{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7Y5ZQUYL3TZO52SD23FOPNJIER","short_pith_number":"pith:7Y5ZQUYL","canonical_record":{"source":{"id":"1508.07357","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-28T21:34:47Z","cross_cats_sorted":[],"title_canon_sha256":"ddb43c2c7af722b6d7ba2c74dfa54c15962100ef74a71d9c7bac91b71a1013eb","abstract_canon_sha256":"364ecafa65d7ce387e0cbd3a3ace1af7ba8c2bb559348549e4004785010e0485"},"schema_version":"1.0"},"canonical_sha256":"fe3b98530bdcf2eeea43d6cae7b528245d5b888d481db97b3723e5374572a455","source":{"kind":"arxiv","id":"1508.07357","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07357","created_at":"2026-05-18T01:34:32Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07357v1","created_at":"2026-05-18T01:34:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07357","created_at":"2026-05-18T01:34:32Z"},{"alias_kind":"pith_short_12","alias_value":"7Y5ZQUYL3TZO","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7Y5ZQUYL3TZO52SD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7Y5ZQUYL","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7Y5ZQUYL3TZO52SD23FOPNJIER","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07357","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-28T21:34:47Z","cross_cats_sorted":[],"title_canon_sha256":"ddb43c2c7af722b6d7ba2c74dfa54c15962100ef74a71d9c7bac91b71a1013eb","abstract_canon_sha256":"364ecafa65d7ce387e0cbd3a3ace1af7ba8c2bb559348549e4004785010e0485"},"schema_version":"1.0"},"canonical_sha256":"fe3b98530bdcf2eeea43d6cae7b528245d5b888d481db97b3723e5374572a455","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:32.479780Z","signature_b64":"JS+wPteimeU8AHzUkyI9CapCqgoB4Td0bG/11hvVc+8MuH0YrVFgSSZs4L98xTynz2mwSrrKF2jL81eiLfYaAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fe3b98530bdcf2eeea43d6cae7b528245d5b888d481db97b3723e5374572a455","last_reissued_at":"2026-05-18T01:34:32.479255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:32.479255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07357","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":"2026-05-18T01:34:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n7BRQrLxCdfq+vNfiZfX3/RdIibOuzp46dPoGu/zNp8C3DRFcbQjVkK+hRd0+xODgknZJoaiTzAp+SK6VI+aDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:24:18.957565Z"},"content_sha256":"8c611ddb915dc18e7145f8d636e7f5ef07b6b7d931f5556b06d7d7b59c373fd7","schema_version":"1.0","event_id":"sha256:8c611ddb915dc18e7145f8d636e7f5ef07b6b7d931f5556b06d7d7b59c373fd7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7Y5ZQUYL3TZO52SD23FOPNJIER","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Compressed Cliques Graphs, Clique Coverings and Positive Zero Forcing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abolghasem Soltani, Boting Yang, Karen Meagher, Shaun Fallat","submitted_at":"2015-08-28T21:34:47Z","abstract_excerpt":"Zero forcing parameters, associated with graphs, have been studied for over a decade, and have gained popularity as the number of related applications grows. In particular, it is well-known that such parameters are related to certain vertex coverings. Continuing along these lines, we investigate positive zero forcing within the context of certain clique coverings. A key object considered here is the compressed cliques graph. We study a number of properties associated with the compressed cliques graph, including: uniqueness, forbidden subgraphs, connections to Johnson graphs, and positive zero "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07357","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":"2026-05-18T01:34:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WPeN71H+mUx57YmxdvZDAsf1V8mq+5NyRjlVJe8gq/l8k4x+PfNay/ho4exPB5fUjVJblBDLZwWSvYNIavmUCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T04:24:18.957932Z"},"content_sha256":"84dbc972cdde5fa05f3ba50c860181b66f80c3fba104a9158c83cd607f7fa1e2","schema_version":"1.0","event_id":"sha256:84dbc972cdde5fa05f3ba50c860181b66f80c3fba104a9158c83cd607f7fa1e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7Y5ZQUYL3TZO52SD23FOPNJIER/bundle.json","state_url":"https://pith.science/pith/7Y5ZQUYL3TZO52SD23FOPNJIER/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7Y5ZQUYL3TZO52SD23FOPNJIER/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":"2026-05-25T04:24:18Z","links":{"resolver":"https://pith.science/pith/7Y5ZQUYL3TZO52SD23FOPNJIER","bundle":"https://pith.science/pith/7Y5ZQUYL3TZO52SD23FOPNJIER/bundle.json","state":"https://pith.science/pith/7Y5ZQUYL3TZO52SD23FOPNJIER/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7Y5ZQUYL3TZO52SD23FOPNJIER/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7Y5ZQUYL3TZO52SD23FOPNJIER","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":"364ecafa65d7ce387e0cbd3a3ace1af7ba8c2bb559348549e4004785010e0485","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-28T21:34:47Z","title_canon_sha256":"ddb43c2c7af722b6d7ba2c74dfa54c15962100ef74a71d9c7bac91b71a1013eb"},"schema_version":"1.0","source":{"id":"1508.07357","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07357","created_at":"2026-05-18T01:34:32Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07357v1","created_at":"2026-05-18T01:34:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07357","created_at":"2026-05-18T01:34:32Z"},{"alias_kind":"pith_short_12","alias_value":"7Y5ZQUYL3TZO","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7Y5ZQUYL3TZO52SD","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7Y5ZQUYL","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:84dbc972cdde5fa05f3ba50c860181b66f80c3fba104a9158c83cd607f7fa1e2","target":"graph","created_at":"2026-05-18T01:34:32Z","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":"Zero forcing parameters, associated with graphs, have been studied for over a decade, and have gained popularity as the number of related applications grows. In particular, it is well-known that such parameters are related to certain vertex coverings. Continuing along these lines, we investigate positive zero forcing within the context of certain clique coverings. A key object considered here is the compressed cliques graph. We study a number of properties associated with the compressed cliques graph, including: uniqueness, forbidden subgraphs, connections to Johnson graphs, and positive zero ","authors_text":"Abolghasem Soltani, Boting Yang, Karen Meagher, Shaun Fallat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-28T21:34:47Z","title":"Compressed Cliques Graphs, Clique Coverings and Positive Zero Forcing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07357","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":"sha256:8c611ddb915dc18e7145f8d636e7f5ef07b6b7d931f5556b06d7d7b59c373fd7","target":"record","created_at":"2026-05-18T01:34:32Z","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":"364ecafa65d7ce387e0cbd3a3ace1af7ba8c2bb559348549e4004785010e0485","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-28T21:34:47Z","title_canon_sha256":"ddb43c2c7af722b6d7ba2c74dfa54c15962100ef74a71d9c7bac91b71a1013eb"},"schema_version":"1.0","source":{"id":"1508.07357","kind":"arxiv","version":1}},"canonical_sha256":"fe3b98530bdcf2eeea43d6cae7b528245d5b888d481db97b3723e5374572a455","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe3b98530bdcf2eeea43d6cae7b528245d5b888d481db97b3723e5374572a455","first_computed_at":"2026-05-18T01:34:32.479255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:32.479255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JS+wPteimeU8AHzUkyI9CapCqgoB4Td0bG/11hvVc+8MuH0YrVFgSSZs4L98xTynz2mwSrrKF2jL81eiLfYaAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:32.479780Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07357","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8c611ddb915dc18e7145f8d636e7f5ef07b6b7d931f5556b06d7d7b59c373fd7","sha256:84dbc972cdde5fa05f3ba50c860181b66f80c3fba104a9158c83cd607f7fa1e2"],"state_sha256":"259fb133d52965689f6e3567136f1f7ba9224d946104219a4e859b75f1951b9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t1lxwRSiAtFOkxfWS1lE8Ld31OAyPKMl0oIFWi90i7Tu07nTD4GN3YgM1NXx/TzuVxllfgKR+/GysFjGoltOCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T04:24:18.960744Z","bundle_sha256":"e5bfe4e2829c53ef9c6c9672b44adc26222f55b61c2c07ad928e088d8748812c"}}