{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RG4OJML6SVPXZTNDBTX2YQONTR","short_pith_number":"pith:RG4OJML6","canonical_record":{"source":{"id":"1307.2198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-08T18:25:26Z","cross_cats_sorted":[],"title_canon_sha256":"09896007ff4fbad40cd6f4785da3f5aa7760a58e067ea659094fcb0df2e5ac9e","abstract_canon_sha256":"3f06d8fde02565f2baab03dcedde45f8834f580becac9a389c515e1621a822b2"},"schema_version":"1.0"},"canonical_sha256":"89b8e4b17e955f7ccda30cefac41cd9c627b670e54022d02c049fcc2aacf75b1","source":{"kind":"arxiv","id":"1307.2198","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2198","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2198v1","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2198","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"pith_short_12","alias_value":"RG4OJML6SVPX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RG4OJML6SVPXZTND","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RG4OJML6","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RG4OJML6SVPXZTNDBTX2YQONTR","target":"record","payload":{"canonical_record":{"source":{"id":"1307.2198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-08T18:25:26Z","cross_cats_sorted":[],"title_canon_sha256":"09896007ff4fbad40cd6f4785da3f5aa7760a58e067ea659094fcb0df2e5ac9e","abstract_canon_sha256":"3f06d8fde02565f2baab03dcedde45f8834f580becac9a389c515e1621a822b2"},"schema_version":"1.0"},"canonical_sha256":"89b8e4b17e955f7ccda30cefac41cd9c627b670e54022d02c049fcc2aacf75b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:02.116440Z","signature_b64":"lN9jYCp/HibeKBdflbSjZCEQWvSnoQzRS+IbUmNAk6zdLtBhXtRZ5USgXNYUSesrHWPkYbEISdJziAfr18ynDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"89b8e4b17e955f7ccda30cefac41cd9c627b670e54022d02c049fcc2aacf75b1","last_reissued_at":"2026-05-18T03:19:02.115648Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:02.115648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.2198","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":"2026-05-18T03:19:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xmsE/xcAvLolaBkZrB/SlW6iW1zlQNsYePgGrWTH7ZCnzF7IWH44QDqh9RxCuWOt13T9pfUERfph5ejikVABBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:46:23.183446Z"},"content_sha256":"357ed3b42b136af6209b60a5a4e4ba2520558b93d5ca6287e826052380fb9e31","schema_version":"1.0","event_id":"sha256:357ed3b42b136af6209b60a5a4e4ba2520558b93d5ca6287e826052380fb9e31"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RG4OJML6SVPXZTNDBTX2YQONTR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zero forcing for sign patterns","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Abraham Berman, Felix Goldberg","submitted_at":"2013-07-08T18:25:26Z","abstract_excerpt":"We introduce a new variant of zero forcing - signed zero forcing. The classical zero forcing number provides an upper bound on the maximum nullity of a matrix with a given graph (i.e. zero-nonzero pattern). Our new variant provides an analo- gous bound for the maximum nullity of a matrix with a given sign pattern. This allows us to compute, for instance, the maximum nullity of a Z-matrix whose graph is L(K_{n}), the line graph of a clique."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2198","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":"2026-05-18T03:19:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4DakVPpQ8ofAyNUGCbq1dwUQaqwDzD+gTdYMqz3nwGKtrzjDjQMwgNfslRNFuEr9rsdy2nLhmlo0+bjSNyVzAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T06:46:23.184194Z"},"content_sha256":"382b3db628f1e5149262b13d941571d768011be205c14c4008e0beacda44c917","schema_version":"1.0","event_id":"sha256:382b3db628f1e5149262b13d941571d768011be205c14c4008e0beacda44c917"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RG4OJML6SVPXZTNDBTX2YQONTR/bundle.json","state_url":"https://pith.science/pith/RG4OJML6SVPXZTNDBTX2YQONTR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RG4OJML6SVPXZTNDBTX2YQONTR/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":"2026-06-06T06:46:23Z","links":{"resolver":"https://pith.science/pith/RG4OJML6SVPXZTNDBTX2YQONTR","bundle":"https://pith.science/pith/RG4OJML6SVPXZTNDBTX2YQONTR/bundle.json","state":"https://pith.science/pith/RG4OJML6SVPXZTNDBTX2YQONTR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RG4OJML6SVPXZTNDBTX2YQONTR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RG4OJML6SVPXZTNDBTX2YQONTR","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":"3f06d8fde02565f2baab03dcedde45f8834f580becac9a389c515e1621a822b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-08T18:25:26Z","title_canon_sha256":"09896007ff4fbad40cd6f4785da3f5aa7760a58e067ea659094fcb0df2e5ac9e"},"schema_version":"1.0","source":{"id":"1307.2198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.2198","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"arxiv_version","alias_value":"1307.2198v1","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.2198","created_at":"2026-05-18T03:19:02Z"},{"alias_kind":"pith_short_12","alias_value":"RG4OJML6SVPX","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"RG4OJML6SVPXZTND","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"RG4OJML6","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:382b3db628f1e5149262b13d941571d768011be205c14c4008e0beacda44c917","target":"graph","created_at":"2026-05-18T03:19:02Z","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 introduce a new variant of zero forcing - signed zero forcing. The classical zero forcing number provides an upper bound on the maximum nullity of a matrix with a given graph (i.e. zero-nonzero pattern). Our new variant provides an analo- gous bound for the maximum nullity of a matrix with a given sign pattern. This allows us to compute, for instance, the maximum nullity of a Z-matrix whose graph is L(K_{n}), the line graph of a clique.","authors_text":"Abraham Berman, Felix Goldberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-08T18:25:26Z","title":"Zero forcing for sign patterns"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2198","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":"sha256:357ed3b42b136af6209b60a5a4e4ba2520558b93d5ca6287e826052380fb9e31","target":"record","created_at":"2026-05-18T03:19:02Z","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":"3f06d8fde02565f2baab03dcedde45f8834f580becac9a389c515e1621a822b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-07-08T18:25:26Z","title_canon_sha256":"09896007ff4fbad40cd6f4785da3f5aa7760a58e067ea659094fcb0df2e5ac9e"},"schema_version":"1.0","source":{"id":"1307.2198","kind":"arxiv","version":1}},"canonical_sha256":"89b8e4b17e955f7ccda30cefac41cd9c627b670e54022d02c049fcc2aacf75b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"89b8e4b17e955f7ccda30cefac41cd9c627b670e54022d02c049fcc2aacf75b1","first_computed_at":"2026-05-18T03:19:02.115648Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:02.115648Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lN9jYCp/HibeKBdflbSjZCEQWvSnoQzRS+IbUmNAk6zdLtBhXtRZ5USgXNYUSesrHWPkYbEISdJziAfr18ynDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:02.116440Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.2198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:357ed3b42b136af6209b60a5a4e4ba2520558b93d5ca6287e826052380fb9e31","sha256:382b3db628f1e5149262b13d941571d768011be205c14c4008e0beacda44c917"],"state_sha256":"b48004e90bf53a5c8e846f3df84e30501f9f13d8692126114ec0a8a166b977db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4ZjEPSfymGdYeG4pY23nEbkCDOvHkHedWrsptcVDsmmjWIoEnHWfPZJlOuHzBxLFU6KARjdfbc2Od7rnuycmCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T06:46:23.187905Z","bundle_sha256":"3c02f4ea6f5c2bec787143fb3e8da6701930d5109340260f498fdacd548179bf"}}