{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:SQGX77ZN7QJKPG2ZLCVOP7LJGI","short_pith_number":"pith:SQGX77ZN","canonical_record":{"source":{"id":"math/0108078","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2001-08-10T18:59:28Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"f3c3c4ada513fab173003cce1f1263f288b057d6710604fd20b57ff3c55ae0ff","abstract_canon_sha256":"1a7b1332d80671a86b93f162d99a74ec5197ce583449ae92d3420834419e2700"},"schema_version":"1.0"},"canonical_sha256":"940d7fff2dfc12a79b5958aae7fd69323d0919c43945ee04635851248c80179d","source":{"kind":"arxiv","id":"math/0108078","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0108078","created_at":"2026-07-04T14:35:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0108078v1","created_at":"2026-07-04T14:35:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0108078","created_at":"2026-07-04T14:35:28Z"},{"alias_kind":"pith_short_12","alias_value":"SQGX77ZN7QJK","created_at":"2026-07-04T14:35:28Z"},{"alias_kind":"pith_short_16","alias_value":"SQGX77ZN7QJKPG2Z","created_at":"2026-07-04T14:35:28Z"},{"alias_kind":"pith_short_8","alias_value":"SQGX77ZN","created_at":"2026-07-04T14:35:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:SQGX77ZN7QJKPG2ZLCVOP7LJGI","target":"record","payload":{"canonical_record":{"source":{"id":"math/0108078","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2001-08-10T18:59:28Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"f3c3c4ada513fab173003cce1f1263f288b057d6710604fd20b57ff3c55ae0ff","abstract_canon_sha256":"1a7b1332d80671a86b93f162d99a74ec5197ce583449ae92d3420834419e2700"},"schema_version":"1.0"},"canonical_sha256":"940d7fff2dfc12a79b5958aae7fd69323d0919c43945ee04635851248c80179d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:35:28.384578Z","signature_b64":"UqvCfs2YcyKUo0KyIbLdA5UX82N+BlwSCXTv6JthjzND5tovmYUdEcPqmYSFqUu7Fvft+CoLLVtK1gpZAfDhBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"940d7fff2dfc12a79b5958aae7fd69323d0919c43945ee04635851248c80179d","last_reissued_at":"2026-07-04T14:35:28.384178Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:35:28.384178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0108078","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":"2026-07-04T14:35:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3QoX9HRg4yU9eWCuCvmVRtZPpdj6lw/aDqu8j7s2Orc7yRSp+nR64xhMWjRwXgVmhuI5FSek4lS7vOCiHPkqAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:42:10.997619Z"},"content_sha256":"f29b29221b6c270bdec2c242f38bba705ff7492050321065051ee1990e203d45","schema_version":"1.0","event_id":"sha256:f29b29221b6c270bdec2c242f38bba705ff7492050321065051ee1990e203d45"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:SQGX77ZN7QJKPG2ZLCVOP7LJGI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric Syzygies of Canonical Curves of even Genus lying on a K3-Surface","license":"","headline":"","cross_cats":["math.AC"],"primary_cat":"math.AG","authors_text":"Hans-Christian v. Bothmer","submitted_at":"2001-08-10T18:59:28Z","abstract_excerpt":"Based on a recent result of Voisin [2001] we describe the last nonzero syzygy space in the linear strand of a canonical curve C of even genus g=2k lying on a K3 surface, as the ambient space of a k-2-uple embedded P^{k+1}. Furthermore the geometric syzygies constructed by Green and Lazarsfeld [1984] from g^1_{k+1}'s form a non degenerate configuration of finitely many rational normal curves on this P^{k+1}. This proves a natural generalization of Green's conjecture [1984], namely that the geometric syzygies should span the space of all syzygies, in this case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0108078","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0108078/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:35:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4llkYP7GnV4SCq1qTxjEaUPsNytOg2j8gYMh+XRXlS4E3XxRaesmroInkRgB5Nt7WWVRS7frXXG4+7ozXlVpBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T00:42:10.998170Z"},"content_sha256":"bca5b69316dc3cb220e2bb5bf8389244181486ff76f325deff418b6b4965d1e4","schema_version":"1.0","event_id":"sha256:bca5b69316dc3cb220e2bb5bf8389244181486ff76f325deff418b6b4965d1e4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SQGX77ZN7QJKPG2ZLCVOP7LJGI/bundle.json","state_url":"https://pith.science/pith/SQGX77ZN7QJKPG2ZLCVOP7LJGI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SQGX77ZN7QJKPG2ZLCVOP7LJGI/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":"2026-08-09T00:42:11Z","links":{"resolver":"https://pith.science/pith/SQGX77ZN7QJKPG2ZLCVOP7LJGI","bundle":"https://pith.science/pith/SQGX77ZN7QJKPG2ZLCVOP7LJGI/bundle.json","state":"https://pith.science/pith/SQGX77ZN7QJKPG2ZLCVOP7LJGI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SQGX77ZN7QJKPG2ZLCVOP7LJGI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:SQGX77ZN7QJKPG2ZLCVOP7LJGI","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":"1a7b1332d80671a86b93f162d99a74ec5197ce583449ae92d3420834419e2700","cross_cats_sorted":["math.AC"],"license":"","primary_cat":"math.AG","submitted_at":"2001-08-10T18:59:28Z","title_canon_sha256":"f3c3c4ada513fab173003cce1f1263f288b057d6710604fd20b57ff3c55ae0ff"},"schema_version":"1.0","source":{"id":"math/0108078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0108078","created_at":"2026-07-04T14:35:28Z"},{"alias_kind":"arxiv_version","alias_value":"math/0108078v1","created_at":"2026-07-04T14:35:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0108078","created_at":"2026-07-04T14:35:28Z"},{"alias_kind":"pith_short_12","alias_value":"SQGX77ZN7QJK","created_at":"2026-07-04T14:35:28Z"},{"alias_kind":"pith_short_16","alias_value":"SQGX77ZN7QJKPG2Z","created_at":"2026-07-04T14:35:28Z"},{"alias_kind":"pith_short_8","alias_value":"SQGX77ZN","created_at":"2026-07-04T14:35:28Z"}],"graph_snapshots":[{"event_id":"sha256:bca5b69316dc3cb220e2bb5bf8389244181486ff76f325deff418b6b4965d1e4","target":"graph","created_at":"2026-07-04T14:35:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0108078/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Based on a recent result of Voisin [2001] we describe the last nonzero syzygy space in the linear strand of a canonical curve C of even genus g=2k lying on a K3 surface, as the ambient space of a k-2-uple embedded P^{k+1}. Furthermore the geometric syzygies constructed by Green and Lazarsfeld [1984] from g^1_{k+1}'s form a non degenerate configuration of finitely many rational normal curves on this P^{k+1}. This proves a natural generalization of Green's conjecture [1984], namely that the geometric syzygies should span the space of all syzygies, in this case.","authors_text":"Hans-Christian v. Bothmer","cross_cats":["math.AC"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2001-08-10T18:59:28Z","title":"Geometric Syzygies of Canonical Curves of even Genus lying on a K3-Surface"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0108078","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:f29b29221b6c270bdec2c242f38bba705ff7492050321065051ee1990e203d45","target":"record","created_at":"2026-07-04T14:35:28Z","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":"1a7b1332d80671a86b93f162d99a74ec5197ce583449ae92d3420834419e2700","cross_cats_sorted":["math.AC"],"license":"","primary_cat":"math.AG","submitted_at":"2001-08-10T18:59:28Z","title_canon_sha256":"f3c3c4ada513fab173003cce1f1263f288b057d6710604fd20b57ff3c55ae0ff"},"schema_version":"1.0","source":{"id":"math/0108078","kind":"arxiv","version":1}},"canonical_sha256":"940d7fff2dfc12a79b5958aae7fd69323d0919c43945ee04635851248c80179d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"940d7fff2dfc12a79b5958aae7fd69323d0919c43945ee04635851248c80179d","first_computed_at":"2026-07-04T14:35:28.384178Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:28.384178Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UqvCfs2YcyKUo0KyIbLdA5UX82N+BlwSCXTv6JthjzND5tovmYUdEcPqmYSFqUu7Fvft+CoLLVtK1gpZAfDhBA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:28.384578Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0108078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f29b29221b6c270bdec2c242f38bba705ff7492050321065051ee1990e203d45","sha256:bca5b69316dc3cb220e2bb5bf8389244181486ff76f325deff418b6b4965d1e4"],"state_sha256":"fe532794b5a5fd2a4842ff9b577a4dea2b0058d588436d7749421cb6ee636789"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g1aWj3mLBri7uIwkFVaUpi/ga96Y+PsOgESLoMcbMfJfZoBYfPu/TBHz2owjLmZBB0bqE/i/JRabCwBcD3R9Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T00:42:11.001823Z","bundle_sha256":"55bb266ba73443e663b3c4307551ad03a76e721bf2c690a0a7765e472423e799"}}