feat: 完善日月食与月掩几何链路并扩展历法接口

- 新增日月食中心带、偏食带、阴影足迹、等时线、食分线及升落边界计算，支持极区与混合食拓扑
- 新增日食单时刻阴影求解器、站心状态查询、批量采样和 ΔT 覆盖接口
- 重构恒星与行星月掩路径，补充有限盘面接触、站心修正、掩带宽度、极区投影及升落边界
- 扩展 SVG 与 GeoJSON 输出，支持详细面板、全球/极区/地球投影、边界闭合、时间标记和拓扑签名
- 扩展日月食候选搜索、局地搜索、沙罗序列预计算与范围外推，补充系列锚点和成员一致性校验
- 补齐古历纪年、儒略历独有闰日、多公历候选、历法改革跨日及精确日期运算接口
- 优化 ΔT、章动、恒星时、月球地平线、事件根搜索和本地星历缓存，降低重复计算开销并提升边界稳定

basic/apsis.go

@@ -145,14 +145,26 @@ func moonApsisSeedTT(k float64) float64 {
 }
 
 func refineDistanceExtremum(seed float64, cfg apsisSearchConfig, distanceFn func(float64) float64) (float64, float64) {
+	if !finite(seed) || !finite(cfg.bracketHalfWidth) || !finite(cfg.sampleStep) || cfg.sampleStep <= 0 {
+		return seed, math.NaN()
+	}
 	best := seed
 	bestDistance := distanceFn(seed)
-	for sample := seed - cfg.bracketHalfWidth; sample <= seed+cfg.bracketHalfWidth+1e-12; sample += cfg.sampleStep {
+	// seed 幅度很大时 sample += sampleStep 可能小于一个 ULP（浮点间隔）而永不推进，
+	// 因此显式检测步长是否真的改变了采样点，避免无界循环。
+	// At a large |seed| the step can fall below one ULP, so `sample += step` would never
+	// advance; detect a step that does not move the sample and stop the sweep instead.
+	for sample, end := seed-cfg.bracketHalfWidth, seed+cfg.bracketHalfWidth+1e-12; sample <= end; {
 		dist := distanceFn(sample)
 		if distanceBetter(dist, bestDistance, cfg.maximize) {
 			best = sample
 			bestDistance = dist
 		}
+		next := sample + cfg.sampleStep
+		if next == sample {
+			break
+		}
+		sample = next
 	}
 
 	left, right, ok := apsisDerivativeBracket(best, seed, cfg, distanceFn)