{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GRZ57OVGVBBYJSCNX43TLHDGW7","short_pith_number":"pith:GRZ57OVG","canonical_record":{"source":{"id":"1110.0405","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-03T16:27:47Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c35c39098476afe9b37ba59295d89b137649eab61317058190b6e47ca8395bb1","abstract_canon_sha256":"0e6d259e1c1dc17273a616aabce180ce253593030ab82384ee8592554dac8532"},"schema_version":"1.0"},"canonical_sha256":"3473dfbaa6a84384c84dbf37359c66b7f3ae1cd3de8074834150d4f53a4aff11","source":{"kind":"arxiv","id":"1110.0405","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0405","created_at":"2026-05-18T04:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0405v1","created_at":"2026-05-18T04:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0405","created_at":"2026-05-18T04:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"GRZ57OVGVBBY","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GRZ57OVGVBBYJSCN","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GRZ57OVG","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GRZ57OVGVBBYJSCNX43TLHDGW7","target":"record","payload":{"canonical_record":{"source":{"id":"1110.0405","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-03T16:27:47Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"c35c39098476afe9b37ba59295d89b137649eab61317058190b6e47ca8395bb1","abstract_canon_sha256":"0e6d259e1c1dc17273a616aabce180ce253593030ab82384ee8592554dac8532"},"schema_version":"1.0"},"canonical_sha256":"3473dfbaa6a84384c84dbf37359c66b7f3ae1cd3de8074834150d4f53a4aff11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:11:50.013498Z","signature_b64":"Qsz6MmDYxgQIWyfCVZ12af/0Q9kYVaCefVEROGbqHI+0ZHLcUBkcqTkSX37r/6AlFNH3/Uk/tOqmgRaUP8Q8Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3473dfbaa6a84384c84dbf37359c66b7f3ae1cd3de8074834150d4f53a4aff11","last_reissued_at":"2026-05-18T04:11:50.012815Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:11:50.012815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1110.0405","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":"2026-05-18T04:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JmlOMipfYWxmcc/K5xZ8VfdV1cAsL9YG7a0a5DpvE5gRJX3aCGZH2xmKLp+ZBoAwdP0dR6+Cx6albuhEyLHfAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:38:08.886147Z"},"content_sha256":"730973184fc75138f097ad7b50a2c97508922eb4c9c40beefdcade2626f62c37","schema_version":"1.0","event_id":"sha256:730973184fc75138f097ad7b50a2c97508922eb4c9c40beefdcade2626f62c37"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GRZ57OVGVBBYJSCNX43TLHDGW7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free loop space and homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.AT","authors_text":"Jean-Louis Loday","submitted_at":"2011-10-03T16:27:47Z","abstract_excerpt":"The aim of this paper is to explain the relationship between the (co)homology of the free loop space and the Hochschild homology of its singular cochain algebra. We introduce all the relevant technical tools, namely simplicial and cyclic objects, and we provide the various steps of the proofs, which are scattered around in the literature. This paper can be seen as a companion to the paper \"Cyclic homology and equivariant homology\" by J.D.S. Jones dealing with the cyclic case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0405","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":"2026-05-18T04:11:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9hTnN23Wuksztx7qQamHB/VYHqRBjvIHcJYiWvAgnPKTq94Jm1u548LcUeE4D6+GwmllIeukQOthMj5ZX2hbBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:38:08.886888Z"},"content_sha256":"36c1ee6b354b645a3d1366de87de3d2fb94e50c557502328ad41535ed75f147a","schema_version":"1.0","event_id":"sha256:36c1ee6b354b645a3d1366de87de3d2fb94e50c557502328ad41535ed75f147a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GRZ57OVGVBBYJSCNX43TLHDGW7/bundle.json","state_url":"https://pith.science/pith/GRZ57OVGVBBYJSCNX43TLHDGW7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GRZ57OVGVBBYJSCNX43TLHDGW7/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":"2026-05-28T23:38:08Z","links":{"resolver":"https://pith.science/pith/GRZ57OVGVBBYJSCNX43TLHDGW7","bundle":"https://pith.science/pith/GRZ57OVGVBBYJSCNX43TLHDGW7/bundle.json","state":"https://pith.science/pith/GRZ57OVGVBBYJSCNX43TLHDGW7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GRZ57OVGVBBYJSCNX43TLHDGW7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GRZ57OVGVBBYJSCNX43TLHDGW7","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":"0e6d259e1c1dc17273a616aabce180ce253593030ab82384ee8592554dac8532","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-03T16:27:47Z","title_canon_sha256":"c35c39098476afe9b37ba59295d89b137649eab61317058190b6e47ca8395bb1"},"schema_version":"1.0","source":{"id":"1110.0405","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.0405","created_at":"2026-05-18T04:11:50Z"},{"alias_kind":"arxiv_version","alias_value":"1110.0405v1","created_at":"2026-05-18T04:11:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.0405","created_at":"2026-05-18T04:11:50Z"},{"alias_kind":"pith_short_12","alias_value":"GRZ57OVGVBBY","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GRZ57OVGVBBYJSCN","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GRZ57OVG","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:36c1ee6b354b645a3d1366de87de3d2fb94e50c557502328ad41535ed75f147a","target":"graph","created_at":"2026-05-18T04:11:50Z","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":"The aim of this paper is to explain the relationship between the (co)homology of the free loop space and the Hochschild homology of its singular cochain algebra. We introduce all the relevant technical tools, namely simplicial and cyclic objects, and we provide the various steps of the proofs, which are scattered around in the literature. This paper can be seen as a companion to the paper \"Cyclic homology and equivariant homology\" by J.D.S. Jones dealing with the cyclic case.","authors_text":"Jean-Louis Loday","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-03T16:27:47Z","title":"Free loop space and homology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0405","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":"sha256:730973184fc75138f097ad7b50a2c97508922eb4c9c40beefdcade2626f62c37","target":"record","created_at":"2026-05-18T04:11:50Z","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":"0e6d259e1c1dc17273a616aabce180ce253593030ab82384ee8592554dac8532","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-10-03T16:27:47Z","title_canon_sha256":"c35c39098476afe9b37ba59295d89b137649eab61317058190b6e47ca8395bb1"},"schema_version":"1.0","source":{"id":"1110.0405","kind":"arxiv","version":1}},"canonical_sha256":"3473dfbaa6a84384c84dbf37359c66b7f3ae1cd3de8074834150d4f53a4aff11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3473dfbaa6a84384c84dbf37359c66b7f3ae1cd3de8074834150d4f53a4aff11","first_computed_at":"2026-05-18T04:11:50.012815Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:11:50.012815Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Qsz6MmDYxgQIWyfCVZ12af/0Q9kYVaCefVEROGbqHI+0ZHLcUBkcqTkSX37r/6AlFNH3/Uk/tOqmgRaUP8Q8Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:11:50.013498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.0405","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:730973184fc75138f097ad7b50a2c97508922eb4c9c40beefdcade2626f62c37","sha256:36c1ee6b354b645a3d1366de87de3d2fb94e50c557502328ad41535ed75f147a"],"state_sha256":"021b23909165c49678b309648f52d51d8099c0cf367cea21f2a3095a860bd8a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8rhFm/vTXNu7nkUEKHIWphTmXmsKIXHqTm2WjSBzk1RWGKJ8xa4iyGkE27rEriTFhAg4ScD0irMKBRvbLcBwDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:38:08.890376Z","bundle_sha256":"931c6f4eafd7a826a4245eee2b5889df4adee1986b2bafc5502e20f402c7c1c5"}}