{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:MIIKYYQ7ZSMRD7V32COMURTKPK","short_pith_number":"pith:MIIKYYQ7","canonical_record":{"source":{"id":"1805.00429","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-01T16:53:06Z","cross_cats_sorted":[],"title_canon_sha256":"98054faf25b6e0012a55c23345062e39f0ed387432a44ebbddf12feee0f8f64b","abstract_canon_sha256":"6c622f60211973b0b7c207932c9e237dc54037712534d8922a88080a3950f886"},"schema_version":"1.0"},"canonical_sha256":"6210ac621fcc9911febbd09cca466a7ab9d8e31de6fb4b7bc5952ebffd79fc96","source":{"kind":"arxiv","id":"1805.00429","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00429","created_at":"2026-07-05T00:46:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00429v3","created_at":"2026-07-05T00:46:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00429","created_at":"2026-07-05T00:46:43Z"},{"alias_kind":"pith_short_12","alias_value":"MIIKYYQ7ZSMR","created_at":"2026-07-05T00:46:43Z"},{"alias_kind":"pith_short_16","alias_value":"MIIKYYQ7ZSMRD7V3","created_at":"2026-07-05T00:46:43Z"},{"alias_kind":"pith_short_8","alias_value":"MIIKYYQ7","created_at":"2026-07-05T00:46:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:MIIKYYQ7ZSMRD7V32COMURTKPK","target":"record","payload":{"canonical_record":{"source":{"id":"1805.00429","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-01T16:53:06Z","cross_cats_sorted":[],"title_canon_sha256":"98054faf25b6e0012a55c23345062e39f0ed387432a44ebbddf12feee0f8f64b","abstract_canon_sha256":"6c622f60211973b0b7c207932c9e237dc54037712534d8922a88080a3950f886"},"schema_version":"1.0"},"canonical_sha256":"6210ac621fcc9911febbd09cca466a7ab9d8e31de6fb4b7bc5952ebffd79fc96","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:46:43.202013Z","signature_b64":"SIDcpYACiZRrohJauT4o2jpZNRIJABKq5tbmxdM6MY0lnZeV/M+GUu/wGO9TaeRhgpu6pOivtNDerE4F8DGVBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6210ac621fcc9911febbd09cca466a7ab9d8e31de6fb4b7bc5952ebffd79fc96","last_reissued_at":"2026-07-05T00:46:43.201506Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:46:43.201506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.00429","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":"2026-07-05T00:46:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wix8sZmHGYAZxa4Ac2QJycAZWjt3H7ClY+2jgk/iG8owFepbISRiQ7lSV2UT+IAbGpDTTMROm5tuQpDjBJFuDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:19:51.867246Z"},"content_sha256":"fe289c75a76d8a629ec7b6114a3e36cb9e99d5f7776cf15f67bf780ef6813d8b","schema_version":"1.0","event_id":"sha256:fe289c75a76d8a629ec7b6114a3e36cb9e99d5f7776cf15f67bf780ef6813d8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:MIIKYYQ7ZSMRD7V32COMURTKPK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Trisections of surface complements and the Price twist","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Maggie Miller, Seungwon Kim","submitted_at":"2018-05-01T16:53:06Z","abstract_excerpt":"Given an $S\\cong \\mathbb{R}P^2$ smoothly embedded in a 4-manifold $X^4$ with Euler number 2 or -2, the Price twist is a surgery operation on $\\nu(S)$ yielding (up to) three different 4-manifolds: $X^4,\\tau_S(X^4),\\Sigma_S(X^4)$. This is of particular interest when $X^4=S^4$, as then $\\Sigma_S(X^4)$ is a homotopy 4-sphere which is not obviously diffeomorphic to $S^4$. In this paper, we show how to produce a trisection description of each Price twist on $S\\subset X^4$ by producing a relative trisection of $X^4\\setminus\\nu(S)$. Moreover, we show how to produce a trisection description of general "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00429","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/1805.00429/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":"2026-07-05T00:46:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TetU0YAfrHJPWKbUmhAHnEvyLqBZBmb/nkU/+6RF1OmTL4taoizYlf7QMEX4I8VQLVZxJw0as8L89rDTOZtOAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-17T01:19:51.867769Z"},"content_sha256":"2d11b51edf55657cedfe87bc834015161dd05496a53a636f8dbc9be30b28d9d2","schema_version":"1.0","event_id":"sha256:2d11b51edf55657cedfe87bc834015161dd05496a53a636f8dbc9be30b28d9d2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIIKYYQ7ZSMRD7V32COMURTKPK/bundle.json","state_url":"https://pith.science/pith/MIIKYYQ7ZSMRD7V32COMURTKPK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIIKYYQ7ZSMRD7V32COMURTKPK/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":"2026-08-17T01:19:51Z","links":{"resolver":"https://pith.science/pith/MIIKYYQ7ZSMRD7V32COMURTKPK","bundle":"https://pith.science/pith/MIIKYYQ7ZSMRD7V32COMURTKPK/bundle.json","state":"https://pith.science/pith/MIIKYYQ7ZSMRD7V32COMURTKPK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIIKYYQ7ZSMRD7V32COMURTKPK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:MIIKYYQ7ZSMRD7V32COMURTKPK","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":"6c622f60211973b0b7c207932c9e237dc54037712534d8922a88080a3950f886","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-01T16:53:06Z","title_canon_sha256":"98054faf25b6e0012a55c23345062e39f0ed387432a44ebbddf12feee0f8f64b"},"schema_version":"1.0","source":{"id":"1805.00429","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.00429","created_at":"2026-07-05T00:46:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.00429v3","created_at":"2026-07-05T00:46:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.00429","created_at":"2026-07-05T00:46:43Z"},{"alias_kind":"pith_short_12","alias_value":"MIIKYYQ7ZSMR","created_at":"2026-07-05T00:46:43Z"},{"alias_kind":"pith_short_16","alias_value":"MIIKYYQ7ZSMRD7V3","created_at":"2026-07-05T00:46:43Z"},{"alias_kind":"pith_short_8","alias_value":"MIIKYYQ7","created_at":"2026-07-05T00:46:43Z"}],"graph_snapshots":[{"event_id":"sha256:2d11b51edf55657cedfe87bc834015161dd05496a53a636f8dbc9be30b28d9d2","target":"graph","created_at":"2026-07-05T00:46:43Z","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/1805.00429/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given an $S\\cong \\mathbb{R}P^2$ smoothly embedded in a 4-manifold $X^4$ with Euler number 2 or -2, the Price twist is a surgery operation on $\\nu(S)$ yielding (up to) three different 4-manifolds: $X^4,\\tau_S(X^4),\\Sigma_S(X^4)$. This is of particular interest when $X^4=S^4$, as then $\\Sigma_S(X^4)$ is a homotopy 4-sphere which is not obviously diffeomorphic to $S^4$. In this paper, we show how to produce a trisection description of each Price twist on $S\\subset X^4$ by producing a relative trisection of $X^4\\setminus\\nu(S)$. Moreover, we show how to produce a trisection description of general ","authors_text":"Maggie Miller, Seungwon Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-01T16:53:06Z","title":"Trisections of surface complements and the Price twist"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.00429","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:fe289c75a76d8a629ec7b6114a3e36cb9e99d5f7776cf15f67bf780ef6813d8b","target":"record","created_at":"2026-07-05T00:46:43Z","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":"6c622f60211973b0b7c207932c9e237dc54037712534d8922a88080a3950f886","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2018-05-01T16:53:06Z","title_canon_sha256":"98054faf25b6e0012a55c23345062e39f0ed387432a44ebbddf12feee0f8f64b"},"schema_version":"1.0","source":{"id":"1805.00429","kind":"arxiv","version":3}},"canonical_sha256":"6210ac621fcc9911febbd09cca466a7ab9d8e31de6fb4b7bc5952ebffd79fc96","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6210ac621fcc9911febbd09cca466a7ab9d8e31de6fb4b7bc5952ebffd79fc96","first_computed_at":"2026-07-05T00:46:43.201506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:46:43.201506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SIDcpYACiZRrohJauT4o2jpZNRIJABKq5tbmxdM6MY0lnZeV/M+GUu/wGO9TaeRhgpu6pOivtNDerE4F8DGVBg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:46:43.202013Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.00429","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fe289c75a76d8a629ec7b6114a3e36cb9e99d5f7776cf15f67bf780ef6813d8b","sha256:2d11b51edf55657cedfe87bc834015161dd05496a53a636f8dbc9be30b28d9d2"],"state_sha256":"183bd5c86701a760af17c9535a47f8fad97faaeff8a31a9cd3f4f8d9b20aeb14"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gTq8beFws9EjaLoyhxXANVGVcV4RLXbbc4kgjFEvhSum+whGw7iYVn0QF8suRYEYWm9P12S2TzP9Ph6grRuLDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-17T01:19:51.873195Z","bundle_sha256":"465d6950e32f3fcef7a10f345c568e772517ad5dd114f6ed4a29525f98abac13"}}