{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YBITVSP3JC5PNZSDSZ3N2A2QTV","short_pith_number":"pith:YBITVSP3","canonical_record":{"source":{"id":"1609.03706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-13T07:13:32Z","cross_cats_sorted":[],"title_canon_sha256":"e53e147f9d563eb6cfefc84560c40dda112b149b0490793878c6df667553c217","abstract_canon_sha256":"9e7cf9dd24bcb5196b2eb34bc76b7db4dc62a9cb5db78f3c8fe098c446401a36"},"schema_version":"1.0"},"canonical_sha256":"c0513ac9fb48baf6e6439676dd03509d482fd6ffdac3c921de16bcd4a8a5b4bf","source":{"kind":"arxiv","id":"1609.03706","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03706","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03706v1","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03706","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"YBITVSP3JC5P","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YBITVSP3JC5PNZSD","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YBITVSP3","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YBITVSP3JC5PNZSDSZ3N2A2QTV","target":"record","payload":{"canonical_record":{"source":{"id":"1609.03706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-13T07:13:32Z","cross_cats_sorted":[],"title_canon_sha256":"e53e147f9d563eb6cfefc84560c40dda112b149b0490793878c6df667553c217","abstract_canon_sha256":"9e7cf9dd24bcb5196b2eb34bc76b7db4dc62a9cb5db78f3c8fe098c446401a36"},"schema_version":"1.0"},"canonical_sha256":"c0513ac9fb48baf6e6439676dd03509d482fd6ffdac3c921de16bcd4a8a5b4bf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:42.654024Z","signature_b64":"Prx8WczkcN4blDyp9QqPYYtEPbR3JYEfPOYEVR3DefrSFPet5xgyYSVzNdFs+fyW9kvgv8H63+SJXpvLhmQWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0513ac9fb48baf6e6439676dd03509d482fd6ffdac3c921de16bcd4a8a5b4bf","last_reissued_at":"2026-05-18T01:04:42.653460Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:42.653460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.03706","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":"2026-05-18T01:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"m0wufn3LCpFXIWesrKq2lpSJ9BvGEHDWlLBb2/9PcI36V3ZyHRz3if5S496By2+ZHndITM+R1egW4d3l/4XSBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:15:58.698585Z"},"content_sha256":"afa1898fc79d7f00e4aabe6fb65aaa5eb2d9be61bb07221ca23afae925089dee","schema_version":"1.0","event_id":"sha256:afa1898fc79d7f00e4aabe6fb65aaa5eb2d9be61bb07221ca23afae925089dee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YBITVSP3JC5PNZSDSZ3N2A2QTV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Surfaces in $\\mathbb{P}^4$ lying on small degree hypersurfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Daniel Naie, Igor Reider","submitted_at":"2016-09-13T07:13:32Z","abstract_excerpt":"Since the work of Ellingsrud and Peskine at the end of 1980s, it has been known that, with the exception of a finite number of families, smooth compact complex surfaces in $\\mathbb{P}^4$ with prescribed Chern classes must lie on hypersurfaces of degree $m\\leq 5$. The study of surfaces lying on a small degree hypersurface in $\\mathbb{P}^4$---small meaning $\\leq5$---seems to be a way of obtaining empirical data leading to a better conceptual understanding of surfaces in $\\mathbb{P}^4$. From this perspective, two main issues are considered in the paper:\n  - an analogue of the Hartshorne-Lichtenba"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03706","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":"2026-05-18T01:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AHFgG2dKWrPISPMZW78nQjnxSfth6kUlohFqp4Ikg2jzEYCQNqkuNn12cIPrgnAw6XfKWSZvjZwpH7bpDZTPBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T21:15:58.699223Z"},"content_sha256":"d074d7c8244b88f9cd43f32be26a3ad9cb389f1d86013282a1e664cb56184981","schema_version":"1.0","event_id":"sha256:d074d7c8244b88f9cd43f32be26a3ad9cb389f1d86013282a1e664cb56184981"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YBITVSP3JC5PNZSDSZ3N2A2QTV/bundle.json","state_url":"https://pith.science/pith/YBITVSP3JC5PNZSDSZ3N2A2QTV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YBITVSP3JC5PNZSDSZ3N2A2QTV/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":"2026-06-10T21:15:58Z","links":{"resolver":"https://pith.science/pith/YBITVSP3JC5PNZSDSZ3N2A2QTV","bundle":"https://pith.science/pith/YBITVSP3JC5PNZSDSZ3N2A2QTV/bundle.json","state":"https://pith.science/pith/YBITVSP3JC5PNZSDSZ3N2A2QTV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YBITVSP3JC5PNZSDSZ3N2A2QTV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YBITVSP3JC5PNZSDSZ3N2A2QTV","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":"9e7cf9dd24bcb5196b2eb34bc76b7db4dc62a9cb5db78f3c8fe098c446401a36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-13T07:13:32Z","title_canon_sha256":"e53e147f9d563eb6cfefc84560c40dda112b149b0490793878c6df667553c217"},"schema_version":"1.0","source":{"id":"1609.03706","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.03706","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"1609.03706v1","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.03706","created_at":"2026-05-18T01:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"YBITVSP3JC5P","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YBITVSP3JC5PNZSD","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YBITVSP3","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:d074d7c8244b88f9cd43f32be26a3ad9cb389f1d86013282a1e664cb56184981","target":"graph","created_at":"2026-05-18T01:04:42Z","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":"Since the work of Ellingsrud and Peskine at the end of 1980s, it has been known that, with the exception of a finite number of families, smooth compact complex surfaces in $\\mathbb{P}^4$ with prescribed Chern classes must lie on hypersurfaces of degree $m\\leq 5$. The study of surfaces lying on a small degree hypersurface in $\\mathbb{P}^4$---small meaning $\\leq5$---seems to be a way of obtaining empirical data leading to a better conceptual understanding of surfaces in $\\mathbb{P}^4$. From this perspective, two main issues are considered in the paper:\n  - an analogue of the Hartshorne-Lichtenba","authors_text":"Daniel Naie, Igor Reider","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-13T07:13:32Z","title":"Surfaces in $\\mathbb{P}^4$ lying on small degree hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03706","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:afa1898fc79d7f00e4aabe6fb65aaa5eb2d9be61bb07221ca23afae925089dee","target":"record","created_at":"2026-05-18T01:04:42Z","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":"9e7cf9dd24bcb5196b2eb34bc76b7db4dc62a9cb5db78f3c8fe098c446401a36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2016-09-13T07:13:32Z","title_canon_sha256":"e53e147f9d563eb6cfefc84560c40dda112b149b0490793878c6df667553c217"},"schema_version":"1.0","source":{"id":"1609.03706","kind":"arxiv","version":1}},"canonical_sha256":"c0513ac9fb48baf6e6439676dd03509d482fd6ffdac3c921de16bcd4a8a5b4bf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0513ac9fb48baf6e6439676dd03509d482fd6ffdac3c921de16bcd4a8a5b4bf","first_computed_at":"2026-05-18T01:04:42.653460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:42.653460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Prx8WczkcN4blDyp9QqPYYtEPbR3JYEfPOYEVR3DefrSFPet5xgyYSVzNdFs+fyW9kvgv8H63+SJXpvLhmQWBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:42.654024Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.03706","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afa1898fc79d7f00e4aabe6fb65aaa5eb2d9be61bb07221ca23afae925089dee","sha256:d074d7c8244b88f9cd43f32be26a3ad9cb389f1d86013282a1e664cb56184981"],"state_sha256":"540de8e1cdbba3e298c32c603bbe881ad523445c82343b1e45d28f2d256e3beb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CatQc/xCjVw/hT27kncY4mf+7hJGWjeEV69Ua+ayzeCJPz+bYsBy2I7ijCQjO2BZgZbXGphZQ1Rqxi0WKGsUDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T21:15:58.702646Z","bundle_sha256":"0526899cc74e542abcf356788484d45bf7e138483789a2694333b36c922336cb"}}