{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:J33GTX774GC5EC5WHI24DUBXRM","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":"09b6f73ce85c47e41a495ab156b67d39cfa6d0c3967bb133caa7d1604aaf28eb","cross_cats_sorted":["math.CO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2025-06-23T23:52:48Z","title_canon_sha256":"3924fb9750787d47d07101666d4756ba8d9f8ed27e51443c41691d2170cdc666"},"schema_version":"1.0","source":{"id":"2506.19197","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.19197","created_at":"2026-07-05T11:49:10Z"},{"alias_kind":"arxiv_version","alias_value":"2506.19197v3","created_at":"2026-07-05T11:49:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.19197","created_at":"2026-07-05T11:49:10Z"},{"alias_kind":"pith_short_12","alias_value":"J33GTX774GC5","created_at":"2026-07-05T11:49:10Z"},{"alias_kind":"pith_short_16","alias_value":"J33GTX774GC5EC5W","created_at":"2026-07-05T11:49:10Z"},{"alias_kind":"pith_short_8","alias_value":"J33GTX77","created_at":"2026-07-05T11:49:10Z"}],"graph_snapshots":[{"event_id":"sha256:873e1f3c89e85fb5b964d9228953234f791a17b3a51dd1ad7178363429960454","target":"graph","created_at":"2026-07-05T11:49:10Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2506.19197/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A unit ball graph consists of a set of vertices, labeled by points in Euclidean space, and edges joining all pairs of points within distance 1. These geometric graphs are used to model a variety of spatial networks, including communication networks between agents in an autonomous swarm. In such an application, vertices and/or edges of the graph may not be perfectly reliable; an agent may experience failure or a communication link rendered inoperable. With the goal of designing robust swarm formations, or unit ball graphs with high reliability (probability of connectedness), in a preliminary co","authors_text":"Calum Buchanan, Hamid R. Ossareh, James Bagrow, Puck Rombach","cross_cats":["math.CO","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2025-06-23T23:52:48Z","title":"Vertex addition to a ball graph with application to reliability and area coverage in autonomous swarms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.19197","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":"sha256:0b40d363ba1e8e62f0860dd3200bef881321b67f6b41115a8b4196d369f98bd1","target":"record","created_at":"2026-07-05T11:49:10Z","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":"09b6f73ce85c47e41a495ab156b67d39cfa6d0c3967bb133caa7d1604aaf28eb","cross_cats_sorted":["math.CO","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DC","submitted_at":"2025-06-23T23:52:48Z","title_canon_sha256":"3924fb9750787d47d07101666d4756ba8d9f8ed27e51443c41691d2170cdc666"},"schema_version":"1.0","source":{"id":"2506.19197","kind":"arxiv","version":3}},"canonical_sha256":"4ef669dfffe185d20bb63a35c1d0378b39f7383d8a3928abd558f1c442b11b00","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ef669dfffe185d20bb63a35c1d0378b39f7383d8a3928abd558f1c442b11b00","first_computed_at":"2026-07-05T11:49:10.968945Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:49:10.968945Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cGZkntZbeauY3YI262CQbTWmBZOYBDCbxL/EoJTh3Ejxmpp3r1NCvP03Ptbl6y9EGTOwwGFEsUEvYRgne2eNDw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:49:10.969416Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.19197","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0b40d363ba1e8e62f0860dd3200bef881321b67f6b41115a8b4196d369f98bd1","sha256:873e1f3c89e85fb5b964d9228953234f791a17b3a51dd1ad7178363429960454"],"state_sha256":"809ae42bc732f2378124a9db53ce01107f9ded1606a6eb227a469492aafa1af5"}