{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:S6MSPRKKMGRQCXF6PQA6R35E7B","short_pith_number":"pith:S6MSPRKK","canonical_record":{"source":{"id":"2309.07041","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.SG","submitted_at":"2023-09-13T15:53:18Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"7664f884d3bdbe3e950afdc5a681219c1d462f0b22d2181815203b54203f1371","abstract_canon_sha256":"511ec229210ea0097702585842b2d6908d633ea4171f5558514bde143c7a3ae2"},"schema_version":"1.0"},"canonical_sha256":"979927c54a61a3015cbe7c01e8efa4f867d0111aafb5fde2087ebb16d0582a95","source":{"kind":"arxiv","id":"2309.07041","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.07041","created_at":"2026-07-05T10:47:24Z"},{"alias_kind":"arxiv_version","alias_value":"2309.07041v3","created_at":"2026-07-05T10:47:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.07041","created_at":"2026-07-05T10:47:24Z"},{"alias_kind":"pith_short_12","alias_value":"S6MSPRKKMGRQ","created_at":"2026-07-05T10:47:24Z"},{"alias_kind":"pith_short_16","alias_value":"S6MSPRKKMGRQCXF6","created_at":"2026-07-05T10:47:24Z"},{"alias_kind":"pith_short_8","alias_value":"S6MSPRKK","created_at":"2026-07-05T10:47:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:S6MSPRKKMGRQCXF6PQA6R35E7B","target":"record","payload":{"canonical_record":{"source":{"id":"2309.07041","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.SG","submitted_at":"2023-09-13T15:53:18Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"7664f884d3bdbe3e950afdc5a681219c1d462f0b22d2181815203b54203f1371","abstract_canon_sha256":"511ec229210ea0097702585842b2d6908d633ea4171f5558514bde143c7a3ae2"},"schema_version":"1.0"},"canonical_sha256":"979927c54a61a3015cbe7c01e8efa4f867d0111aafb5fde2087ebb16d0582a95","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:47:24.098940Z","signature_b64":"Vq1Z1ewGpTO62yQn3c2QUFS5kTCQxgEv76VUL6F6MvSbJ1ni+98NKI8TiGESUuciGeuvfH84P5mCV9RE9k5OBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"979927c54a61a3015cbe7c01e8efa4f867d0111aafb5fde2087ebb16d0582a95","last_reissued_at":"2026-07-05T10:47:24.098466Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:47:24.098466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.07041","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":"2026-07-05T10:47:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xNT65+nj7FTRDPqDIFmdMUPzOQBEJ2epFh0EKHSMcBXDJG3o6rH/cgLbsyJ2Clw9y4DCJz1y348DHYxA0AIRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:30:38.232870Z"},"content_sha256":"e3ee34a2833c8dca0f609d07d1cd7cc5024d9039bee512292e204d33342e2ec6","schema_version":"1.0","event_id":"sha256:e3ee34a2833c8dca0f609d07d1cd7cc5024d9039bee512292e204d33342e2ec6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:S6MSPRKKMGRQCXF6PQA6R35E7B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Donaldson's 4-6 question","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Amanda Hirschi, Luya Wang","submitted_at":"2023-09-13T15:53:18Z","abstract_excerpt":"We prove that the examples by Smith and McMullen-Taubes provide infinitely many counterexamples to one direction of Donaldson's 4-6 question and the closely related Stabilising Conjecture. These are the first known counterexamples. In the other direction, we show that the Gromov-Witten invariants of two simply-connected closed symplectic $4$-manifolds, whose products with $(S^2,\\omega_{\\text{std}})$ are deformation equivalent, agree. In particular, when $b_2^+ \\geq 2$, these $4$-manifolds have the same Seiberg-Witten invariants. Furthermore, one can replace $(S^2,\\omega_{\\text{std}})$ by $(S^2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.07041","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2309.07041/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":"2026-07-05T10:47:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0Ib1loe6JE46X0JxBSuM5Z5JyFp2K1OWzGHckMh1Q5pmIwZQWAiwibYMmu4n8STWWfDvVrjLB7Fd+kO04LazDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T16:30:38.233383Z"},"content_sha256":"c43b024e4775c51df350754090ae700d48f8c74b542255c9eccbbf91a79729c3","schema_version":"1.0","event_id":"sha256:c43b024e4775c51df350754090ae700d48f8c74b542255c9eccbbf91a79729c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S6MSPRKKMGRQCXF6PQA6R35E7B/bundle.json","state_url":"https://pith.science/pith/S6MSPRKKMGRQCXF6PQA6R35E7B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S6MSPRKKMGRQCXF6PQA6R35E7B/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":"2026-08-03T16:30:38Z","links":{"resolver":"https://pith.science/pith/S6MSPRKKMGRQCXF6PQA6R35E7B","bundle":"https://pith.science/pith/S6MSPRKKMGRQCXF6PQA6R35E7B/bundle.json","state":"https://pith.science/pith/S6MSPRKKMGRQCXF6PQA6R35E7B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S6MSPRKKMGRQCXF6PQA6R35E7B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:S6MSPRKKMGRQCXF6PQA6R35E7B","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":"511ec229210ea0097702585842b2d6908d633ea4171f5558514bde143c7a3ae2","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.SG","submitted_at":"2023-09-13T15:53:18Z","title_canon_sha256":"7664f884d3bdbe3e950afdc5a681219c1d462f0b22d2181815203b54203f1371"},"schema_version":"1.0","source":{"id":"2309.07041","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.07041","created_at":"2026-07-05T10:47:24Z"},{"alias_kind":"arxiv_version","alias_value":"2309.07041v3","created_at":"2026-07-05T10:47:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.07041","created_at":"2026-07-05T10:47:24Z"},{"alias_kind":"pith_short_12","alias_value":"S6MSPRKKMGRQ","created_at":"2026-07-05T10:47:24Z"},{"alias_kind":"pith_short_16","alias_value":"S6MSPRKKMGRQCXF6","created_at":"2026-07-05T10:47:24Z"},{"alias_kind":"pith_short_8","alias_value":"S6MSPRKK","created_at":"2026-07-05T10:47:24Z"}],"graph_snapshots":[{"event_id":"sha256:c43b024e4775c51df350754090ae700d48f8c74b542255c9eccbbf91a79729c3","target":"graph","created_at":"2026-07-05T10:47:24Z","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/2309.07041/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that the examples by Smith and McMullen-Taubes provide infinitely many counterexamples to one direction of Donaldson's 4-6 question and the closely related Stabilising Conjecture. These are the first known counterexamples. In the other direction, we show that the Gromov-Witten invariants of two simply-connected closed symplectic $4$-manifolds, whose products with $(S^2,\\omega_{\\text{std}})$ are deformation equivalent, agree. In particular, when $b_2^+ \\geq 2$, these $4$-manifolds have the same Seiberg-Witten invariants. Furthermore, one can replace $(S^2,\\omega_{\\text{std}})$ by $(S^2","authors_text":"Amanda Hirschi, Luya Wang","cross_cats":["math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.SG","submitted_at":"2023-09-13T15:53:18Z","title":"On Donaldson's 4-6 question"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.07041","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:e3ee34a2833c8dca0f609d07d1cd7cc5024d9039bee512292e204d33342e2ec6","target":"record","created_at":"2026-07-05T10:47:24Z","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":"511ec229210ea0097702585842b2d6908d633ea4171f5558514bde143c7a3ae2","cross_cats_sorted":["math.GT"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.SG","submitted_at":"2023-09-13T15:53:18Z","title_canon_sha256":"7664f884d3bdbe3e950afdc5a681219c1d462f0b22d2181815203b54203f1371"},"schema_version":"1.0","source":{"id":"2309.07041","kind":"arxiv","version":3}},"canonical_sha256":"979927c54a61a3015cbe7c01e8efa4f867d0111aafb5fde2087ebb16d0582a95","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"979927c54a61a3015cbe7c01e8efa4f867d0111aafb5fde2087ebb16d0582a95","first_computed_at":"2026-07-05T10:47:24.098466Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:47:24.098466Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Vq1Z1ewGpTO62yQn3c2QUFS5kTCQxgEv76VUL6F6MvSbJ1ni+98NKI8TiGESUuciGeuvfH84P5mCV9RE9k5OBg==","signature_status":"signed_v1","signed_at":"2026-07-05T10:47:24.098940Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.07041","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e3ee34a2833c8dca0f609d07d1cd7cc5024d9039bee512292e204d33342e2ec6","sha256:c43b024e4775c51df350754090ae700d48f8c74b542255c9eccbbf91a79729c3"],"state_sha256":"2b11efcf7500e45fe886f8217072c3a0bf1408679c069d1117400096ae2fa976"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ON+P4CFSLzQgU6dyi5ShKIoGy3bSJTx1AzTu2WskifNDw127on69T9Gw0h70NwJK/e/fqjGpm8K1dzj+oP4yDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T16:30:38.238916Z","bundle_sha256":"b178ebe67a0597eec7b7a05f148e55d71f8dd19af09889e02687b1a59c7784de"}}