{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:4IKYFUYECDFCTZJL6KOS5JKZBA","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":"1becc6949544253326c766d6e04bc1460569f806c860dbc52801d30e1361a0ff","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-30T14:57:41Z","title_canon_sha256":"fd04e9c54949779e9be3c4e6112d22dda652f3285a56540141f336ad7716e080"},"schema_version":"1.0","source":{"id":"1409.0119","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.0119","created_at":"2026-05-18T02:43:53Z"},{"alias_kind":"arxiv_version","alias_value":"1409.0119v1","created_at":"2026-05-18T02:43:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.0119","created_at":"2026-05-18T02:43:53Z"},{"alias_kind":"pith_short_12","alias_value":"4IKYFUYECDFC","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_16","alias_value":"4IKYFUYECDFCTZJL","created_at":"2026-05-18T12:28:14Z"},{"alias_kind":"pith_short_8","alias_value":"4IKYFUYE","created_at":"2026-05-18T12:28:14Z"}],"graph_snapshots":[{"event_id":"sha256:10264e9c22514f1bf416ef8d47aaa03fd5c978c029967dddc16c102e1719f4bf","target":"graph","created_at":"2026-05-18T02:43:53Z","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":"We prove that elements of the Hanoi Towers groups $\\mathcal{H}_m$ have depth bounded from above by a poly-logarithmic function $O(\\log^{m-2} n)$, where $n$ is the length of an element. Therefore the word problem in groups $\\mathcal{H}_m$ is solvable in subexponential time $\\exp(O(\\log^{m-2} n))$.","authors_text":"Ievgen Bondarenko","cross_cats":["cs.FL"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-30T14:57:41Z","title":"The word problem in Hanoi Towers groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0119","kind":"arxiv","version":1},"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":"sha256:9878f62fff9e4bfee1fa1cde2bd63842322d8b9d05224c82aa4ae85da00bb9f8","target":"record","created_at":"2026-05-18T02:43:53Z","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":"1becc6949544253326c766d6e04bc1460569f806c860dbc52801d30e1361a0ff","cross_cats_sorted":["cs.FL"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2014-08-30T14:57:41Z","title_canon_sha256":"fd04e9c54949779e9be3c4e6112d22dda652f3285a56540141f336ad7716e080"},"schema_version":"1.0","source":{"id":"1409.0119","kind":"arxiv","version":1}},"canonical_sha256":"e21582d30410ca29e52bf29d2ea5590811bcb3218c37b53edfa4181f79129f8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e21582d30410ca29e52bf29d2ea5590811bcb3218c37b53edfa4181f79129f8e","first_computed_at":"2026-05-18T02:43:53.306291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:53.306291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xv9LvnWX6S+g5gDch9LiYhwf9s6dZH4Pj6emFheXLv+UXAHsbYmeQwmuDdmUaSTiP9viMzR1TmcE19TrQwj9Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:53.306840Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.0119","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9878f62fff9e4bfee1fa1cde2bd63842322d8b9d05224c82aa4ae85da00bb9f8","sha256:10264e9c22514f1bf416ef8d47aaa03fd5c978c029967dddc16c102e1719f4bf"],"state_sha256":"4b8bb9b7a166811805acb3833098446eb18df3c98b160809914b5e9f49fcb880"}