{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:O4GETRMC7YTRP6ZUF2BW7PWK3L","short_pith_number":"pith:O4GETRMC","canonical_record":{"source":{"id":"1304.5314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-04-19T05:45:54Z","cross_cats_sorted":[],"title_canon_sha256":"fa3057677859492e804e3c4ae1165ed87dc49c0538e1e095292a32f0c3b141b9","abstract_canon_sha256":"c851349356483d9bff2245fc0b744b97bce611aff74333e5bbd422cfb3dac65a"},"schema_version":"1.0"},"canonical_sha256":"770c49c582fe2717fb342e836fbecadaf7d1f5daef2c3ad29dabe56bd1e1ca42","source":{"kind":"arxiv","id":"1304.5314","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5314","created_at":"2026-05-18T01:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5314v1","created_at":"2026-05-18T01:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5314","created_at":"2026-05-18T01:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"O4GETRMC7YTR","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O4GETRMC7YTRP6ZU","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O4GETRMC","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:O4GETRMC7YTRP6ZUF2BW7PWK3L","target":"record","payload":{"canonical_record":{"source":{"id":"1304.5314","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-04-19T05:45:54Z","cross_cats_sorted":[],"title_canon_sha256":"fa3057677859492e804e3c4ae1165ed87dc49c0538e1e095292a32f0c3b141b9","abstract_canon_sha256":"c851349356483d9bff2245fc0b744b97bce611aff74333e5bbd422cfb3dac65a"},"schema_version":"1.0"},"canonical_sha256":"770c49c582fe2717fb342e836fbecadaf7d1f5daef2c3ad29dabe56bd1e1ca42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:24.914155Z","signature_b64":"djhlwEwU0BnAGkSzcvUewVoQ+Dwp6wj0+Y3FoiIgICTkkKDjbG4CLvAQ7aZVKAa/2Xg8uqEPZGUpCcogoiQgCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"770c49c582fe2717fb342e836fbecadaf7d1f5daef2c3ad29dabe56bd1e1ca42","last_reissued_at":"2026-05-18T01:04:24.913708Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:24.913708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.5314","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":"2026-05-18T01:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0urwvpqO7PUu/oRBtmA2xlb/3w/4u1K0ag4TkAahxdhUeFovKdWdQZyxi8mloLsVa3HzsLW4wUv+lcf30l04Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T00:08:03.715105Z"},"content_sha256":"eeedecf1562481f815ddfbb991d026ef7a36d1622900c562058733ab350acbe9","schema_version":"1.0","event_id":"sha256:eeedecf1562481f815ddfbb991d026ef7a36d1622900c562058733ab350acbe9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:O4GETRMC7YTRP6ZUF2BW7PWK3L","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derived Representation Schemes and Noncommutative Geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Ajay Ramadoss, Giovanni Felder, Yuri Berest","submitted_at":"2013-04-19T05:45:54Z","abstract_excerpt":"Some 15 years ago M. Kontsevich and A. Rosenberg [KR] proposed a heuristic principle according to which the family of schemes ${Rep_n(A)}$ parametrizing the finite-dimensional represen- tations of a noncommutative algebra A should be thought of as a substitute or \"approximation\" for Spec(A). The idea is that every property or noncommutative geometric structure on A should induce a corresponding geometric property or structure on $Rep_n(A)$ for all n. In recent years, many interesting structures in noncommutative geometry have originated from this idea. In practice, however, if an associative a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5314","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":"2026-05-18T01:04:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IOKrsN5RLw51Mjf/OHDG/n7ANlit0DWtWNLIb0xr6FnTSX8Wvow21npFFyQQQE4iECp0VvdKHCtnLJ7SrTWxDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T00:08:03.715729Z"},"content_sha256":"0df47d3a5ff56a44db0d7ae614916b2aaa78d76c9ca6744b9d6bb31a88db7eb8","schema_version":"1.0","event_id":"sha256:0df47d3a5ff56a44db0d7ae614916b2aaa78d76c9ca6744b9d6bb31a88db7eb8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O4GETRMC7YTRP6ZUF2BW7PWK3L/bundle.json","state_url":"https://pith.science/pith/O4GETRMC7YTRP6ZUF2BW7PWK3L/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O4GETRMC7YTRP6ZUF2BW7PWK3L/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":"2026-05-22T00:08:03Z","links":{"resolver":"https://pith.science/pith/O4GETRMC7YTRP6ZUF2BW7PWK3L","bundle":"https://pith.science/pith/O4GETRMC7YTRP6ZUF2BW7PWK3L/bundle.json","state":"https://pith.science/pith/O4GETRMC7YTRP6ZUF2BW7PWK3L/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O4GETRMC7YTRP6ZUF2BW7PWK3L/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:O4GETRMC7YTRP6ZUF2BW7PWK3L","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":"c851349356483d9bff2245fc0b744b97bce611aff74333e5bbd422cfb3dac65a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-04-19T05:45:54Z","title_canon_sha256":"fa3057677859492e804e3c4ae1165ed87dc49c0538e1e095292a32f0c3b141b9"},"schema_version":"1.0","source":{"id":"1304.5314","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.5314","created_at":"2026-05-18T01:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1304.5314v1","created_at":"2026-05-18T01:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.5314","created_at":"2026-05-18T01:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"O4GETRMC7YTR","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"O4GETRMC7YTRP6ZU","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"O4GETRMC","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:0df47d3a5ff56a44db0d7ae614916b2aaa78d76c9ca6744b9d6bb31a88db7eb8","target":"graph","created_at":"2026-05-18T01:04:24Z","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":"Some 15 years ago M. Kontsevich and A. Rosenberg [KR] proposed a heuristic principle according to which the family of schemes ${Rep_n(A)}$ parametrizing the finite-dimensional represen- tations of a noncommutative algebra A should be thought of as a substitute or \"approximation\" for Spec(A). The idea is that every property or noncommutative geometric structure on A should induce a corresponding geometric property or structure on $Rep_n(A)$ for all n. In recent years, many interesting structures in noncommutative geometry have originated from this idea. In practice, however, if an associative a","authors_text":"Ajay Ramadoss, Giovanni Felder, Yuri Berest","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-04-19T05:45:54Z","title":"Derived Representation Schemes and Noncommutative Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.5314","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:eeedecf1562481f815ddfbb991d026ef7a36d1622900c562058733ab350acbe9","target":"record","created_at":"2026-05-18T01:04:24Z","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":"c851349356483d9bff2245fc0b744b97bce611aff74333e5bbd422cfb3dac65a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2013-04-19T05:45:54Z","title_canon_sha256":"fa3057677859492e804e3c4ae1165ed87dc49c0538e1e095292a32f0c3b141b9"},"schema_version":"1.0","source":{"id":"1304.5314","kind":"arxiv","version":1}},"canonical_sha256":"770c49c582fe2717fb342e836fbecadaf7d1f5daef2c3ad29dabe56bd1e1ca42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"770c49c582fe2717fb342e836fbecadaf7d1f5daef2c3ad29dabe56bd1e1ca42","first_computed_at":"2026-05-18T01:04:24.913708Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:24.913708Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"djhlwEwU0BnAGkSzcvUewVoQ+Dwp6wj0+Y3FoiIgICTkkKDjbG4CLvAQ7aZVKAa/2Xg8uqEPZGUpCcogoiQgCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:24.914155Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.5314","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eeedecf1562481f815ddfbb991d026ef7a36d1622900c562058733ab350acbe9","sha256:0df47d3a5ff56a44db0d7ae614916b2aaa78d76c9ca6744b9d6bb31a88db7eb8"],"state_sha256":"9782aa48ed47f8b923a55fa679721cfe8c58ee6dff483d177f107b0a7cd28a27"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yyw2qf28vO0zbq9DVrM8A3h9vENOCjrTZSnU+LRNGqhm359MXcjPR0lID5CjLhmAHp01LW0nXFcGYCR7h4P5Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T00:08:03.718653Z","bundle_sha256":"ea0842265a26f08cf36855252ff7cfd1fa71849412a28c97826bcc785ae93973"}}