{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4JWWRXVXQUUOKKWRMBLQ25GOOA","short_pith_number":"pith:4JWWRXVX","schema_version":"1.0","canonical_sha256":"e26d68deb78528e52ad160570d74ce7033fc3025f26e5325d61ed33bf140ba92","source":{"kind":"arxiv","id":"2606.01017","version":1},"attestation_state":"computed","paper":{"title":"Real analytic lift of foliations of Thurston and Tsuboi","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Shigeyuki Morita, Teruaki Kitano, Yoshihiko Mitsumatsu","submitted_at":"2026-05-31T05:21:08Z","abstract_excerpt":"Thurston constructed codimension one foliations on $S^3$ thereby proved that the homomorphism $gv: \\pi_3(B\\overline{\\Gamma}^\\infty_1)\\rightarrow \\mathbb{R}$ induced by the Godbillon-Vey invariant is surjective. By another real analytic construction, he proved that the homomorphism $gv: H_3(B\\overline{\\Gamma}^\\omega_1)\\rightarrow \\mathbb{R}$ is also surjective where $B\\overline{\\Gamma}^\\omega_1$ is a $K(\\pi,1)$ space by Haefliger.\n  Tsuboi proved that the former surjection splits so that $\\pi_3(B\\overline{\\Gamma}^\\infty_1)= \\mathbb{R}\\oplus \\mathrm{Ker}\\,gv$. He further showed that the subgroup"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.01017","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2026-05-31T05:21:08Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"eb4f182f0fe9d68cf6888923a161bf18a111fa7bf9197f258639d7538b22df57","abstract_canon_sha256":"4ec0459fe0f6a655a61cf4e9627a80929e3f12f17bc99f652b1618298002f3fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:18.535289Z","signature_b64":"Jxp16HAALjNCg+OF2/auyvI3Lxy2nc51P7OkyM2y/NKo8gGO/tEvPbQztlosinkZS0gomzABBvP1Y7q2GG1XBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e26d68deb78528e52ad160570d74ce7033fc3025f26e5325d61ed33bf140ba92","last_reissued_at":"2026-06-02T01:04:18.534869Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:18.534869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Real analytic lift of foliations of Thurston and Tsuboi","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Shigeyuki Morita, Teruaki Kitano, Yoshihiko Mitsumatsu","submitted_at":"2026-05-31T05:21:08Z","abstract_excerpt":"Thurston constructed codimension one foliations on $S^3$ thereby proved that the homomorphism $gv: \\pi_3(B\\overline{\\Gamma}^\\infty_1)\\rightarrow \\mathbb{R}$ induced by the Godbillon-Vey invariant is surjective. By another real analytic construction, he proved that the homomorphism $gv: H_3(B\\overline{\\Gamma}^\\omega_1)\\rightarrow \\mathbb{R}$ is also surjective where $B\\overline{\\Gamma}^\\omega_1$ is a $K(\\pi,1)$ space by Haefliger.\n  Tsuboi proved that the former surjection splits so that $\\pi_3(B\\overline{\\Gamma}^\\infty_1)= \\mathbb{R}\\oplus \\mathrm{Ker}\\,gv$. He further showed that the subgroup"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01017","kind":"arxiv","version":1},"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/2606.01017/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.01017","created_at":"2026-06-02T01:04:18.534929+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.01017v1","created_at":"2026-06-02T01:04:18.534929+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.01017","created_at":"2026-06-02T01:04:18.534929+00:00"},{"alias_kind":"pith_short_12","alias_value":"4JWWRXVXQUUO","created_at":"2026-06-02T01:04:18.534929+00:00"},{"alias_kind":"pith_short_16","alias_value":"4JWWRXVXQUUOKKWR","created_at":"2026-06-02T01:04:18.534929+00:00"},{"alias_kind":"pith_short_8","alias_value":"4JWWRXVX","created_at":"2026-06-02T01:04:18.534929+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4JWWRXVXQUUOKKWRMBLQ25GOOA","json":"https://pith.science/pith/4JWWRXVXQUUOKKWRMBLQ25GOOA.json","graph_json":"https://pith.science/api/pith-number/4JWWRXVXQUUOKKWRMBLQ25GOOA/graph.json","events_json":"https://pith.science/api/pith-number/4JWWRXVXQUUOKKWRMBLQ25GOOA/events.json","paper":"https://pith.science/paper/4JWWRXVX"},"agent_actions":{"view_html":"https://pith.science/pith/4JWWRXVXQUUOKKWRMBLQ25GOOA","download_json":"https://pith.science/pith/4JWWRXVXQUUOKKWRMBLQ25GOOA.json","view_paper":"https://pith.science/paper/4JWWRXVX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.01017&json=true","fetch_graph":"https://pith.science/api/pith-number/4JWWRXVXQUUOKKWRMBLQ25GOOA/graph.json","fetch_events":"https://pith.science/api/pith-number/4JWWRXVXQUUOKKWRMBLQ25GOOA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4JWWRXVXQUUOKKWRMBLQ25GOOA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4JWWRXVXQUUOKKWRMBLQ25GOOA/action/storage_attestation","attest_author":"https://pith.science/pith/4JWWRXVXQUUOKKWRMBLQ25GOOA/action/author_attestation","sign_citation":"https://pith.science/pith/4JWWRXVXQUUOKKWRMBLQ25GOOA/action/citation_signature","submit_replication":"https://pith.science/pith/4JWWRXVXQUUOKKWRMBLQ25GOOA/action/replication_record"}},"created_at":"2026-06-02T01:04:18.534929+00:00","updated_at":"2026-06-02T01:04:18.534929+00:00"}