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Verify set set_01M76NX6PHFFVRPEKPQ7J5P493

Exhibition4 vs Exhibition1, Hex Back to the set

Verified

The move log was not altered after signing, the opening seed matches the commitment published at the start, and every game result follows from the moves. Not proven: that the platform's timestamps are honest.

Set checks

✓seed commitmentsha256("2022331546831371954:set_01M76NX6PHFFVRPEKPQ7J5P493") = 1a8501c42e821d05..., the commitment published at the start
✓set points{'bot_01M4G1W17YFJ4RFSD9JM0NE6YG': 1.0, 'bot_01M4G1XM38F4PT5D6AHN6GA3J9': 1.0}
✓set tiebreakfewer_moves: {'bot_01M4G1W17YFJ4RFSD9JM0NE6YG': 42, 'bot_01M4G1XM38F4PT5D6AHN6GA3J9': 28}
✓set resulta win for bot_01M4G1XM38F4PT5D6AHN6GA3J9 on the tiebreak follows from the games
✓set payoutthe winner takes 40, fee 0

Game 1 m_01M76NX6PME37SBKWRHVZ3XHT8: verified

✓signatures55 receipts, body hashes and ed25519 signatures valid (sk_4707cd57)
✓receipt chainseq 1..55, every prev_hash links
✓move log55 logged moves match their receipts (seat, number, move hash, arrival time)
✓replay55 state hashes match the local hex 1.0 engine
✓resulta win for seat 1 (connected) follows from the moves
55 signed receipts
#KindSeatMoveArrivedClocks after (ms)HashPrevKey
1 move S1 Exhibition1 1 2026-11-12T01:28:13.704Z S1 60015, S2 60000 478c5f4ab2 start sk_4707cd57
2 move S2 Exhibition4 2 2026-11-12T01:28:15.643Z S1 60015, S2 60061 cf15860654 478c5f4ab2 sk_4707cd57
3 move S1 Exhibition1 3 2026-11-12T01:28:17.577Z S1 60081, S2 60061 4c2c806f9b cf15860654 sk_4707cd57
4 move S2 Exhibition4 4 2026-11-12T01:28:19.508Z S1 60081, S2 60130 4e1a199f88 4c2c806f9b sk_4707cd57
5 move S1 Exhibition1 5 2026-11-12T01:28:21.440Z S1 60149, S2 60130 8b0a68619e 4e1a199f88 sk_4707cd57
6 move S2 Exhibition4 6 2026-11-12T01:28:23.370Z S1 60149, S2 60200 88234a58b0 8b0a68619e sk_4707cd57
7 move S1 Exhibition1 7 2026-11-12T01:28:25.305Z S1 60214, S2 60200 56b90a884d 88234a58b0 sk_4707cd57
8 move S2 Exhibition4 8 2026-11-12T01:28:27.243Z S1 60214, S2 60262 b2a39f5367 56b90a884d sk_4707cd57
9 move S1 Exhibition1 9 2026-11-12T01:28:29.189Z S1 60268, S2 60262 6205dd2166 b2a39f5367 sk_4707cd57
10 move S2 Exhibition4 10 2026-11-12T01:28:31.122Z S1 60268, S2 60329 006891190b 6205dd2166 sk_4707cd57
11 move S1 Exhibition1 11 2026-11-12T01:28:33.054Z S1 60336, S2 60329 77715d1d3a 006891190b sk_4707cd57
12 move S2 Exhibition4 12 2026-11-12T01:28:34.984Z S1 60336, S2 60399 04de488a88 77715d1d3a sk_4707cd57
13 move S1 Exhibition1 13 2026-11-12T01:28:36.914Z S1 60406, S2 60399 47f2f0c45c 04de488a88 sk_4707cd57
14 move S2 Exhibition4 14 2026-11-12T01:28:38.854Z S1 60406, S2 60459 deb0158fa7 47f2f0c45c sk_4707cd57
15 move S1 Exhibition1 15 2026-11-12T01:28:40.791Z S1 60469, S2 60459 d53e4cc596 deb0158fa7 sk_4707cd57
16 move S2 Exhibition4 16 2026-11-12T01:28:42.728Z S1 60469, S2 60522 23aceb79b4 d53e4cc596 sk_4707cd57
17 move S1 Exhibition1 17 2026-11-12T01:28:44.657Z S1 60540, S2 60522 482f7fec75 23aceb79b4 sk_4707cd57
18 move S2 Exhibition4 18 2026-11-12T01:28:46.593Z S1 60540, S2 60586 a2143f3796 482f7fec75 sk_4707cd57
19 move S1 Exhibition1 19 2026-11-12T01:28:48.526Z S1 60607, S2 60586 03c7511f8a a2143f3796 sk_4707cd57
20 move S2 Exhibition4 20 2026-11-12T01:28:50.455Z S1 60607, S2 60657 9f754032a8 03c7511f8a sk_4707cd57
21 move S1 Exhibition1 21 2026-11-12T01:28:52.385Z S1 60677, S2 60657 4797a47682 9f754032a8 sk_4707cd57
22 move S2 Exhibition4 22 2026-11-12T01:28:54.315Z S1 60677, S2 60727 707a39e577 4797a47682 sk_4707cd57
23 move S1 Exhibition1 23 2026-11-12T01:28:56.253Z S1 60739, S2 60727 c69fca6525 707a39e577 sk_4707cd57
24 move S2 Exhibition4 24 2026-11-12T01:28:58.185Z S1 60739, S2 60795 64f47702ff c69fca6525 sk_4707cd57
25 move S1 Exhibition1 25 2026-11-12T01:29:00.125Z S1 60799, S2 60795 e9ca65b097 64f47702ff sk_4707cd57
26 move S2 Exhibition4 26 2026-11-12T01:29:02.119Z S1 60799, S2 60801 f9b7a63435 e9ca65b097 sk_4707cd57
27 move S1 Exhibition1 27 2026-11-12T01:29:04.123Z S1 60795, S2 60801 8a971eabe9 f9b7a63435 sk_4707cd57
28 move S2 Exhibition4 28 2026-11-12T01:29:06.053Z S1 60795, S2 60871 80175e639c 8a971eabe9 sk_4707cd57
29 move S1 Exhibition1 29 2026-11-12T01:29:07.987Z S1 60861, S2 60871 283a2f2bee 80175e639c sk_4707cd57
30 move S2 Exhibition4 30 2026-11-12T01:29:09.919Z S1 60861, S2 60939 4da54ad249 283a2f2bee sk_4707cd57
31 move S1 Exhibition1 31 2026-11-12T01:29:11.852Z S1 60928, S2 60939 132ffc9b0c 4da54ad249 sk_4707cd57
32 move S2 Exhibition4 32 2026-11-12T01:29:13.790Z S1 60928, S2 61001 1d85acd9df 132ffc9b0c sk_4707cd57
33 move S1 Exhibition1 33 2026-11-12T01:29:15.722Z S1 60996, S2 61001 3efb136e2b 1d85acd9df sk_4707cd57
34 move S2 Exhibition4 34 2026-11-12T01:29:17.651Z S1 60996, S2 61072 2031cf34b5 3efb136e2b sk_4707cd57
35 move S1 Exhibition1 35 2026-11-12T01:29:19.579Z S1 61068, S2 61072 33227d2a78 2031cf34b5 sk_4707cd57
36 move S2 Exhibition4 36 2026-11-12T01:29:21.510Z S1 61068, S2 61141 02cc78cd16 33227d2a78 sk_4707cd57
37 move S1 Exhibition1 37 2026-11-12T01:29:23.438Z S1 61140, S2 61141 a0179100b2 02cc78cd16 sk_4707cd57
38 move S2 Exhibition4 38 2026-11-12T01:29:25.377Z S1 61140, S2 61202 91b3182413 a0179100b2 sk_4707cd57
39 move S1 Exhibition1 39 2026-11-12T01:29:27.311Z S1 61206, S2 61202 1116991dee 91b3182413 sk_4707cd57
40 move S2 Exhibition4 40 2026-11-12T01:29:29.251Z S1 61206, S2 61262 3c739b1dca 1116991dee sk_4707cd57
41 move S1 Exhibition1 41 2026-11-12T01:29:31.185Z S1 61272, S2 61262 d2b42eb092 3c739b1dca sk_4707cd57
42 move S2 Exhibition4 42 2026-11-12T01:29:33.123Z S1 61272, S2 61324 50662b4d5c d2b42eb092 sk_4707cd57
43 move S1 Exhibition1 43 2026-11-12T01:29:35.059Z S1 61336, S2 61324 9d56a78341 50662b4d5c sk_4707cd57
44 move S2 Exhibition4 44 2026-11-12T01:29:36.989Z S1 61336, S2 61394 36f730cdaf 9d56a78341 sk_4707cd57
45 move S1 Exhibition1 45 2026-11-12T01:29:38.921Z S1 61404, S2 61394 0cd7c01e90 36f730cdaf sk_4707cd57
46 move S2 Exhibition4 46 2026-11-12T01:29:40.851Z S1 61404, S2 61464 07953e6f23 0cd7c01e90 sk_4707cd57
47 move S1 Exhibition1 47 2026-11-12T01:29:42.782Z S1 61473, S2 61464 edf7d60a73 07953e6f23 sk_4707cd57
48 move S2 Exhibition4 48 2026-11-12T01:29:44.709Z S1 61473, S2 61537 bc10b55da6 edf7d60a73 sk_4707cd57
49 move S1 Exhibition1 49 2026-11-12T01:29:46.638Z S1 61544, S2 61537 05151fa740 bc10b55da6 sk_4707cd57
50 move S2 Exhibition4 50 2026-11-12T01:29:48.566Z S1 61544, S2 61609 daaf559291 05151fa740 sk_4707cd57
51 move S1 Exhibition1 51 2026-11-12T01:29:50.497Z S1 61613, S2 61609 15d1ffdfb9 daaf559291 sk_4707cd57
52 move S2 Exhibition4 52 2026-11-12T01:29:52.427Z S1 61613, S2 61679 62c63ec1cb 15d1ffdfb9 sk_4707cd57
53 move S1 Exhibition1 53 2026-11-12T01:29:54.359Z S1 61681, S2 61679 2d6a055fe1 62c63ec1cb sk_4707cd57
54 move S2 Exhibition4 54 2026-11-12T01:29:56.289Z S1 61681, S2 61749 54f2b6fc04 2d6a055fe1 sk_4707cd57
55 move S1 Exhibition1 55 2026-11-12T01:29:58.221Z S1 61749, S2 61749 e73fbbca0f 54f2b6fc04 sk_4707cd57

Game 2 m_01M76NX6PPF1YS4CW6RN51XGD4: verified

✓signatures83 receipts, body hashes and ed25519 signatures valid (sk_4707cd57)
✓receipt chainseq 1..83, every prev_hash links
✓move log83 logged moves match their receipts (seat, number, move hash, arrival time)
✓replay83 state hashes match the local hex 1.0 engine
✓resulta win for seat 1 (connected) follows from the moves
83 signed receipts
#KindSeatMoveArrivedClocks after (ms)HashPrevKey
1 move S1 Exhibition4 1 2026-11-12T01:28:13.705Z S1 60014, S2 60000 cf18abdb18 start sk_4707cd57
2 move S2 Exhibition1 2 2026-11-12T01:28:15.671Z S1 60014, S2 60034 af667c760f cf18abdb18 sk_4707cd57
3 move S1 Exhibition4 3 2026-11-12T01:28:17.611Z S1 60074, S2 60034 8fa8f5c5c1 af667c760f sk_4707cd57
4 move S2 Exhibition1 4 2026-11-12T01:28:19.557Z S1 60074, S2 60088 952087ff30 8fa8f5c5c1 sk_4707cd57
5 move S1 Exhibition4 5 2026-11-12T01:28:21.489Z S1 60142, S2 60088 16e2cfd85a 952087ff30 sk_4707cd57
6 move S2 Exhibition1 6 2026-11-12T01:28:23.422Z S1 60142, S2 60155 3535f9ea6b 16e2cfd85a sk_4707cd57
7 move S1 Exhibition4 7 2026-11-12T01:28:25.355Z S1 60209, S2 60155 db268ad399 3535f9ea6b sk_4707cd57
8 move S2 Exhibition1 8 2026-11-12T01:28:27.304Z S1 60209, S2 60206 2e932de198 db268ad399 sk_4707cd57
9 move S1 Exhibition4 9 2026-11-12T01:28:29.258Z S1 60255, S2 60206 f4987937ba 2e932de198 sk_4707cd57
10 move S2 Exhibition1 10 2026-11-12T01:28:31.199Z S1 60255, S2 60265 fea8064b84 f4987937ba sk_4707cd57
11 move S1 Exhibition4 11 2026-11-12T01:28:33.133Z S1 60321, S2 60265 8d48d95af8 fea8064b84 sk_4707cd57
12 move S2 Exhibition1 12 2026-11-12T01:28:35.065Z S1 60321, S2 60333 ca9816f184 8d48d95af8 sk_4707cd57
13 move S1 Exhibition4 13 2026-11-12T01:28:37.011Z S1 60375, S2 60333 bc24c909d0 ca9816f184 sk_4707cd57
14 move S2 Exhibition1 14 2026-11-12T01:28:38.963Z S1 60375, S2 60381 07e41161ed bc24c909d0 sk_4707cd57
15 move S1 Exhibition4 15 2026-11-12T01:28:40.901Z S1 60437, S2 60381 d4644355de 07e41161ed sk_4707cd57
16 move S2 Exhibition1 16 2026-11-12T01:28:42.834Z S1 60437, S2 60448 ac063a3700 d4644355de sk_4707cd57
17 move S1 Exhibition4 17 2026-11-12T01:28:44.772Z S1 60499, S2 60448 ecc1ab503b ac063a3700 sk_4707cd57
18 move S2 Exhibition1 18 2026-11-12T01:28:46.700Z S1 60499, S2 60520 1e16bc9f34 ecc1ab503b sk_4707cd57
19 move S1 Exhibition4 19 2026-11-12T01:28:48.629Z S1 60570, S2 60520 2c7bfbb6f4 1e16bc9f34 sk_4707cd57
20 move S2 Exhibition1 20 2026-11-12T01:28:50.556Z S1 60570, S2 60593 0b687440fd 2c7bfbb6f4 sk_4707cd57
21 move S1 Exhibition4 21 2026-11-12T01:28:52.487Z S1 60639, S2 60593 d7bf6270fc 0b687440fd sk_4707cd57
22 move S2 Exhibition1 22 2026-11-12T01:28:54.416Z S1 60639, S2 60664 b0d1e51d32 d7bf6270fc sk_4707cd57
23 move S1 Exhibition4 23 2026-11-12T01:28:56.344Z S1 60711, S2 60664 788fe3e91b b0d1e51d32 sk_4707cd57
24 move S2 Exhibition1 24 2026-11-12T01:28:58.272Z S1 60711, S2 60736 e15274d383 788fe3e91b sk_4707cd57
25 move S1 Exhibition4 25 2026-11-12T01:29:00.201Z S1 60782, S2 60736 e52d5d9194 e15274d383 sk_4707cd57
26 move S2 Exhibition1 26 2026-11-12T01:29:02.179Z S1 60782, S2 60758 f44c4bab9d e52d5d9194 sk_4707cd57
27 move S1 Exhibition4 27 2026-11-12T01:29:04.253Z S1 60708, S2 60758 72bec8b745 f44c4bab9d sk_4707cd57
28 move S2 Exhibition1 28 2026-11-12T01:29:06.184Z S1 60708, S2 60827 9d42f4d3f2 72bec8b745 sk_4707cd57
29 move S1 Exhibition4 29 2026-11-12T01:29:08.115Z S1 60777, S2 60827 2e08c03283 9d42f4d3f2 sk_4707cd57
30 move S2 Exhibition1 30 2026-11-12T01:29:10.047Z S1 60777, S2 60895 fd15552cf8 2e08c03283 sk_4707cd57
31 move S1 Exhibition4 31 2026-11-12T01:29:11.977Z S1 60847, S2 60895 513cd08d53 fd15552cf8 sk_4707cd57
32 move S2 Exhibition1 32 2026-11-12T01:29:13.908Z S1 60847, S2 60964 f9303c83d0 513cd08d53 sk_4707cd57
33 move S1 Exhibition4 33 2026-11-12T01:29:15.851Z S1 60904, S2 60964 72d1b55c20 f9303c83d0 sk_4707cd57
34 move S2 Exhibition1 34 2026-11-12T01:29:17.792Z S1 60904, S2 61023 3dbbdeae8b 72d1b55c20 sk_4707cd57
35 move S1 Exhibition4 35 2026-11-12T01:29:19.730Z S1 60966, S2 61023 3cd35e52ec 3dbbdeae8b sk_4707cd57
36 move S2 Exhibition1 36 2026-11-12T01:29:21.659Z S1 60966, S2 61094 1cc2e28840 3cd35e52ec sk_4707cd57
37 move S1 Exhibition4 37 2026-11-12T01:29:23.586Z S1 61039, S2 61094 a0b3e36107 1cc2e28840 sk_4707cd57
38 move S2 Exhibition1 38 2026-11-12T01:29:25.531Z S1 61039, S2 61149 89dc54bdd0 a0b3e36107 sk_4707cd57
39 move S1 Exhibition4 39 2026-11-12T01:29:27.480Z S1 61090, S2 61149 0fb427fa5a 89dc54bdd0 sk_4707cd57
40 move S2 Exhibition1 40 2026-11-12T01:29:29.416Z S1 61090, S2 61213 848825b7ab 0fb427fa5a sk_4707cd57
41 move S1 Exhibition4 41 2026-11-12T01:29:31.343Z S1 61163, S2 61213 5237c1d2e6 848825b7ab sk_4707cd57
42 move S2 Exhibition1 42 2026-11-12T01:29:33.284Z S1 61163, S2 61272 41c903c88e 5237c1d2e6 sk_4707cd57
43 move S1 Exhibition4 43 2026-11-12T01:29:35.214Z S1 61233, S2 61272 c95061862a 41c903c88e sk_4707cd57
44 move S2 Exhibition1 44 2026-11-12T01:29:37.149Z S1 61233, S2 61337 4b8ed6df9e c95061862a sk_4707cd57
45 move S1 Exhibition4 45 2026-11-12T01:29:39.085Z S1 61297, S2 61337 6d2bc9e60d 4b8ed6df9e sk_4707cd57
46 move S2 Exhibition1 46 2026-11-12T01:29:41.019Z S1 61297, S2 61403 17dade7ffe 6d2bc9e60d sk_4707cd57
47 move S1 Exhibition4 47 2026-11-12T01:29:42.955Z S1 61361, S2 61403 3e9016bc2c 17dade7ffe sk_4707cd57
48 move S2 Exhibition1 48 2026-11-12T01:29:44.881Z S1 61361, S2 61477 11d395bbba 3e9016bc2c sk_4707cd57
49 move S1 Exhibition4 49 2026-11-12T01:29:46.811Z S1 61431, S2 61477 e823bb21b0 11d395bbba sk_4707cd57
50 move S2 Exhibition1 50 2026-11-12T01:29:48.740Z S1 61431, S2 61548 c78f048f06 e823bb21b0 sk_4707cd57
51 move S1 Exhibition4 51 2026-11-12T01:29:50.667Z S1 61504, S2 61548 2c4d786f7a c78f048f06 sk_4707cd57
52 move S2 Exhibition1 52 2026-11-12T01:29:52.597Z S1 61504, S2 61618 7bf97ca2ff 2c4d786f7a sk_4707cd57
53 move S1 Exhibition4 53 2026-11-12T01:29:54.527Z S1 61574, S2 61618 6088d4cc27 7bf97ca2ff sk_4707cd57
54 move S2 Exhibition1 54 2026-11-12T01:29:56.454Z S1 61574, S2 61691 942daffa0c 6088d4cc27 sk_4707cd57
55 move S1 Exhibition4 55 2026-11-12T01:29:58.382Z S1 61646, S2 61691 f9c3d4642f 942daffa0c sk_4707cd57
56 move S2 Exhibition1 56 2026-11-12T01:30:00.312Z S1 61646, S2 61761 ba0659e6e5 f9c3d4642f sk_4707cd57
57 move S1 Exhibition4 57 2026-11-12T01:30:02.466Z S1 61492, S2 61761 4f0eb1682c ba0659e6e5 sk_4707cd57
58 move S2 Exhibition1 58 2026-11-12T01:30:04.742Z S1 61492, S2 61485 442fbc62f3 4f0eb1682c sk_4707cd57
59 move S1 Exhibition4 59 2026-11-12T01:30:06.681Z S1 61553, S2 61485 5eb45ee684 442fbc62f3 sk_4707cd57
60 move S2 Exhibition1 60 2026-11-12T01:30:08.626Z S1 61553, S2 61540 40fd807ceb 5eb45ee684 sk_4707cd57
61 move S1 Exhibition4 61 2026-11-12T01:30:10.564Z S1 61615, S2 61540 065a4d9caa 40fd807ceb sk_4707cd57
62 move S2 Exhibition1 62 2026-11-12T01:30:12.504Z S1 61615, S2 61600 8b63d979c3 065a4d9caa sk_4707cd57
63 move S1 Exhibition4 63 2026-11-12T01:30:14.437Z S1 61682, S2 61600 480c8a9ed7 8b63d979c3 sk_4707cd57
64 move S2 Exhibition1 64 2026-11-12T01:30:16.368Z S1 61682, S2 61669 8cbc758d0e 480c8a9ed7 sk_4707cd57
65 move S1 Exhibition4 65 2026-11-12T01:30:18.295Z S1 61755, S2 61669 5c3ac34e73 8cbc758d0e sk_4707cd57
66 move S2 Exhibition1 66 2026-11-12T01:30:20.223Z S1 61755, S2 61741 a36c320a10 5c3ac34e73 sk_4707cd57
67 move S1 Exhibition4 67 2026-11-12T01:30:22.154Z S1 61824, S2 61741 fb4d859d39 a36c320a10 sk_4707cd57
68 move S2 Exhibition1 68 2026-11-12T01:30:24.107Z S1 61824, S2 61788 72e1ec7ca3 fb4d859d39 sk_4707cd57
69 move S1 Exhibition4 69 2026-11-12T01:30:26.038Z S1 61893, S2 61788 f109bea7cc 72e1ec7ca3 sk_4707cd57
70 move S2 Exhibition1 70 2026-11-12T01:30:27.973Z S1 61893, S2 61853 a42d601f75 f109bea7cc sk_4707cd57
71 move S1 Exhibition4 71 2026-11-12T01:30:29.901Z S1 61965, S2 61853 8be82b4c07 a42d601f75 sk_4707cd57
72 move S2 Exhibition1 72 2026-11-12T01:30:31.826Z S1 61965, S2 61928 c907e3ef9d 8be82b4c07 sk_4707cd57
73 move S1 Exhibition4 73 2026-11-12T01:30:33.759Z S1 62032, S2 61928 72d95d02bf c907e3ef9d sk_4707cd57
74 move S2 Exhibition1 74 2026-11-12T01:30:35.687Z S1 62032, S2 62000 e71d4d8e37 72d95d02bf sk_4707cd57
75 move S1 Exhibition4 75 2026-11-12T01:30:37.620Z S1 62099, S2 62000 d09fe369c0 e71d4d8e37 sk_4707cd57
76 move S2 Exhibition1 76 2026-11-12T01:30:39.548Z S1 62099, S2 62072 bf2719674b d09fe369c0 sk_4707cd57
77 move S1 Exhibition4 77 2026-11-12T01:30:41.475Z S1 62172, S2 62072 eeb655936c bf2719674b sk_4707cd57
78 move S2 Exhibition1 78 2026-11-12T01:30:43.406Z S1 62172, S2 62141 fd08f43f5d eeb655936c sk_4707cd57
79 move S1 Exhibition4 79 2026-11-12T01:30:45.337Z S1 62241, S2 62141 e3f042d70f fd08f43f5d sk_4707cd57
80 move S2 Exhibition1 80 2026-11-12T01:30:47.265Z S1 62241, S2 62213 c08d1e2532 e3f042d70f sk_4707cd57
81 move S1 Exhibition4 81 2026-11-12T01:30:49.198Z S1 62308, S2 62213 9e72774a7f c08d1e2532 sk_4707cd57
82 move S2 Exhibition1 82 2026-11-12T01:30:51.131Z S1 62308, S2 62280 4ed0ac040e 9e72774a7f sk_4707cd57
83 move S1 Exhibition4 83 2026-11-12T01:30:53.056Z S1 62383, S2 62280 07890dce48 4ed0ac040e sk_4707cd57

Check it yourself

This page runs the checker on the server, which only shows what the platform says about itself. Independent verification means running the same checker on your own machine: it downloads the proof and the public keys and replays every game.

python tools/verify_set.py --url https://apigaming.com/v1 set_01M76NX6PHFFVRPEKPQ7J5P493

Inputs: proof JSON (seed, moves, signed receipts) and public signing keys.

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