Kinematic Cross-Correlation of Gaia DR3 Stellar Halo with Totani (2025) 21 GeV Gamma-Ray Halo: Spectral Analysis and Multi-Test Validation

Version 4.0 — Major update. Supersedes v3.0. CORRECTIONS FROM v3.0:(1) read_fort200 corrected from pixel-summation to pixel-averaging (Δρ~7% for reliable bins, Spearman invariant confirmed). (2) MI=21.4σ from v2.0 retracted — implementation error; correct values: raw MI=11.8–14.5σ (k-dependent), conditional MI(|b|)=1.6σ. (3) Five post-hoc exclusions documented explicitly (§4.3). (4) SFD E(B-V) dust control added. (5) Sagittarius stream exclusion test added. (6) read_fort200_avg verified symmetric via Spearman invariance test. KEY RESULTS:Main result (ring region, 20°<|l|<60°, 10°<|b|<60°): partial(|b|) = +0.154 ± 0.016, 9.4σ raw, 9.1σ after Bonferroni correction (22 tests). Monotonic stringency: disk 2.2σ → standard 3.9σ → strict 4.6σ → very strict 9.1σ. Disk/halo signal ratio = 0.23. Spectral analysis (reliable bins): 12 GeV: +0.135 (7.4σ); 21 GeV: +0.154 (9.4σ); 35 GeV: +0.048 (2.5σ); 59 GeV: +0.052 (2.2σ). Profile consistent with bb̄ annihilation at m_χ~0.6 TeV. Bins below 5 GeV excluded (GALPROP oversubtraction). ICS test at 21 GeV: signal survives PCA-based partial correlation control (CMB component: 97% survival, 8.4σ). ICS optical/infrared/CMB files show ρ=0.95 (effectively one template). Robustness: scramble p=0.0000; SFD dust control 9.7σ; Sgr stream exclusion 7.7σ; hemisphere N≈S (6.4σ vs 6.1σ); N=10 subsamples std=0.016; fragility Δ=2.7%; NSIDE 32/64/128 stable. Consilium v5 (14 agents, 4 cycles): GREEN=30, YELLOW=21, RED=0. Document audit: GREEN=54, YELLOW=4, RED=0. LIMITATIONS: Single GALPROP model; ICS(E) only at 21 GeV; MSP template absent; no metallicity cut; no preregistration. 21 limitations documented in §5. PENDING: ICS(E) maps at 8 energies (T. Totani); skyFACT MSP template (C. Eckner); LAMOST DR9 metallicity cross-match.