{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:OQQ4UJRINE343JSILYRYEBS2KP","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":"debbdb68773d5ed0a14d7deea31ad033be924f91397fa6c95f6724ea395bf20e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-30T09:24:45Z","title_canon_sha256":"535c94deabb5c4ca597d498533c304182520922ac35f60a17919fe7bc0405d4a"},"schema_version":"1.0","source":{"id":"1804.11094","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.11094","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"arxiv_version","alias_value":"1804.11094v1","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.11094","created_at":"2026-05-18T00:17:14Z"},{"alias_kind":"pith_short_12","alias_value":"OQQ4UJRINE34","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"OQQ4UJRINE343JSI","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"OQQ4UJRI","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:de0a519c1bcd3f886dd2c35d09bf1312682090af22ebfe4cba9bfed84f7650f5","target":"graph","created_at":"2026-05-18T00:17:14Z","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":"An Any graph obtained by deleting a Hamming code of length n from a n-cube Qn is called as a Hamming shell. It is well known that a Hamming shell is vertex-transitive, edge-transitive, distance preserving. Moreover, it is Hamiltonian and connected. In this paper, we prove that a Hamming shell is edge-bipancyclic and (n-1)-connected.","authors_text":"B. N. Waphare, S. A. Mane","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-30T09:24:45Z","title":"Connectivity and edge-bipancyclicity of hamming shell"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11094","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":"sha256:2e65cca858e5061b208c6bf9336987eb752f68fe31954e509a561ecb1dc6aea3","target":"record","created_at":"2026-05-18T00:17:14Z","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":"debbdb68773d5ed0a14d7deea31ad033be924f91397fa6c95f6724ea395bf20e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-30T09:24:45Z","title_canon_sha256":"535c94deabb5c4ca597d498533c304182520922ac35f60a17919fe7bc0405d4a"},"schema_version":"1.0","source":{"id":"1804.11094","kind":"arxiv","version":1}},"canonical_sha256":"7421ca26286937cda6485e2382065a53fd346af64b3ad11e836e62ccd96da397","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7421ca26286937cda6485e2382065a53fd346af64b3ad11e836e62ccd96da397","first_computed_at":"2026-05-18T00:17:14.633604Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:14.633604Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZRLY+jb4HSiaMVK/bWmp4GEwGNwE+WH0WT8/0vE6Cb62jUIWziG/sW31w0Cg+UhDNYNBl+y2LNing19eD4ejBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:14.634313Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.11094","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2e65cca858e5061b208c6bf9336987eb752f68fe31954e509a561ecb1dc6aea3","sha256:de0a519c1bcd3f886dd2c35d09bf1312682090af22ebfe4cba9bfed84f7650f5"],"state_sha256":"3eeed9c401db03d18b3309426cf0e12aed00705942de610aa39e8024c2a5dab7"}