{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1997:QHSBPLRPUU76YN5Z3JQZYNRQDO","short_pith_number":"pith:QHSBPLRP","canonical_record":{"source":{"id":"alg-geom/9710025","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1997-10-20T10:49:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e4fb0aef015230964db8b302aea59c799a569d2bc661109dce3bd6273af0edf5","abstract_canon_sha256":"e57580c7b6558bbe635b429c2fc4b4feeade89901f9f21b00114cf07e364e158"},"schema_version":"1.0"},"canonical_sha256":"81e417ae2fa53fec37b9da619c36301b836980985533e59d377f480806a08910","source":{"kind":"arxiv","id":"alg-geom/9710025","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9710025","created_at":"2026-07-04T14:10:03Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9710025v1","created_at":"2026-07-04T14:10:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9710025","created_at":"2026-07-04T14:10:03Z"},{"alias_kind":"pith_short_12","alias_value":"QHSBPLRPUU76","created_at":"2026-07-04T14:10:03Z"},{"alias_kind":"pith_short_16","alias_value":"QHSBPLRPUU76YN5Z","created_at":"2026-07-04T14:10:03Z"},{"alias_kind":"pith_short_8","alias_value":"QHSBPLRP","created_at":"2026-07-04T14:10:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1997:QHSBPLRPUU76YN5Z3JQZYNRQDO","target":"record","payload":{"canonical_record":{"source":{"id":"alg-geom/9710025","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"alg-geom","submitted_at":"1997-10-20T10:49:54Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e4fb0aef015230964db8b302aea59c799a569d2bc661109dce3bd6273af0edf5","abstract_canon_sha256":"e57580c7b6558bbe635b429c2fc4b4feeade89901f9f21b00114cf07e364e158"},"schema_version":"1.0"},"canonical_sha256":"81e417ae2fa53fec37b9da619c36301b836980985533e59d377f480806a08910","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:10:03.404673Z","signature_b64":"Ng04FIsdHb5lpBaFNlfOyAi/kPpsh4TF+vLpha9NRkeEvCx2x7J/og7nwup7miZ4tuVva3G5WMea+W9AaEnTAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"81e417ae2fa53fec37b9da619c36301b836980985533e59d377f480806a08910","last_reissued_at":"2026-07-04T14:10:03.404291Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:10:03.404291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"alg-geom/9710025","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":"2026-07-04T14:10:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"osBJ0IaZOHlsXE3fCgOoDuXER3aoa16E68ID9IqMkIYkprEJdjtgZcSNmZWQ6neDsgy10xFlmvz7ZV/dp9zXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:06:39.388769Z"},"content_sha256":"b00b43156a7c45e5f56a885ebedb95ed4b2a689e7688d12101cedcb6ebd3e414","schema_version":"1.0","event_id":"sha256:b00b43156a7c45e5f56a885ebedb95ed4b2a689e7688d12101cedcb6ebd3e414"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1997:QHSBPLRPUU76YN5Z3JQZYNRQDO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal even sets of nodes","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"Stephan Endrass","submitted_at":"1997-10-20T10:49:54Z","abstract_excerpt":"We extend some results on even sets of nodes which have been proved for surfaces up to degree 6 to surfaces up to degree 10. In particular, we give a formula for the minimal cardinality of a nonempty even set of nodes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9710025","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/alg-geom/9710025/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":"2026-07-04T14:10:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zUZ1OWQZ2VJZnGqzJpkHxcKp+qFLIBwePG3PZblZVlJxX6FIKqiP88eQY9tlDyV+NXDPNxg66Jpl03Xk/00nDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:06:39.389286Z"},"content_sha256":"9741743010c3b845af052cef0526f1191557a560da8c3bd1d8a38e3dcfe0403d","schema_version":"1.0","event_id":"sha256:9741743010c3b845af052cef0526f1191557a560da8c3bd1d8a38e3dcfe0403d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QHSBPLRPUU76YN5Z3JQZYNRQDO/bundle.json","state_url":"https://pith.science/pith/QHSBPLRPUU76YN5Z3JQZYNRQDO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QHSBPLRPUU76YN5Z3JQZYNRQDO/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":"2026-08-11T21:06:39Z","links":{"resolver":"https://pith.science/pith/QHSBPLRPUU76YN5Z3JQZYNRQDO","bundle":"https://pith.science/pith/QHSBPLRPUU76YN5Z3JQZYNRQDO/bundle.json","state":"https://pith.science/pith/QHSBPLRPUU76YN5Z3JQZYNRQDO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QHSBPLRPUU76YN5Z3JQZYNRQDO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1997:QHSBPLRPUU76YN5Z3JQZYNRQDO","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":"e57580c7b6558bbe635b429c2fc4b4feeade89901f9f21b00114cf07e364e158","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1997-10-20T10:49:54Z","title_canon_sha256":"e4fb0aef015230964db8b302aea59c799a569d2bc661109dce3bd6273af0edf5"},"schema_version":"1.0","source":{"id":"alg-geom/9710025","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"alg-geom/9710025","created_at":"2026-07-04T14:10:03Z"},{"alias_kind":"arxiv_version","alias_value":"alg-geom/9710025v1","created_at":"2026-07-04T14:10:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.alg-geom/9710025","created_at":"2026-07-04T14:10:03Z"},{"alias_kind":"pith_short_12","alias_value":"QHSBPLRPUU76","created_at":"2026-07-04T14:10:03Z"},{"alias_kind":"pith_short_16","alias_value":"QHSBPLRPUU76YN5Z","created_at":"2026-07-04T14:10:03Z"},{"alias_kind":"pith_short_8","alias_value":"QHSBPLRP","created_at":"2026-07-04T14:10:03Z"}],"graph_snapshots":[{"event_id":"sha256:9741743010c3b845af052cef0526f1191557a560da8c3bd1d8a38e3dcfe0403d","target":"graph","created_at":"2026-07-04T14:10:03Z","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/alg-geom/9710025/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We extend some results on even sets of nodes which have been proved for surfaces up to degree 6 to surfaces up to degree 10. In particular, we give a formula for the minimal cardinality of a nonempty even set of nodes.","authors_text":"Stephan Endrass","cross_cats":["math.AG"],"headline":"","license":"","primary_cat":"alg-geom","submitted_at":"1997-10-20T10:49:54Z","title":"Minimal even sets of nodes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9710025","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:b00b43156a7c45e5f56a885ebedb95ed4b2a689e7688d12101cedcb6ebd3e414","target":"record","created_at":"2026-07-04T14:10:03Z","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":"e57580c7b6558bbe635b429c2fc4b4feeade89901f9f21b00114cf07e364e158","cross_cats_sorted":["math.AG"],"license":"","primary_cat":"alg-geom","submitted_at":"1997-10-20T10:49:54Z","title_canon_sha256":"e4fb0aef015230964db8b302aea59c799a569d2bc661109dce3bd6273af0edf5"},"schema_version":"1.0","source":{"id":"alg-geom/9710025","kind":"arxiv","version":1}},"canonical_sha256":"81e417ae2fa53fec37b9da619c36301b836980985533e59d377f480806a08910","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"81e417ae2fa53fec37b9da619c36301b836980985533e59d377f480806a08910","first_computed_at":"2026-07-04T14:10:03.404291Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:10:03.404291Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ng04FIsdHb5lpBaFNlfOyAi/kPpsh4TF+vLpha9NRkeEvCx2x7J/og7nwup7miZ4tuVva3G5WMea+W9AaEnTAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:10:03.404673Z","signed_message":"canonical_sha256_bytes"},"source_id":"alg-geom/9710025","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b00b43156a7c45e5f56a885ebedb95ed4b2a689e7688d12101cedcb6ebd3e414","sha256:9741743010c3b845af052cef0526f1191557a560da8c3bd1d8a38e3dcfe0403d"],"state_sha256":"9bdf6166793b72ce34f254c025e2c72cdca2313a57e43669d4ec27751d9b5b6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rhiYpMoa8CCf/seu23liHuVmpJzWoLsCnEGLI1mYa+I1VPFqhx9h3jEUebEuNUlNHjh1dHIjSQecVQei9nSHDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T21:06:39.393665Z","bundle_sha256":"fd8c880d1b1359515bd6c0ff365acd4b1722efaa04b754528782da454723bd6c"}}