{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WJOUH2RL4A2UJIVZBVDNHB5UJI","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":"7d273da9836af153d9b27d37c4662234558cba8ee4b21e7b6d1d48215425f07c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-03T11:07:05Z","title_canon_sha256":"486261cf8bf7ee71514d964a048a7bd9a3b93e884dbbc017a9ecc5fcf1097337"},"schema_version":"1.0","source":{"id":"1705.01358","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.01358","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"arxiv_version","alias_value":"1705.01358v1","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.01358","created_at":"2026-05-18T00:45:05Z"},{"alias_kind":"pith_short_12","alias_value":"WJOUH2RL4A2U","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WJOUH2RL4A2UJIVZ","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WJOUH2RL","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:d9803a0acdd08213ae35dd45a117e682aec6d93c19c02e3d56420f53d1243864","target":"graph","created_at":"2026-05-18T00:45:05Z","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":"Let T1, T2,..., Tk be spanning trees in a graph G. If for any pair of vertices {u, v} of G, the paths between u and v in every Ti( 0 < i < k+1) do not contain common edges and common vertices, except the vertices u and v, then T1, T2,..., Tk are called completely independent spanning trees in G. The n-dimensional augmented cube, denoted as AQn, a variation of the hypercube possesses several embeddable properties that the hypercube and its variations do not possess. For AQn (n > 5), construction of 4 completely independent spanning trees of which two trees with diameters 2n - 5 and two trees wi","authors_text":"B. N. Waphare, S. A. Kandekar, S. A. Mane","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-03T11:07:05Z","title":"Construction of Four Completely Independent Spanning Trees on Augmented Cubes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01358","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":"sha256:963afabe9f75c9c0baed08598b818bf1c3ebad0da0abdb45a52850a17fbfc21f","target":"record","created_at":"2026-05-18T00:45:05Z","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":"7d273da9836af153d9b27d37c4662234558cba8ee4b21e7b6d1d48215425f07c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-05-03T11:07:05Z","title_canon_sha256":"486261cf8bf7ee71514d964a048a7bd9a3b93e884dbbc017a9ecc5fcf1097337"},"schema_version":"1.0","source":{"id":"1705.01358","kind":"arxiv","version":1}},"canonical_sha256":"b25d43ea2be03544a2b90d46d387b44a1b0f2d9e5de12bed72b9d360f5f991f5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b25d43ea2be03544a2b90d46d387b44a1b0f2d9e5de12bed72b9d360f5f991f5","first_computed_at":"2026-05-18T00:45:05.337169Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:05.337169Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GoaIVIAQITpvydVpM3sHNXuI2yodjiW1JTGuLTtvUVWq5cgOwpDuh+P3rpYgUDkuC09OmfkMrF3NnZi/mkVEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:05.337564Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.01358","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:963afabe9f75c9c0baed08598b818bf1c3ebad0da0abdb45a52850a17fbfc21f","sha256:d9803a0acdd08213ae35dd45a117e682aec6d93c19c02e3d56420f53d1243864"],"state_sha256":"34f37eda134ee63b5546a87e42988eed9c79cad90a4e60f5afac4f616e86f4f2"}