{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:XGBXK2OULRX7IJDEDKV7HR64Y3","short_pith_number":"pith:XGBXK2OU","canonical_record":{"source":{"id":"0808.0457","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-08-04T16:28:41Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"5a42d671da35f2f12bccf2c68f46dfc698070db9263c2829e14f066a641d15f4","abstract_canon_sha256":"1a12fff1eb0c92f31863d1099442792ba394a171bd8292c4a5ac8ba2227cf162"},"schema_version":"1.0"},"canonical_sha256":"b9837569d45c6ff424641aabf3c7dcc6db393b0ecc0301ff206b7f018bb3ce53","source":{"kind":"arxiv","id":"0808.0457","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.0457","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"0808.0457v3","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.0457","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"XGBXK2OULRX7","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"XGBXK2OULRX7IJDE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"XGBXK2OU","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:XGBXK2OULRX7IJDEDKV7HR64Y3","target":"record","payload":{"canonical_record":{"source":{"id":"0808.0457","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-08-04T16:28:41Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"5a42d671da35f2f12bccf2c68f46dfc698070db9263c2829e14f066a641d15f4","abstract_canon_sha256":"1a12fff1eb0c92f31863d1099442792ba394a171bd8292c4a5ac8ba2227cf162"},"schema_version":"1.0"},"canonical_sha256":"b9837569d45c6ff424641aabf3c7dcc6db393b0ecc0301ff206b7f018bb3ce53","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:24:57.154811Z","signature_b64":"YMFnlaEAywqVdWx/4+lOvhktDf77pwZ6I6i+kXWxbKktepYYQlrSlEhW4J8e+6J9jtbGe50ZIy29XcfX6gwcDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9837569d45c6ff424641aabf3c7dcc6db393b0ecc0301ff206b7f018bb3ce53","last_reissued_at":"2026-05-18T02:24:57.153918Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:24:57.153918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0808.0457","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:24:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ojY5UKUqhQwcJVFqOA/CdKX1C6LlVRvxOpdkclLe8enR9tDjwiRwdlERxMJYW+fMLVbTC+GBAvHYTlbyvlQ+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:16:44.192670Z"},"content_sha256":"a444fe0245e9de8608a29f5ab4aff3ac99853383b0c56879c563cd744f2ebf9c","schema_version":"1.0","event_id":"sha256:a444fe0245e9de8608a29f5ab4aff3ac99853383b0c56879c563cd744f2ebf9c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:XGBXK2OULRX7IJDEDKV7HR64Y3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Formality of the little N-disks operad","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.AT","authors_text":"Ismar Volic, Pascal Lambrechts","submitted_at":"2008-08-04T16:28:41Z","abstract_excerpt":"We develop the details of Kontsevich's proof of the formality of little N-disks operad over the field of real numbers. Formality holds in the category of operads of chain complexes and also in some sense in the category of commutative differential graded algebras, which is the category encoding \"real\" homotopy theory. We also prove a relative version of the formality for the inclusion of the little m-disks operad in the little N-disks operad for N>=2m+1."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.0457","kind":"arxiv","version":3},"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":"2026-05-18T02:24:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IQ6y7G+oaWcd7FxpdG6qK0p2LeExUdvkK9g95bgDunZcRZ3AAQKU0hi71u2l5w/9XYLw7jUQ/r/tn2FYm7OwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-01T23:16:44.193242Z"},"content_sha256":"c716da2c10d60130412b81152806b479627f4942bbeffc69baa82475eb6fc824","schema_version":"1.0","event_id":"sha256:c716da2c10d60130412b81152806b479627f4942bbeffc69baa82475eb6fc824"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XGBXK2OULRX7IJDEDKV7HR64Y3/bundle.json","state_url":"https://pith.science/pith/XGBXK2OULRX7IJDEDKV7HR64Y3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XGBXK2OULRX7IJDEDKV7HR64Y3/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":"2026-07-01T23:16:44Z","links":{"resolver":"https://pith.science/pith/XGBXK2OULRX7IJDEDKV7HR64Y3","bundle":"https://pith.science/pith/XGBXK2OULRX7IJDEDKV7HR64Y3/bundle.json","state":"https://pith.science/pith/XGBXK2OULRX7IJDEDKV7HR64Y3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XGBXK2OULRX7IJDEDKV7HR64Y3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:XGBXK2OULRX7IJDEDKV7HR64Y3","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":"1a12fff1eb0c92f31863d1099442792ba394a171bd8292c4a5ac8ba2227cf162","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-08-04T16:28:41Z","title_canon_sha256":"5a42d671da35f2f12bccf2c68f46dfc698070db9263c2829e14f066a641d15f4"},"schema_version":"1.0","source":{"id":"0808.0457","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.0457","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"arxiv_version","alias_value":"0808.0457v3","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.0457","created_at":"2026-05-18T02:24:57Z"},{"alias_kind":"pith_short_12","alias_value":"XGBXK2OULRX7","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"XGBXK2OULRX7IJDE","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"XGBXK2OU","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:c716da2c10d60130412b81152806b479627f4942bbeffc69baa82475eb6fc824","target":"graph","created_at":"2026-05-18T02:24:57Z","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":"We develop the details of Kontsevich's proof of the formality of little N-disks operad over the field of real numbers. Formality holds in the category of operads of chain complexes and also in some sense in the category of commutative differential graded algebras, which is the category encoding \"real\" homotopy theory. We also prove a relative version of the formality for the inclusion of the little m-disks operad in the little N-disks operad for N>=2m+1.","authors_text":"Ismar Volic, Pascal Lambrechts","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-08-04T16:28:41Z","title":"Formality of the little N-disks operad"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.0457","kind":"arxiv","version":3},"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:a444fe0245e9de8608a29f5ab4aff3ac99853383b0c56879c563cd744f2ebf9c","target":"record","created_at":"2026-05-18T02:24:57Z","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":"1a12fff1eb0c92f31863d1099442792ba394a171bd8292c4a5ac8ba2227cf162","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2008-08-04T16:28:41Z","title_canon_sha256":"5a42d671da35f2f12bccf2c68f46dfc698070db9263c2829e14f066a641d15f4"},"schema_version":"1.0","source":{"id":"0808.0457","kind":"arxiv","version":3}},"canonical_sha256":"b9837569d45c6ff424641aabf3c7dcc6db393b0ecc0301ff206b7f018bb3ce53","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9837569d45c6ff424641aabf3c7dcc6db393b0ecc0301ff206b7f018bb3ce53","first_computed_at":"2026-05-18T02:24:57.153918Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:24:57.153918Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YMFnlaEAywqVdWx/4+lOvhktDf77pwZ6I6i+kXWxbKktepYYQlrSlEhW4J8e+6J9jtbGe50ZIy29XcfX6gwcDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:24:57.154811Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.0457","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a444fe0245e9de8608a29f5ab4aff3ac99853383b0c56879c563cd744f2ebf9c","sha256:c716da2c10d60130412b81152806b479627f4942bbeffc69baa82475eb6fc824"],"state_sha256":"f4599d11dc85cecf4d88c9874db9cc5410bcee992cfb15745db381139ab963a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7+hSUul6wLQbuhpkEXjPmIrQ9UEbMIiq9dPwaGjm+iDOiM2fQuI/qtyDcrqpwMKm9rP1aTqK7HbgBEhZX5hNBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-01T23:16:44.197250Z","bundle_sha256":"2720e65e6dfbca3c7ebcced6608edb5282b2feb48698e0c9744d42552d9620fc"}}