{"success":true,"version":"v1","request":{"tool":"describe_luoshu_square","calculator_id":"luoshu-square","inputs":{"number":5},"request_id":"req_a61c5d4a5ce44247885e","received_at":"2026-09-24T08:32:24Z"},"result":{"entity_type":"calculation","id":"calc_luoshu-square","calculator_id":"luoshu-square","calculator_name":"Luoshu Square (洛书)","category":"yijing","status":"completed","values":{"number":5,"color_name":"5 五黄 (Wu Huang, Yellow)","trigram":"none (centre, 中宫)","direction":"Centre (中)","element":"Earth (土)","season":"Transitions between seasons (四季土)","family_member":"none (centre)","grid":["4 9 2","3 5 7","8 1 6"],"magic_constant":15,"hetu_pair":10,"hetu_element":"Earth (土)","opposite_palace":5,"all_palaces":[{"number":1,"color_name":"1 一白 (Yi Bai, White)","trigram":"坎 Kan ☵ (Water)","direction":"North (N, 北)","element":"Water (水)"},{"number":2,"color_name":"2 二黑 (Er Hei, Black)","trigram":"坤 Kun ☷ (Earth)","direction":"Southwest (SW, 西南)","element":"Earth (土)"},{"number":3,"color_name":"3 三碧 (San Bi, Jade green)","trigram":"震 Zhen ☳ (Thunder)","direction":"East (E, 东)","element":"Wood (木)"},{"number":4,"color_name":"4 四绿 (Si Lü, Green)","trigram":"巽 Xun ☴ (Wind)","direction":"Southeast (SE, 东南)","element":"Wood (木)"},{"number":5,"color_name":"5 五黄 (Wu Huang, Yellow)","trigram":"none (centre, 中宫)","direction":"Centre (中)","element":"Earth (土)"},{"number":6,"color_name":"6 六白 (Liu Bai, White)","trigram":"乾 Qian ☰ (Heaven)","direction":"Northwest (NW, 西北)","element":"Metal (金)"},{"number":7,"color_name":"7 七赤 (Qi Chi, Red)","trigram":"兑 Dui ☱ (Lake)","direction":"West (W, 西)","element":"Metal (金)"},{"number":8,"color_name":"8 八白 (Ba Bai, White)","trigram":"艮 Gen ☶ (Mountain)","direction":"Northeast (NE, 东北)","element":"Earth (土)"},{"number":9,"color_name":"9 九紫 (Jiu Zi, Purple)","trigram":"离 Li ☲ (Fire)","direction":"South (S, 南)","element":"Fire (火)"}]},"units":{},"formula":"grid = [4 9 2; 3 5 7; 8 1 6], magic constant = 3·(1+…+9)/9 = 15; opposite = 10 − number (5 → 5); Hetu partner = number ± 5","notes":[],"summary":"Number: 5; Colour name (紫白): 5 五黄 (Wu Huang, Yellow); Trigram (后天): none (centre, 中宫); Direction: Centre (中); Element: Earth (土); Season: Transitions between seasons (四季土); Family member: none (centre); Grid (south at top): 4 9 2, 3 5 7, 8 1 6; Magic constant: 15; Hetu partner (河图): 10; Hetu element: Earth (土); Opposite palace: 5; All nine palaces: 9 values"},"warnings":[],"sources":[{"name":"Wikipedia – Lo Shu Square","url":"https://en.wikipedia.org/wiki/Lo_Shu_Square","type":"reference","retrieved_at":"2026-09-24"},{"name":"Wikipedia – Bagua","url":"https://en.wikipedia.org/wiki/Bagua","type":"reference","retrieved_at":"2026-09-24"}],"freshness":{"type":"static","max_age_seconds":null,"note":"Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output."},"cache":{"hit":false,"cacheable":true,"deterministic":true,"note":"Same inputs always produce the same result; safe to cache indefinitely."},"timestamp":"2026-09-24T08:32:24Z","duration_ms":0,"next_actions":[{"tool":"lookup_bagua_trigram","calculator_id":"bagua","reason":"Full attributes of the palace's trigram.","url":"https://tttkmbb.com/api/v1/calculate/bagua","docs":"https://tttkmbb.com/yijing/bagua.md"},{"tool":"calculate_ming_gua","calculator_id":"ming-gua","reason":"Personal Kua number defined by these palaces.","url":"https://tttkmbb.com/api/v1/calculate/ming-gua","docs":"https://tttkmbb.com/yijing/ming-gua.md"},{"tool":"analyze_five_element_relation","calculator_id":"five-elements","reason":"Relations between the elements of two palaces.","url":"https://tttkmbb.com/api/v1/calculate/five-elements","docs":"https://tttkmbb.com/yijing/five-elements.md"}],"links":{"self":"https://tttkmbb.com/api/v1/calculate/luoshu-square?number=5","html":"https://tttkmbb.com/yijing/luoshu-square?number=5","markdown":"https://tttkmbb.com/yijing/luoshu-square.md","schema":"https://tttkmbb.com/api/v1/calculators/luoshu-square","openapi":"https://tttkmbb.com/openapi.json","mcp":"https://tttkmbb.com/mcp","task":"https://tttkmbb.com/api/v1/tasks/task_eyJjIjoibHVvc2h1LXNxdWFyZSIsImkiOnsibnVtYmVyIjo1fSwidCI6IjIwMjYtMDktMjRUMDg6MzI6MjRaIn0"}}