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/moon_precision_test.go

@@ -0,0 +1,81 @@
+package basic
+
+import (
+	"math"
+	"testing"
+)
+
+func TestMoonSeriesNumericalPrecision(t *testing.T) {
+	// The existing binary64 coefficients evaluated at 70 decimal digits.
+	// These check arithmetic precision, not the lunar theory's physical error.
+	for _, sample := range []struct{ jd, longitude, latitude, distance, velocity float64 }{
+		{990647.125, 48.68531043735905108, -3.208940888099671943, 365328.8143785083007, 14.53542662716284001},
+		{1730647.9333686847, 346.3227699608293767, -2.151500042672265917, 368450.7410464923284, 14.30553896629878483},
+		{2451545.0, 223.3189003731153751, 5.170885995272171723, 402448.7431750887777, 12.02142669184144213},
+		{2460770.123456789, 99.20516643712787636, 5.156920731462777075, 378303.2056716878878, 13.57356557811076973},
+		{2817000.99999, 256.0031142427467021, 3.438015761341575242, 402219.0739759512533, 11.99285384469081927},
+		{3191874.3956256355, 178.1121054545695063, 1.37109140818496243, 379219.9689425243825, 13.41568168416747773},
+		{3547272.75, 167.6849402044916958, 5.088592207858965847, 374590.3971822900352, 13.85120063917007945},
+	} {
+		longitude := HMoonTrueLo(sample.jd)
+		latitude := HMoonTrueBo(sample.jd)
+		distance := HMoonAway(sample.jd)
+		if error := math.Abs(math.Remainder(longitude-sample.longitude, 360)); error > 2e-11 {
+			t.Errorf("jd=%.12f longitude error=%g degrees", sample.jd, error)
+		}
+		if error := math.Abs(latitude - sample.latitude); error > 2e-11 {
+			t.Errorf("jd=%.12f latitude error=%g degrees", sample.jd, error)
+		}
+		if error := math.Abs(distance - sample.distance); error > 1e-5 {
+			t.Errorf("jd=%.12f distance error=%g km", sample.jd, error)
+		}
+		const step = 5.0 / 86400
+		before, after := sample.jd-step, sample.jd+step
+		velocity := math.Remainder(HMoonTrueLo(after)-HMoonTrueLo(before), 360) / (after - before)
+		if error := math.Abs(velocity - sample.velocity); error > 2e-7 {
+			t.Errorf("jd=%.12f velocity error=%g degrees/day", sample.jd, error)
+		}
+	}
+}
+
+func TestOccultationContactDerivativeNumericalStability(t *testing.T) {
+	config, _ := planetOccultationConfigFor(OccultationMercury)
+	cache := newPlanetOccultationEventCache(config)
+	const tt = 1730647.933368684724
+	const longitude = 90.88806942770216
+	const latitude = 29.603106445560446
+	evaluations := newOccultationRiseSetEvaluationCache(cache.riseSetContextAt)
+	derivative := func(jd float64) float64 {
+		return evaluations.evaluation(jd).contactDerivative(longitude, latitude)
+	}
+	center := derivative(tt)
+	const trendStep = 0.5 / 86400
+	trend := (derivative(tt+trendStep) - derivative(tt-trendStep)) / (2 * trendStep)
+	ulp := math.Nextafter(tt, math.Inf(1)) - tt
+	for i := -16; i <= 16; i++ {
+		offset := float64(i) * ulp
+		jitter := derivative(tt+offset) - center - trend*offset
+		if math.Abs(jitter) > occultationRiseSetJunctionDerivativeTolerance {
+			t.Fatalf("offset=%g seconds: derivative jitter=%g degrees/day", offset*86400, jitter)
+		}
+	}
+	cache.preparePathEphemeris(tt, OccultationPathAlgorithmOptimized)
+	if cache.local == nil || !cache.local.dense {
+		t.Fatal("smooth exact states must support the checked dense ephemeris")
+	}
+}
+
+// MoonCalcNew 与 HMoonTrueLo 是同一个物理量的两个入口，必须给出同一个值（此前只有一个入口
+// 走线性相位补偿，两者差约 1e-9 度）。
+func TestMoonCalcNewMatchesHMoonTrueLo(t *testing.T) {
+	for _, jd := range []float64{2451545.0, 2460310.5, 2415020.5, 2299160.5, 2500000.5} {
+		direct := math.Mod(MoonCalcNew(0, jd)*180/math.Pi, 360)
+		if direct < 0 {
+			direct += 360
+		}
+		high := HMoonTrueLo(jd)
+		if diff := math.Abs(direct - high); diff > 1e-12 {
+			t.Errorf("jd %.1f: MoonCalcNew=%0.15f HMoonTrueLo=%0.15f diff=%.3g deg", jd, direct, high, diff)
+		}
+	}
+}