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This is a raw source document. Integrity tags [E] [M] [O] [F] are coloured for readability. Content is as written in the research file.

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.
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