{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:QAOOWSW3XZVUZUY3AVGUPWE2DJ","short_pith_number":"pith:QAOOWSW3","schema_version":"1.0","canonical_sha256":"801ceb4adbbe6b4cd31b054d47d89a1a430fbb3c7d73d6039c8973e71f34a28d","source":{"kind":"arxiv","id":"1702.04397","version":2},"attestation_state":"computed","paper":{"title":"The infinity Quillen functor, Maurer-Cartan elements and DGL realizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Aniceto Murillo, Daniel Tanr\\'e, Urtzi Buijs, Yves F\\'elix","submitted_at":"2017-02-14T21:30:12Z","abstract_excerpt":"We show an alternative construction of the cosimplicial free complete diferential graded Lie algebra $\\mathfrak{L}_\\bullet=\\widehat{\\mathbb{L}}(s^{-1}\\Delta^\\bullet)$ based on a new Lie bracket formulae for Lie polynomials on a general tensor algebra. Based on it,we prove that for any complete differential graded Lie algebra $L$, its geometrical realization $\\langle L\\rangle=\\text{Hom}_{\\text{cdgl}}(\\mathfrak{L}_\\bullet,L)$ is isomorphic to its nerve $\\gamma_\\bullet(L)$, a deformation retract of the Getzler-Hinich realization $\\text{MC}(\\mathscr{A}_\\bullet\\widehat{\\otimes} L)$."},"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":"1702.04397","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-02-14T21:30:12Z","cross_cats_sorted":[],"title_canon_sha256":"6cfc6e53b4d8eed693d8bc3f2784c68cdd8f221da4a79087fcfe367a0ac15ce9","abstract_canon_sha256":"c9452020b1ac8db31998b3e6f339072ac66920c2b8d1671f8f513d9c3d1f8a30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:16:09.313554Z","signature_b64":"4ZX7h4FnelQNHkF/8kpXHUM9lVbdYs4Po7OgASoEikkH/LOth5+hCeFgKNepxzGnibpejpnrlYEChAvZp5EyAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"801ceb4adbbe6b4cd31b054d47d89a1a430fbb3c7d73d6039c8973e71f34a28d","last_reissued_at":"2026-05-18T00:16:09.312835Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:16:09.312835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The infinity Quillen functor, Maurer-Cartan elements and DGL realizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Aniceto Murillo, Daniel Tanr\\'e, Urtzi Buijs, Yves F\\'elix","submitted_at":"2017-02-14T21:30:12Z","abstract_excerpt":"We show an alternative construction of the cosimplicial free complete diferential graded Lie algebra $\\mathfrak{L}_\\bullet=\\widehat{\\mathbb{L}}(s^{-1}\\Delta^\\bullet)$ based on a new Lie bracket formulae for Lie polynomials on a general tensor algebra. Based on it,we prove that for any complete differential graded Lie algebra $L$, its geometrical realization $\\langle L\\rangle=\\text{Hom}_{\\text{cdgl}}(\\mathfrak{L}_\\bullet,L)$ is isomorphic to its nerve $\\gamma_\\bullet(L)$, a deformation retract of the Getzler-Hinich realization $\\text{MC}(\\mathscr{A}_\\bullet\\widehat{\\otimes} L)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04397","kind":"arxiv","version":2},"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":"1702.04397","created_at":"2026-05-18T00:16:09.312962+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.04397v2","created_at":"2026-05-18T00:16:09.312962+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.04397","created_at":"2026-05-18T00:16:09.312962+00:00"},{"alias_kind":"pith_short_12","alias_value":"QAOOWSW3XZVU","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_16","alias_value":"QAOOWSW3XZVUZUY3","created_at":"2026-05-18T12:31:37.085036+00:00"},{"alias_kind":"pith_short_8","alias_value":"QAOOWSW3","created_at":"2026-05-18T12:31:37.085036+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/QAOOWSW3XZVUZUY3AVGUPWE2DJ","json":"https://pith.science/pith/QAOOWSW3XZVUZUY3AVGUPWE2DJ.json","graph_json":"https://pith.science/api/pith-number/QAOOWSW3XZVUZUY3AVGUPWE2DJ/graph.json","events_json":"https://pith.science/api/pith-number/QAOOWSW3XZVUZUY3AVGUPWE2DJ/events.json","paper":"https://pith.science/paper/QAOOWSW3"},"agent_actions":{"view_html":"https://pith.science/pith/QAOOWSW3XZVUZUY3AVGUPWE2DJ","download_json":"https://pith.science/pith/QAOOWSW3XZVUZUY3AVGUPWE2DJ.json","view_paper":"https://pith.science/paper/QAOOWSW3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.04397&json=true","fetch_graph":"https://pith.science/api/pith-number/QAOOWSW3XZVUZUY3AVGUPWE2DJ/graph.json","fetch_events":"https://pith.science/api/pith-number/QAOOWSW3XZVUZUY3AVGUPWE2DJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QAOOWSW3XZVUZUY3AVGUPWE2DJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QAOOWSW3XZVUZUY3AVGUPWE2DJ/action/storage_attestation","attest_author":"https://pith.science/pith/QAOOWSW3XZVUZUY3AVGUPWE2DJ/action/author_attestation","sign_citation":"https://pith.science/pith/QAOOWSW3XZVUZUY3AVGUPWE2DJ/action/citation_signature","submit_replication":"https://pith.science/pith/QAOOWSW3XZVUZUY3AVGUPWE2DJ/action/replication_record"}},"created_at":"2026-05-18T00:16:09.312962+00:00","updated_at":"2026-05-18T00:16:09.312962+00:00"}