Results — T-SH Kerr Envelope + RT Residual
GR Kerr silhouette vs spin · literature RT floor · NZ GRMHD/spin OPEN · no false GRMHD · no EHT discovery · no promote
CPT Framework — spin-2 decisive tests · T-SH-K Date: 2026-08-14 Status: BANKED ·PASS_T_SH_KERR_RT_ENVELOPE
Design: a_geom_spin2_t_sh_kerr_rt_envelope_design.md
Parent: T-SH forecast + plasma honesty · S6 board
Census: scripts/investigations/s3_geometry/spin2_t_sh_kerr_rt_envelope_census.py · data/spin2_t_sh_kerr_rt_envelope_census.json
Tags: [E honesty] · [P prediction] · [Programme]
0. One-line
T-SH-K delivers what can be done without inventing physics: GR Kerr geometric diameter envelope \(b_{\mathrm{eff}}\in[4.48,5.20]\,M\) (half-range ~6.9% of Schwarzschild; max shrink ~13.8% at high spin); literature RT bias floor ~4–8%; static NZ \(b_c=2e\) sits above the entire Kerr band at fixed \(M/D\); full NZ GRMHD and spinning NZ metric remain OPEN (no in-repo GRMHD, no free NZ Kerr); EHT still does not select NZ once RT floors are included; ngEHT remains a TARGET not auto-3σ; no promote.
1. Integrity (held)
| Rule | Held | |------|:----:| | No false claim of NZ GRMHD in this repo | Yes | | No invented spinning NZ metric | Yes · status OPEN | | Kerr envelope is GR geometry only | Yes | | RT envelope is literature honesty, not a new simulation | Yes | | No EHT discovery claim | Yes | | No promote | Yes |
2. What was requested vs what was delivered
| Requested | Delivered | Not delivered | |-----------|-----------|---------------| | Kerr envelope | GR critical-curve diameter vs \(a,i\) | — | | Full NZ GRMHD ray-trace | Prerequisites + OPEN chip | Fluid + RT + NZ metric imaging | | Combined honesty | Updated \(n_\sigma\) (one- and two-sided) | NZ-side spinning \(b_c(a)\) |
Repo fact: no BHAC / ipole / RAPTOR / EHT imaging stack; no banked spinning compression metric.3. GR Kerr geometric envelope (computed)
Spherical photon orbits (Teo / Bardeen, \(M=1\)); celestial critical curve; mean diameter proxy \(D=(D_h+D_v)/2\), \(b_{\mathrm{eff}}=D/2\).
| Check | Result | |-------|--------| | \(a=0\) | \(b_{\mathrm{eff}}=3\sqrt{3}\) PASS | | Grid | \(a\in\{0\ldots 0.998\}\), \(i\in\{1^\circ,17^\circ,60^\circ,90^\circ\}\) · 36 points |
| Quantity | Value | |----------|------:| | \(b_{\mathrm{eff}}\) min / max | 4.479 / 5.196 | | Half-range \(\sigma_b\) | 0.359 (~6.9% of \(3\sqrt{3}\)) | | Max \|dev\| from Schwarzschild | 0.717 (~13.8%) |
Structural fact on this grid: Kerr spin shrinks the geometric diameter relative to Schwarzschild (\(b_{\mathrm{eff}}(a)\le b_{\mathrm{eff}}(0)\)). The upper edge of the Kerr family at fixed \(M/D\) is the non-spinning GR value.Absolute µas (banked \(\theta_g\))
| Source | \(\sigma_{\mathrm{Kerr}}\) half-range | max shrink vs \(a=0\) | |--------|--------------------------------------:|----------------------:| | Sgr A | ~3.61 µas | ~7.22 µas | | M87 | ~2.74 µas | ~5.48 µas |
4. Literature RT / plasma envelope (not a simulation)
| Floor | Fractional | Sgr A (µas) | M87 (µas) | |-------|------------:|-------------:|-----------:| | Typical | 4% of \(\theta_{\mathrm{GR}}\) | ~2.09 | ~1.59 | | Ceiling | 8% of \(\theta_{\mathrm{GR}}\) | ~4.18 | ~3.18 |
These are honesty ceilings aligned with EHT model-library practice (ring vs pure geometry can differ by O(few–10%)). They are not an in-repo GRMHD run.
5. Static NZ vs GR Kerr family
| Object | \(b_c\) / \(b_{\mathrm{eff}}\) | |--------|-------------------------------:| | GR Kerr band | [4.48, 5.20] | | NZ static | \(2e \approx 5.437\) |
At fixed \(M/D\): static NZ lies above the entire GR Kerr geometric band. Spin does not let GR “reach up” to NZ; it moves GR down. Spin is therefore not an escape that makes NZ look like a high-spin Kerr silhouette at the same mass scale.| Source | \(\theta_{\mathrm{NZ}}-\theta_{\mathrm{GR}}(a=0)\) | Kerr can close that gap? | |--------|--------------------------------------------------:|:------------------------:| | Sgr A | +2.42 µas | No (spin widens the gap) | | M87 | +1.84 µas | No |
6. Discrimination (updated honesty)
6.1 Two-sided Kerr half-range (pessimistic if misread)
If one naively puts \(\sigma_{\mathrm{Kerr}}\) two-sided into the NZ−GR error budget, ngEHT \(n_\sigma\) collapses to \(\sim 0.5\)–\(0.6\). That is misleading for an “NZ above GR” test, because Kerr variation is one-sided downward.
6.2 One-sided (correct for geometric family test) + RT
Use gap = NZ − GR(\(a=0\)) with RT as two-sided emission uncertainty:
| Source | EHT \(n_\sigma\) (RT typ) | ngEHT \(n_\sigma\) (RT typ) | Auto \(>3\sigma\) ngEHT? | |--------|-------------------------:|---------------------------:|:------------------------:| | Sgr A | ~0.78 | ~1.12 | No | | M87 | ~0.54 | ~1.10 | No |
| Instrument | Verdict | |------------|---------| | Current EHT | Still does not select NZ (RT floors dominate) | | ngEHT ~0.5 µas | Still a TARGET; with RT ~4% floors, \(n_\sigma\sim 1\) — not automatic discovery | | Geometric-only multi-\(\sigma\) (T-SH old) | Optimistic upper bound only |
7. NZ GRMHD + spinning NZ — OPEN checklist
| Prerequisite | Status | |--------------|--------| | Freeze spinning NZ metric (slow-rotation / KS-like / other) | DESIGN FROZEN · Class A dual-book · SNZ-a PASS_SNZ_A · a_geom_spin2_spinning_nz_metric_design.md | | Photon critical curve \(b_{\mathrm{eff}}(a)\) in that metric | DONE · SNZ-c | | Emission model + radiative transfer | DONE as GRRT · T-RT named \(n(r)\) · not BHAC | | Synthetic imaging / ring fit | PARTIAL · 1-D \(I(b)\) + static curves · no EHT pipeline | | In-repo GRMHD fluid evolution | Not present |
8. Gates
| Gate | Status | |------|--------| | PASS_KERR_A0 | PASS | | PASS_KERR_ENVELOPE | PASS | | PASS_RT_ENVELOPE | PASS | | PASS_NZ_SPIN_OPEN | PASS | | PASS_NO_FALSE_GRMHD | PASS | | PASS_NO_DISCOVERY | PASS | | PASS_INTEGRITY | PASS |
Status:PASS_T_SH_KERR_RT_ENVELOPE
9. Relation to T-SH pack
| Layer | Role | |-------|------| | T-SH geometric \(b_c\) | Static NZ vs Schw TARGET | | T-SH plasma honesty (§5) | Flat 1.5 µas floor | | T-SH-K (this) | GR Kerr band + literature RT + NZ GRMHD OPEN | | T-RT GRRT | In-repo geodesic + named emission · PASS_T_RT_GRRT · not fluid GRMHD | | True NZ GRMHD | Still OPEN · external cube / public pipeline only |
10. One-line
§T-SH-K: Kerr \(b_{\mathrm{eff}}\in[4.48,5.20]\); NZ static above Kerr band; RT 4–8% floor; NZ GRMHD OPEN; no false GRMHD; no EHT discovery; no promote.