{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:QI6SLHQZHSLFU5Z6NSR6UFAVZC","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":"12ab5d21001167a2d0c14da1d9ba0dd28d3a2e24f7616fe6e385cfd5bff9630f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-04T14:33:31Z","title_canon_sha256":"a1da96e6b85aa05d6b42c634465af2048cf69c54be1125c8cb6f166565e1863b"},"schema_version":"1.0","source":{"id":"1411.0923","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.0923","created_at":"2026-05-18T00:36:41Z"},{"alias_kind":"arxiv_version","alias_value":"1411.0923v2","created_at":"2026-05-18T00:36:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.0923","created_at":"2026-05-18T00:36:41Z"},{"alias_kind":"pith_short_12","alias_value":"QI6SLHQZHSLF","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"QI6SLHQZHSLFU5Z6","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"QI6SLHQZ","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:9c614837012d5197a50736d3fc3b9173020c34eece608dd8d0d632e1d01d9772","target":"graph","created_at":"2026-05-18T00:36:41Z","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":"A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move, one pebble each is removed at vertices $v$ and $w$ adjacent to a vertex $u$, and an extra pebble is added at vertex $u$. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using rubbling moves. The optimal rubbling number is the smallest number $m$ needed to guarantee a pebble distribution of $m$ pebbles from which any vertex is reachable. We determine the op","authors_text":"Gyula Y. Katona, L\\'aszl\\'o F. Papp","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-04T14:33:31Z","title":"The Optimal Rubbling Number of Ladders, Prisms and M\\\"obius-ladders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.0923","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":"sha256:46cbf600d6f2b35114e8ee8cb742504d97ef4a527191871c795dd7101f46eacd","target":"record","created_at":"2026-05-18T00:36:41Z","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":"12ab5d21001167a2d0c14da1d9ba0dd28d3a2e24f7616fe6e385cfd5bff9630f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-11-04T14:33:31Z","title_canon_sha256":"a1da96e6b85aa05d6b42c634465af2048cf69c54be1125c8cb6f166565e1863b"},"schema_version":"1.0","source":{"id":"1411.0923","kind":"arxiv","version":2}},"canonical_sha256":"823d259e193c965a773e6ca3ea1415c8af1885288aede3b5c04249a537174e2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"823d259e193c965a773e6ca3ea1415c8af1885288aede3b5c04249a537174e2d","first_computed_at":"2026-05-18T00:36:41.739417Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:41.739417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9nHkj2CXMZlPTL1UDwzQkBb1Kzom/RbQHfZf1Qa83ibrlobWigUJR+soVHzs/eethgzDqGlTmu8fwYRs8M8jBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:41.739881Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.0923","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46cbf600d6f2b35114e8ee8cb742504d97ef4a527191871c795dd7101f46eacd","sha256:9c614837012d5197a50736d3fc3b9173020c34eece608dd8d0d632e1d01d9772"],"state_sha256":"25e740eaef292ccf4c55703a730d3ac7ab21a3f19e8a78f6554ceb0855dc74a5"}