{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HXNSZ5LRYHF6F4HKSFXZMXHFF4","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":"d6214bd52d6762618e2ee1eac9cb03965bcc2751dcaf878b38077be8bd965fd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-04T19:41:17Z","title_canon_sha256":"6ec19337408236c5e5d654da50ddd6ef82f229eee65410cb4e4c2c582987dea6"},"schema_version":"1.0","source":{"id":"1308.0844","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.0844","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"arxiv_version","alias_value":"1308.0844v1","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.0844","created_at":"2026-05-18T03:16:48Z"},{"alias_kind":"pith_short_12","alias_value":"HXNSZ5LRYHF6","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HXNSZ5LRYHF6F4HK","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HXNSZ5LR","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:0be0e7910e291fd556a1fa0b94faabbaf656af6ee058710230001ed0e4ea426f","target":"graph","created_at":"2026-05-18T03:16:48Z","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":"We obtain an explicit analytical sufficient condition on $E$ that ensures the monotonicity of the matrix $M+E$, where $M$ is an $M$-matrix.","authors_text":"Felix Goldberg","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-04T19:41:17Z","title":"On monotonicity-preserving perturbations of $M$-matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.0844","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:ae98e42673f8653a53c3ee68261ff59e6c55026979096496adefceb9024dd8d0","target":"record","created_at":"2026-05-18T03:16:48Z","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":"d6214bd52d6762618e2ee1eac9cb03965bcc2751dcaf878b38077be8bd965fd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-04T19:41:17Z","title_canon_sha256":"6ec19337408236c5e5d654da50ddd6ef82f229eee65410cb4e4c2c582987dea6"},"schema_version":"1.0","source":{"id":"1308.0844","kind":"arxiv","version":1}},"canonical_sha256":"3ddb2cf571c1cbe2f0ea916f965ce52f31ec21313a36f85c031c76f130644501","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3ddb2cf571c1cbe2f0ea916f965ce52f31ec21313a36f85c031c76f130644501","first_computed_at":"2026-05-18T03:16:48.010881Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:16:48.010881Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SAKgQlJnLWJ43b1DGF6puSmyjuDn3OSZixvXbBu5L3YwzIjFGBTlmqYmIX1qHkosWUWR4JUggmJR0u1RUIKhCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:16:48.011584Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.0844","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae98e42673f8653a53c3ee68261ff59e6c55026979096496adefceb9024dd8d0","sha256:0be0e7910e291fd556a1fa0b94faabbaf656af6ee058710230001ed0e4ea426f"],"state_sha256":"1ae08f493de06b0d3e69e9ba80c9b10cd54690dbfc4e76ce21ed26f07396875c"}