{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:R3UC6VEPGRVU5OK4D2HOIWPUMU","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":"192461639eb4575f7acf5cbe04a8e94f2361ea6972a687ba7a1205ec8d5899e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-25T11:33:15Z","title_canon_sha256":"e242aba72493bf3544cc42259664f8c66c9a4ea1ef54bcaa2416fc119c66578c"},"schema_version":"1.0","source":{"id":"1107.4902","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.4902","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"arxiv_version","alias_value":"1107.4902v1","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.4902","created_at":"2026-05-18T04:16:54Z"},{"alias_kind":"pith_short_12","alias_value":"R3UC6VEPGRVU","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"R3UC6VEPGRVU5OK4","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"R3UC6VEP","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:85f3667a8924b4d62a9ef22c36ba60c60c1cfffcb4afffcd4823552a182e25a4","target":"graph","created_at":"2026-05-18T04:16:54Z","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":"Graph pebbling considers the problem of transforming configurations of discrete pebbles to certain target configurations on the vertices of a graph, using the so-called pebbling move. This paper provides counterexamples to a monotonicity conjecture stated by Hurlbert et al. concerning the pebbling number compared to the pebbling threshold.","authors_text":"Cecilia Holmgren, Johan Bj\\\"orklund","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-25T11:33:15Z","title":"Counterexamples to a Monotonicity Conjecture for the Threshold Pebbling Number"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.4902","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:c51231f62f1a46c45f90d514391e21ca87c0647cb79bb89947c0cb6e109453a0","target":"record","created_at":"2026-05-18T04:16:54Z","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":"192461639eb4575f7acf5cbe04a8e94f2361ea6972a687ba7a1205ec8d5899e5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-07-25T11:33:15Z","title_canon_sha256":"e242aba72493bf3544cc42259664f8c66c9a4ea1ef54bcaa2416fc119c66578c"},"schema_version":"1.0","source":{"id":"1107.4902","kind":"arxiv","version":1}},"canonical_sha256":"8ee82f548f346b4eb95c1e8ee459f4653f62b92b74f6c79b237714b7d9fe9a35","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8ee82f548f346b4eb95c1e8ee459f4653f62b92b74f6c79b237714b7d9fe9a35","first_computed_at":"2026-05-18T04:16:54.315389Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:16:54.315389Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"anf6O6OwHMbRmAoYFD6ogKUcJf2TMK2k6gw5/1Txa4vx2MwjM6D3bPzYYl9lDvHHIpGNlKHUO2LVglovwaJNAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:16:54.316029Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.4902","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c51231f62f1a46c45f90d514391e21ca87c0647cb79bb89947c0cb6e109453a0","sha256:85f3667a8924b4d62a9ef22c36ba60c60c1cfffcb4afffcd4823552a182e25a4"],"state_sha256":"ab36e1498816985e1514980a4fa923270aa0309d1647d46287b0f0f1bea0ef71"}