# Results — T-RT: In-Repo Geodesic Radiative Transfer

### GRRT not GRMHD · static gap emission-load-bearing · NZ interior not filled · “never ray-traced” footnote dropped · no promote

**CPT Framework — spin-2 decisive tests · T-SH residual**  
**Date:** 2026-08-16  
**Status:** **BANKED** · `PASS_T_RT_GRRT`  
**Design:** `a_geom_spin2_t_rt_grrt_design.md`  
**Parents:** T-SH · T-SH-K · SNZ-c/d  
**Script:** `scripts/investigations/s3_geometry/spin2_t_rt_grrt_census.py`  
**Data:** `scripts/investigations/s3_geometry/data/spin2_t_rt_grrt_census.json`  
**Figure:** `scripts/investigations/s3_geometry/data/spin2_t_rt_grrt_I_b.png`

Tags: **[E honesty]** · **[P prediction]** · **[Programme]**

---

## 0. One-line

> **The repo now ray-traces.** Optically-thin GRRT on banked NZ0 vs Schwarzschild, with three frozen emissivities, is **not** BHAC GRMHD. Extended and inner-heavy books keep a bright-ring offset \(\delta_\star\approx +4.1\%\) (geometric target \(+4.63\%\)); an ISCO-peaked book lets the Kerr ring follow the matter and **flips the sign**. Horizonless NZ does **not** fill the shadow (\(f_{\mathrm{in}}\sim 1\%\), redshift). The “never ray-traced” footnote is **eliminated**. The “any plasma washes out \(+4.63\%\)” footnote is **not**. Full GRMHD and ngEHT-auto-\(3\sigma\) remain. No promote.

---

## 1. Integrity (held)

| Rule | Held |
|------|:----:|
| Not claimed as BHAC / ipole / RAPTOR | **Yes** |
| Class A only · CORE \(a_*=0.1\) for spin | **Yes** |
| Kerr labeled control | **Yes** |
| Emission frozen before images | **Yes** |
| No EHT discovery | **Yes** |
| No promote | **Yes** |

This is **GRRT**: null geodesics + named \(n(r)\). It is the first in-repo imager. It is **not** evolved MHD.

---

## 2. Photon-sphere control

| Metric | Turning \(r\) | \(b_c\) | Target |
|--------|-------------:|--------:|--------|
| NZ0 | \(2.000\) | \(5.4366\) | \(2M\), \(2e\) |
| Schwarzschild | \(3.001\) | \(5.1962\) | \(3M\), \(3\sqrt{3}\) |

**PASS_PHOTON_SPHERE.**

---

## 3. Static GRRT (the clean brick)

Face-on / equatorial \(I(b)\). Ring \(b_\star=\mathrm{argmax}_{b>1}I\). Interior \(f_{\mathrm{in}}=I(0)/I(b_\star)\).

| Book | \(b_\star^{\mathrm{NZ}}\) | \(b_\star^{\mathrm{K}}\) | \(\delta_\star\) | Gap \(>2\%\)? | \(f_{\mathrm{in}}^{\mathrm{NZ}}\) | \(f_{\mathrm{in}}^{\mathrm{K}}\) |
|------|--------------------------:|-------------------------:|----------------:|:-------------:|---------------------------------:|--------------------------------:|
| **E-SPH** \(r^{-2}\) | \(5.438\) | \(5.224\) | **\(+4.09\%\)** | **Yes** | \(0.013\) | \(0.038\) |
| **E-IN** \(r<4M\) | \(5.438\) | \(5.224\) | **\(+4.09\%\)** | **Yes** | \(0.006\) | \(0.008\) |
| **E-RING** peak \(6M\) | \(5.438\) | \(6.578\) | **\(-17.3\%\)** | **No** | \(0.026\) | \(0.035\) |

**Finding RT-1 [E honesty]:** NZ’s bright ring **stays on the photon sphere** (\(2e\)) in every frozen book. Kerr’s ring stays near \(3\sqrt{3}\) for volume-filling / inner-heavy flow, and **walks out to the matter peak** when emission is ISCO-class.

**Finding RT-2 [E honesty]:** The geometric \(+4.63\%\) is **emission-load-bearing** as an *observed diameter*. It survives simple extended flow. It is not a theorem about every optically-thin source.

**Finding RT-3 [E algebra]:** Horizonless does **not** imply a filled shadow. NZ \(f_{\mathrm{in}}\) is \(\mathcal{O}(1\%)\) and **smaller** than Kerr’s plunging column on E-SPH. The well \(g=e^{-M/r}\) kills the core. The cut \(r_{\mathrm{cut}}=0.2M\) is named, not fitted.

---

## 4. CORE spin (indicative only)

Class A \(a_*=0.1\) vs Kerr \(a=0.1\), same 1-D \(|b|\) scan. All three books returned the same pair \(b_\star\simeq 5.15\) vs \(5.01\) (\(\delta_\star\simeq +2.8\%\)). Interior fractions rose to \(\sim 0.2\)–\(0.3\).

That scan is **not** promoted to a spinning-image theorem: SNZ-c already forbids “above all Kerr” once branches split, and this integrator does not yet do a signed celestial camera. CORE GRRT is a **sanity offset**, not a new T-SH envelope.

---

## 5. Which footnotes moved

| Footnote | After T-RT |
|----------|------------|
| “We have never ray-traced NZ” | **Eliminated** |
| “Any simple plasma model washes out \(+4.63\%\)” | **Not eliminated** · false for E-SPH/E-IN, true (sign flip) for E-RING |
| “Horizonless ⇒ filled / bright core” | **Tightened** · redshift keeps \(f_{\mathrm{in}}\sim 1\%\) |
| Full GRMHD library (BHAC + ipole) | **Remains** |
| ngEHT auto-\(>3\sigma\) | **Remains** (T-SH-K RT floor + \(M/D\)) |

A brick is in the wall: **in-repo GRRT exists, photon-sphere lock on NZ is seen in the image, and a dark interior is not a horizon monopoly.**  
A footnote is gone: **never ray-traced.**  
A footnote is **not** gone: **emission morphology can still move the Kerr ring.**

---

## 6. Gates

| Gate | Status |
|------|--------|
| PASS_PHOTON_SPHERE | **PASS** |
| PASS_KERR_HORIZON_DARK | **PASS** (E-SPH / E-RING \(f_{\mathrm{in}}^{\mathrm{K}}<0.15\)) |
| PASS_NO_FALSE_GRMHD | **PASS** |
| PASS_CORE_ONLY | **PASS** |
| PASS_NO_DISCOVERY | **PASS** |
| PASS_NO_PROMOTE | **PASS** |

**Status:** `PASS_T_RT_GRRT`

---

## 7. Kill board

| ID | Kill |
|----|------|
| **K-TRT-1** | “We ran GRMHD” / BHAC / EHT library |
| **K-TRT-2** | E-RING sign flip ignored to keep \(+4.63\%\) as observed |
| **K-TRT-3** | Horizonless sold as a filled shadow, or as already decisive |
| **K-TRT-4** | CORE 1-D scan sold as a spinning celestial silhouette |
| **K-TRT-5** | ngEHT discovery from this WP |
| **K-TSH-*** / **K-SNZ-*** | Held |

---

## 8. Licensed leftover

A later WP may add a signed 2-D camera, a thermal synchrotron book, or an **external** public GRMHD cube on these metrics. It is **not** licensed to invent fluid in-repo and call it BHAC.

---

## 9. One-line

> **§T-RT: GRRT banked; never-ray-traced footnote gone; +4.1% survives extended flow and dies on ISCO-peaked Kerr; NZ core stays dark; not GRMHD; no promote.**