{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:JWB6IPXU4RLFKAGIHGYYPJQMZ3","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":"b80c4642da605f8276008e8ad2f82ade8adda28c5bec99232b858f51c57a81f0","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-12T15:01:47Z","title_canon_sha256":"d98d809524898a2e0fae2d49474603083e81f8e2af0787ece97fbb15888168e7"},"schema_version":"1.0","source":{"id":"2505.07632","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.07632","created_at":"2026-07-05T11:29:34Z"},{"alias_kind":"arxiv_version","alias_value":"2505.07632v2","created_at":"2026-07-05T11:29:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.07632","created_at":"2026-07-05T11:29:34Z"},{"alias_kind":"pith_short_12","alias_value":"JWB6IPXU4RLF","created_at":"2026-07-05T11:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"JWB6IPXU4RLFKAGI","created_at":"2026-07-05T11:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"JWB6IPXU","created_at":"2026-07-05T11:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:961c1ad8fac8bc0a0a7f1bca4242543821fab391c362865301a87f0dae3cfc4b","target":"graph","created_at":"2026-07-05T11:29:34Z","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/2505.07632/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let X be a normal quasi-projective variety over $\\mathbb{C}$. We study its higher Albanese manifolds, introduced by Hain and Zucker, from the point of view of o-minimal geometry. We show that for each $s$ the higher Albanese manifold $\\operatorname{Alb}^s(X)$ can be functorially endowed with a structure of an $\\mathbb{R}_{\\operatorname{alg}}$-definable complex manifold in such a way that the natural projections $\\operatorname{Alb}^s(X) \\to \\operatorname{Alb}^{s-1}(X)$ are $\\mathbb{R}_{\\operatorname{alg}}$-definable and the higher Albanese maps $\\operatorname{alb}^s \\colon X^{\\operatorname{an}}","authors_text":"Vasily Rogov","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-12T15:01:47Z","title":"O-minimal geometry of higher Albanese manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.07632","kind":"arxiv","version":2},"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:ad67b6db41e4485b5e879c092c40903f0b3058df3c64664ecc52d581405c796b","target":"record","created_at":"2026-07-05T11:29:34Z","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":"b80c4642da605f8276008e8ad2f82ade8adda28c5bec99232b858f51c57a81f0","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-05-12T15:01:47Z","title_canon_sha256":"d98d809524898a2e0fae2d49474603083e81f8e2af0787ece97fbb15888168e7"},"schema_version":"1.0","source":{"id":"2505.07632","kind":"arxiv","version":2}},"canonical_sha256":"4d83e43ef4e4565500c839b187a60cced3fcfd557ee97e1953eb0e8d3a705093","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d83e43ef4e4565500c839b187a60cced3fcfd557ee97e1953eb0e8d3a705093","first_computed_at":"2026-07-05T11:29:34.682272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:29:34.682272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/3oolL/XylqT6zaQ7bJVmcUxTAZKc+L4ttIwRzf0y69SQp3SWkr/X9hlCvy9cWFps/Gs27G+OhAvlwIsVgGMAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:29:34.682791Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.07632","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ad67b6db41e4485b5e879c092c40903f0b3058df3c64664ecc52d581405c796b","sha256:961c1ad8fac8bc0a0a7f1bca4242543821fab391c362865301a87f0dae3cfc4b"],"state_sha256":"b6b4cf58234ea774bb2469e73d310d923f10117da88dffda80fed39f3261511c"}