{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JGZZ4FVTQLOH2ODNZLT2QHYI4J","short_pith_number":"pith:JGZZ4FVT","canonical_record":{"source":{"id":"1510.05832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-20T10:54:21Z","cross_cats_sorted":[],"title_canon_sha256":"09a8e50db4f6b9d7ab61041d08e49c207e7c3aab4106ec571105e20f7c41528c","abstract_canon_sha256":"fca23d42d7851077d135757fe566f9637d1377756812e7f93a059d09af2ddb2e"},"schema_version":"1.0"},"canonical_sha256":"49b39e16b382dc7d386dcae7a81f08e266b183ff91c863ea3cf6d5275581e672","source":{"kind":"arxiv","id":"1510.05832","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05832","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05832v1","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05832","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"JGZZ4FVTQLOH","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JGZZ4FVTQLOH2ODN","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JGZZ4FVT","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JGZZ4FVTQLOH2ODNZLT2QHYI4J","target":"record","payload":{"canonical_record":{"source":{"id":"1510.05832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-20T10:54:21Z","cross_cats_sorted":[],"title_canon_sha256":"09a8e50db4f6b9d7ab61041d08e49c207e7c3aab4106ec571105e20f7c41528c","abstract_canon_sha256":"fca23d42d7851077d135757fe566f9637d1377756812e7f93a059d09af2ddb2e"},"schema_version":"1.0"},"canonical_sha256":"49b39e16b382dc7d386dcae7a81f08e266b183ff91c863ea3cf6d5275581e672","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:39.572746Z","signature_b64":"FCba4qoueFhUgzpwwDXORF/BNE6TwFacnGSK/KAqDuD5cz7m5yaNn33wh4jsCaW0LNSL5JsGrnSsNLfK2qinCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49b39e16b382dc7d386dcae7a81f08e266b183ff91c863ea3cf6d5275581e672","last_reissued_at":"2026-05-18T01:29:39.572254Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:39.572254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.05832","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":"2026-05-18T01:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a79Q9veu5PT4DarvS0zsbkBQ6FEr18Z/qBESJ+ZowR26mwJUPkXj8BaTohrOwX0+0C8JDHCFEH+Ub+XtZ58+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:01:39.167228Z"},"content_sha256":"ea8989165d22951969605ea9939e9bec0d94e863c42162f494ba708b47abda6f","schema_version":"1.0","event_id":"sha256:ea8989165d22951969605ea9939e9bec0d94e863c42162f494ba708b47abda6f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JGZZ4FVTQLOH2ODNZLT2QHYI4J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bloch's conjecture and valences of correspondences for K3 surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Claudio Pedrini","submitted_at":"2015-10-20T10:54:21Z","abstract_excerpt":"Bloch's conjecture for a surface $X$ over an algebraically closed field $k$ states that every homologically trivial correspondence $\\Gamma $ acts as 0 on the Albanese kernel $T(X_{\\Omega})$, where $\\Omega $ is a universal domain containing $k$. Here we prove that, for a complex K3 surface $X$, Bloch's conjecture is equivalent to the existence of a valence for every correspondence. We also give applications of this result to the case of a correspondence associated to an automorphisms of finite order and to the existence of constant cycle curves on $X$. Finally we show that Franchetta's conjectu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05832","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":"2026-05-18T01:29:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3I67wKbIqUllqp5l3Xopums6gWnkL5jcOHUWFIw6AvdjidUK0s7/saXUMmtICnLJjeMVhcerDWNJ7/Ru68cBDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T11:01:39.168409Z"},"content_sha256":"629f7993c48a8f0c112f402e1bf96f1da6258958348d452f2eb2118e9689dfec","schema_version":"1.0","event_id":"sha256:629f7993c48a8f0c112f402e1bf96f1da6258958348d452f2eb2118e9689dfec"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JGZZ4FVTQLOH2ODNZLT2QHYI4J/bundle.json","state_url":"https://pith.science/pith/JGZZ4FVTQLOH2ODNZLT2QHYI4J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JGZZ4FVTQLOH2ODNZLT2QHYI4J/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":"2026-05-31T11:01:39Z","links":{"resolver":"https://pith.science/pith/JGZZ4FVTQLOH2ODNZLT2QHYI4J","bundle":"https://pith.science/pith/JGZZ4FVTQLOH2ODNZLT2QHYI4J/bundle.json","state":"https://pith.science/pith/JGZZ4FVTQLOH2ODNZLT2QHYI4J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JGZZ4FVTQLOH2ODNZLT2QHYI4J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JGZZ4FVTQLOH2ODNZLT2QHYI4J","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":"fca23d42d7851077d135757fe566f9637d1377756812e7f93a059d09af2ddb2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-20T10:54:21Z","title_canon_sha256":"09a8e50db4f6b9d7ab61041d08e49c207e7c3aab4106ec571105e20f7c41528c"},"schema_version":"1.0","source":{"id":"1510.05832","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.05832","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"arxiv_version","alias_value":"1510.05832v1","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.05832","created_at":"2026-05-18T01:29:39Z"},{"alias_kind":"pith_short_12","alias_value":"JGZZ4FVTQLOH","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JGZZ4FVTQLOH2ODN","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JGZZ4FVT","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:629f7993c48a8f0c112f402e1bf96f1da6258958348d452f2eb2118e9689dfec","target":"graph","created_at":"2026-05-18T01:29:39Z","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":"Bloch's conjecture for a surface $X$ over an algebraically closed field $k$ states that every homologically trivial correspondence $\\Gamma $ acts as 0 on the Albanese kernel $T(X_{\\Omega})$, where $\\Omega $ is a universal domain containing $k$. Here we prove that, for a complex K3 surface $X$, Bloch's conjecture is equivalent to the existence of a valence for every correspondence. We also give applications of this result to the case of a correspondence associated to an automorphisms of finite order and to the existence of constant cycle curves on $X$. Finally we show that Franchetta's conjectu","authors_text":"Claudio Pedrini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-20T10:54:21Z","title":"Bloch's conjecture and valences of correspondences for K3 surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.05832","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:ea8989165d22951969605ea9939e9bec0d94e863c42162f494ba708b47abda6f","target":"record","created_at":"2026-05-18T01:29:39Z","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":"fca23d42d7851077d135757fe566f9637d1377756812e7f93a059d09af2ddb2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-20T10:54:21Z","title_canon_sha256":"09a8e50db4f6b9d7ab61041d08e49c207e7c3aab4106ec571105e20f7c41528c"},"schema_version":"1.0","source":{"id":"1510.05832","kind":"arxiv","version":1}},"canonical_sha256":"49b39e16b382dc7d386dcae7a81f08e266b183ff91c863ea3cf6d5275581e672","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"49b39e16b382dc7d386dcae7a81f08e266b183ff91c863ea3cf6d5275581e672","first_computed_at":"2026-05-18T01:29:39.572254Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:39.572254Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FCba4qoueFhUgzpwwDXORF/BNE6TwFacnGSK/KAqDuD5cz7m5yaNn33wh4jsCaW0LNSL5JsGrnSsNLfK2qinCg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:39.572746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.05832","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ea8989165d22951969605ea9939e9bec0d94e863c42162f494ba708b47abda6f","sha256:629f7993c48a8f0c112f402e1bf96f1da6258958348d452f2eb2118e9689dfec"],"state_sha256":"be14dada3f731bee73be0ecd66f7a1eee604a4df37b82bd99eeb0c71209f6e3b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9zhhHJ87Tl07Zynt5HfLv06hsTsMFt9ajGsEUjPMuTuYiif/6fC+nY9abEtY/W/QQlJLav7nnq6m8yrloH76Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T11:01:39.171939Z","bundle_sha256":"f0e70eb0da56b443a426cd95a3105132591c0a7622c3ffd3d09139a9115a21c3"}}