{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:UQRZFZQ3GKLDZIMAKOCG2ZKO7O","short_pith_number":"pith:UQRZFZQ3","canonical_record":{"source":{"id":"0809.4837","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-09-28T11:39:57Z","cross_cats_sorted":[],"title_canon_sha256":"77252d5409e7656a54ce96fdb0ebbef5b7b91fcf56fcb55eb75baee134a246b2","abstract_canon_sha256":"c7b8cc2538dcc0a54529226b9cb27861852573600c9dbce6e938f69dbd3e9873"},"schema_version":"1.0"},"canonical_sha256":"a42392e61b32963ca18053846d654efb940d7e8eef8ed7ee2fcdbf20da7d9aab","source":{"kind":"arxiv","id":"0809.4837","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.4837","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"arxiv_version","alias_value":"0809.4837v3","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.4837","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"pith_short_12","alias_value":"UQRZFZQ3GKLD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"UQRZFZQ3GKLDZIMA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"UQRZFZQ3","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:UQRZFZQ3GKLDZIMAKOCG2ZKO7O","target":"record","payload":{"canonical_record":{"source":{"id":"0809.4837","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-09-28T11:39:57Z","cross_cats_sorted":[],"title_canon_sha256":"77252d5409e7656a54ce96fdb0ebbef5b7b91fcf56fcb55eb75baee134a246b2","abstract_canon_sha256":"c7b8cc2538dcc0a54529226b9cb27861852573600c9dbce6e938f69dbd3e9873"},"schema_version":"1.0"},"canonical_sha256":"a42392e61b32963ca18053846d654efb940d7e8eef8ed7ee2fcdbf20da7d9aab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:03:07.652553Z","signature_b64":"8fY+ox1clQRrz7xwyW54ub7H4HYifAMmwFo2hyrpCwRi3byrlQz/PalvPmomzDOP4MVs+UWRAhEpMSY9zHoPBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a42392e61b32963ca18053846d654efb940d7e8eef8ed7ee2fcdbf20da7d9aab","last_reissued_at":"2026-05-18T04:03:07.652004Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:03:07.652004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0809.4837","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":"2026-05-18T04:03:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ql9eqFXGL3nzaY+e/JsSx4nJ4RpICeWUBzhuHV6Er3/yhJZdw3ALrqs4ZZvIqCtT8oyO8eXVuzhzcwi6WVNwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:15:34.047974Z"},"content_sha256":"293be550b6710726bf715439579ed32100f4a1788ff5777522a362b85620c07d","schema_version":"1.0","event_id":"sha256:293be550b6710726bf715439579ed32100f4a1788ff5777522a362b85620c07d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:UQRZFZQ3GKLDZIMAKOCG2ZKO7O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Secant varieties of Segre-Veronese varieties P^m x P^n embedded by O(1,2)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Hirotachi Abo, Maria Chiara Brambilla","submitted_at":"2008-09-28T11:39:57Z","abstract_excerpt":"Let $X_{m,n}$ be the Segre-Veronese variety $\\mathbb{P}^m \\times \\mathbb{P}^n$ embedded by the morphism given by $\\mathcal{O}(1,2)$. In this paper, we provide two functions $\\underline{s}(m,n)\\le \\bar{s}(m,n)$ such that the $s^{\\mathrm{th}}$ secant variety of $X_{m,n}$ has the expected dimension if $s \\leq \\underline{s}(m,n)$ or $ \\bar{s}(m,n) \\leq s$. We also present a conjecturally complete list of defective secant varieties of such Segre-Veronese varieties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4837","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":"2026-05-18T04:03:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ujsp7Wr7ABy0cv56KEgYocC8mHAsNxWdu6f3dYeHJ8R8vLnE3+2IlxyaF4GnwsqY5qxmY/aG4fmMgbKkJkQRCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T12:15:34.048709Z"},"content_sha256":"82106ea2ca9b44549f83a2d62c6e23ff0080483ec23a82244de10597d1e645b3","schema_version":"1.0","event_id":"sha256:82106ea2ca9b44549f83a2d62c6e23ff0080483ec23a82244de10597d1e645b3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UQRZFZQ3GKLDZIMAKOCG2ZKO7O/bundle.json","state_url":"https://pith.science/pith/UQRZFZQ3GKLDZIMAKOCG2ZKO7O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UQRZFZQ3GKLDZIMAKOCG2ZKO7O/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":"2026-05-30T12:15:34Z","links":{"resolver":"https://pith.science/pith/UQRZFZQ3GKLDZIMAKOCG2ZKO7O","bundle":"https://pith.science/pith/UQRZFZQ3GKLDZIMAKOCG2ZKO7O/bundle.json","state":"https://pith.science/pith/UQRZFZQ3GKLDZIMAKOCG2ZKO7O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UQRZFZQ3GKLDZIMAKOCG2ZKO7O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:UQRZFZQ3GKLDZIMAKOCG2ZKO7O","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":"c7b8cc2538dcc0a54529226b9cb27861852573600c9dbce6e938f69dbd3e9873","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-09-28T11:39:57Z","title_canon_sha256":"77252d5409e7656a54ce96fdb0ebbef5b7b91fcf56fcb55eb75baee134a246b2"},"schema_version":"1.0","source":{"id":"0809.4837","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0809.4837","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"arxiv_version","alias_value":"0809.4837v3","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0809.4837","created_at":"2026-05-18T04:03:07Z"},{"alias_kind":"pith_short_12","alias_value":"UQRZFZQ3GKLD","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"UQRZFZQ3GKLDZIMA","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"UQRZFZQ3","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:82106ea2ca9b44549f83a2d62c6e23ff0080483ec23a82244de10597d1e645b3","target":"graph","created_at":"2026-05-18T04:03:07Z","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 $X_{m,n}$ be the Segre-Veronese variety $\\mathbb{P}^m \\times \\mathbb{P}^n$ embedded by the morphism given by $\\mathcal{O}(1,2)$. In this paper, we provide two functions $\\underline{s}(m,n)\\le \\bar{s}(m,n)$ such that the $s^{\\mathrm{th}}$ secant variety of $X_{m,n}$ has the expected dimension if $s \\leq \\underline{s}(m,n)$ or $ \\bar{s}(m,n) \\leq s$. We also present a conjecturally complete list of defective secant varieties of such Segre-Veronese varieties.","authors_text":"Hirotachi Abo, Maria Chiara Brambilla","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-09-28T11:39:57Z","title":"Secant varieties of Segre-Veronese varieties P^m x P^n embedded by O(1,2)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.4837","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":"sha256:293be550b6710726bf715439579ed32100f4a1788ff5777522a362b85620c07d","target":"record","created_at":"2026-05-18T04:03:07Z","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":"c7b8cc2538dcc0a54529226b9cb27861852573600c9dbce6e938f69dbd3e9873","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2008-09-28T11:39:57Z","title_canon_sha256":"77252d5409e7656a54ce96fdb0ebbef5b7b91fcf56fcb55eb75baee134a246b2"},"schema_version":"1.0","source":{"id":"0809.4837","kind":"arxiv","version":3}},"canonical_sha256":"a42392e61b32963ca18053846d654efb940d7e8eef8ed7ee2fcdbf20da7d9aab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a42392e61b32963ca18053846d654efb940d7e8eef8ed7ee2fcdbf20da7d9aab","first_computed_at":"2026-05-18T04:03:07.652004Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:03:07.652004Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8fY+ox1clQRrz7xwyW54ub7H4HYifAMmwFo2hyrpCwRi3byrlQz/PalvPmomzDOP4MVs+UWRAhEpMSY9zHoPBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:03:07.652553Z","signed_message":"canonical_sha256_bytes"},"source_id":"0809.4837","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:293be550b6710726bf715439579ed32100f4a1788ff5777522a362b85620c07d","sha256:82106ea2ca9b44549f83a2d62c6e23ff0080483ec23a82244de10597d1e645b3"],"state_sha256":"e4411a9975d3aed26cb7270955d72bbe0afdb4c4980f23106b5e4a35166db16b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2d0fZaHmvUuItC2RdPeo8asw6rbPC1yeMGB+fpD+v/Eincb7i12f3TyiWrQS3odkbAPhhqQbOW3ZBgDw+3hiAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T12:15:34.053586Z","bundle_sha256":"c7e79f8beaa40afc24bff044df4ed091fe127a0c12b55a188f1605f713ddec71"}}