{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XTB6WW72PPKGBC6JUH5OAGFENG","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":"1f0b8ea70766b5dff293f3727bcc93b7d244de278061a6dd8266ef014d66b983","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-15T12:07:34Z","title_canon_sha256":"2c5f3dc8d867e860d74aa4e148128862fcd6d07e1a28ee2d0937e0cbedf8db52"},"schema_version":"1.0","source":{"id":"1905.06107","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1905.06107","created_at":"2026-05-17T23:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1905.06107v1","created_at":"2026-05-17T23:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.06107","created_at":"2026-05-17T23:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"XTB6WW72PPKG","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XTB6WW72PPKGBC6J","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XTB6WW72","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:9e10645b4c6148c543b8426faca385deb15beb6a6ae5bd75737c7fdf3544fc60","target":"graph","created_at":"2026-05-17T23:46:07Z","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":"We study the rich structure of periodic stationary solutions of Nagumo reaction diffusion equation on lattices. By exploring the relationship with Nagumo equations on cyclic graphs we are able to divide these periodic solutions into equivalence classes that can be partially ordered and counted. In order to accomplish this, we use combinatorial concepts such as necklaces, bracelets and Lyndon words.","authors_text":"Hermen Jan Hupkes, Leonardo Morelli, Petr Stehl\\'ik, Vladim\\'ir \\v{S}v\\'igler","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-15T12:07:34Z","title":"Counting and ordering periodic stationary solutions of lattice Nagumo equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.06107","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":"sha256:9150a508fa5839736623a6987b0fb9c5225913ff4336906aa1be8e37a3a795ad","target":"record","created_at":"2026-05-17T23:46:07Z","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":"1f0b8ea70766b5dff293f3727bcc93b7d244de278061a6dd8266ef014d66b983","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2019-05-15T12:07:34Z","title_canon_sha256":"2c5f3dc8d867e860d74aa4e148128862fcd6d07e1a28ee2d0937e0cbedf8db52"},"schema_version":"1.0","source":{"id":"1905.06107","kind":"arxiv","version":1}},"canonical_sha256":"bcc3eb5bfa7bd4608bc9a1fae018a469827a2f0020c46ff73977ee62b4fbb050","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bcc3eb5bfa7bd4608bc9a1fae018a469827a2f0020c46ff73977ee62b4fbb050","first_computed_at":"2026-05-17T23:46:07.483730Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:07.483730Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bP7FooR9/67Y5JDMPqt8+XR3AKYpikg3MowMGE3H7DgsJeud6FihWY45pQtoslJ4Hm6bRKPQiXnVjCmA8p8DDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:07.484230Z","signed_message":"canonical_sha256_bytes"},"source_id":"1905.06107","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9150a508fa5839736623a6987b0fb9c5225913ff4336906aa1be8e37a3a795ad","sha256:9e10645b4c6148c543b8426faca385deb15beb6a6ae5bd75737c7fdf3544fc60"],"state_sha256":"3a7d1a5822a32688ff4626351d7e45e70fd7cb35ae9dfb0c5a3904d0bbeeabf6"}