{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:UHVNDNNEKNJIHVDTR2XEWT36SY","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":"c2b8c003c44a8f57813adcff26302880c6cd2249501cbe23dd828101ed3a2099","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-09T10:35:25Z","title_canon_sha256":"dac02afaedcf5321f9bdd8fe95c1d946258f8b2f0756d6605c685278ba933701"},"schema_version":"1.0","source":{"id":"1007.1553","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1553","created_at":"2026-05-18T04:31:42Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1553v2","created_at":"2026-05-18T04:31:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1553","created_at":"2026-05-18T04:31:42Z"},{"alias_kind":"pith_short_12","alias_value":"UHVNDNNEKNJI","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"UHVNDNNEKNJIHVDT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"UHVNDNNE","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:54d23a00ed840b25182cdfb42a1db23cbb1489f2612995755047e69928c8ad1e","target":"graph","created_at":"2026-05-18T04:31:42Z","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 give a counting based proof of the Graham Pollak Theorem","authors_text":"Sundar Vishwanathan","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-09T10:35:25Z","title":"A Counting Proof of the Graham Pollak Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1553","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":"sha256:8d9f40ba91238fdf8c7309fe1c249f5a1f9c0806baa4f5f1169b2524bb7283ba","target":"record","created_at":"2026-05-18T04:31:42Z","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":"c2b8c003c44a8f57813adcff26302880c6cd2249501cbe23dd828101ed3a2099","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-07-09T10:35:25Z","title_canon_sha256":"dac02afaedcf5321f9bdd8fe95c1d946258f8b2f0756d6605c685278ba933701"},"schema_version":"1.0","source":{"id":"1007.1553","kind":"arxiv","version":2}},"canonical_sha256":"a1ead1b5a4535283d4738eae4b4f7e9603ec32552520ae367d14d3e4cc37f666","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1ead1b5a4535283d4738eae4b4f7e9603ec32552520ae367d14d3e4cc37f666","first_computed_at":"2026-05-18T04:31:42.171848Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:42.171848Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3SXaCX4NW6HGCq+1OpJiP0PCmHG2s/4hjHTkIOwpNQz6GytNGHWTH0+SAnOGqH6cq1TT0BFnoqUXXEpjm8LdAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:42.172273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.1553","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d9f40ba91238fdf8c7309fe1c249f5a1f9c0806baa4f5f1169b2524bb7283ba","sha256:54d23a00ed840b25182cdfb42a1db23cbb1489f2612995755047e69928c8ad1e"],"state_sha256":"e2858fac37c82bd0010da6cedb8cb590b08320767c36470965dc7571d095be54"}