{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UCWZTBTU2JQEV7YWFYGEHOW2CW","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":"c6bf0a31c5c4483dfa0d3511765572f5474c932369628a935d1ca91063c51865","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-12T15:08:52Z","title_canon_sha256":"24a37a2716334eceb5197a990d233cbe27fe3c4fced1a1a128adf74e30e93653"},"schema_version":"1.0","source":{"id":"1601.02896","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.02896","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"arxiv_version","alias_value":"1601.02896v2","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.02896","created_at":"2026-05-18T01:04:50Z"},{"alias_kind":"pith_short_12","alias_value":"UCWZTBTU2JQE","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UCWZTBTU2JQEV7YW","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UCWZTBTU","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:1aa73842e15cbd8c4bb42bbb572480bc080fdc498cb9cfbc135fbf3f8f17c7b5","target":"graph","created_at":"2026-05-18T01:04:50Z","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 define what appears to be a new construction. Given a graph $G$ and a positive integer $k$, the reduced $k$th power of $G$, denoted $G^{(k)}$, is the configuration space in which $k$ indistinguishable tokens are placed on the vertices of $G$, so that any vertex can hold up to $k$ tokens. Two configurations are adjacent if one can be transformed to the other by moving a single token along an edge to an adjacent vertex.\n  The reduced power $G^{(k)}$ is the transition graph of the master Markov chain for $k$ identical and indistinguishable stochastic automata with transition graph $G$. We pres","authors_text":"Gregory D. Smith, Richard H. Hammack","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-12T15:08:52Z","title":"Cycle bases of reduced powers of graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02896","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:de103d020bab1f98d0dcc939c0ad8fd3467511d15e94463d15e469866e92b35e","target":"record","created_at":"2026-05-18T01:04:50Z","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":"c6bf0a31c5c4483dfa0d3511765572f5474c932369628a935d1ca91063c51865","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-01-12T15:08:52Z","title_canon_sha256":"24a37a2716334eceb5197a990d233cbe27fe3c4fced1a1a128adf74e30e93653"},"schema_version":"1.0","source":{"id":"1601.02896","kind":"arxiv","version":2}},"canonical_sha256":"a0ad998674d2604aff162e0c43bada15ae7304c36fb7a6f414fd877568641606","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0ad998674d2604aff162e0c43bada15ae7304c36fb7a6f414fd877568641606","first_computed_at":"2026-05-18T01:04:50.201908Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:50.201908Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"waz/OwuGZfuh5hQJ7NI83QplDZ7cIw1kvvcgNmtOwK4UhEWJEEqwu+ephuCJfk6UrW4XAtpXEPEFJVkaUxuyBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:50.202303Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.02896","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de103d020bab1f98d0dcc939c0ad8fd3467511d15e94463d15e469866e92b35e","sha256:1aa73842e15cbd8c4bb42bbb572480bc080fdc498cb9cfbc135fbf3f8f17c7b5"],"state_sha256":"d85148655fa43d7e41101bfad12c0cad284f4cd64841221b335a48d11414b1e2"}