{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:IUDGKJLKVCCVNNELJ2WAG4YO6O","short_pith_number":"pith:IUDGKJLK","canonical_record":{"source":{"id":"1005.3560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-19T21:03:39Z","cross_cats_sorted":[],"title_canon_sha256":"b4a37f2d159a64814e13d4183d85e720c030f15e209fd958666193b8553a81ee","abstract_canon_sha256":"278b3f85238bcecf12e39635deb7546dcc9fa10043a8f45862ba18fbf589a78b"},"schema_version":"1.0"},"canonical_sha256":"450665256aa88556b48b4eac03730ef394984fc5437a44de3ead16dfa1b05606","source":{"kind":"arxiv","id":"1005.3560","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.3560","created_at":"2026-05-18T03:29:51Z"},{"alias_kind":"arxiv_version","alias_value":"1005.3560v2","created_at":"2026-05-18T03:29:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3560","created_at":"2026-05-18T03:29:51Z"},{"alias_kind":"pith_short_12","alias_value":"IUDGKJLKVCCV","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IUDGKJLKVCCVNNEL","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IUDGKJLK","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:IUDGKJLKVCCVNNELJ2WAG4YO6O","target":"record","payload":{"canonical_record":{"source":{"id":"1005.3560","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-19T21:03:39Z","cross_cats_sorted":[],"title_canon_sha256":"b4a37f2d159a64814e13d4183d85e720c030f15e209fd958666193b8553a81ee","abstract_canon_sha256":"278b3f85238bcecf12e39635deb7546dcc9fa10043a8f45862ba18fbf589a78b"},"schema_version":"1.0"},"canonical_sha256":"450665256aa88556b48b4eac03730ef394984fc5437a44de3ead16dfa1b05606","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:51.373163Z","signature_b64":"asLq32u+8uJeUdD3eDP+p/WP7sz89bXNoYNE33HyiJ/mAJX1/sJvL2vfuQTgrGv299m/sHzF/Iph8MptUzR8AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"450665256aa88556b48b4eac03730ef394984fc5437a44de3ead16dfa1b05606","last_reissued_at":"2026-05-18T03:29:51.372451Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:51.372451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1005.3560","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:29:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VSTf2QHN3u2zB5v+Mqg+KDszLEHpTnUN/poArxqtY+y4kmPrqNWtB5ZflNkUehRrxBR/m3AY0JoPfu3VPEz2Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:25:56.940959Z"},"content_sha256":"752c4cf79fca58025eb77434ebbe584bd61ea4790f60c17d15b6cdf3d6f193ad","schema_version":"1.0","event_id":"sha256:752c4cf79fca58025eb77434ebbe584bd61ea4790f60c17d15b6cdf3d6f193ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:IUDGKJLKVCCVNNELJ2WAG4YO6O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Foundations for a theory of complex matroids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Emanuele Delucchi, Laura Anderson","submitted_at":"2010-05-19T21:03:39Z","abstract_excerpt":"We explore a combinatorial theory of linear dependency in complex space, \"complex matroids\", with foundations analogous to those for oriented matroids. We give multiple equivalent axiomatizations of complex matroids, showing that this theory captures properties of linear dependency, orthogonality, and determinants over C in much the same way that oriented matroids capture the same properties over R. In addition, our complex matroids come with a canonical circle action analogous to the action of C* on a complex vector space. Our phirotopes (analogues of determinants) are the same as those studi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3560","kind":"arxiv","version":2},"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":"2026-05-18T03:29:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XG7p8jHr4j2uo4Crt27GXj5Gi0r+fBcnA/j0ipxKa5OFXslcnoSniLjfyYS5GiZbonS5kcotKu7I0Vt5b/EiDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T16:25:56.941340Z"},"content_sha256":"f9a0d3833210f52c60674e5e9b69d417927b56c8907f3bbfede6cd0f78d17d22","schema_version":"1.0","event_id":"sha256:f9a0d3833210f52c60674e5e9b69d417927b56c8907f3bbfede6cd0f78d17d22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IUDGKJLKVCCVNNELJ2WAG4YO6O/bundle.json","state_url":"https://pith.science/pith/IUDGKJLKVCCVNNELJ2WAG4YO6O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IUDGKJLKVCCVNNELJ2WAG4YO6O/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":"2026-06-23T16:25:56Z","links":{"resolver":"https://pith.science/pith/IUDGKJLKVCCVNNELJ2WAG4YO6O","bundle":"https://pith.science/pith/IUDGKJLKVCCVNNELJ2WAG4YO6O/bundle.json","state":"https://pith.science/pith/IUDGKJLKVCCVNNELJ2WAG4YO6O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IUDGKJLKVCCVNNELJ2WAG4YO6O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:IUDGKJLKVCCVNNELJ2WAG4YO6O","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":"278b3f85238bcecf12e39635deb7546dcc9fa10043a8f45862ba18fbf589a78b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-19T21:03:39Z","title_canon_sha256":"b4a37f2d159a64814e13d4183d85e720c030f15e209fd958666193b8553a81ee"},"schema_version":"1.0","source":{"id":"1005.3560","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.3560","created_at":"2026-05-18T03:29:51Z"},{"alias_kind":"arxiv_version","alias_value":"1005.3560v2","created_at":"2026-05-18T03:29:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.3560","created_at":"2026-05-18T03:29:51Z"},{"alias_kind":"pith_short_12","alias_value":"IUDGKJLKVCCV","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"IUDGKJLKVCCVNNEL","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"IUDGKJLK","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:f9a0d3833210f52c60674e5e9b69d417927b56c8907f3bbfede6cd0f78d17d22","target":"graph","created_at":"2026-05-18T03:29:51Z","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 explore a combinatorial theory of linear dependency in complex space, \"complex matroids\", with foundations analogous to those for oriented matroids. We give multiple equivalent axiomatizations of complex matroids, showing that this theory captures properties of linear dependency, orthogonality, and determinants over C in much the same way that oriented matroids capture the same properties over R. In addition, our complex matroids come with a canonical circle action analogous to the action of C* on a complex vector space. Our phirotopes (analogues of determinants) are the same as those studi","authors_text":"Emanuele Delucchi, Laura Anderson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-19T21:03:39Z","title":"Foundations for a theory of complex matroids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.3560","kind":"arxiv","version":2},"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":"sha256:752c4cf79fca58025eb77434ebbe584bd61ea4790f60c17d15b6cdf3d6f193ad","target":"record","created_at":"2026-05-18T03:29:51Z","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":"278b3f85238bcecf12e39635deb7546dcc9fa10043a8f45862ba18fbf589a78b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-05-19T21:03:39Z","title_canon_sha256":"b4a37f2d159a64814e13d4183d85e720c030f15e209fd958666193b8553a81ee"},"schema_version":"1.0","source":{"id":"1005.3560","kind":"arxiv","version":2}},"canonical_sha256":"450665256aa88556b48b4eac03730ef394984fc5437a44de3ead16dfa1b05606","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"450665256aa88556b48b4eac03730ef394984fc5437a44de3ead16dfa1b05606","first_computed_at":"2026-05-18T03:29:51.372451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:51.372451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"asLq32u+8uJeUdD3eDP+p/WP7sz89bXNoYNE33HyiJ/mAJX1/sJvL2vfuQTgrGv299m/sHzF/Iph8MptUzR8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:51.373163Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.3560","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:752c4cf79fca58025eb77434ebbe584bd61ea4790f60c17d15b6cdf3d6f193ad","sha256:f9a0d3833210f52c60674e5e9b69d417927b56c8907f3bbfede6cd0f78d17d22"],"state_sha256":"186f677d05c43c641c1b3d14d7300dbeef8442b112cdd41db4a199468a74ae55"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oPL7ZKlGl/LX2PexMgLk/l/Wc+nWXbJjXF+ANSYdQumGrS2ClcKu49J6GWhxGZdhMz0JvGyq/WLEYMYtI30CDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T16:25:56.943354Z","bundle_sha256":"22c5a6f9f856174f339f59b0dab430e02e2133efa26411e7a234fbbc9a8f031b"}}