{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:J3KGMNSBAV2EVNIMNSSQNKDYSI","short_pith_number":"pith:J3KGMNSB","canonical_record":{"source":{"id":"1009.5262","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-27T14:11:52Z","cross_cats_sorted":[],"title_canon_sha256":"81dda4865a77a3ef0c3b692f968544a556803505a0436c8d13239680bd2f913b","abstract_canon_sha256":"ebf8b50a0b4eb3c9728a26536160d8faad1e5b40c29726c9c3b0f41e605f4847"},"schema_version":"1.0"},"canonical_sha256":"4ed466364105744ab50c6ca506a8789223738a288aee094ab5d5cf20e2d881bc","source":{"kind":"arxiv","id":"1009.5262","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5262","created_at":"2026-05-18T03:43:42Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5262v3","created_at":"2026-05-18T03:43:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5262","created_at":"2026-05-18T03:43:42Z"},{"alias_kind":"pith_short_12","alias_value":"J3KGMNSBAV2E","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"J3KGMNSBAV2EVNIM","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"J3KGMNSB","created_at":"2026-05-18T12:26:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:J3KGMNSBAV2EVNIMNSSQNKDYSI","target":"record","payload":{"canonical_record":{"source":{"id":"1009.5262","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-27T14:11:52Z","cross_cats_sorted":[],"title_canon_sha256":"81dda4865a77a3ef0c3b692f968544a556803505a0436c8d13239680bd2f913b","abstract_canon_sha256":"ebf8b50a0b4eb3c9728a26536160d8faad1e5b40c29726c9c3b0f41e605f4847"},"schema_version":"1.0"},"canonical_sha256":"4ed466364105744ab50c6ca506a8789223738a288aee094ab5d5cf20e2d881bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:42.724906Z","signature_b64":"5tSRN0ocDzRxtFGbF8Poz9mGkCCikiXs2n9EHKPiBYIDaJnrW+QdlYdSnRG9zMgJK/igugbRLD9jTeJG9cnECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4ed466364105744ab50c6ca506a8789223738a288aee094ab5d5cf20e2d881bc","last_reissued_at":"2026-05-18T03:43:42.724331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:42.724331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1009.5262","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B0kdxgodqtHe2awxEVo7+K9CgsvNdt3iPllGxPPGekG60NDsVeSx5pEUrQAwEnLfr6Ns/025dEiOzIcw93L+DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:44:41.557463Z"},"content_sha256":"75aec0387d6034698606ac3ad1f1f10100debc8ea1a9471536ac805b344a375e","schema_version":"1.0","event_id":"sha256:75aec0387d6034698606ac3ad1f1f10100debc8ea1a9471536ac805b344a375e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:J3KGMNSBAV2EVNIMNSSQNKDYSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A remark on the Generalized Hodge Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Dario Portelli","submitted_at":"2010-09-27T14:11:52Z","abstract_excerpt":"Let X be a smooth, projective variety over the field of complex numbers. On the space H of its rational cohomology of degree i we have the arithmetic filtration F^p. On the other hand, on the space of cohomology of degree i of X with complex coefficients we have the Hodge filtration G^p. It is well known that F^p is contained in the intersection of G^p with H, and that, in general, this inclusion is strict. In this paper we propose a natural substitute S^p for the Hodge filtration space G^p such that the intersection of S^p with H is the space F^p of the arithmetic filtration. In particular, S"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5262","kind":"arxiv","version":3},"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":"2026-05-18T03:43:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"A4rtwUl6Pd/fi+zRXKwiu9AU/b517Kmm84QnZqC65gwmT9FZ4srvc2smotCWrZsqeHJRhKN90Pr4PzPGUVpLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:44:41.557811Z"},"content_sha256":"a342b4c1b79b8b99d5a783371ed88b780437474609b38293ee947bc3b84c9fd2","schema_version":"1.0","event_id":"sha256:a342b4c1b79b8b99d5a783371ed88b780437474609b38293ee947bc3b84c9fd2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J3KGMNSBAV2EVNIMNSSQNKDYSI/bundle.json","state_url":"https://pith.science/pith/J3KGMNSBAV2EVNIMNSSQNKDYSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J3KGMNSBAV2EVNIMNSSQNKDYSI/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":"2026-06-24T18:44:41Z","links":{"resolver":"https://pith.science/pith/J3KGMNSBAV2EVNIMNSSQNKDYSI","bundle":"https://pith.science/pith/J3KGMNSBAV2EVNIMNSSQNKDYSI/bundle.json","state":"https://pith.science/pith/J3KGMNSBAV2EVNIMNSSQNKDYSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J3KGMNSBAV2EVNIMNSSQNKDYSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:J3KGMNSBAV2EVNIMNSSQNKDYSI","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":"ebf8b50a0b4eb3c9728a26536160d8faad1e5b40c29726c9c3b0f41e605f4847","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-27T14:11:52Z","title_canon_sha256":"81dda4865a77a3ef0c3b692f968544a556803505a0436c8d13239680bd2f913b"},"schema_version":"1.0","source":{"id":"1009.5262","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.5262","created_at":"2026-05-18T03:43:42Z"},{"alias_kind":"arxiv_version","alias_value":"1009.5262v3","created_at":"2026-05-18T03:43:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.5262","created_at":"2026-05-18T03:43:42Z"},{"alias_kind":"pith_short_12","alias_value":"J3KGMNSBAV2E","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_16","alias_value":"J3KGMNSBAV2EVNIM","created_at":"2026-05-18T12:26:09Z"},{"alias_kind":"pith_short_8","alias_value":"J3KGMNSB","created_at":"2026-05-18T12:26:09Z"}],"graph_snapshots":[{"event_id":"sha256:a342b4c1b79b8b99d5a783371ed88b780437474609b38293ee947bc3b84c9fd2","target":"graph","created_at":"2026-05-18T03:43:42Z","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":"Let X be a smooth, projective variety over the field of complex numbers. On the space H of its rational cohomology of degree i we have the arithmetic filtration F^p. On the other hand, on the space of cohomology of degree i of X with complex coefficients we have the Hodge filtration G^p. It is well known that F^p is contained in the intersection of G^p with H, and that, in general, this inclusion is strict. In this paper we propose a natural substitute S^p for the Hodge filtration space G^p such that the intersection of S^p with H is the space F^p of the arithmetic filtration. In particular, S","authors_text":"Dario Portelli","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-27T14:11:52Z","title":"A remark on the Generalized Hodge Conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.5262","kind":"arxiv","version":3},"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":"sha256:75aec0387d6034698606ac3ad1f1f10100debc8ea1a9471536ac805b344a375e","target":"record","created_at":"2026-05-18T03:43:42Z","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":"ebf8b50a0b4eb3c9728a26536160d8faad1e5b40c29726c9c3b0f41e605f4847","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-09-27T14:11:52Z","title_canon_sha256":"81dda4865a77a3ef0c3b692f968544a556803505a0436c8d13239680bd2f913b"},"schema_version":"1.0","source":{"id":"1009.5262","kind":"arxiv","version":3}},"canonical_sha256":"4ed466364105744ab50c6ca506a8789223738a288aee094ab5d5cf20e2d881bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4ed466364105744ab50c6ca506a8789223738a288aee094ab5d5cf20e2d881bc","first_computed_at":"2026-05-18T03:43:42.724331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:42.724331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5tSRN0ocDzRxtFGbF8Poz9mGkCCikiXs2n9EHKPiBYIDaJnrW+QdlYdSnRG9zMgJK/igugbRLD9jTeJG9cnECg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:42.724906Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.5262","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75aec0387d6034698606ac3ad1f1f10100debc8ea1a9471536ac805b344a375e","sha256:a342b4c1b79b8b99d5a783371ed88b780437474609b38293ee947bc3b84c9fd2"],"state_sha256":"19354e240353d8b5dda8550fece3455aea056d983b85f6d3adee45c3254caa95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CL/alAEPjwdNvSu/FjrS1HHuBkYe9NX8qgj3QpgUVSqKrF9Aq1N8zx7+XyQ1YoWBsg0FoMeHghzDyuPYPAh0AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:44:41.559744Z","bundle_sha256":"0a67459af9e50be897ac63912b9d6a023c00d177fa962fa7bf983c4866df051a"}}