to upload (recommended set)
- **FTL_Einstein_Audit_SHARE_PACKAGE_v9_ZenodoReady.zip** (main everything-in-one package)
- **FTL_Einstein_Audit_FTLonly_v2.pdf** (technical paper PDF)
- **FTL_Einstein_Audit_PUBLIC_ARTICLE.pdf** (public explainer PDF)