{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:32HVKIU5CQD2J3EVDW6MVZ7LKI","short_pith_number":"pith:32HVKIU5","schema_version":"1.0","canonical_sha256":"de8f55229d1407a4ec951dbccae7eb52338f4f2a8861ce8f2b5e03fccd0b8e30","source":{"kind":"arxiv","id":"math/0510045","version":1},"attestation_state":"computed","paper":{"title":"Improved Pebbling Bounds","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anant P. Godbole, Melody Chan","submitted_at":"2005-10-03T13:59:59Z","abstract_excerpt":"Consider a configuration of pebbles distributed on the vertices of a connected graph of order $n$. A pebbling step consists of removing two pebbles from a given vertex and placing one pebble on an adjacent vertex. A distribution of pebbles on a graph is called solvable if it is possible to place a pebble on any given vertex using a sequence of pebbling steps. The pebbling number of a graph, denoted $f(G)$, is the minimal number of pebbles such that every configuration of $f(G)$ pebbles on $G$ is solvable. We derive several general upper bounds on the pebbling number, improving previous results"},"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":"math/0510045","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2005-10-03T13:59:59Z","cross_cats_sorted":[],"title_canon_sha256":"49d2a1ce9d3be536560303c49d1ff47692fd4f568cb8f1ef490910744890aaad","abstract_canon_sha256":"5776f844e859889d5aa0cfd7b173465f1d1e38469834dd512c39a937cafb34b3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:04.814599Z","signature_b64":"TkI9en6TlHR3RQ4yEc6trHCbTaVmVfoJzGlnbfDrpsG5kpz9xn98z3Z1UL5Obd9La8Td6IG6E6OoBcBCNLutBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de8f55229d1407a4ec951dbccae7eb52338f4f2a8861ce8f2b5e03fccd0b8e30","last_reissued_at":"2026-05-18T03:58:04.813991Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:04.813991Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Improved Pebbling Bounds","license":"","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Anant P. Godbole, Melody Chan","submitted_at":"2005-10-03T13:59:59Z","abstract_excerpt":"Consider a configuration of pebbles distributed on the vertices of a connected graph of order $n$. A pebbling step consists of removing two pebbles from a given vertex and placing one pebble on an adjacent vertex. A distribution of pebbles on a graph is called solvable if it is possible to place a pebble on any given vertex using a sequence of pebbling steps. The pebbling number of a graph, denoted $f(G)$, is the minimal number of pebbles such that every configuration of $f(G)$ pebbles on $G$ is solvable. We derive several general upper bounds on the pebbling number, improving previous results"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510045","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":"math/0510045","created_at":"2026-05-18T03:58:04.814079+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0510045v1","created_at":"2026-05-18T03:58:04.814079+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510045","created_at":"2026-05-18T03:58:04.814079+00:00"},{"alias_kind":"pith_short_12","alias_value":"32HVKIU5CQD2","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"32HVKIU5CQD2J3EV","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"32HVKIU5","created_at":"2026-05-18T12:25:52.687210+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/32HVKIU5CQD2J3EVDW6MVZ7LKI","json":"https://pith.science/pith/32HVKIU5CQD2J3EVDW6MVZ7LKI.json","graph_json":"https://pith.science/api/pith-number/32HVKIU5CQD2J3EVDW6MVZ7LKI/graph.json","events_json":"https://pith.science/api/pith-number/32HVKIU5CQD2J3EVDW6MVZ7LKI/events.json","paper":"https://pith.science/paper/32HVKIU5"},"agent_actions":{"view_html":"https://pith.science/pith/32HVKIU5CQD2J3EVDW6MVZ7LKI","download_json":"https://pith.science/pith/32HVKIU5CQD2J3EVDW6MVZ7LKI.json","view_paper":"https://pith.science/paper/32HVKIU5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0510045&json=true","fetch_graph":"https://pith.science/api/pith-number/32HVKIU5CQD2J3EVDW6MVZ7LKI/graph.json","fetch_events":"https://pith.science/api/pith-number/32HVKIU5CQD2J3EVDW6MVZ7LKI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/32HVKIU5CQD2J3EVDW6MVZ7LKI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/32HVKIU5CQD2J3EVDW6MVZ7LKI/action/storage_attestation","attest_author":"https://pith.science/pith/32HVKIU5CQD2J3EVDW6MVZ7LKI/action/author_attestation","sign_citation":"https://pith.science/pith/32HVKIU5CQD2J3EVDW6MVZ7LKI/action/citation_signature","submit_replication":"https://pith.science/pith/32HVKIU5CQD2J3EVDW6MVZ7LKI/action/replication_record"}},"created_at":"2026-05-18T03:58:04.814079+00:00","updated_at":"2026-05-18T03:58:04.814079+00:00"}