{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:OL2ET3GDYQMIM6IVXT7KHHHCYB","short_pith_number":"pith:OL2ET3GD","schema_version":"1.0","canonical_sha256":"72f449ecc3c418867915bcfea39ce2c07c478740f12b9c50cea3eff7900cfcc4","source":{"kind":"arxiv","id":"2505.16285","version":1},"attestation_state":"computed","paper":{"title":"Maps between circle bundles: Fiber-preserving, Finiteness and Realization of mapping degree sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR","math.NT"],"primary_cat":"math.GT","authors_text":"Christoforos Neofytidis, Hongbin Sun, Shicheng Wang, Ye Tian, Zhongzi Wang","submitted_at":"2025-05-22T06:32:03Z","abstract_excerpt":"Let $E_i$ be an oriented circle bundle over a closed oriented aspherical $n$-manifold $M_i$ with Euler class $e_i\\in H^2(M_i;\\mathbb{Z})$, $i=1,2$. We prove the following:\n  (i) If every finite-index subgroup of $\\pi_1(M_2)$ has trivial center, then any non-zero degree map from $E_1$ to $E_2$ is homotopic to a fiber-preserving map.\n  (ii) The mapping degree set of fiber-preserving maps from $E_1$ to $E_2$ is given by $$\\{0\\} \\cup\\{k\\cdot \\mathrm{deg}(f) \\ | \\, k\\ne 0, \\ f\\colon M_1\\to M_2 \\, \\text{with} \\, \\mathrm{deg}(f)\\ne 0 \\ \\text{such that}\\, f^\\#(e_2)=ke_1\\},$$ where $f^\\# \\colon H^2(M_2"},"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":"2505.16285","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-05-22T06:32:03Z","cross_cats_sorted":["math.AT","math.GR","math.NT"],"title_canon_sha256":"97ac0b2cd51e7d9564d1364e17ffcc9378ef710926b741a6c92f665cb81ea159","abstract_canon_sha256":"c1e616834bd37fd8cb2b71f7d0c7910e8f86170a4940f7adf1333aaf92502174"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:07:32.759148Z","signature_b64":"3fJ2WFF4PAATY1ejoRZl97A03r6oVogu0J/vy5jJC2GqMbL02OcaAQiiiSMCI2cyXfB9w0qpys19SZ7tyTLBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72f449ecc3c418867915bcfea39ce2c07c478740f12b9c50cea3eff7900cfcc4","last_reissued_at":"2026-07-05T11:07:32.758746Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:07:32.758746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maps between circle bundles: Fiber-preserving, Finiteness and Realization of mapping degree sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.GR","math.NT"],"primary_cat":"math.GT","authors_text":"Christoforos Neofytidis, Hongbin Sun, Shicheng Wang, Ye Tian, Zhongzi Wang","submitted_at":"2025-05-22T06:32:03Z","abstract_excerpt":"Let $E_i$ be an oriented circle bundle over a closed oriented aspherical $n$-manifold $M_i$ with Euler class $e_i\\in H^2(M_i;\\mathbb{Z})$, $i=1,2$. We prove the following:\n  (i) If every finite-index subgroup of $\\pi_1(M_2)$ has trivial center, then any non-zero degree map from $E_1$ to $E_2$ is homotopic to a fiber-preserving map.\n  (ii) The mapping degree set of fiber-preserving maps from $E_1$ to $E_2$ is given by $$\\{0\\} \\cup\\{k\\cdot \\mathrm{deg}(f) \\ | \\, k\\ne 0, \\ f\\colon M_1\\to M_2 \\, \\text{with} \\, \\mathrm{deg}(f)\\ne 0 \\ \\text{such that}\\, f^\\#(e_2)=ke_1\\},$$ where $f^\\# \\colon H^2(M_2"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.16285","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/2505.16285/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":"2505.16285","created_at":"2026-07-05T11:07:32.758804+00:00"},{"alias_kind":"arxiv_version","alias_value":"2505.16285v1","created_at":"2026-07-05T11:07:32.758804+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.16285","created_at":"2026-07-05T11:07:32.758804+00:00"},{"alias_kind":"pith_short_12","alias_value":"OL2ET3GDYQMI","created_at":"2026-07-05T11:07:32.758804+00:00"},{"alias_kind":"pith_short_16","alias_value":"OL2ET3GDYQMIM6IV","created_at":"2026-07-05T11:07:32.758804+00:00"},{"alias_kind":"pith_short_8","alias_value":"OL2ET3GD","created_at":"2026-07-05T11:07:32.758804+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/OL2ET3GDYQMIM6IVXT7KHHHCYB","json":"https://pith.science/pith/OL2ET3GDYQMIM6IVXT7KHHHCYB.json","graph_json":"https://pith.science/api/pith-number/OL2ET3GDYQMIM6IVXT7KHHHCYB/graph.json","events_json":"https://pith.science/api/pith-number/OL2ET3GDYQMIM6IVXT7KHHHCYB/events.json","paper":"https://pith.science/paper/OL2ET3GD"},"agent_actions":{"view_html":"https://pith.science/pith/OL2ET3GDYQMIM6IVXT7KHHHCYB","download_json":"https://pith.science/pith/OL2ET3GDYQMIM6IVXT7KHHHCYB.json","view_paper":"https://pith.science/paper/OL2ET3GD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2505.16285&json=true","fetch_graph":"https://pith.science/api/pith-number/OL2ET3GDYQMIM6IVXT7KHHHCYB/graph.json","fetch_events":"https://pith.science/api/pith-number/OL2ET3GDYQMIM6IVXT7KHHHCYB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OL2ET3GDYQMIM6IVXT7KHHHCYB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OL2ET3GDYQMIM6IVXT7KHHHCYB/action/storage_attestation","attest_author":"https://pith.science/pith/OL2ET3GDYQMIM6IVXT7KHHHCYB/action/author_attestation","sign_citation":"https://pith.science/pith/OL2ET3GDYQMIM6IVXT7KHHHCYB/action/citation_signature","submit_replication":"https://pith.science/pith/OL2ET3GDYQMIM6IVXT7KHHHCYB/action/replication_record"}},"created_at":"2026-07-05T11:07:32.758804+00:00","updated_at":"2026-07-05T11:07:32.758804+00:00"}