{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:3BBA4R3JNTMQFQMMXDZ7QQGQS4","short_pith_number":"pith:3BBA4R3J","canonical_record":{"source":{"id":"1209.4756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-09-21T09:28:34Z","cross_cats_sorted":[],"title_canon_sha256":"1ad3d493af4a181700a21b2dac504fa956d42841f59fcad6ab2c59f045e66571","abstract_canon_sha256":"6ffe2b6d5ab7be816d509c078d61d2ed31bcdb863fa890c6f55a242b7f46c332"},"schema_version":"1.0"},"canonical_sha256":"d8420e47696cd902c18cb8f3f840d09723a931c664d5a6468168b634f719df8f","source":{"kind":"arxiv","id":"1209.4756","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4756","created_at":"2026-05-18T03:45:10Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4756v1","created_at":"2026-05-18T03:45:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4756","created_at":"2026-05-18T03:45:10Z"},{"alias_kind":"pith_short_12","alias_value":"3BBA4R3JNTMQ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3BBA4R3JNTMQFQMM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3BBA4R3J","created_at":"2026-05-18T12:26:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:3BBA4R3JNTMQFQMMXDZ7QQGQS4","target":"record","payload":{"canonical_record":{"source":{"id":"1209.4756","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-09-21T09:28:34Z","cross_cats_sorted":[],"title_canon_sha256":"1ad3d493af4a181700a21b2dac504fa956d42841f59fcad6ab2c59f045e66571","abstract_canon_sha256":"6ffe2b6d5ab7be816d509c078d61d2ed31bcdb863fa890c6f55a242b7f46c332"},"schema_version":"1.0"},"canonical_sha256":"d8420e47696cd902c18cb8f3f840d09723a931c664d5a6468168b634f719df8f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:45:10.047145Z","signature_b64":"5ny3iUd6xbwnVnElAdLlYe0JGJ/v1gsFQL0gtNwQw6noF9VuPuWjDTzKheK12AbbcRW9UChWhzr3B9lWqqA9Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8420e47696cd902c18cb8f3f840d09723a931c664d5a6468168b634f719df8f","last_reissued_at":"2026-05-18T03:45:10.046480Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:45:10.046480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1209.4756","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fYA+bXCjnItl1ws5G2l/S4ODSZzYbzigGi4vPU9OAbcX9L7ErYkC9okvPwnoa9HBhMk8MlMXk5RVTHPabbBlAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:13:20.769530Z"},"content_sha256":"2b9c73882373d31b370581265da41e859b2e771fdeb4dd01ab78b8a412298797","schema_version":"1.0","event_id":"sha256:2b9c73882373d31b370581265da41e859b2e771fdeb4dd01ab78b8a412298797"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:3BBA4R3JNTMQFQMMXDZ7QQGQS4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$L_infty$ rational homotopy of mapping spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Aniceto Murillo, Urtzi Buijs, Yves F\\'elix","submitted_at":"2012-09-21T09:28:34Z","abstract_excerpt":"In this paper we describe explicit $L_\\infty$ algebras modeling the rational homotopy type of any component of the spaces $\\map(X,Y)$ and $\\map^*(X,Y)$ of free and pointed maps between the finite nilpotent CW-complex $X$ and the finite type nilpotent CW-complex $Y$. When $X$ is of finite type, non necessarily finite, we also show that the algebraic covers of these $L_\\infty$ algebras model the universal covers of the corresponding mapping spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4756","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:45:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eu0aWz/NxMKC7DPB230tYJQdF7P1gAehHGGkoYgfS/tTcuKb34MCID/3ZxeRfuOBKA25xGIKfTJcndi3yKNRBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T13:13:20.769888Z"},"content_sha256":"1c0e9b18ced7e6f4547f1e86b1c57e5be4f68f27c2c35cd236c8512946b05aac","schema_version":"1.0","event_id":"sha256:1c0e9b18ced7e6f4547f1e86b1c57e5be4f68f27c2c35cd236c8512946b05aac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3BBA4R3JNTMQFQMMXDZ7QQGQS4/bundle.json","state_url":"https://pith.science/pith/3BBA4R3JNTMQFQMMXDZ7QQGQS4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3BBA4R3JNTMQFQMMXDZ7QQGQS4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-02T13:13:20Z","links":{"resolver":"https://pith.science/pith/3BBA4R3JNTMQFQMMXDZ7QQGQS4","bundle":"https://pith.science/pith/3BBA4R3JNTMQFQMMXDZ7QQGQS4/bundle.json","state":"https://pith.science/pith/3BBA4R3JNTMQFQMMXDZ7QQGQS4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3BBA4R3JNTMQFQMMXDZ7QQGQS4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:3BBA4R3JNTMQFQMMXDZ7QQGQS4","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":"6ffe2b6d5ab7be816d509c078d61d2ed31bcdb863fa890c6f55a242b7f46c332","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-09-21T09:28:34Z","title_canon_sha256":"1ad3d493af4a181700a21b2dac504fa956d42841f59fcad6ab2c59f045e66571"},"schema_version":"1.0","source":{"id":"1209.4756","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.4756","created_at":"2026-05-18T03:45:10Z"},{"alias_kind":"arxiv_version","alias_value":"1209.4756v1","created_at":"2026-05-18T03:45:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.4756","created_at":"2026-05-18T03:45:10Z"},{"alias_kind":"pith_short_12","alias_value":"3BBA4R3JNTMQ","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_16","alias_value":"3BBA4R3JNTMQFQMM","created_at":"2026-05-18T12:26:50Z"},{"alias_kind":"pith_short_8","alias_value":"3BBA4R3J","created_at":"2026-05-18T12:26:50Z"}],"graph_snapshots":[{"event_id":"sha256:1c0e9b18ced7e6f4547f1e86b1c57e5be4f68f27c2c35cd236c8512946b05aac","target":"graph","created_at":"2026-05-18T03:45:10Z","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 describe explicit $L_\\infty$ algebras modeling the rational homotopy type of any component of the spaces $\\map(X,Y)$ and $\\map^*(X,Y)$ of free and pointed maps between the finite nilpotent CW-complex $X$ and the finite type nilpotent CW-complex $Y$. When $X$ is of finite type, non necessarily finite, we also show that the algebraic covers of these $L_\\infty$ algebras model the universal covers of the corresponding mapping spaces.","authors_text":"Aniceto Murillo, Urtzi Buijs, Yves F\\'elix","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-09-21T09:28:34Z","title":"$L_infty$ rational homotopy of mapping spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4756","kind":"arxiv","version":1},"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":"sha256:2b9c73882373d31b370581265da41e859b2e771fdeb4dd01ab78b8a412298797","target":"record","created_at":"2026-05-18T03:45:10Z","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":"6ffe2b6d5ab7be816d509c078d61d2ed31bcdb863fa890c6f55a242b7f46c332","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2012-09-21T09:28:34Z","title_canon_sha256":"1ad3d493af4a181700a21b2dac504fa956d42841f59fcad6ab2c59f045e66571"},"schema_version":"1.0","source":{"id":"1209.4756","kind":"arxiv","version":1}},"canonical_sha256":"d8420e47696cd902c18cb8f3f840d09723a931c664d5a6468168b634f719df8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8420e47696cd902c18cb8f3f840d09723a931c664d5a6468168b634f719df8f","first_computed_at":"2026-05-18T03:45:10.046480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:45:10.046480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5ny3iUd6xbwnVnElAdLlYe0JGJ/v1gsFQL0gtNwQw6noF9VuPuWjDTzKheK12AbbcRW9UChWhzr3B9lWqqA9Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T03:45:10.047145Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.4756","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b9c73882373d31b370581265da41e859b2e771fdeb4dd01ab78b8a412298797","sha256:1c0e9b18ced7e6f4547f1e86b1c57e5be4f68f27c2c35cd236c8512946b05aac"],"state_sha256":"3b89e3da7fa72f13ecd96bf8a80647ccb870f1b366453d05674494b4ed228219"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Xp0L7NaKzsOhPbbjaw9k1NDL9Tlimo7/B5WW8eMZyYpBqvcIK52DLzU3hr+BatO+TLIvrtVACxV8EeczmDyCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T13:13:20.771927Z","bundle_sha256":"64bc6816947ca466e0707c8e5bde3c5e3600faa340b010fb1d8447abc7d8e9f0"}}