{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:YLVNIYMIOGYJAK6644MNLJESSO","short_pith_number":"pith:YLVNIYMI","canonical_record":{"source":{"id":"1202.6297","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-28T17:36:34Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"8384b5dbe971bb69dfb8fecda3420a8789da9754764ba55ee768fca2116ec9c9","abstract_canon_sha256":"cede470d3a1dbfb486d979e5d60c042966ce309a51fbcf7516e024dc0cac579f"},"schema_version":"1.0"},"canonical_sha256":"c2ead4618871b0902bdee718d5a49293945ea0c0a31fb0701d5026a215090a55","source":{"kind":"arxiv","id":"1202.6297","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6297","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6297v3","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6297","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"pith_short_12","alias_value":"YLVNIYMIOGYJ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YLVNIYMIOGYJAK66","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YLVNIYMI","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:YLVNIYMIOGYJAK6644MNLJESSO","target":"record","payload":{"canonical_record":{"source":{"id":"1202.6297","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-28T17:36:34Z","cross_cats_sorted":["math.AT","math.KT"],"title_canon_sha256":"8384b5dbe971bb69dfb8fecda3420a8789da9754764ba55ee768fca2116ec9c9","abstract_canon_sha256":"cede470d3a1dbfb486d979e5d60c042966ce309a51fbcf7516e024dc0cac579f"},"schema_version":"1.0"},"canonical_sha256":"c2ead4618871b0902bdee718d5a49293945ea0c0a31fb0701d5026a215090a55","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:06.930273Z","signature_b64":"0VMMw7YVN0utvT+voTtU0UQf3j6T74P5XPfEkNeOppUVVa/lHVGRbV1wwqJtxar3MJbMBkFmtEXKnLTZ5CgRDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c2ead4618871b0902bdee718d5a49293945ea0c0a31fb0701d5026a215090a55","last_reissued_at":"2026-05-18T03:31:06.929592Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:06.929592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1202.6297","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":"2026-05-18T03:31:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2BjiUBJ4hQqyPkjKikVgG1jhUMyD9+F6Lhpjnx6RsHSb0iJIZJKT7H2v4bJqK7e5i6iUy+vSIxdXAbPqFuhHAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:40:01.867888Z"},"content_sha256":"005b0e6b208ebb37d01c0626973d9d72dd6c17e983c0dd00a0e17e8749e61bbc","schema_version":"1.0","event_id":"sha256:005b0e6b208ebb37d01c0626973d9d72dd6c17e983c0dd00a0e17e8749e61bbc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:YLVNIYMIOGYJAK6644MNLJESSO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From exceptional collections to motivic decompositions via noncommutative motives","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"Goncalo Tabuada, Matilde Marcolli","submitted_at":"2012-02-28T17:36:34Z","abstract_excerpt":"Making use of noncommutative motives we relate exceptional collections (and more generally semi-orthogonal decompositions) to motivic decompositions. On one hand we prove that the Chow motive M(X) of every smooth proper Deligne-Mumford stack X, whose bounded derived category D(X) of coherent schemes admits a full exceptional collection, decomposes into a direct sum of tensor powers of the Lefschetz motive. Examples include projective spaces, quadrics, toric varieties, homogeneous spaces, Fano threefolds, and moduli spaces. On the other hand we prove that if M(X) decomposes into a direct sum of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6297","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":"2026-05-18T03:31:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+EMZDPFYaphY0K7PzoB+Z7+A4dE3+ON6Odg/1/pjvMKZWn+2tsH0+6ufKJGUw4HSVudesi+8Jj4w5r9AZZZwBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:40:01.868621Z"},"content_sha256":"e3619cb4c6ddab26ea8e34b2838dfcc39aa2726a5fbda90cccf9990b54f33b2e","schema_version":"1.0","event_id":"sha256:e3619cb4c6ddab26ea8e34b2838dfcc39aa2726a5fbda90cccf9990b54f33b2e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YLVNIYMIOGYJAK6644MNLJESSO/bundle.json","state_url":"https://pith.science/pith/YLVNIYMIOGYJAK6644MNLJESSO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YLVNIYMIOGYJAK6644MNLJESSO/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":"2026-06-09T02:40:01Z","links":{"resolver":"https://pith.science/pith/YLVNIYMIOGYJAK6644MNLJESSO","bundle":"https://pith.science/pith/YLVNIYMIOGYJAK6644MNLJESSO/bundle.json","state":"https://pith.science/pith/YLVNIYMIOGYJAK6644MNLJESSO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YLVNIYMIOGYJAK6644MNLJESSO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:YLVNIYMIOGYJAK6644MNLJESSO","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":"cede470d3a1dbfb486d979e5d60c042966ce309a51fbcf7516e024dc0cac579f","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-28T17:36:34Z","title_canon_sha256":"8384b5dbe971bb69dfb8fecda3420a8789da9754764ba55ee768fca2116ec9c9"},"schema_version":"1.0","source":{"id":"1202.6297","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6297","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6297v3","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6297","created_at":"2026-05-18T03:31:06Z"},{"alias_kind":"pith_short_12","alias_value":"YLVNIYMIOGYJ","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"YLVNIYMIOGYJAK66","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"YLVNIYMI","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:e3619cb4c6ddab26ea8e34b2838dfcc39aa2726a5fbda90cccf9990b54f33b2e","target":"graph","created_at":"2026-05-18T03:31:06Z","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":"Making use of noncommutative motives we relate exceptional collections (and more generally semi-orthogonal decompositions) to motivic decompositions. On one hand we prove that the Chow motive M(X) of every smooth proper Deligne-Mumford stack X, whose bounded derived category D(X) of coherent schemes admits a full exceptional collection, decomposes into a direct sum of tensor powers of the Lefschetz motive. Examples include projective spaces, quadrics, toric varieties, homogeneous spaces, Fano threefolds, and moduli spaces. On the other hand we prove that if M(X) decomposes into a direct sum of","authors_text":"Goncalo Tabuada, Matilde Marcolli","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-28T17:36:34Z","title":"From exceptional collections to motivic decompositions via noncommutative motives"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6297","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":"sha256:005b0e6b208ebb37d01c0626973d9d72dd6c17e983c0dd00a0e17e8749e61bbc","target":"record","created_at":"2026-05-18T03:31:06Z","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":"cede470d3a1dbfb486d979e5d60c042966ce309a51fbcf7516e024dc0cac579f","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2012-02-28T17:36:34Z","title_canon_sha256":"8384b5dbe971bb69dfb8fecda3420a8789da9754764ba55ee768fca2116ec9c9"},"schema_version":"1.0","source":{"id":"1202.6297","kind":"arxiv","version":3}},"canonical_sha256":"c2ead4618871b0902bdee718d5a49293945ea0c0a31fb0701d5026a215090a55","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c2ead4618871b0902bdee718d5a49293945ea0c0a31fb0701d5026a215090a55","first_computed_at":"2026-05-18T03:31:06.929592Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:31:06.929592Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0VMMw7YVN0utvT+voTtU0UQf3j6T74P5XPfEkNeOppUVVa/lHVGRbV1wwqJtxar3MJbMBkFmtEXKnLTZ5CgRDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:31:06.930273Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6297","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:005b0e6b208ebb37d01c0626973d9d72dd6c17e983c0dd00a0e17e8749e61bbc","sha256:e3619cb4c6ddab26ea8e34b2838dfcc39aa2726a5fbda90cccf9990b54f33b2e"],"state_sha256":"c0deb72d1269d18fb73243bf1fd04e0ee0988018423a1e6dc68a56ac6ebb0543"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aK1uzEv4M9wmUlh4Igk0XVVPmGaSkVtq9Md8tvDwxPfjGHQNhqotYhOckt/TILxW3dggcyTwrfJLF+3iDW4uDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:40:01.872554Z","bundle_sha256":"59f55673d5a7143c4823d628ce16decea890a9fa1a31a391186f834ac820dbba"}}