{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:U7YD3XSTJFNRIJOJ7XESOH7HKY","short_pith_number":"pith:U7YD3XST","schema_version":"1.0","canonical_sha256":"a7f03dde53495b1425c9fdc9271fe7560ec2170e5c6c739bb840e34593fb42d0","source":{"kind":"arxiv","id":"1804.03717","version":1},"attestation_state":"computed","paper":{"title":"Optimal pebbling number of graphs with given minimum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Czygrinow, Glenn Hurlbert, Gyula Y. Katona, L\\'aszl\\'o F. Papp","submitted_at":"2018-04-10T21:00:52Z","abstract_excerpt":"Consider a distribution of pebbles on a connected graph $G$. A pebbling move removes two pebbles from a vertex and places one to an adjacent vertex. A vertex is reachable under a pebbling distribution if it has a pebble after the application of a sequence of pebbling moves. The optimal pebbling number $\\pi^*(G)$ is the smallest number of pebbles which we can distribute in such a way that each vertex is reachable. It was known that the optimal pebbling number of any connected graph is at most $\\frac{4n}{\\delta+1}$, where $\\delta$ is the minimum degree of the graph. We strengthen this bound by s"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1804.03717","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-10T21:00:52Z","cross_cats_sorted":[],"title_canon_sha256":"cd3ce940920e8f3c3360923bf6bbd650f6ad439fbe568235ac8ca1a1794fbfbc","abstract_canon_sha256":"0e65bc3f73026746b9494eb8438362cd95b548bb56e94e738bdf805eefb72c6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:45.198301Z","signature_b64":"V3NO2FUGnjt+yUv2NMrcBWyGBrqJFt1jU2Rcn22GBQgAuBJVFx3G+SHT8VlX4egHj46h5lffZUG+lFmI21jwDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a7f03dde53495b1425c9fdc9271fe7560ec2170e5c6c739bb840e34593fb42d0","last_reissued_at":"2026-05-18T00:18:45.197733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:45.197733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal pebbling number of graphs with given minimum degree","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Andrzej Czygrinow, Glenn Hurlbert, Gyula Y. Katona, L\\'aszl\\'o F. Papp","submitted_at":"2018-04-10T21:00:52Z","abstract_excerpt":"Consider a distribution of pebbles on a connected graph $G$. A pebbling move removes two pebbles from a vertex and places one to an adjacent vertex. A vertex is reachable under a pebbling distribution if it has a pebble after the application of a sequence of pebbling moves. The optimal pebbling number $\\pi^*(G)$ is the smallest number of pebbles which we can distribute in such a way that each vertex is reachable. It was known that the optimal pebbling number of any connected graph is at most $\\frac{4n}{\\delta+1}$, where $\\delta$ is the minimum degree of the graph. We strengthen this bound by s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03717","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1804.03717","created_at":"2026-05-18T00:18:45.197822+00:00"},{"alias_kind":"arxiv_version","alias_value":"1804.03717v1","created_at":"2026-05-18T00:18:45.197822+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.03717","created_at":"2026-05-18T00:18:45.197822+00:00"},{"alias_kind":"pith_short_12","alias_value":"U7YD3XSTJFNR","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"U7YD3XSTJFNRIJOJ","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"U7YD3XST","created_at":"2026-05-18T12:32:56.356000+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/U7YD3XSTJFNRIJOJ7XESOH7HKY","json":"https://pith.science/pith/U7YD3XSTJFNRIJOJ7XESOH7HKY.json","graph_json":"https://pith.science/api/pith-number/U7YD3XSTJFNRIJOJ7XESOH7HKY/graph.json","events_json":"https://pith.science/api/pith-number/U7YD3XSTJFNRIJOJ7XESOH7HKY/events.json","paper":"https://pith.science/paper/U7YD3XST"},"agent_actions":{"view_html":"https://pith.science/pith/U7YD3XSTJFNRIJOJ7XESOH7HKY","download_json":"https://pith.science/pith/U7YD3XSTJFNRIJOJ7XESOH7HKY.json","view_paper":"https://pith.science/paper/U7YD3XST","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1804.03717&json=true","fetch_graph":"https://pith.science/api/pith-number/U7YD3XSTJFNRIJOJ7XESOH7HKY/graph.json","fetch_events":"https://pith.science/api/pith-number/U7YD3XSTJFNRIJOJ7XESOH7HKY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/U7YD3XSTJFNRIJOJ7XESOH7HKY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/U7YD3XSTJFNRIJOJ7XESOH7HKY/action/storage_attestation","attest_author":"https://pith.science/pith/U7YD3XSTJFNRIJOJ7XESOH7HKY/action/author_attestation","sign_citation":"https://pith.science/pith/U7YD3XSTJFNRIJOJ7XESOH7HKY/action/citation_signature","submit_replication":"https://pith.science/pith/U7YD3XSTJFNRIJOJ7XESOH7HKY/action/replication_record"}},"created_at":"2026-05-18T00:18:45.197822+00:00","updated_at":"2026-05-18T00:18:45.197822+00:00"}