{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:C6N74KZDOBTYOAD27T4M3IF4GZ","short_pith_number":"pith:C6N74KZD","schema_version":"1.0","canonical_sha256":"179bfe2b23706787007afcf8cda0bc366702e0b2d52daabce51a88d967372d75","source":{"kind":"arxiv","id":"1809.02582","version":1},"attestation_state":"computed","paper":{"title":"Pebbling on Directed Graphs with Fixed Diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Franklin Kenter, John Asplund","submitted_at":"2018-09-07T17:15:38Z","abstract_excerpt":"Pebbling is a game played on a graph. The single player is given a graph and a configuration of pebbles and may make pebbling moves by removing 2 pebbles from one vertex and placing one at an adjacent vertex to eventually have one pebble reach a predetermined vertex. The pebbling number, $\\pi(G)$, is the minimum number of pebbles such that regardless of their exact configuration, the player can use pebbling moves to have a pebble reach any predetermined vertex.\n  Previous work has related $\\pi(G)$ to the diameter of $G$. Clarke, Hochberg, and Hurlbert demonstrated that every connected undirect"},"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":"1809.02582","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-09-07T17:15:38Z","cross_cats_sorted":[],"title_canon_sha256":"ff72b3b841f0feefdff08ea7755011a02a1dbe45d65001e97dda46a00965a8fa","abstract_canon_sha256":"5b793c05a6acf9f9ea6873b59932c0a8d24eb6e8a5d63af95dddef7425e089b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:16.699942Z","signature_b64":"G7zo37dndgYvm0nQRJtgP0pSrKmHzKxTpBPNkwf7J4I+03ZqH5f5Fe8A4PwH2nMTZkYcHyEXE2uOnkP3bsnUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"179bfe2b23706787007afcf8cda0bc366702e0b2d52daabce51a88d967372d75","last_reissued_at":"2026-05-18T00:06:16.699336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:16.699336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Pebbling on Directed Graphs with Fixed Diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Franklin Kenter, John Asplund","submitted_at":"2018-09-07T17:15:38Z","abstract_excerpt":"Pebbling is a game played on a graph. The single player is given a graph and a configuration of pebbles and may make pebbling moves by removing 2 pebbles from one vertex and placing one at an adjacent vertex to eventually have one pebble reach a predetermined vertex. The pebbling number, $\\pi(G)$, is the minimum number of pebbles such that regardless of their exact configuration, the player can use pebbling moves to have a pebble reach any predetermined vertex.\n  Previous work has related $\\pi(G)$ to the diameter of $G$. Clarke, Hochberg, and Hurlbert demonstrated that every connected undirect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.02582","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":"1809.02582","created_at":"2026-05-18T00:06:16.699438+00:00"},{"alias_kind":"arxiv_version","alias_value":"1809.02582v1","created_at":"2026-05-18T00:06:16.699438+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.02582","created_at":"2026-05-18T00:06:16.699438+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6N74KZDOBTY","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6N74KZDOBTYOAD2","created_at":"2026-05-18T12:32:16.446611+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6N74KZD","created_at":"2026-05-18T12:32:16.446611+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/C6N74KZDOBTYOAD27T4M3IF4GZ","json":"https://pith.science/pith/C6N74KZDOBTYOAD27T4M3IF4GZ.json","graph_json":"https://pith.science/api/pith-number/C6N74KZDOBTYOAD27T4M3IF4GZ/graph.json","events_json":"https://pith.science/api/pith-number/C6N74KZDOBTYOAD27T4M3IF4GZ/events.json","paper":"https://pith.science/paper/C6N74KZD"},"agent_actions":{"view_html":"https://pith.science/pith/C6N74KZDOBTYOAD27T4M3IF4GZ","download_json":"https://pith.science/pith/C6N74KZDOBTYOAD27T4M3IF4GZ.json","view_paper":"https://pith.science/paper/C6N74KZD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1809.02582&json=true","fetch_graph":"https://pith.science/api/pith-number/C6N74KZDOBTYOAD27T4M3IF4GZ/graph.json","fetch_events":"https://pith.science/api/pith-number/C6N74KZDOBTYOAD27T4M3IF4GZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6N74KZDOBTYOAD27T4M3IF4GZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6N74KZDOBTYOAD27T4M3IF4GZ/action/storage_attestation","attest_author":"https://pith.science/pith/C6N74KZDOBTYOAD27T4M3IF4GZ/action/author_attestation","sign_citation":"https://pith.science/pith/C6N74KZDOBTYOAD27T4M3IF4GZ/action/citation_signature","submit_replication":"https://pith.science/pith/C6N74KZDOBTYOAD27T4M3IF4GZ/action/replication_record"}},"created_at":"2026-05-18T00:06:16.699438+00:00","updated_at":"2026-05-18T00:06:16.699438+00:00"}