{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:76CYVY3ZPZGFCZKXE4OZHPJ4YL","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":"16a6c7134d0bd37e9348524f18b9fe9830588090370569f896c6090d319a83ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-13T17:04:12Z","title_canon_sha256":"6c36054de5e63b4766e2ad300f8ce604ff33adff567fd21f64a69f76881694a1"},"schema_version":"1.0","source":{"id":"1010.2704","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.2704","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"arxiv_version","alias_value":"1010.2704v1","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.2704","created_at":"2026-05-18T02:38:18Z"},{"alias_kind":"pith_short_12","alias_value":"76CYVY3ZPZGF","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"76CYVY3ZPZGFCZKX","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"76CYVY3Z","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:c30acbfeaff8262864aec0fcc014fff524934009f378b5ae86e11c626cc3cf4a","target":"graph","created_at":"2026-05-18T02:38:18Z","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 $p:F\\to G$ be a morphism of stacks of positive \\emph{virtual} relative dimension $k$ and let $\\gamma\\in H^k(F)$. We give sufficient conditions for $p_*\\gamma\\cdot[F]^{virt}$ to be a multiple of $[G]^{virt}$. We apply this result to show an analogue of the conservation of number for virtually smooth families. We show implications to Gromov-Witten invariants and give a new proof of a theorem of Marian, Oprea and Pandharipande which compares the virtual classes of moduli spaces of stable maps and moduli spaces of stable quotients.","authors_text":"Cristina Manolache","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-13T17:04:12Z","title":"Virtual push-forwards"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2704","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":"sha256:430cf599ffd0403d37f823ef7b25311987a3f9d0fc5712734d14c644024f62c5","target":"record","created_at":"2026-05-18T02:38:18Z","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":"16a6c7134d0bd37e9348524f18b9fe9830588090370569f896c6090d319a83ce","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-10-13T17:04:12Z","title_canon_sha256":"6c36054de5e63b4766e2ad300f8ce604ff33adff567fd21f64a69f76881694a1"},"schema_version":"1.0","source":{"id":"1010.2704","kind":"arxiv","version":1}},"canonical_sha256":"ff858ae3797e4c516557271d93bd3cc2d0b6cd117b03071429a8cd6500dd1dd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff858ae3797e4c516557271d93bd3cc2d0b6cd117b03071429a8cd6500dd1dd4","first_computed_at":"2026-05-18T02:38:18.372691Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:38:18.372691Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uGJtBmXA+emCjBP4cbbJc7XXrkFboQhb7C4pS0pB8uRsdTf5QSiQW79OIpT6M0e0A6v0dosywRApub55zAAdAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:38:18.373253Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.2704","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:430cf599ffd0403d37f823ef7b25311987a3f9d0fc5712734d14c644024f62c5","sha256:c30acbfeaff8262864aec0fcc014fff524934009f378b5ae86e11c626cc3cf4a"],"state_sha256":"6efb7b6a6da121b070504c649804f294f0a20d2747024c953fa282078bd37845"}