{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HSQDKAW7UQ5NPE4CVU5O3Y4ATI","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":"acd3bdaeef92202b749c56a566f3d25d42fe9ba88bcc4caccefad483d6e22045","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-10-20T18:43:24Z","title_canon_sha256":"695bb0d09619f9783351de14f5d8a44ba48203902cff8d244c8e2a3af26b6411"},"schema_version":"1.0","source":{"id":"2510.18010","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2510.18010","created_at":"2026-06-29T00:14:00Z"},{"alias_kind":"arxiv_version","alias_value":"2510.18010v2","created_at":"2026-06-29T00:14:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.18010","created_at":"2026-06-29T00:14:00Z"},{"alias_kind":"pith_short_12","alias_value":"HSQDKAW7UQ5N","created_at":"2026-06-29T00:14:00Z"},{"alias_kind":"pith_short_16","alias_value":"HSQDKAW7UQ5NPE4C","created_at":"2026-06-29T00:14:00Z"},{"alias_kind":"pith_short_8","alias_value":"HSQDKAW7","created_at":"2026-06-29T00:14:00Z"}],"graph_snapshots":[{"event_id":"sha256:7d9f83885990e842102648761b2a03a72e3d9036706e387f51559d5e0eb933d2","target":"graph","created_at":"2026-06-29T00:14:00Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2510.18010/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The famous Tower of Hanoi puzzle involves moving $n$ discs of distinct sizes from one of $p\\geq 3$ pegs (traditionally $p=3$) to another of the pegs, subject to the constraints that only one disc may be moved at a time, and no disc can ever be placed on a disc smaller than itself. Much is known about the Hanoi graph $H_p^n$, whose $p^n$ vertices represent the configurations of the puzzle, and whose edges represent the pairs of configurations separated by a single legal move. In a previous paper, the present authors presented nearly tight asymptotic bounds of $O((p-2)^n)$ and $\\Omega(n^{(1-p)/2","authors_text":"Daniel Frishberg, David Eppstein, William Maxwell","cross_cats":["cs.DM"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-10-20T18:43:24Z","title":"On the expansion of Hanoi graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.18010","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":"sha256:7003fb48836966db411378ff41ba02a939355c5e70c2c4293279efed1c83a0fc","target":"record","created_at":"2026-06-29T00:14:00Z","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":"acd3bdaeef92202b749c56a566f3d25d42fe9ba88bcc4caccefad483d6e22045","cross_cats_sorted":["cs.DM"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-10-20T18:43:24Z","title_canon_sha256":"695bb0d09619f9783351de14f5d8a44ba48203902cff8d244c8e2a3af26b6411"},"schema_version":"1.0","source":{"id":"2510.18010","kind":"arxiv","version":2}},"canonical_sha256":"3ca03502dfa43ad79382ad3aede3809a204d953b17c57f96415f98b852179d7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ca03502dfa43ad79382ad3aede3809a204d953b17c57f96415f98b852179d7b","first_computed_at":"2026-06-29T00:14:00.609219Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-29T00:14:00.609219Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JPyIw45khdYzAtp/CwGUbUKA2hpqwcR6s2kd8oIjUdEHWnkZLzrWfrBB+zDxPb4xwsiusF9eghrlXYqfcNo1Cg==","signature_status":"signed_v1","signed_at":"2026-06-29T00:14:00.609682Z","signed_message":"canonical_sha256_bytes"},"source_id":"2510.18010","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7003fb48836966db411378ff41ba02a939355c5e70c2c4293279efed1c83a0fc","sha256:7d9f83885990e842102648761b2a03a72e3d9036706e387f51559d5e0eb933d2"],"state_sha256":"3204e1a656eee506284969fb2ad57ee98e062e5c2470dc04b0b81fb7d4e45ff8"}