{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:PGB4QYZAHRSAZ5TOXOF242FB4W","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":"a79e60cf1b6f36c982f52ea2536bd428ce5e08010189b511f85e5eda0b07b9e5","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-06-21T23:12:29Z","title_canon_sha256":"b619f7c3bba93ad9a26eec60687a3dacd8e64086fb4f4b11e5ecac01aa73892d"},"schema_version":"1.0","source":{"id":"2506.17854","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.17854","created_at":"2026-07-05T11:25:24Z"},{"alias_kind":"arxiv_version","alias_value":"2506.17854v1","created_at":"2026-07-05T11:25:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.17854","created_at":"2026-07-05T11:25:24Z"},{"alias_kind":"pith_short_12","alias_value":"PGB4QYZAHRSA","created_at":"2026-07-05T11:25:24Z"},{"alias_kind":"pith_short_16","alias_value":"PGB4QYZAHRSAZ5TO","created_at":"2026-07-05T11:25:24Z"},{"alias_kind":"pith_short_8","alias_value":"PGB4QYZA","created_at":"2026-07-05T11:25:24Z"}],"graph_snapshots":[{"event_id":"sha256:69b76574c95e6985d88c81b035c8a0373cf62f650dce704c061e01b6be2a23f2","target":"graph","created_at":"2026-07-05T11:25:24Z","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/2506.17854/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Quadratic Gromov--Witten invariants allow one to obtain an arithmetically meaningful count of curves satisfying constraints over a field $k$ without assuming that $k$ is the field of complex or real numbers. This paper studies the behavior of quadratic genus $0$ Gromov--Witten invariants during an algebraic analogue of surgery on del Pezzo surfaces. For this, we define and study (twisted) binomial coefficients in the Grothendieck--Witt group, building on work of Serre. We obtain a formula expressing the quadratic genus $0$ Gromov--Witten invariants of surfaces obtained as a smoothing of a give","authors_text":"Erwan Brugall\\'e, Kirsten Wickelgren","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-06-21T23:12:29Z","title":"A quadratic Abramovich-Bertram formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.17854","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:b5b8500007e7d4e8132f68ddda2093e3dbe52f6bb4c4ff48d375071522e5f62c","target":"record","created_at":"2026-07-05T11:25:24Z","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":"a79e60cf1b6f36c982f52ea2536bd428ce5e08010189b511f85e5eda0b07b9e5","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-06-21T23:12:29Z","title_canon_sha256":"b619f7c3bba93ad9a26eec60687a3dacd8e64086fb4f4b11e5ecac01aa73892d"},"schema_version":"1.0","source":{"id":"2506.17854","kind":"arxiv","version":1}},"canonical_sha256":"7983c863203c640cf66ebb8bae68a1e58764e97c44066db32848214f445180ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7983c863203c640cf66ebb8bae68a1e58764e97c44066db32848214f445180ce","first_computed_at":"2026-07-05T11:25:24.436005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:25:24.436005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bxYN6fJyTMZ3Zjb/uXnlu+2Qu8T+Yq+LZzQ8PisK06a+EF7ahpVrkm6Pyanfrp1nrg+1ZEbvkRGQjdPubHqvBw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:25:24.436427Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.17854","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5b8500007e7d4e8132f68ddda2093e3dbe52f6bb4c4ff48d375071522e5f62c","sha256:69b76574c95e6985d88c81b035c8a0373cf62f650dce704c061e01b6be2a23f2"],"state_sha256":"c815ee3a6ff73bbe2ca48e93b0020fbbdd7d680f22ecb9768e6ada5865964739"}