{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:PDYIAF5H4JYEZCBTGJ7Q6JOCNT","short_pith_number":"pith:PDYIAF5H","canonical_record":{"source":{"id":"1808.04227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-13T14:01:21Z","cross_cats_sorted":[],"title_canon_sha256":"d380cb40533c33f7f1645505071cae29bad1a9be976bbda40b230955cce427d5","abstract_canon_sha256":"cee6a9928aa5badc53292a3b15922ff85bc6aec22cfdac11c501fc20864b53d5"},"schema_version":"1.0"},"canonical_sha256":"78f08017a7e2704c8833327f0f25c26cedfa8d2dd26d7e220416b788768c383a","source":{"kind":"arxiv","id":"1808.04227","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04227","created_at":"2026-05-18T00:08:18Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04227v1","created_at":"2026-05-18T00:08:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04227","created_at":"2026-05-18T00:08:18Z"},{"alias_kind":"pith_short_12","alias_value":"PDYIAF5H4JYE","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PDYIAF5H4JYEZCBT","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PDYIAF5H","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:PDYIAF5H4JYEZCBTGJ7Q6JOCNT","target":"record","payload":{"canonical_record":{"source":{"id":"1808.04227","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-13T14:01:21Z","cross_cats_sorted":[],"title_canon_sha256":"d380cb40533c33f7f1645505071cae29bad1a9be976bbda40b230955cce427d5","abstract_canon_sha256":"cee6a9928aa5badc53292a3b15922ff85bc6aec22cfdac11c501fc20864b53d5"},"schema_version":"1.0"},"canonical_sha256":"78f08017a7e2704c8833327f0f25c26cedfa8d2dd26d7e220416b788768c383a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:18.546253Z","signature_b64":"s2vHqjm+LxtZCjGZuzpMEnud8PNkHj8ZOc9Dy7E3c2ut1rRbMrcZ93pcTMB7K2bjdek20GV76fzXMERrUdISAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78f08017a7e2704c8833327f0f25c26cedfa8d2dd26d7e220416b788768c383a","last_reissued_at":"2026-05-18T00:08:18.545814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:18.545814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.04227","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a65ORL6pLBPGcQBU5iLQytXlnapjcfgpzVHOy0TZcKKAVlX4YwH7cyqPYAZpG+GiXKdlNzB0Y171RbMnUZfYDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:29:02.210460Z"},"content_sha256":"32fd96767b08163be6408f07f52e05fdb95fa8c7e4d2f8d451fb9265c2247d4f","schema_version":"1.0","event_id":"sha256:32fd96767b08163be6408f07f52e05fdb95fa8c7e4d2f8d451fb9265c2247d4f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:PDYIAF5H4JYEZCBTGJ7Q6JOCNT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Miquel Dynamics, Clifford Lattices and the Dimer Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Niklas C. Affolter","submitted_at":"2018-08-13T14:01:21Z","abstract_excerpt":"Miquel dynamics were introduced by Ramassamy as a discrete time evolution of square grid circle patterns on the torus. In each time step every second circle in the pattern is replaced with a new one by employing Miquel's six circle theorem. Inspired by these dynamics we define the Miquel move, which changes the combinatorics and geometry of a circle pattern locally. We prove that the circle centers under Miquel dynamics are Clifford lattices, considered as an integrable system by Konopelchenko and Schief. Clifford lattices have the combinatorics of an octahedral lattice and every octahedron co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04227","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:08:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QNQmUsEqG0kx08VB5WHkI0A6suiuvH+HkAPnk4016maLqog7FyNZNm2/CWBUuxlmDx/F9qEpbxlakzARBLKtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T17:29:02.210999Z"},"content_sha256":"88a874eec56977d486199a962187be64a8aba156a3eecf43e161c8afd5fa0101","schema_version":"1.0","event_id":"sha256:88a874eec56977d486199a962187be64a8aba156a3eecf43e161c8afd5fa0101"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PDYIAF5H4JYEZCBTGJ7Q6JOCNT/bundle.json","state_url":"https://pith.science/pith/PDYIAF5H4JYEZCBTGJ7Q6JOCNT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PDYIAF5H4JYEZCBTGJ7Q6JOCNT/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T17:29:02Z","links":{"resolver":"https://pith.science/pith/PDYIAF5H4JYEZCBTGJ7Q6JOCNT","bundle":"https://pith.science/pith/PDYIAF5H4JYEZCBTGJ7Q6JOCNT/bundle.json","state":"https://pith.science/pith/PDYIAF5H4JYEZCBTGJ7Q6JOCNT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PDYIAF5H4JYEZCBTGJ7Q6JOCNT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:PDYIAF5H4JYEZCBTGJ7Q6JOCNT","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"cee6a9928aa5badc53292a3b15922ff85bc6aec22cfdac11c501fc20864b53d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-13T14:01:21Z","title_canon_sha256":"d380cb40533c33f7f1645505071cae29bad1a9be976bbda40b230955cce427d5"},"schema_version":"1.0","source":{"id":"1808.04227","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.04227","created_at":"2026-05-18T00:08:18Z"},{"alias_kind":"arxiv_version","alias_value":"1808.04227v1","created_at":"2026-05-18T00:08:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.04227","created_at":"2026-05-18T00:08:18Z"},{"alias_kind":"pith_short_12","alias_value":"PDYIAF5H4JYE","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"PDYIAF5H4JYEZCBT","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"PDYIAF5H","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:88a874eec56977d486199a962187be64a8aba156a3eecf43e161c8afd5fa0101","target":"graph","created_at":"2026-05-18T00:08:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Miquel dynamics were introduced by Ramassamy as a discrete time evolution of square grid circle patterns on the torus. In each time step every second circle in the pattern is replaced with a new one by employing Miquel's six circle theorem. Inspired by these dynamics we define the Miquel move, which changes the combinatorics and geometry of a circle pattern locally. We prove that the circle centers under Miquel dynamics are Clifford lattices, considered as an integrable system by Konopelchenko and Schief. Clifford lattices have the combinatorics of an octahedral lattice and every octahedron co","authors_text":"Niklas C. Affolter","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-13T14:01:21Z","title":"Miquel Dynamics, Clifford Lattices and the Dimer Model"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04227","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:32fd96767b08163be6408f07f52e05fdb95fa8c7e4d2f8d451fb9265c2247d4f","target":"record","created_at":"2026-05-18T00:08:18Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"cee6a9928aa5badc53292a3b15922ff85bc6aec22cfdac11c501fc20864b53d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-08-13T14:01:21Z","title_canon_sha256":"d380cb40533c33f7f1645505071cae29bad1a9be976bbda40b230955cce427d5"},"schema_version":"1.0","source":{"id":"1808.04227","kind":"arxiv","version":1}},"canonical_sha256":"78f08017a7e2704c8833327f0f25c26cedfa8d2dd26d7e220416b788768c383a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78f08017a7e2704c8833327f0f25c26cedfa8d2dd26d7e220416b788768c383a","first_computed_at":"2026-05-18T00:08:18.545814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:08:18.545814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s2vHqjm+LxtZCjGZuzpMEnud8PNkHj8ZOc9Dy7E3c2ut1rRbMrcZ93pcTMB7K2bjdek20GV76fzXMERrUdISAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:08:18.546253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.04227","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32fd96767b08163be6408f07f52e05fdb95fa8c7e4d2f8d451fb9265c2247d4f","sha256:88a874eec56977d486199a962187be64a8aba156a3eecf43e161c8afd5fa0101"],"state_sha256":"0f88d970bf84f1d0b0b2eff06e4fb5f101e76c16db4b0e39ab0941f5b68cfa3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ySwNGFYEYtBWCVM6i2JT5Kha3UswWocEOU4J+CkuZpO9D2QeczUK4Pz8A/V0Tunbydgoe90njGw2uTTdsOLAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T17:29:02.216167Z","bundle_sha256":"208df8ae0625ef92925e76efbf7da3d200e12e2f8f1e20c658ddc6c350d676e5"}}