{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HWHZ72GY34YYJZUJV6KLCYXKNK","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":"5929e7ed75ddb3ca45bf2fe932ff8dd1252b5682cece09094e6586764041b97c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-01-30T07:13:09Z","title_canon_sha256":"2b2e1e7845823fc04fa26dd516cc56df5e246a44156a32e9fe8a047f0ddacea8"},"schema_version":"1.0","source":{"id":"1701.08500","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.08500","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"arxiv_version","alias_value":"1701.08500v1","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08500","created_at":"2026-05-18T00:51:29Z"},{"alias_kind":"pith_short_12","alias_value":"HWHZ72GY34YY","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HWHZ72GY34YYJZUJ","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HWHZ72GY","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:b2a11133b4c9c5b0bcec84c47907843d700438d749fb7dcdf4abb5a41e432436","target":"graph","created_at":"2026-05-18T00:51:29Z","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 is an iterative graph coloring process where at each discrete time step, a colored vertex with a single uncolored neighbor forces that neighbor to become colored. The zero forcing number of a graph is the cardinality of the smallest set of initially colored vertices which forces the entire graph to eventually become colored. Connected forcing is a variant of zero forcing in which the initially colored set of vertices induces a connected subgraph; the analogous parameter of interest is the connected forcing number. In this paper, we characterize the graphs with connected forcing nu","authors_text":"Boris Brimkov, Caleb C. Fast, Illya V. Hicks","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-01-30T07:13:09Z","title":"Graphs with Extremal Connected Forcing Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08500","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:aae7cbb63cddde5329e88d7c65f8a0b21b5e85a31e77a7202ee0ce2a878a281d","target":"record","created_at":"2026-05-18T00:51:29Z","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":"5929e7ed75ddb3ca45bf2fe932ff8dd1252b5682cece09094e6586764041b97c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-01-30T07:13:09Z","title_canon_sha256":"2b2e1e7845823fc04fa26dd516cc56df5e246a44156a32e9fe8a047f0ddacea8"},"schema_version":"1.0","source":{"id":"1701.08500","kind":"arxiv","version":1}},"canonical_sha256":"3d8f9fe8d8df3184e689af94b162ea6aa5e9f2adbc97c413e1980d2820e7b2de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d8f9fe8d8df3184e689af94b162ea6aa5e9f2adbc97c413e1980d2820e7b2de","first_computed_at":"2026-05-18T00:51:29.842447Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:29.842447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P/BSZ1t4s1T92SotwUjth/MkQSULgDZgv5Ob2g9JGhOvV7QDyJi2+7vMlVl1V0sGiKUaW/TgZXpobq+5/xYADQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:29.842884Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.08500","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aae7cbb63cddde5329e88d7c65f8a0b21b5e85a31e77a7202ee0ce2a878a281d","sha256:b2a11133b4c9c5b0bcec84c47907843d700438d749fb7dcdf4abb5a41e432436"],"state_sha256":"18d79edc716a63c0f2e52e10945cc0ff7163eae942f7b5ad737fc26870c3facf"}