{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OFEPEGWFELJGX27CJLHBK4IC6N","short_pith_number":"pith:OFEPEGWF","canonical_record":{"source":{"id":"1212.1515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-07T01:46:22Z","cross_cats_sorted":[],"title_canon_sha256":"e3608606082ed560db8829f44a173f7ef1334b19457ffe03df49169a4114619f","abstract_canon_sha256":"71d6be67cf1c3772339fd0c859adfd0eb80cb9a6ef3fe87639ec8ead0524385d"},"schema_version":"1.0"},"canonical_sha256":"7148f21ac522d26bebe24ace157102f35da0c2671ee223ca10b96081102e1595","source":{"kind":"arxiv","id":"1212.1515","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1515","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1515v2","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1515","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"OFEPEGWFELJG","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OFEPEGWFELJGX27C","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OFEPEGWF","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OFEPEGWFELJGX27CJLHBK4IC6N","target":"record","payload":{"canonical_record":{"source":{"id":"1212.1515","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-07T01:46:22Z","cross_cats_sorted":[],"title_canon_sha256":"e3608606082ed560db8829f44a173f7ef1334b19457ffe03df49169a4114619f","abstract_canon_sha256":"71d6be67cf1c3772339fd0c859adfd0eb80cb9a6ef3fe87639ec8ead0524385d"},"schema_version":"1.0"},"canonical_sha256":"7148f21ac522d26bebe24ace157102f35da0c2671ee223ca10b96081102e1595","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:36.390676Z","signature_b64":"xPlfhXvrw4F3tOAZ9v5AfvNZekhrjLEuUCHcoQAalHGDZliLOcqhDZ6fSoAz36Q3xey0dFo2O7NIR5gm1kkECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7148f21ac522d26bebe24ace157102f35da0c2671ee223ca10b96081102e1595","last_reissued_at":"2026-05-18T01:14:36.390010Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:36.390010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.1515","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":"2026-05-18T01:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Os4MydMQyRDrtWkTJbrqr9tL//M7R5gb6MEhX9zHKRatp3/cA/D112e5mnjvjejp/ZjU455cWDQMuABilJtoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T11:18:55.562878Z"},"content_sha256":"fe4eaf4e4d177809ae7d1027047d03d27721e74fe698ad0b39582f6451d28e92","schema_version":"1.0","event_id":"sha256:fe4eaf4e4d177809ae7d1027047d03d27721e74fe698ad0b39582f6451d28e92"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OFEPEGWFELJGX27CJLHBK4IC6N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Secant cumulants and toric geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Luke Oeding, Mateusz Michalek, Piotr Zwiernik","submitted_at":"2012-12-07T01:46:22Z","abstract_excerpt":"We study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant coordinates its ideal is generated by binomial quadrics. We present new results on the local structure of the secant variety. In particular, we show that it has rational singularities and we give a description of the singular locus. We also classify all secant varieties that are Gorenstein. Moreover, generalizing (Sturmfels and Zwiernik 2012), we obtain ana"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1515","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":"2026-05-18T01:14:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YGp9t9IKAG8LMuDAlj5W4MpbT5su3R9Qk2dcCCXn/0O57jXyIaI8NIrWi59PX7aAA1e9XZUHRhcJ384UDReZBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T11:18:55.563222Z"},"content_sha256":"ec854b91360ce2ace9c8d06f3f12f8c5d2f8156d8d316656c2cd353f6f5f185e","schema_version":"1.0","event_id":"sha256:ec854b91360ce2ace9c8d06f3f12f8c5d2f8156d8d316656c2cd353f6f5f185e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OFEPEGWFELJGX27CJLHBK4IC6N/bundle.json","state_url":"https://pith.science/pith/OFEPEGWFELJGX27CJLHBK4IC6N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OFEPEGWFELJGX27CJLHBK4IC6N/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":"2026-05-20T11:18:55Z","links":{"resolver":"https://pith.science/pith/OFEPEGWFELJGX27CJLHBK4IC6N","bundle":"https://pith.science/pith/OFEPEGWFELJGX27CJLHBK4IC6N/bundle.json","state":"https://pith.science/pith/OFEPEGWFELJGX27CJLHBK4IC6N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OFEPEGWFELJGX27CJLHBK4IC6N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OFEPEGWFELJGX27CJLHBK4IC6N","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":"71d6be67cf1c3772339fd0c859adfd0eb80cb9a6ef3fe87639ec8ead0524385d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-07T01:46:22Z","title_canon_sha256":"e3608606082ed560db8829f44a173f7ef1334b19457ffe03df49169a4114619f"},"schema_version":"1.0","source":{"id":"1212.1515","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.1515","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"arxiv_version","alias_value":"1212.1515v2","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.1515","created_at":"2026-05-18T01:14:36Z"},{"alias_kind":"pith_short_12","alias_value":"OFEPEGWFELJG","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OFEPEGWFELJGX27C","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OFEPEGWF","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:ec854b91360ce2ace9c8d06f3f12f8c5d2f8156d8d316656c2cd353f6f5f185e","target":"graph","created_at":"2026-05-18T01:14:36Z","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 study the secant line variety of the Segre product of projective spaces using special cumulant coordinates adapted for secant varieties. We show that the secant variety is covered by open normal toric varieties. We prove that in cumulant coordinates its ideal is generated by binomial quadrics. We present new results on the local structure of the secant variety. In particular, we show that it has rational singularities and we give a description of the singular locus. We also classify all secant varieties that are Gorenstein. Moreover, generalizing (Sturmfels and Zwiernik 2012), we obtain ana","authors_text":"Luke Oeding, Mateusz Michalek, Piotr Zwiernik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-07T01:46:22Z","title":"Secant cumulants and toric geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.1515","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:fe4eaf4e4d177809ae7d1027047d03d27721e74fe698ad0b39582f6451d28e92","target":"record","created_at":"2026-05-18T01:14:36Z","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":"71d6be67cf1c3772339fd0c859adfd0eb80cb9a6ef3fe87639ec8ead0524385d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-12-07T01:46:22Z","title_canon_sha256":"e3608606082ed560db8829f44a173f7ef1334b19457ffe03df49169a4114619f"},"schema_version":"1.0","source":{"id":"1212.1515","kind":"arxiv","version":2}},"canonical_sha256":"7148f21ac522d26bebe24ace157102f35da0c2671ee223ca10b96081102e1595","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7148f21ac522d26bebe24ace157102f35da0c2671ee223ca10b96081102e1595","first_computed_at":"2026-05-18T01:14:36.390010Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:36.390010Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xPlfhXvrw4F3tOAZ9v5AfvNZekhrjLEuUCHcoQAalHGDZliLOcqhDZ6fSoAz36Q3xey0dFo2O7NIR5gm1kkECg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:36.390676Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.1515","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe4eaf4e4d177809ae7d1027047d03d27721e74fe698ad0b39582f6451d28e92","sha256:ec854b91360ce2ace9c8d06f3f12f8c5d2f8156d8d316656c2cd353f6f5f185e"],"state_sha256":"ea27f4870e31361912bef0aca3336fa4006d767e7c65eb44a0ddb163bd5f6b89"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AiEfiwLg3oQyn8zWZNBFiVAhQC83ktNIyl27j2kmO1P9Hi/DPOR55gOJUwZWDnDO1mJBFgVywSZj8EyLPO7BAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T11:18:55.566657Z","bundle_sha256":"13855932a858fbd62733a8add487eda0ca4f887bf56069a5fe0b8b53d656622e"}}