{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Q2QBAVHPFAVAAJ5MMIXAS6TWNK","short_pith_number":"pith:Q2QBAVHP","canonical_record":{"source":{"id":"1305.2355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-10T14:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"284089e1d3b6262777800496dbfe85bdc1ada8a1d209f2b4090daf1b2cfdcb7e","abstract_canon_sha256":"2b86358c52609eed845d8ca0670022c465b6a694d5b0c1afc75b5010905631a6"},"schema_version":"1.0"},"canonical_sha256":"86a01054ef282a0027ac622e097a766a8228c129867291e04a6503a48c88d525","source":{"kind":"arxiv","id":"1305.2355","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2355","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2355v1","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2355","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"pith_short_12","alias_value":"Q2QBAVHPFAVA","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q2QBAVHPFAVAAJ5M","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q2QBAVHP","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Q2QBAVHPFAVAAJ5MMIXAS6TWNK","target":"record","payload":{"canonical_record":{"source":{"id":"1305.2355","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-10T14:49:10Z","cross_cats_sorted":[],"title_canon_sha256":"284089e1d3b6262777800496dbfe85bdc1ada8a1d209f2b4090daf1b2cfdcb7e","abstract_canon_sha256":"2b86358c52609eed845d8ca0670022c465b6a694d5b0c1afc75b5010905631a6"},"schema_version":"1.0"},"canonical_sha256":"86a01054ef282a0027ac622e097a766a8228c129867291e04a6503a48c88d525","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:00.232150Z","signature_b64":"CHCoh+8bqHo/IYSWIDt8J9S8j07wc9nq7vXJxLvMudMKRVSVco7a5EmwfQDcfyhNNqtosCpKIO0UyCbD+H1+Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86a01054ef282a0027ac622e097a766a8228c129867291e04a6503a48c88d525","last_reissued_at":"2026-05-18T03:26:00.231679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:00.231679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.2355","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":"2026-05-18T03:26:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LVp7LHAw1XECKOayZHtH6i/QSqbTuKPupAZVMnWMwZoxe9SH6e6KyoOUkmD+ytBax5c8XJlRw0nQ00SeL9MkCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:20:46.590034Z"},"content_sha256":"e4591b0291786037219604dd7c77353b4c0e1459c7d4c4fbe5d62ac0cf13836f","schema_version":"1.0","event_id":"sha256:e4591b0291786037219604dd7c77353b4c0e1459c7d4c4fbe5d62ac0cf13836f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Q2QBAVHPFAVAAJ5MMIXAS6TWNK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Projective surfaces of maximal sectional regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Euisung Park, Markus Brodmann, Peter Schenzel, Wanseok Lee","submitted_at":"2013-05-10T14:49:10Z","abstract_excerpt":"We study projective surfaces $X \\subset \\mathbb{P}^r$ (with $r \\geq 5$) of maximal sectional regularity and degree $d > r$, hence surfaces for which the Castelnuovo-Mumford regularity $\\reg(C)$ of a general hyperplane section curve $C = X \\cap \\mathbb{P}^{r-1}$ takes the maximally possible value $d-r+3$. We show that each of these surfaces is either a cone over a curve $C \\subset \\mathbb{P}^{r-1}$ of maximal regularity or else a birational outer linear projection of a smooth rational surface scroll $\\widetilde{X} \\subset \\mathbb{P}^{d+1}$. We prove that the Castelnuovo-Mumford regularity of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2355","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":"2026-05-18T03:26:00Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JE09T0D8fCCa2KJT6Jstt1UZLmjcscw0HBcPYSu7Kuv1y1oXc2o9gYkAhv7ij1DG8d741dfzFoQPMRKPhpy2AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:20:46.590392Z"},"content_sha256":"38c3bc1c3e8f3b775925be6ce26196ccb106215e461deec9f9db741dcd5306d2","schema_version":"1.0","event_id":"sha256:38c3bc1c3e8f3b775925be6ce26196ccb106215e461deec9f9db741dcd5306d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q2QBAVHPFAVAAJ5MMIXAS6TWNK/bundle.json","state_url":"https://pith.science/pith/Q2QBAVHPFAVAAJ5MMIXAS6TWNK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q2QBAVHPFAVAAJ5MMIXAS6TWNK/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":"2026-06-03T05:20:46Z","links":{"resolver":"https://pith.science/pith/Q2QBAVHPFAVAAJ5MMIXAS6TWNK","bundle":"https://pith.science/pith/Q2QBAVHPFAVAAJ5MMIXAS6TWNK/bundle.json","state":"https://pith.science/pith/Q2QBAVHPFAVAAJ5MMIXAS6TWNK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q2QBAVHPFAVAAJ5MMIXAS6TWNK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Q2QBAVHPFAVAAJ5MMIXAS6TWNK","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":"2b86358c52609eed845d8ca0670022c465b6a694d5b0c1afc75b5010905631a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-10T14:49:10Z","title_canon_sha256":"284089e1d3b6262777800496dbfe85bdc1ada8a1d209f2b4090daf1b2cfdcb7e"},"schema_version":"1.0","source":{"id":"1305.2355","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2355","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2355v1","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2355","created_at":"2026-05-18T03:26:00Z"},{"alias_kind":"pith_short_12","alias_value":"Q2QBAVHPFAVA","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"Q2QBAVHPFAVAAJ5M","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"Q2QBAVHP","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:38c3bc1c3e8f3b775925be6ce26196ccb106215e461deec9f9db741dcd5306d2","target":"graph","created_at":"2026-05-18T03:26:00Z","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 projective surfaces $X \\subset \\mathbb{P}^r$ (with $r \\geq 5$) of maximal sectional regularity and degree $d > r$, hence surfaces for which the Castelnuovo-Mumford regularity $\\reg(C)$ of a general hyperplane section curve $C = X \\cap \\mathbb{P}^{r-1}$ takes the maximally possible value $d-r+3$. We show that each of these surfaces is either a cone over a curve $C \\subset \\mathbb{P}^{r-1}$ of maximal regularity or else a birational outer linear projection of a smooth rational surface scroll $\\widetilde{X} \\subset \\mathbb{P}^{d+1}$. We prove that the Castelnuovo-Mumford regularity of th","authors_text":"Euisung Park, Markus Brodmann, Peter Schenzel, Wanseok Lee","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-10T14:49:10Z","title":"Projective surfaces of maximal sectional regularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2355","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:e4591b0291786037219604dd7c77353b4c0e1459c7d4c4fbe5d62ac0cf13836f","target":"record","created_at":"2026-05-18T03:26:00Z","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":"2b86358c52609eed845d8ca0670022c465b6a694d5b0c1afc75b5010905631a6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-10T14:49:10Z","title_canon_sha256":"284089e1d3b6262777800496dbfe85bdc1ada8a1d209f2b4090daf1b2cfdcb7e"},"schema_version":"1.0","source":{"id":"1305.2355","kind":"arxiv","version":1}},"canonical_sha256":"86a01054ef282a0027ac622e097a766a8228c129867291e04a6503a48c88d525","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86a01054ef282a0027ac622e097a766a8228c129867291e04a6503a48c88d525","first_computed_at":"2026-05-18T03:26:00.231679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:00.231679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CHCoh+8bqHo/IYSWIDt8J9S8j07wc9nq7vXJxLvMudMKRVSVco7a5EmwfQDcfyhNNqtosCpKIO0UyCbD+H1+Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:00.232150Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.2355","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e4591b0291786037219604dd7c77353b4c0e1459c7d4c4fbe5d62ac0cf13836f","sha256:38c3bc1c3e8f3b775925be6ce26196ccb106215e461deec9f9db741dcd5306d2"],"state_sha256":"83b716ff16dfd11c2a8a0c92bafc17718b9f6544b265ba9e60eaf2ededfd58f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x2TSwGqFoa4iYo4tqMh9t+dZ9LgpDjqKzAy/nkOgk5wcSB9dglQR6J7JsCdv6GIwdhqeZOTjwj2YGM57z0C7Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:20:46.592384Z","bundle_sha256":"51897cb7f756fa0cbbb6556699d5aa967e15480e7989b56b53d50d00f5d6077f"}}