{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:I77FG3ZE5OPGZ5TL7NGQE73HEV","short_pith_number":"pith:I77FG3ZE","canonical_record":{"source":{"id":"1111.4404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-11-18T16:01:19Z","cross_cats_sorted":[],"title_canon_sha256":"d88e020dc0fa3964f548367c35255a7e03318ed067996c021c4110bf1fab2bdb","abstract_canon_sha256":"236df98a22d4061bc6bc851461ca589e9f33ebf294c082919e71b2889e909178"},"schema_version":"1.0"},"canonical_sha256":"47fe536f24eb9e6cf66bfb4d027f67254a8243145473c8c44df0d428f6807a68","source":{"kind":"arxiv","id":"1111.4404","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4404","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4404v1","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4404","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"I77FG3ZE5OPG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"I77FG3ZE5OPGZ5TL","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"I77FG3ZE","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:I77FG3ZE5OPGZ5TL7NGQE73HEV","target":"record","payload":{"canonical_record":{"source":{"id":"1111.4404","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-11-18T16:01:19Z","cross_cats_sorted":[],"title_canon_sha256":"d88e020dc0fa3964f548367c35255a7e03318ed067996c021c4110bf1fab2bdb","abstract_canon_sha256":"236df98a22d4061bc6bc851461ca589e9f33ebf294c082919e71b2889e909178"},"schema_version":"1.0"},"canonical_sha256":"47fe536f24eb9e6cf66bfb4d027f67254a8243145473c8c44df0d428f6807a68","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:08:04.461137Z","signature_b64":"jgxDw8v+FnS8ZgfMX5KDA4xuAOUcDgH7hMnDZjZYO90wVRhu8zMmKLTBtCMS1wR2kNUa0A71t0jiGwv+uIyFAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"47fe536f24eb9e6cf66bfb4d027f67254a8243145473c8c44df0d428f6807a68","last_reissued_at":"2026-05-18T04:08:04.460674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:08:04.460674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.4404","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":"2026-05-18T04:08:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"97xW3O18j8xgIZmOikLlBeYb5YiV1pZu3cDsYRYmk9L/q4sbIabj0RSSqeKrU+bwwOwNDiVoT1BAP/bw/SBAAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:55:50.048863Z"},"content_sha256":"c524d14fde684a5094abe1bce9383bd7ff9fa31b69395c41a1a32377c71be78f","schema_version":"1.0","event_id":"sha256:c524d14fde684a5094abe1bce9383bd7ff9fa31b69395c41a1a32377c71be78f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:I77FG3ZE5OPGZ5TL7NGQE73HEV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rational Homotopy Type of the Classifying Space for Fibrewise Self-Equivalences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Samuel B. Smith, Urtzi Buijs","submitted_at":"2011-11-18T16:01:19Z","abstract_excerpt":"Let p be a fibration of simply connected CW complexes with finite base B and fibre F. Let aut_1(p) denote the identity component of the space of all fibre-homotopy self-equivalences of p and Baut_1(p) the classifying space for this topological monoid. We give a differential graded Lie algebra model for Baut_1(p). We use this model to give classification results for the rational homotopy types represented by Baut_1(p) and also to obtain conditions under which the monoid aut_1(p) is a double loop-space after rationalization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4404","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":"2026-05-18T04:08:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iF1ERsahSm4vifGM9PxD6xM5JQ9Nb/miOoFfWlPuwvfclfL1STQk7CWRkyzjGu9kqgs5C72kUQNnSyGHT4yXDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T06:55:50.049234Z"},"content_sha256":"7096162259646a08b3c0c2ab63260276e246958506144a4de8bff08ac3deac37","schema_version":"1.0","event_id":"sha256:7096162259646a08b3c0c2ab63260276e246958506144a4de8bff08ac3deac37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I77FG3ZE5OPGZ5TL7NGQE73HEV/bundle.json","state_url":"https://pith.science/pith/I77FG3ZE5OPGZ5TL7NGQE73HEV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I77FG3ZE5OPGZ5TL7NGQE73HEV/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":"2026-06-02T06:55:50Z","links":{"resolver":"https://pith.science/pith/I77FG3ZE5OPGZ5TL7NGQE73HEV","bundle":"https://pith.science/pith/I77FG3ZE5OPGZ5TL7NGQE73HEV/bundle.json","state":"https://pith.science/pith/I77FG3ZE5OPGZ5TL7NGQE73HEV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I77FG3ZE5OPGZ5TL7NGQE73HEV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:I77FG3ZE5OPGZ5TL7NGQE73HEV","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":"236df98a22d4061bc6bc851461ca589e9f33ebf294c082919e71b2889e909178","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-11-18T16:01:19Z","title_canon_sha256":"d88e020dc0fa3964f548367c35255a7e03318ed067996c021c4110bf1fab2bdb"},"schema_version":"1.0","source":{"id":"1111.4404","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4404","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4404v1","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4404","created_at":"2026-05-18T04:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"I77FG3ZE5OPG","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"I77FG3ZE5OPGZ5TL","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"I77FG3ZE","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:7096162259646a08b3c0c2ab63260276e246958506144a4de8bff08ac3deac37","target":"graph","created_at":"2026-05-18T04:08:04Z","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":"Let p be a fibration of simply connected CW complexes with finite base B and fibre F. Let aut_1(p) denote the identity component of the space of all fibre-homotopy self-equivalences of p and Baut_1(p) the classifying space for this topological monoid. We give a differential graded Lie algebra model for Baut_1(p). We use this model to give classification results for the rational homotopy types represented by Baut_1(p) and also to obtain conditions under which the monoid aut_1(p) is a double loop-space after rationalization.","authors_text":"Samuel B. Smith, Urtzi Buijs","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-11-18T16:01:19Z","title":"Rational Homotopy Type of the Classifying Space for Fibrewise Self-Equivalences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4404","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:c524d14fde684a5094abe1bce9383bd7ff9fa31b69395c41a1a32377c71be78f","target":"record","created_at":"2026-05-18T04:08:04Z","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":"236df98a22d4061bc6bc851461ca589e9f33ebf294c082919e71b2889e909178","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-11-18T16:01:19Z","title_canon_sha256":"d88e020dc0fa3964f548367c35255a7e03318ed067996c021c4110bf1fab2bdb"},"schema_version":"1.0","source":{"id":"1111.4404","kind":"arxiv","version":1}},"canonical_sha256":"47fe536f24eb9e6cf66bfb4d027f67254a8243145473c8c44df0d428f6807a68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"47fe536f24eb9e6cf66bfb4d027f67254a8243145473c8c44df0d428f6807a68","first_computed_at":"2026-05-18T04:08:04.460674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:04.460674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jgxDw8v+FnS8ZgfMX5KDA4xuAOUcDgH7hMnDZjZYO90wVRhu8zMmKLTBtCMS1wR2kNUa0A71t0jiGwv+uIyFAw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:04.461137Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4404","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c524d14fde684a5094abe1bce9383bd7ff9fa31b69395c41a1a32377c71be78f","sha256:7096162259646a08b3c0c2ab63260276e246958506144a4de8bff08ac3deac37"],"state_sha256":"fa0ae1b26f3e3b240460fb840331088c34308408b95f3aa370ce5cdadb7759c5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nJwyJv4CSaHIrHkCMUwvX9uFj9JVUIykbIouN+UuBEBubnB+QA1uMHWVaZ7+5meLgCgqJ00gsepE75Q6Z8f8BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T06:55:50.051234Z","bundle_sha256":"f932e224b870f8e4438dc6e7be1f232ae38fc8e8812ece2051c4fd98242de811"}}