{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:4XCT2RT6DDGYFFDA5LIN65SVEC","short_pith_number":"pith:4XCT2RT6","canonical_record":{"source":{"id":"2607.16364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-07-17T13:19:46Z","cross_cats_sorted":[],"title_canon_sha256":"fd69e6732c8c7a45ef10be2fd2d5047fc8e6fe1be0fe308dd58cabe0c2a07a72","abstract_canon_sha256":"a4a1e0ea7ba0b277fcbbdfccb9f72c94f6a94e9c4792c5249481a700c2b33aa8"},"schema_version":"1.0"},"canonical_sha256":"e5c53d467e18cd829460ead0df76552090bbfcf26724ad49cb1dbe4917409c3a","source":{"kind":"arxiv","id":"2607.16364","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16364","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16364v1","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16364","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"4XCT2RT6DDGY","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"pith_short_16","alias_value":"4XCT2RT6DDGYFFDA","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"pith_short_8","alias_value":"4XCT2RT6","created_at":"2026-07-21T00:20:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:4XCT2RT6DDGYFFDA5LIN65SVEC","target":"record","payload":{"canonical_record":{"source":{"id":"2607.16364","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-07-17T13:19:46Z","cross_cats_sorted":[],"title_canon_sha256":"fd69e6732c8c7a45ef10be2fd2d5047fc8e6fe1be0fe308dd58cabe0c2a07a72","abstract_canon_sha256":"a4a1e0ea7ba0b277fcbbdfccb9f72c94f6a94e9c4792c5249481a700c2b33aa8"},"schema_version":"1.0"},"canonical_sha256":"e5c53d467e18cd829460ead0df76552090bbfcf26724ad49cb1dbe4917409c3a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-21T00:20:14.250737Z","signature_b64":"IadFUqdQ27emtnWKD4ng80/jlfQyOc21JyD/+y+dZ+lIoj8MSRnBvmSS0Wtz2TEwI/7tOO+Jnu3WU892uOMHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e5c53d467e18cd829460ead0df76552090bbfcf26724ad49cb1dbe4917409c3a","last_reissued_at":"2026-07-21T00:20:14.249873Z","signature_status":"signed_v1","first_computed_at":"2026-07-21T00:20:14.249873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.16364","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":"2026-07-21T00:20:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BZZXi95ib2rbt56YcvRsPUtMBNWoCsy4NStaPR4K2XDcCHpruy2M0ED0OYzDwEmaRhZxOXX+dMRqdOwrDEN2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:57:07.519323Z"},"content_sha256":"39865eb6e100a6099674c8d16be304c001c4c5a870bb263a21f5115b80076fe8","schema_version":"1.0","event_id":"sha256:39865eb6e100a6099674c8d16be304c001c4c5a870bb263a21f5115b80076fe8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:4XCT2RT6DDGYFFDA5LIN65SVEC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$0$-cycles and sheaves on abelian surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Gianluca Pacienza, Giovanni Mongardi, Laura Pertusi","submitted_at":"2026-07-17T13:19:46Z","abstract_excerpt":"We introduce a filtration on the Chow ring of an abelian surface $A$, inspired by O'Grady's filtration on K3 surfaces. We give a geometric description of the filtration, and we prove that it is deeply linked with the rational orbit of points in the generalized Kummer variety of $A$. We propose a conjecture on the second Chern class of sheaves on this abelian surface, and we provide some evidence for the conjecture and prove some of its applications."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16364","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/2607.16364/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":"2026-07-21T00:20:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JFwFCYN/QNqcFlm0rtakWlXz1hxjkPAamFRfH6QgaEHyYUr4GN8FqAbFIS6Dl0lS1dZ4eE9ZpHcKmE/4bFOjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-06T08:57:07.519820Z"},"content_sha256":"eab1cdb63c42c4938484d1089bcb95a0069e21a506f06b2ba1ea289c76205d6f","schema_version":"1.0","event_id":"sha256:eab1cdb63c42c4938484d1089bcb95a0069e21a506f06b2ba1ea289c76205d6f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4XCT2RT6DDGYFFDA5LIN65SVEC/bundle.json","state_url":"https://pith.science/pith/4XCT2RT6DDGYFFDA5LIN65SVEC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4XCT2RT6DDGYFFDA5LIN65SVEC/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":"2026-08-06T08:57:07Z","links":{"resolver":"https://pith.science/pith/4XCT2RT6DDGYFFDA5LIN65SVEC","bundle":"https://pith.science/pith/4XCT2RT6DDGYFFDA5LIN65SVEC/bundle.json","state":"https://pith.science/pith/4XCT2RT6DDGYFFDA5LIN65SVEC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4XCT2RT6DDGYFFDA5LIN65SVEC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4XCT2RT6DDGYFFDA5LIN65SVEC","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":"a4a1e0ea7ba0b277fcbbdfccb9f72c94f6a94e9c4792c5249481a700c2b33aa8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-07-17T13:19:46Z","title_canon_sha256":"fd69e6732c8c7a45ef10be2fd2d5047fc8e6fe1be0fe308dd58cabe0c2a07a72"},"schema_version":"1.0","source":{"id":"2607.16364","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16364","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16364v1","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16364","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"pith_short_12","alias_value":"4XCT2RT6DDGY","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"pith_short_16","alias_value":"4XCT2RT6DDGYFFDA","created_at":"2026-07-21T00:20:14Z"},{"alias_kind":"pith_short_8","alias_value":"4XCT2RT6","created_at":"2026-07-21T00:20:14Z"}],"graph_snapshots":[{"event_id":"sha256:eab1cdb63c42c4938484d1089bcb95a0069e21a506f06b2ba1ea289c76205d6f","target":"graph","created_at":"2026-07-21T00:20:14Z","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/2607.16364/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a filtration on the Chow ring of an abelian surface $A$, inspired by O'Grady's filtration on K3 surfaces. We give a geometric description of the filtration, and we prove that it is deeply linked with the rational orbit of points in the generalized Kummer variety of $A$. We propose a conjecture on the second Chern class of sheaves on this abelian surface, and we provide some evidence for the conjecture and prove some of its applications.","authors_text":"Gianluca Pacienza, Giovanni Mongardi, Laura Pertusi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-07-17T13:19:46Z","title":"$0$-cycles and sheaves on abelian surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16364","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":"sha256:39865eb6e100a6099674c8d16be304c001c4c5a870bb263a21f5115b80076fe8","target":"record","created_at":"2026-07-21T00:20:14Z","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":"a4a1e0ea7ba0b277fcbbdfccb9f72c94f6a94e9c4792c5249481a700c2b33aa8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-07-17T13:19:46Z","title_canon_sha256":"fd69e6732c8c7a45ef10be2fd2d5047fc8e6fe1be0fe308dd58cabe0c2a07a72"},"schema_version":"1.0","source":{"id":"2607.16364","kind":"arxiv","version":1}},"canonical_sha256":"e5c53d467e18cd829460ead0df76552090bbfcf26724ad49cb1dbe4917409c3a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5c53d467e18cd829460ead0df76552090bbfcf26724ad49cb1dbe4917409c3a","first_computed_at":"2026-07-21T00:20:14.249873Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T00:20:14.249873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IadFUqdQ27emtnWKD4ng80/jlfQyOc21JyD/+y+dZ+lIoj8MSRnBvmSS0Wtz2TEwI/7tOO+Jnu3WU892uOMHAg==","signature_status":"signed_v1","signed_at":"2026-07-21T00:20:14.250737Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16364","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39865eb6e100a6099674c8d16be304c001c4c5a870bb263a21f5115b80076fe8","sha256:eab1cdb63c42c4938484d1089bcb95a0069e21a506f06b2ba1ea289c76205d6f"],"state_sha256":"d380c659f741b874cfb3a59ce35c9edeee1dfc0d6719e78afd13eea961fa71a8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JMFCOigB2TG/jW+rOrFPbaWWufG6dQDscLgsefh4oeD/1dfnY+wtxZQgaipkknBn1oVgIjrbip6SVuvWq0/3Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-06T08:57:07.524500Z","bundle_sha256":"bccbefa46ee84d92b234384027b3f0cb46bd9ece48e1e39da1465c432d6b3b37"}}