{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3EJZWEIYZU43356LUGMUY7WMYW","short_pith_number":"pith:3EJZWEIY","schema_version":"1.0","canonical_sha256":"d9139b1118cd39bdf7cba1994c7eccc58955657f1f0a88beaee2ebfc7b69d42f","source":{"kind":"arxiv","id":"1310.0096","version":1},"attestation_state":"computed","paper":{"title":"A rational realization problem in Gottlieb group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Toshihiro Yamaguchi","submitted_at":"2013-09-30T23:54:18Z","abstract_excerpt":"We define the fibre-restricted Gottlieb group with respect to a fibration $\\xi :X\\to E\\to Y$ in CW complexes. It is a subgroup of the Gottlieb group of $X$. When $X$ and $E$ are finite simply connected, its rationalized model is given by the arguments of derivations of Sullivan models based on F\\'{e}lix, Lupton and Smith \\cite{FLS}. We consider the realization problem of groups in a Gottlieb group as fibre-restricted Gottlieb groups in rational homotoy theory. Especially we define an invariant named as (Gottlieb) depth of $X$ over $Y$. In particular, when $Y=BS^1$, it is related to the rationa"},"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":"1310.0096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2013-09-30T23:54:18Z","cross_cats_sorted":[],"title_canon_sha256":"1875bcc0da17e4c57a001b78cf47a5426b653e31793721d519892a71635f0952","abstract_canon_sha256":"a5d339a0aecffdebaecc9dffe877d842c324edc20d7f54a2e004f47c8c0a6b68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:45.646951Z","signature_b64":"LWC4KD7xME5EP6EccmR9TRPfFebhWN8ohdmzA4SkJCsBvN8oSZPseEEmhn2hKSoZqf2h8UrN+v3p7/tvH9MwDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9139b1118cd39bdf7cba1994c7eccc58955657f1f0a88beaee2ebfc7b69d42f","last_reissued_at":"2026-05-18T03:11:45.646271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:45.646271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A rational realization problem in Gottlieb group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Toshihiro Yamaguchi","submitted_at":"2013-09-30T23:54:18Z","abstract_excerpt":"We define the fibre-restricted Gottlieb group with respect to a fibration $\\xi :X\\to E\\to Y$ in CW complexes. It is a subgroup of the Gottlieb group of $X$. When $X$ and $E$ are finite simply connected, its rationalized model is given by the arguments of derivations of Sullivan models based on F\\'{e}lix, Lupton and Smith \\cite{FLS}. We consider the realization problem of groups in a Gottlieb group as fibre-restricted Gottlieb groups in rational homotoy theory. Especially we define an invariant named as (Gottlieb) depth of $X$ over $Y$. In particular, when $Y=BS^1$, it is related to the rationa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0096","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":""},"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":"1310.0096","created_at":"2026-05-18T03:11:45.646396+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.0096v1","created_at":"2026-05-18T03:11:45.646396+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0096","created_at":"2026-05-18T03:11:45.646396+00:00"},{"alias_kind":"pith_short_12","alias_value":"3EJZWEIYZU43","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3EJZWEIYZU43356L","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3EJZWEIY","created_at":"2026-05-18T12:27:32.513160+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/3EJZWEIYZU43356LUGMUY7WMYW","json":"https://pith.science/pith/3EJZWEIYZU43356LUGMUY7WMYW.json","graph_json":"https://pith.science/api/pith-number/3EJZWEIYZU43356LUGMUY7WMYW/graph.json","events_json":"https://pith.science/api/pith-number/3EJZWEIYZU43356LUGMUY7WMYW/events.json","paper":"https://pith.science/paper/3EJZWEIY"},"agent_actions":{"view_html":"https://pith.science/pith/3EJZWEIYZU43356LUGMUY7WMYW","download_json":"https://pith.science/pith/3EJZWEIYZU43356LUGMUY7WMYW.json","view_paper":"https://pith.science/paper/3EJZWEIY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.0096&json=true","fetch_graph":"https://pith.science/api/pith-number/3EJZWEIYZU43356LUGMUY7WMYW/graph.json","fetch_events":"https://pith.science/api/pith-number/3EJZWEIYZU43356LUGMUY7WMYW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3EJZWEIYZU43356LUGMUY7WMYW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3EJZWEIYZU43356LUGMUY7WMYW/action/storage_attestation","attest_author":"https://pith.science/pith/3EJZWEIYZU43356LUGMUY7WMYW/action/author_attestation","sign_citation":"https://pith.science/pith/3EJZWEIYZU43356LUGMUY7WMYW/action/citation_signature","submit_replication":"https://pith.science/pith/3EJZWEIYZU43356LUGMUY7WMYW/action/replication_record"}},"created_at":"2026-05-18T03:11:45.646396+00:00","updated_at":"2026-05-18T03:11:45.646396+00:00"}