{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:N2CQURUGNGUNZURNUDOF2ATITM","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":"97f19b14c2574606165fdf7bd50027677f13f6804870a0b6c65c4f68a97d1b11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-19T22:53:10Z","title_canon_sha256":"d3f57402a46859c7b58f3e527de43f0ace26c48038031a7d707c17751399c175"},"schema_version":"1.0","source":{"id":"1211.4618","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.4618","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"arxiv_version","alias_value":"1211.4618v1","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.4618","created_at":"2026-05-18T03:40:26Z"},{"alias_kind":"pith_short_12","alias_value":"N2CQURUGNGUN","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N2CQURUGNGUNZURN","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N2CQURUG","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:fbebc5e61117522d10aafbd09b5325d5445a35a2be40b8fb03a2a332f883001b","target":"graph","created_at":"2026-05-18T03:40:26Z","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 a combinatorial game played on a graph with a goal of turning all of the vertices of the graph black while having to use as few \"unforced\" moves as possible. This leads to a parameter known as the zero forcing number which can be used to give an upper bound for the maximum nullity of a matrix associated with the graph.\n  We introduce a new variation on the zero forcing game which can be used to give an upper bound for the maximum nullity of a matrix associated with a graph that has $q$ negative eigenvalues. This gives some limits to the number of positive eigenvalues that such ","authors_text":"H. Tracy Hall, Jason Grout, Steve Butler","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-19T22:53:10Z","title":"Zero forcing for inertia sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.4618","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":"sha256:2cef624067d5da9022a7f68d30c417304d3890f91cd77b40ab0d5a358e72c4e1","target":"record","created_at":"2026-05-18T03:40:26Z","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":"97f19b14c2574606165fdf7bd50027677f13f6804870a0b6c65c4f68a97d1b11","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-11-19T22:53:10Z","title_canon_sha256":"d3f57402a46859c7b58f3e527de43f0ace26c48038031a7d707c17751399c175"},"schema_version":"1.0","source":{"id":"1211.4618","kind":"arxiv","version":1}},"canonical_sha256":"6e850a468669a8dcd22da0dc5d02689b066700eebb9bd0c2cea6a2b3b5e4fbe0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e850a468669a8dcd22da0dc5d02689b066700eebb9bd0c2cea6a2b3b5e4fbe0","first_computed_at":"2026-05-18T03:40:26.179490Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:26.179490Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2/ccNfTWFTHlgje+31lYZQjON5/cciiIJD3OmQhXefjyggvp90uu2Z9+smyWDp19fT7ablUTWRTbaeN4eaXEDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:26.180010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.4618","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2cef624067d5da9022a7f68d30c417304d3890f91cd77b40ab0d5a358e72c4e1","sha256:fbebc5e61117522d10aafbd09b5325d5445a35a2be40b8fb03a2a332f883001b"],"state_sha256":"ff0835b029fd14c560d696b0603cf7a79e18d184fcda657a9c52fd11d55a6c65"}