{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:GBVOAIPTVTMB32FIUJKLJJB62Q","short_pith_number":"pith:GBVOAIPT","canonical_record":{"source":{"id":"1308.4308","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-08-20T13:47:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4c73dabf0901c413cb52672624f93a9a61697c0ba29fe610540e2d225ccdaa34","abstract_canon_sha256":"361cce26ce5101fb4a0d09e187488d829e60f683876d7d9d5d640fc5c193d220"},"schema_version":"1.0"},"canonical_sha256":"306ae021f3acd81de8a8a254b4a43ed40ee250898a437e0d2a037b8dd6c736b1","source":{"kind":"arxiv","id":"1308.4308","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4308","created_at":"2026-05-18T01:10:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4308v3","created_at":"2026-05-18T01:10:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4308","created_at":"2026-05-18T01:10:38Z"},{"alias_kind":"pith_short_12","alias_value":"GBVOAIPTVTMB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GBVOAIPTVTMB32FI","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GBVOAIPT","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:GBVOAIPTVTMB32FIUJKLJJB62Q","target":"record","payload":{"canonical_record":{"source":{"id":"1308.4308","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-08-20T13:47:08Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4c73dabf0901c413cb52672624f93a9a61697c0ba29fe610540e2d225ccdaa34","abstract_canon_sha256":"361cce26ce5101fb4a0d09e187488d829e60f683876d7d9d5d640fc5c193d220"},"schema_version":"1.0"},"canonical_sha256":"306ae021f3acd81de8a8a254b4a43ed40ee250898a437e0d2a037b8dd6c736b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:38.960616Z","signature_b64":"kwAD3Zznb3x6xL41ZQmhsRxk0G0JWjNfVhG+zGrDcOb7NFdi6dnAIWgkwl8v2iZYawVzXXobi/8AYzmAM3/mDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"306ae021f3acd81de8a8a254b4a43ed40ee250898a437e0d2a037b8dd6c736b1","last_reissued_at":"2026-05-18T01:10:38.960146Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:38.960146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1308.4308","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:10:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y/QIQFs0GmfhELGmrF6ZKuWbyxAj4l0o+TyzIF9dIy9maj8bYE0Zm1+F9Ap1sKSIkF7Nw5VUOPujCvZQH+VcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:31:15.619182Z"},"content_sha256":"725f71360eca7695a745be559836e09873a6df7882afc9af1addf6edc0ba41d7","schema_version":"1.0","event_id":"sha256:725f71360eca7695a745be559836e09873a6df7882afc9af1addf6edc0ba41d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:GBVOAIPTVTMB32FIUJKLJJB62Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Toric ideals and diagonal 2-minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Anargyros Katsabekis","submitted_at":"2013-08-20T13:47:08Z","abstract_excerpt":"Let $G$ be a simple graph on the vertex set $\\{1,\\ldots,n\\}$ with $m$ edges. An algebraic object attached to $G$ is the ideal $P_{G}$ generated by diagonal 2-minors of an $n \\times n$ matrix of variables. In this paper we prove that if $G$ is bipartite, then every initial ideal of $P_{G}$ is generated by squarefree monomials of degree at most $\\left \\lfloor{\\frac{m+n+1}{2}} \\right \\rfloor$. Furthermore, we completely characterize all connected graphs $G$ for which $P_{G}$ is the toric ideal associated to a finite simple graph. Finally we compute in certain cases the universal Gr{\\\"o}bner basis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4308","kind":"arxiv","version":3},"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":"2026-05-18T01:10:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"p2lr8ucLI/Zf6R/XnnntLuCSdD0bHl9p0jWOwEkBV99uex3T5q6pLX1XnBs2OjE5hgbX5fJG+0Xcd+oxLs98AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T13:31:15.619561Z"},"content_sha256":"440c5e72ec68b39d0939a3755e7dfbfdf49d40ad8e992fbe438f6cf741968008","schema_version":"1.0","event_id":"sha256:440c5e72ec68b39d0939a3755e7dfbfdf49d40ad8e992fbe438f6cf741968008"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GBVOAIPTVTMB32FIUJKLJJB62Q/bundle.json","state_url":"https://pith.science/pith/GBVOAIPTVTMB32FIUJKLJJB62Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GBVOAIPTVTMB32FIUJKLJJB62Q/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":"2026-06-21T13:31:15Z","links":{"resolver":"https://pith.science/pith/GBVOAIPTVTMB32FIUJKLJJB62Q","bundle":"https://pith.science/pith/GBVOAIPTVTMB32FIUJKLJJB62Q/bundle.json","state":"https://pith.science/pith/GBVOAIPTVTMB32FIUJKLJJB62Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GBVOAIPTVTMB32FIUJKLJJB62Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:GBVOAIPTVTMB32FIUJKLJJB62Q","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":"361cce26ce5101fb4a0d09e187488d829e60f683876d7d9d5d640fc5c193d220","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-08-20T13:47:08Z","title_canon_sha256":"4c73dabf0901c413cb52672624f93a9a61697c0ba29fe610540e2d225ccdaa34"},"schema_version":"1.0","source":{"id":"1308.4308","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.4308","created_at":"2026-05-18T01:10:38Z"},{"alias_kind":"arxiv_version","alias_value":"1308.4308v3","created_at":"2026-05-18T01:10:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.4308","created_at":"2026-05-18T01:10:38Z"},{"alias_kind":"pith_short_12","alias_value":"GBVOAIPTVTMB","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"GBVOAIPTVTMB32FI","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"GBVOAIPT","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:440c5e72ec68b39d0939a3755e7dfbfdf49d40ad8e992fbe438f6cf741968008","target":"graph","created_at":"2026-05-18T01:10:38Z","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":"Let $G$ be a simple graph on the vertex set $\\{1,\\ldots,n\\}$ with $m$ edges. An algebraic object attached to $G$ is the ideal $P_{G}$ generated by diagonal 2-minors of an $n \\times n$ matrix of variables. In this paper we prove that if $G$ is bipartite, then every initial ideal of $P_{G}$ is generated by squarefree monomials of degree at most $\\left \\lfloor{\\frac{m+n+1}{2}} \\right \\rfloor$. Furthermore, we completely characterize all connected graphs $G$ for which $P_{G}$ is the toric ideal associated to a finite simple graph. Finally we compute in certain cases the universal Gr{\\\"o}bner basis","authors_text":"Anargyros Katsabekis","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-08-20T13:47:08Z","title":"Toric ideals and diagonal 2-minors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.4308","kind":"arxiv","version":3},"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":"sha256:725f71360eca7695a745be559836e09873a6df7882afc9af1addf6edc0ba41d7","target":"record","created_at":"2026-05-18T01:10:38Z","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":"361cce26ce5101fb4a0d09e187488d829e60f683876d7d9d5d640fc5c193d220","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-08-20T13:47:08Z","title_canon_sha256":"4c73dabf0901c413cb52672624f93a9a61697c0ba29fe610540e2d225ccdaa34"},"schema_version":"1.0","source":{"id":"1308.4308","kind":"arxiv","version":3}},"canonical_sha256":"306ae021f3acd81de8a8a254b4a43ed40ee250898a437e0d2a037b8dd6c736b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"306ae021f3acd81de8a8a254b4a43ed40ee250898a437e0d2a037b8dd6c736b1","first_computed_at":"2026-05-18T01:10:38.960146Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:38.960146Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kwAD3Zznb3x6xL41ZQmhsRxk0G0JWjNfVhG+zGrDcOb7NFdi6dnAIWgkwl8v2iZYawVzXXobi/8AYzmAM3/mDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:38.960616Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.4308","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:725f71360eca7695a745be559836e09873a6df7882afc9af1addf6edc0ba41d7","sha256:440c5e72ec68b39d0939a3755e7dfbfdf49d40ad8e992fbe438f6cf741968008"],"state_sha256":"36ad160129df83abd3a634649878fca7dc17c68d70a06afc809b8db80da8b85e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W14r1klrDR5zxw0Uq49ZJkyAOegBHrH32f3kIPX3IJQuijhKN6+d42TOSrPSDcdj4SXvLso6IsA17aue+cXgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T13:31:15.621502Z","bundle_sha256":"a0a262c9b3c408006d1e4cfc5ea8ae017b84d4dff8cd904e78e9b1e1e554d3e2"}}