{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:V4JMUZE6ZAKJDWLWX5LQQSV4FF","short_pith_number":"pith:V4JMUZE6","canonical_record":{"source":{"id":"1211.1647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-07T19:45:18Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"b3fc4f92d903f1ccc4b7d8254c74dbe929f8fcb8163022545abf25a6eb9c5f87","abstract_canon_sha256":"def15166117b5fd48b997bd8dd1db841c68f9492bc042e079975e91be1c97f42"},"schema_version":"1.0"},"canonical_sha256":"af12ca649ec81491d976bf57084abc29749d9dae3556f947958ac9ccf85a1228","source":{"kind":"arxiv","id":"1211.1647","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1647","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1647v1","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1647","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"pith_short_12","alias_value":"V4JMUZE6ZAKJ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"V4JMUZE6ZAKJDWLW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"V4JMUZE6","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:V4JMUZE6ZAKJDWLWX5LQQSV4FF","target":"record","payload":{"canonical_record":{"source":{"id":"1211.1647","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-07T19:45:18Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"b3fc4f92d903f1ccc4b7d8254c74dbe929f8fcb8163022545abf25a6eb9c5f87","abstract_canon_sha256":"def15166117b5fd48b997bd8dd1db841c68f9492bc042e079975e91be1c97f42"},"schema_version":"1.0"},"canonical_sha256":"af12ca649ec81491d976bf57084abc29749d9dae3556f947958ac9ccf85a1228","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:41:20.586512Z","signature_b64":"qS/Op2icqa1Bt1S0eywnyWj+iKvETedeU1R3r/sJy911Z2hY2Qef68YZJnrOYBpdyuLin48p8HUZN6SIATJfBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af12ca649ec81491d976bf57084abc29749d9dae3556f947958ac9ccf85a1228","last_reissued_at":"2026-05-18T03:41:20.585931Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:41:20.585931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1211.1647","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":"2026-05-18T03:41:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eVHa4nruNMtdFoScGdVdtneHVG1aXZ1tILvxs48so1+NqL3awKxxCD6H8qCpd1BUvwRGZjOXGF2pD1p9ayruDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:10:55.133379Z"},"content_sha256":"27953f2f638ff051deb67b43f052123e2531fdbc290978eb886f497108e1939b","schema_version":"1.0","event_id":"sha256:27953f2f638ff051deb67b43f052123e2531fdbc290978eb886f497108e1939b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:V4JMUZE6ZAKJDWLWX5LQQSV4FF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Deformation theory and rational homotopy type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.QA","authors_text":"Jim Stasheff, Mike Schlessinger","submitted_at":"2012-11-07T19:45:18Z","abstract_excerpt":"We regard the classification of rational homotopy types as a problem in algebraic deformation theory: any space with given cohomology is a perturbation, or deformation, of the \"formal\" space with that cohomology. The classifying space is then a \"moduli\" space --- a certain quotient of an algebraic variety of perturbations. The description we give of this moduli space links it with corresponding structures in homotopy theory, especially the classification of fibres spaces with fixed fibre F in terms of homotopy classes of maps of the base B into a classifying space constructed from the monoid o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1647","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":"2026-05-18T03:41:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zZ19obBynOesBNzH8//SqLGcVYtd6eZONUJk+rztp199F1nQ3jzJJa+xzaWFO5dmtFmLAXrw1/VBeYiqwKDxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T08:10:55.133727Z"},"content_sha256":"f92173e640e6fe277e61efda51ac2c1fc32de38d11007c70132dfc3a58808306","schema_version":"1.0","event_id":"sha256:f92173e640e6fe277e61efda51ac2c1fc32de38d11007c70132dfc3a58808306"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4JMUZE6ZAKJDWLWX5LQQSV4FF/bundle.json","state_url":"https://pith.science/pith/V4JMUZE6ZAKJDWLWX5LQQSV4FF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4JMUZE6ZAKJDWLWX5LQQSV4FF/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":"2026-06-02T08:10:55Z","links":{"resolver":"https://pith.science/pith/V4JMUZE6ZAKJDWLWX5LQQSV4FF","bundle":"https://pith.science/pith/V4JMUZE6ZAKJDWLWX5LQQSV4FF/bundle.json","state":"https://pith.science/pith/V4JMUZE6ZAKJDWLWX5LQQSV4FF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4JMUZE6ZAKJDWLWX5LQQSV4FF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:V4JMUZE6ZAKJDWLWX5LQQSV4FF","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":"def15166117b5fd48b997bd8dd1db841c68f9492bc042e079975e91be1c97f42","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-07T19:45:18Z","title_canon_sha256":"b3fc4f92d903f1ccc4b7d8254c74dbe929f8fcb8163022545abf25a6eb9c5f87"},"schema_version":"1.0","source":{"id":"1211.1647","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1647","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1647v1","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1647","created_at":"2026-05-18T03:41:20Z"},{"alias_kind":"pith_short_12","alias_value":"V4JMUZE6ZAKJ","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"V4JMUZE6ZAKJDWLW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"V4JMUZE6","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:f92173e640e6fe277e61efda51ac2c1fc32de38d11007c70132dfc3a58808306","target":"graph","created_at":"2026-05-18T03:41:20Z","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 regard the classification of rational homotopy types as a problem in algebraic deformation theory: any space with given cohomology is a perturbation, or deformation, of the \"formal\" space with that cohomology. The classifying space is then a \"moduli\" space --- a certain quotient of an algebraic variety of perturbations. The description we give of this moduli space links it with corresponding structures in homotopy theory, especially the classification of fibres spaces with fixed fibre F in terms of homotopy classes of maps of the base B into a classifying space constructed from the monoid o","authors_text":"Jim Stasheff, Mike Schlessinger","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-07T19:45:18Z","title":"Deformation theory and rational homotopy type"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1647","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":"sha256:27953f2f638ff051deb67b43f052123e2531fdbc290978eb886f497108e1939b","target":"record","created_at":"2026-05-18T03:41:20Z","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":"def15166117b5fd48b997bd8dd1db841c68f9492bc042e079975e91be1c97f42","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2012-11-07T19:45:18Z","title_canon_sha256":"b3fc4f92d903f1ccc4b7d8254c74dbe929f8fcb8163022545abf25a6eb9c5f87"},"schema_version":"1.0","source":{"id":"1211.1647","kind":"arxiv","version":1}},"canonical_sha256":"af12ca649ec81491d976bf57084abc29749d9dae3556f947958ac9ccf85a1228","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af12ca649ec81491d976bf57084abc29749d9dae3556f947958ac9ccf85a1228","first_computed_at":"2026-05-18T03:41:20.585931Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:20.585931Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qS/Op2icqa1Bt1S0eywnyWj+iKvETedeU1R3r/sJy911Z2hY2Qef68YZJnrOYBpdyuLin48p8HUZN6SIATJfBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:20.586512Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1647","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:27953f2f638ff051deb67b43f052123e2531fdbc290978eb886f497108e1939b","sha256:f92173e640e6fe277e61efda51ac2c1fc32de38d11007c70132dfc3a58808306"],"state_sha256":"3eff05ed0f4afd3ac40578998ffc9e8a9b61ea82dedeb79d3ac94fb3cd30bae9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PWUbozdx9J5sH3lg/gF5eU9rnpo3JBowwz5kFujbfJuY23l2iMOq9Zr5yRtOFhadpd/UvbYkRHBhWY1vRtjeBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T08:10:55.135756Z","bundle_sha256":"4bf7334240b67893a388af8b0cd1774dfb1043bd8c4bf55020dab4c4baa1f24e"}}