{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:XMT3GZSJGXFDBTFB6VKI66RP2R","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":"d41058a986a34503c82c9fe9b24d7574b5a4816674ead4181d9586e96f8941b3","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-05T21:10:28Z","title_canon_sha256":"4f75fd95ac413db3b4c9352a6fa5d7313776ffe1913265acac90e73c09d300ef"},"schema_version":"1.0","source":{"id":"1408.1115","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1115","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1115v2","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1115","created_at":"2026-05-18T02:43:00Z"},{"alias_kind":"pith_short_12","alias_value":"XMT3GZSJGXFD","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_16","alias_value":"XMT3GZSJGXFDBTFB","created_at":"2026-05-18T12:28:57Z"},{"alias_kind":"pith_short_8","alias_value":"XMT3GZSJ","created_at":"2026-05-18T12:28:57Z"}],"graph_snapshots":[{"event_id":"sha256:9cfe0eebcd9798970752aa8ab12fc954cc8c28e28937b9d1dcda4e38eb1e9306","target":"graph","created_at":"2026-05-18T02:43:00Z","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":"In this paper, we prove that we can recover the genus of a closed compact surface $S$ in $\\mathbb{R}^3$ from the restriction to a generic line of the Fourier transform of the canonical measure carried by $S$. We also show that the restriction on some line in Minkowski space of the solution of a linear wave equation whose Cauchy data comes from the canonical measure carried by $S$, allows to recover the Euler characteristic of $S$.","authors_text":"Nguyen Viet Dang","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-05T21:10:28Z","title":"The Euler characteristic of a surface from its Fourier analysis in one direction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1115","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":"sha256:503609227e20bc6f7b2b2a853fd74ae40e4b27fd758f1c5f078db1d4e2daceb9","target":"record","created_at":"2026-05-18T02:43:00Z","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":"d41058a986a34503c82c9fe9b24d7574b5a4816674ead4181d9586e96f8941b3","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-08-05T21:10:28Z","title_canon_sha256":"4f75fd95ac413db3b4c9352a6fa5d7313776ffe1913265acac90e73c09d300ef"},"schema_version":"1.0","source":{"id":"1408.1115","kind":"arxiv","version":2}},"canonical_sha256":"bb27b3664935ca30cca1f5548f7a2fd460bae292c9db5d31599a015268b19787","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bb27b3664935ca30cca1f5548f7a2fd460bae292c9db5d31599a015268b19787","first_computed_at":"2026-05-18T02:43:00.295342Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:00.295342Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4/hC8Wg2WmLHDu+DmMzirFkuhlBG7jSUIuGIRh5fBAsNgak26Q8rskC17s349HahLyTKIqmaz+kJfw7gNX2FCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:00.295987Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1115","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:503609227e20bc6f7b2b2a853fd74ae40e4b27fd758f1c5f078db1d4e2daceb9","sha256:9cfe0eebcd9798970752aa8ab12fc954cc8c28e28937b9d1dcda4e38eb1e9306"],"state_sha256":"7e7da1232611c27a8bedf28d4b617bc49f5f2857500b73da6ea4f329cf91e336"}