{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:3GTKEQIDRVPRDBPLYODVSLQNCK","short_pith_number":"pith:3GTKEQID","canonical_record":{"source":{"id":"1902.03115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-08T14:48:31Z","cross_cats_sorted":[],"title_canon_sha256":"1c5d3d7a482f89597d0d88ee3f88f6e722b73b7de99107eeeb9a0aeac9d3305a","abstract_canon_sha256":"fee065c2d7bbd1e4d98ea58e6e9ad91f680204fb8bc0056d7a38d6cfd0ec4dc6"},"schema_version":"1.0"},"canonical_sha256":"d9a6a241038d5f1185ebc387592e0d12b90e7fc008d069a76d37faa48655eba3","source":{"kind":"arxiv","id":"1902.03115","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03115","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03115v1","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03115","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"3GTKEQIDRVPR","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3GTKEQIDRVPRDBPL","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3GTKEQID","created_at":"2026-05-18T12:33:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:3GTKEQIDRVPRDBPLYODVSLQNCK","target":"record","payload":{"canonical_record":{"source":{"id":"1902.03115","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-08T14:48:31Z","cross_cats_sorted":[],"title_canon_sha256":"1c5d3d7a482f89597d0d88ee3f88f6e722b73b7de99107eeeb9a0aeac9d3305a","abstract_canon_sha256":"fee065c2d7bbd1e4d98ea58e6e9ad91f680204fb8bc0056d7a38d6cfd0ec4dc6"},"schema_version":"1.0"},"canonical_sha256":"d9a6a241038d5f1185ebc387592e0d12b90e7fc008d069a76d37faa48655eba3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:27.923266Z","signature_b64":"4XTYYiRnS5fZsTIt1e0HBEKedTKGSsAot3yldx2cqGTT8l69/lVzxIpQ6yqbuE2n+KKfNhWatBiSyQseH5gECA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9a6a241038d5f1185ebc387592e0d12b90e7fc008d069a76d37faa48655eba3","last_reissued_at":"2026-05-17T23:54:27.922773Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:27.922773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.03115","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":"2026-05-17T23:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4AJ9bekQKa2me5q4jkNVO4LWpMTd0/o0Ox49FPqB3Yv3wjxdLMQUW7oLrFAiqfwcyuer5mmYiDEG1oARiZ4qDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:21:31.632775Z"},"content_sha256":"bdbb70da52baadd237216e23bc17e47649573d00a07392d92bb70653a795b2ea","schema_version":"1.0","event_id":"sha256:bdbb70da52baadd237216e23bc17e47649573d00a07392d92bb70653a795b2ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:3GTKEQIDRVPRDBPLYODVSLQNCK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Circuits and circulant minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Graciela Nasini, Luis Miguel Torres, Paola Tolomei, Silvia Bianchi","submitted_at":"2019-02-08T14:48:31Z","abstract_excerpt":"Circulant contraction minors play a key role for characterizing ideal circular matrices in terms of minimally non ideal structures. In this article we prove necessary and sufficient conditions for a circular matrix $A$ to have circulant contraction minors in terms of circuits in a digraph associated with $A$. In the particular case when $A$ itself is a circulant matrix, our result provides an alternative characterization to the one previously known from the literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03115","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":"2026-05-17T23:54:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4+EE76t5pi7IJMzYnRcw0m59JGKDyR7pwayJ0OH1enia/u9fcDa0XDXVg1Vvs9UHhyC615SB49ZebTm0HWpdAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T10:21:31.633400Z"},"content_sha256":"3a63ca52c6fdfa5beeea1c966f2e458c616bd852f1e2608d7f472c4f716841db","schema_version":"1.0","event_id":"sha256:3a63ca52c6fdfa5beeea1c966f2e458c616bd852f1e2608d7f472c4f716841db"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3GTKEQIDRVPRDBPLYODVSLQNCK/bundle.json","state_url":"https://pith.science/pith/3GTKEQIDRVPRDBPLYODVSLQNCK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3GTKEQIDRVPRDBPLYODVSLQNCK/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":"2026-05-31T10:21:31Z","links":{"resolver":"https://pith.science/pith/3GTKEQIDRVPRDBPLYODVSLQNCK","bundle":"https://pith.science/pith/3GTKEQIDRVPRDBPLYODVSLQNCK/bundle.json","state":"https://pith.science/pith/3GTKEQIDRVPRDBPLYODVSLQNCK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3GTKEQIDRVPRDBPLYODVSLQNCK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:3GTKEQIDRVPRDBPLYODVSLQNCK","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":"fee065c2d7bbd1e4d98ea58e6e9ad91f680204fb8bc0056d7a38d6cfd0ec4dc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-08T14:48:31Z","title_canon_sha256":"1c5d3d7a482f89597d0d88ee3f88f6e722b73b7de99107eeeb9a0aeac9d3305a"},"schema_version":"1.0","source":{"id":"1902.03115","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.03115","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"arxiv_version","alias_value":"1902.03115v1","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.03115","created_at":"2026-05-17T23:54:27Z"},{"alias_kind":"pith_short_12","alias_value":"3GTKEQIDRVPR","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_16","alias_value":"3GTKEQIDRVPRDBPL","created_at":"2026-05-18T12:33:07Z"},{"alias_kind":"pith_short_8","alias_value":"3GTKEQID","created_at":"2026-05-18T12:33:07Z"}],"graph_snapshots":[{"event_id":"sha256:3a63ca52c6fdfa5beeea1c966f2e458c616bd852f1e2608d7f472c4f716841db","target":"graph","created_at":"2026-05-17T23:54:27Z","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":"Circulant contraction minors play a key role for characterizing ideal circular matrices in terms of minimally non ideal structures. In this article we prove necessary and sufficient conditions for a circular matrix $A$ to have circulant contraction minors in terms of circuits in a digraph associated with $A$. In the particular case when $A$ itself is a circulant matrix, our result provides an alternative characterization to the one previously known from the literature.","authors_text":"Graciela Nasini, Luis Miguel Torres, Paola Tolomei, Silvia Bianchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-08T14:48:31Z","title":"Circuits and circulant minors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03115","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:bdbb70da52baadd237216e23bc17e47649573d00a07392d92bb70653a795b2ea","target":"record","created_at":"2026-05-17T23:54:27Z","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":"fee065c2d7bbd1e4d98ea58e6e9ad91f680204fb8bc0056d7a38d6cfd0ec4dc6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-08T14:48:31Z","title_canon_sha256":"1c5d3d7a482f89597d0d88ee3f88f6e722b73b7de99107eeeb9a0aeac9d3305a"},"schema_version":"1.0","source":{"id":"1902.03115","kind":"arxiv","version":1}},"canonical_sha256":"d9a6a241038d5f1185ebc387592e0d12b90e7fc008d069a76d37faa48655eba3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9a6a241038d5f1185ebc387592e0d12b90e7fc008d069a76d37faa48655eba3","first_computed_at":"2026-05-17T23:54:27.922773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:54:27.922773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4XTYYiRnS5fZsTIt1e0HBEKedTKGSsAot3yldx2cqGTT8l69/lVzxIpQ6yqbuE2n+KKfNhWatBiSyQseH5gECA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:54:27.923266Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.03115","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdbb70da52baadd237216e23bc17e47649573d00a07392d92bb70653a795b2ea","sha256:3a63ca52c6fdfa5beeea1c966f2e458c616bd852f1e2608d7f472c4f716841db"],"state_sha256":"52e75bdfd1282df2d10818dc3285dcdc8edf05acf1043fb603ae4745a9058bd6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Dx+2tVxYFGzyug5Od9s7dEXI2TasXoGuoquXhWlhwpXyVKi2UEltTdZf00yP9QpizKZ68i4n0cTB1axn+/0CBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T10:21:31.636153Z","bundle_sha256":"7d416266dc4f050f5973bc776883f3ed6416cb9109b7a7d1243d358d68354c1d"}}