{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:XAQ7AOMMVBFSLRVPGENCFNZTVV","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":"4d64983e6e375b1603b8622904af6584666e086c50b366d9766708a9d76ce034","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-11-03T14:22:54Z","title_canon_sha256":"56709fef8a87a0a7f8dc75aaa291ffbb95de84263a0a1bae8fd75cd9372d47be"},"schema_version":"1.0","source":{"id":"0811.0308","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.0308","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"arxiv_version","alias_value":"0811.0308v2","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.0308","created_at":"2026-05-18T04:03:20Z"},{"alias_kind":"pith_short_12","alias_value":"XAQ7AOMMVBFS","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"XAQ7AOMMVBFSLRVP","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"XAQ7AOMM","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:68d1527634cbea3330a916dd962472bb28080354bd463c265af14060763b5c72","target":"graph","created_at":"2026-05-18T04:03:20Z","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":"Let N be distributed as a Poisson random set on R^d with intensity comparable to the Lebesgue measure. Consider the Voronoi tiling of R^d, (C_v)_{v\\in N}, where C_v is composed by points x in R^d that are closer to v than to any other v' in N. A polyomino P of size n is a connected union (in the usual R^d topological sense) of n tiles, and we denote by Pi_n the collection of all polyominos P of size n containing the origin. Assume that the weight of a Voronoi tile C_v is given by F(C_v), where F is a nonnegative functional on Voronoi tiles. In this paper we investigate the tail behavior of the","authors_text":"Leandro P. R. Pimentel, Raphael Rossignol","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-11-03T14:22:54Z","title":"Greedy Polyominoes and first-passage times on random Voronoi tilings"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.0308","kind":"arxiv","version":2},"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:c5d8b7233cfb40badf6e9c8e2717ed2c9cb02e74d9cf85217db71a5686e8422b","target":"record","created_at":"2026-05-18T04:03:20Z","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":"4d64983e6e375b1603b8622904af6584666e086c50b366d9766708a9d76ce034","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-11-03T14:22:54Z","title_canon_sha256":"56709fef8a87a0a7f8dc75aaa291ffbb95de84263a0a1bae8fd75cd9372d47be"},"schema_version":"1.0","source":{"id":"0811.0308","kind":"arxiv","version":2}},"canonical_sha256":"b821f0398ca84b25c6af311a22b733ad49342730049fdbc1dcd501d0c2bc86c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b821f0398ca84b25c6af311a22b733ad49342730049fdbc1dcd501d0c2bc86c1","first_computed_at":"2026-05-18T04:03:20.411011Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:20.411011Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UrjJO6x40cS0qz6SNFz3ay8dVsN1f1Z/mRTIU+dXr5bzXGpp+VlIYs9t0pkofa5LTPsQ4osNJP3j2p/aRmQ6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:20.411429Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.0308","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5d8b7233cfb40badf6e9c8e2717ed2c9cb02e74d9cf85217db71a5686e8422b","sha256:68d1527634cbea3330a916dd962472bb28080354bd463c265af14060763b5c72"],"state_sha256":"61fa2e76d0f0d1a188cce8830b9dae78410e52a3955824b07830a189218aa571"}