{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:N7KLM4WZR3GGEGXQ53MQXGNMUD","short_pith_number":"pith:N7KLM4WZ","canonical_record":{"source":{"id":"1505.02837","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-11T23:57:49Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"70a71c58a573afc51ac85a93666f99dc2ba2e8ba00d961709ad0e85b41ab71d1","abstract_canon_sha256":"a75e2e8c4355095b0ccbbb3b7004e53b20ffcc72a046a7b02d15d88902b0ee35"},"schema_version":"1.0"},"canonical_sha256":"6fd4b672d98ecc621af0eed90b99aca0e6831fcf4b6439fa00acaa7294524d2e","source":{"kind":"arxiv","id":"1505.02837","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02837","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02837v1","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02837","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"N7KLM4WZR3GG","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N7KLM4WZR3GGEGXQ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N7KLM4WZ","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:N7KLM4WZR3GGEGXQ53MQXGNMUD","target":"record","payload":{"canonical_record":{"source":{"id":"1505.02837","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-11T23:57:49Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"70a71c58a573afc51ac85a93666f99dc2ba2e8ba00d961709ad0e85b41ab71d1","abstract_canon_sha256":"a75e2e8c4355095b0ccbbb3b7004e53b20ffcc72a046a7b02d15d88902b0ee35"},"schema_version":"1.0"},"canonical_sha256":"6fd4b672d98ecc621af0eed90b99aca0e6831fcf4b6439fa00acaa7294524d2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:14:15.903806Z","signature_b64":"en3EWJ84wCnucKASMxeAs8GNyU7/aTEIyLz4/PcmySaTO2N0Ja+hUBpPaRQllAeKgQFjUdclls2SXFJbbZT8Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fd4b672d98ecc621af0eed90b99aca0e6831fcf4b6439fa00acaa7294524d2e","last_reissued_at":"2026-05-18T02:14:15.903142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:14:15.903142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1505.02837","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:14:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mmj06yPiKpjVXXD4gWOo82ChJq8j6DDVJ7mIdjF4THSXTl/Cbtjd1GTxZ0JREYd/HTk9yvYxYflN5AqQRwvPAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:00:18.343940Z"},"content_sha256":"03237229aa89f16152fa4dd6fec32dc919579d1c0a899e5b7b55aeab663c6453","schema_version":"1.0","event_id":"sha256:03237229aa89f16152fa4dd6fec32dc919579d1c0a899e5b7b55aeab663c6453"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:N7KLM4WZR3GGEGXQ53MQXGNMUD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Independence complexes of well-covered circulant graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Adam Van Tuyl, Jonathan Earl, Kevin N. Vander Meulen","submitted_at":"2015-05-11T23:57:49Z","abstract_excerpt":"We study the independence complexes of families of well-covered circulant graphs discovered by Boros-Gurvich-Milani\\v{c}, Brown-Hoshino, and Moussi. Because these graphs are well-covered, their independence complexes are pure simplicial complexes. We determine when these pure complexes have extra combinatorial (e.g. vertex decomposable, shellable) or topological (e.g. Cohen-Macaulay, Buchsbaum) structure. We also provide a table of all well-covered circulant graphs on 16 or less vertices, and for each such graph, determine if it is vertex decomposable, shellable, Cohen-Macaulay, and/or Buchsba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02837","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:14:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QybSAr2Zys9DPKsKk04nCvnCrKHofc7+gilqfMoURxFQQPId6I+dKXY9hQcMxdedDC5E93t8MOtcW4ZtDyNFCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T15:00:18.344287Z"},"content_sha256":"d14020c8457eea394bcf1db9241c51b365bdf6095570d02ceca9e2c59dd60e54","schema_version":"1.0","event_id":"sha256:d14020c8457eea394bcf1db9241c51b365bdf6095570d02ceca9e2c59dd60e54"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7KLM4WZR3GGEGXQ53MQXGNMUD/bundle.json","state_url":"https://pith.science/pith/N7KLM4WZR3GGEGXQ53MQXGNMUD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7KLM4WZR3GGEGXQ53MQXGNMUD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T15:00:18Z","links":{"resolver":"https://pith.science/pith/N7KLM4WZR3GGEGXQ53MQXGNMUD","bundle":"https://pith.science/pith/N7KLM4WZR3GGEGXQ53MQXGNMUD/bundle.json","state":"https://pith.science/pith/N7KLM4WZR3GGEGXQ53MQXGNMUD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7KLM4WZR3GGEGXQ53MQXGNMUD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:N7KLM4WZR3GGEGXQ53MQXGNMUD","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":"a75e2e8c4355095b0ccbbb3b7004e53b20ffcc72a046a7b02d15d88902b0ee35","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-11T23:57:49Z","title_canon_sha256":"70a71c58a573afc51ac85a93666f99dc2ba2e8ba00d961709ad0e85b41ab71d1"},"schema_version":"1.0","source":{"id":"1505.02837","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1505.02837","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"arxiv_version","alias_value":"1505.02837v1","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02837","created_at":"2026-05-18T02:14:15Z"},{"alias_kind":"pith_short_12","alias_value":"N7KLM4WZR3GG","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"N7KLM4WZR3GGEGXQ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"N7KLM4WZ","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:d14020c8457eea394bcf1db9241c51b365bdf6095570d02ceca9e2c59dd60e54","target":"graph","created_at":"2026-05-18T02:14:15Z","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 study the independence complexes of families of well-covered circulant graphs discovered by Boros-Gurvich-Milani\\v{c}, Brown-Hoshino, and Moussi. Because these graphs are well-covered, their independence complexes are pure simplicial complexes. We determine when these pure complexes have extra combinatorial (e.g. vertex decomposable, shellable) or topological (e.g. Cohen-Macaulay, Buchsbaum) structure. We also provide a table of all well-covered circulant graphs on 16 or less vertices, and for each such graph, determine if it is vertex decomposable, shellable, Cohen-Macaulay, and/or Buchsba","authors_text":"Adam Van Tuyl, Jonathan Earl, Kevin N. Vander Meulen","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-11T23:57:49Z","title":"Independence complexes of well-covered circulant graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02837","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":"sha256:03237229aa89f16152fa4dd6fec32dc919579d1c0a899e5b7b55aeab663c6453","target":"record","created_at":"2026-05-18T02:14:15Z","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":"a75e2e8c4355095b0ccbbb3b7004e53b20ffcc72a046a7b02d15d88902b0ee35","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-05-11T23:57:49Z","title_canon_sha256":"70a71c58a573afc51ac85a93666f99dc2ba2e8ba00d961709ad0e85b41ab71d1"},"schema_version":"1.0","source":{"id":"1505.02837","kind":"arxiv","version":1}},"canonical_sha256":"6fd4b672d98ecc621af0eed90b99aca0e6831fcf4b6439fa00acaa7294524d2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fd4b672d98ecc621af0eed90b99aca0e6831fcf4b6439fa00acaa7294524d2e","first_computed_at":"2026-05-18T02:14:15.903142Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:14:15.903142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"en3EWJ84wCnucKASMxeAs8GNyU7/aTEIyLz4/PcmySaTO2N0Ja+hUBpPaRQllAeKgQFjUdclls2SXFJbbZT8Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:14:15.903806Z","signed_message":"canonical_sha256_bytes"},"source_id":"1505.02837","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:03237229aa89f16152fa4dd6fec32dc919579d1c0a899e5b7b55aeab663c6453","sha256:d14020c8457eea394bcf1db9241c51b365bdf6095570d02ceca9e2c59dd60e54"],"state_sha256":"1d72bf4204650e072504a99457d70ce296b4002e825dfcd715bea5306e0192f4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y6LpycpeWsSjBzAX7IttDjSr31xpb8fvQE/7DGRbVwG2M3d78XIXy6oDePUJvZgMJj6fIaDhtMSu+Y/GBI3BDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T15:00:18.346584Z","bundle_sha256":"0260c29457e2e60cfc528183ed44021f5878cae4a35f96f244eb0c91e494d78b"}}