{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:45G5PDDMCHJQKPJJY7H6OSXKDU","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":"604ec6b4e2adf8c9d4935804bf87d334244c38046864d08d991bba8874cdd5f1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-13T21:04:46Z","title_canon_sha256":"bf27aef341916598d9bf42e76b0a631fb2bb212571b2f5bed6968134cda40871"},"schema_version":"1.0","source":{"id":"1009.2523","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2523","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2523v3","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2523","created_at":"2026-05-18T03:31:07Z"},{"alias_kind":"pith_short_12","alias_value":"45G5PDDMCHJQ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"45G5PDDMCHJQKPJJ","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"45G5PDDM","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:dc8af8c1473955c97d6ce346c64f4e2236ee1735294ea44e172c572944c1c675","target":"graph","created_at":"2026-05-18T03:31:07Z","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 construct an edge-weight distribution for i.i.d. first-passage percolation on $\\mathbb{Z}^2$ whose limit shape is not a polygon and whose extreme points are arbitrarily dense in the boundary. Consequently, the associated Richardson-type growth model can support coexistence of a countably infinite number of distinct species, and the graph of infection has infinitely many ends.","authors_text":"Michael Damron, Michael Hochman","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-13T21:04:46Z","title":"Examples of nonpolygonal limit shapes in i.i.d. first-passage percolation and infinite coexistence in spatial growth models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2523","kind":"arxiv","version":3},"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":"sha256:70f5c64e43f2359698148435b2fb6445b795fb1bcc1702723f58fd64f0282eee","target":"record","created_at":"2026-05-18T03:31:07Z","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":"604ec6b4e2adf8c9d4935804bf87d334244c38046864d08d991bba8874cdd5f1","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-09-13T21:04:46Z","title_canon_sha256":"bf27aef341916598d9bf42e76b0a631fb2bb212571b2f5bed6968134cda40871"},"schema_version":"1.0","source":{"id":"1009.2523","kind":"arxiv","version":3}},"canonical_sha256":"e74dd78c6c11d3053d29c7cfe74aea1d3123c28b5bdb45beeff0fb898de23812","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e74dd78c6c11d3053d29c7cfe74aea1d3123c28b5bdb45beeff0fb898de23812","first_computed_at":"2026-05-18T03:31:07.153629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:07.153629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b9cPgJWDje+SVGGbMfn80xKx2A4i6ILc1X1tOB1dX1yJUMOZRlEtIkVIKSlm9owR7SJET+tsHStCHPNhgDJIAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:07.154192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2523","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70f5c64e43f2359698148435b2fb6445b795fb1bcc1702723f58fd64f0282eee","sha256:dc8af8c1473955c97d6ce346c64f4e2236ee1735294ea44e172c572944c1c675"],"state_sha256":"1928494f916c2f914b86fb188a242c9f52f99afbef77bb74f210167f65ce3367"}