光子环延迟时间层析成像：Mahakal现象
Photon-Ring Retarded- Time Tomography: The Mahakal Phenomenon
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中文总结 AI 辅助
本文提出光子环延迟时间层析成像方法，利用近临界零测地线的多阶图像通道扩展历史可达范围，揭示源富集导致秩与稳定性崩溃的Mahakal现象，并验证了分辨阶数在形态恢复中的有限增益。
中文摘要 AI 辅助
近临界零测地线产生具有不同映射、延迟和权重的图像阶通道，因此一个观测者时间数据集可采样多个源历元。我们按历史可达范围、维度和保留集恢复来组织逆问题。使用连续噪声一致、无矩阵的Kerr/Schwarzschild算子，针对阶数n=0、1、2，我们审计了12种自旋-倾角几何构型。在归一化信噪比SNR0=100时，分辨阶数在所有单元中将锚定连接的历史扩展到直接成像之外，在倾角20度、50度和75度下分别增加40 M、24 M和一个4 M网格步长。操作秩从153升至202，老历元创新从8.29 M增至40.72 M；完整阶数求和仅保留9.66 M。紧凑的时间支撑给出精确结果：直接延迟时间足迹之外的时间基函数生成全零的直接列，而更高阶可提升那些老历元盲块。直接旧结构秩为零，而分辨阶数在三个类别中支持38、93和185个操作方向。然而，源富集使可达范围几乎不变，而秩分数和奇异值稳定性崩溃；这就是Mahakal现象。保留集测试显示收益有限，而非电影般的效果。分辨阶数将稳定的基线包含发射率级跨度从48 M扩展到80 M，但该端点由水平主导。在60条历史上，物理形态误差在TSVD下降低13.3%，在岭回归下降低16.4%。可靠的双特征恢复失败，稳定形态区间为零。完整阶数求和未带来实质性的形态增益。因此，正面结果是理想阶数分离下已知几何图像域基准的最佳情况；SNR0是算子归一化，而非观测。
英文摘要
Near-critical null geodesics generate image-order channels with distinct mappings, delays, and weights, so one observer-time data set samples multiple source epochs. We organize the inverse problem by historical reach, dimension, and held-out recovery. Using continuum-noise-consistent, matrix-free Kerr/Schwarzschild operators for orders n = 0, 1, 2, we audit 12 spin-inclination geometries. At normalized SNR0 = 100, resolved orders extend anchor-connected history beyond direct imaging in all cells by 40 M, 24 M, and one 4 M grid step at inclinations 20 degrees, 50 degrees, and 75 degrees. Operational rank rises from 153 to 202 and old-age innovation from 8.29 M to 40.72 M; complete order summation retains only 9.66 M. Compact temporal support gives an exact result: temporal basis functions outside the direct retarded-time footprint generate identically zero direct columns, while higher orders can lift those old-epoch blind blocks. Direct old-structure rank is zero, while resolved orders support 38, 93, and 185 operational directions across three classes. Yet source enrichment leaves reach nearly fixed while rank fraction and singular-value stability collapse; this is the Mahakal phenomenon. Held-out tests show bounded benefit, not a movie. Resolved orders extend stable baseline-inclusive emissivity-level span from 48 M to 80 M, but that endpoint is level dominated. On 60 histories, physical morphology error falls by 13.3 percent with TSVD and 16.4 percent with ridge. Reliable two-feature recovery fails and the stable morphology interval is zero. Complete order summation yields no material morphology gain. The positive results are therefore best-case, known-geometry image-domain benchmarks under ideal order separation; SNR0 is an operator normalization, not an observation.
