{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:GARPS3K7ZZPFCUB6N2I2U2O63M","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":"95a7cd3787dae360e3cac448c29c5f6588e3b136ad94ecb3e64feafd01c8eb2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-23T17:46:26Z","title_canon_sha256":"b6c4709b494ea68bf15f310e8e89670ad423c005e963b8b95e4c187f264970fc"},"schema_version":"1.0","source":{"id":"1708.07118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.07118","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1708.07118v1","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.07118","created_at":"2026-05-18T00:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"GARPS3K7ZZPF","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"GARPS3K7ZZPFCUB6","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"GARPS3K7","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:c60ff70ef0704b8d377f55ef5a7ca8847f79c22e89f35ec9c1b0d3ac7361a58a","target":"graph","created_at":"2026-05-18T00:36:48Z","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":"A weighted graph $G^{\\omega}$ consists of a simple graph $G$ with a weight $\\omega$, which is a mapping,$\\omega$: $E(G)\\rightarrow\\mathbb{Z}\\backslash\\{0\\}$. A signed graph is a graph whose edges are labeled with $-1$ or $1$. In this paper, we characterize graphs which have a sign such that their signed adjacency matrix has full rank, and graphs which have a weight such that their weighted adjacency matrix does not have full rank. We show that for any arbitrary simple graph $G$, there is a sign $\\sigma$ so that $G^{\\sigma}$ has full rank if and only if $G$ has a $\\{1,2\\}$-factor. We also show ","authors_text":"A. Ghafari, K. Kazemian, M. Nahvi, S. Akbari","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-23T17:46:26Z","title":"Some Criteria for a Signed Graph to Have Full Rank"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07118","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":"sha256:4bd3f6e5884789f6ea7cea6f494708ef92db8cbeddc047416940b2e08ec946b5","target":"record","created_at":"2026-05-18T00:36:48Z","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":"95a7cd3787dae360e3cac448c29c5f6588e3b136ad94ecb3e64feafd01c8eb2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-08-23T17:46:26Z","title_canon_sha256":"b6c4709b494ea68bf15f310e8e89670ad423c005e963b8b95e4c187f264970fc"},"schema_version":"1.0","source":{"id":"1708.07118","kind":"arxiv","version":1}},"canonical_sha256":"3022f96d5fce5e51503e6e91aa69dedb3f5c7c6b6db4ec7d933e64964d1e9d3e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3022f96d5fce5e51503e6e91aa69dedb3f5c7c6b6db4ec7d933e64964d1e9d3e","first_computed_at":"2026-05-18T00:36:48.354187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:48.354187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PuSoPievuO4MmR8FkUKurQMDRkrn8YXzrliDRRePam4nreExaHVjBdJVlZZF29DLINqDIMo/sTIxhGq5pGB+Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:48.354851Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.07118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4bd3f6e5884789f6ea7cea6f494708ef92db8cbeddc047416940b2e08ec946b5","sha256:c60ff70ef0704b8d377f55ef5a7ca8847f79c22e89f35ec9c1b0d3ac7361a58a"],"state_sha256":"08e88337514ed461fd0cd5f842acbb9652ce0d1fa08444561dce5170ff50357a"}