{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:PR4YLZ4TO7H7KQ2MBAV2WNPVEM","short_pith_number":"pith:PR4YLZ4T","canonical_record":{"source":{"id":"0706.0493","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-06-04T18:32:28Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"11cd2c2a4cd734db63d053779be4ab8569360cfc8c4334ccdc5d9c0299d5c79a","abstract_canon_sha256":"0ab665c8a750e8ebff38f2ee9a7791c544b133605cced2864b9a0f199a54c8ef"},"schema_version":"1.0"},"canonical_sha256":"7c7985e79377cff5434c082bab35f52329256f4445e6984c6059fb80185f77b4","source":{"kind":"arxiv","id":"0706.0493","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.0493","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"0706.0493v3","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0493","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"PR4YLZ4TO7H7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"PR4YLZ4TO7H7KQ2M","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"PR4YLZ4T","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:PR4YLZ4TO7H7KQ2MBAV2WNPVEM","target":"record","payload":{"canonical_record":{"source":{"id":"0706.0493","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.AG","submitted_at":"2007-06-04T18:32:28Z","cross_cats_sorted":["math.AT"],"title_canon_sha256":"11cd2c2a4cd734db63d053779be4ab8569360cfc8c4334ccdc5d9c0299d5c79a","abstract_canon_sha256":"0ab665c8a750e8ebff38f2ee9a7791c544b133605cced2864b9a0f199a54c8ef"},"schema_version":"1.0"},"canonical_sha256":"7c7985e79377cff5434c082bab35f52329256f4445e6984c6059fb80185f77b4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:45:35.544401Z","signature_b64":"pHQEYR+ajg6wFfvXtGW3AfCBL6IRyTr6bdarFG4utg8iRhjIHDTmXoFKbz+R+dik+ZCyTdYYg1+wZ4SsnHK1BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c7985e79377cff5434c082bab35f52329256f4445e6984c6059fb80185f77b4","last_reissued_at":"2026-05-18T00:45:35.542992Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:45:35.542992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.0493","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":"2026-05-18T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yXS3dT6w/ZTfKs6BZpPJQLTXFzjnzsb7G/4Mc538eyGd+6CmmOM00lLOG8J0sLrCGysqz4kGZAcXGvsyKBRQAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:20:23.989582Z"},"content_sha256":"f78890f54e7c35550dc5c3fe6bd6659ea3d9554e478b91c8d6d4ec1472499871","schema_version":"1.0","event_id":"sha256:f78890f54e7c35550dc5c3fe6bd6659ea3d9554e478b91c8d6d4ec1472499871"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:PR4YLZ4TO7H7KQ2MBAV2WNPVEM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The derived category of quasi-coherent sheaves and axiomatic stable homotopy","license":"","headline":"","cross_cats":["math.AT"],"primary_cat":"math.AG","authors_text":"Ana Jeremias, Leovigildo Alonso, Maria J. Vale, Marta Perez","submitted_at":"2007-06-04T18:32:28Z","abstract_excerpt":"We prove in this paper that for a quasi-compact and semi-separated (non necessarily noetherian) scheme X, the derived category of quasi-coherent sheaves over X, D(A_qc(X)), is a stable homotopy category in the sense of Hovey, Palmieri and Strickland, answering a question posed by Strickland. Moreover we show that it is unital and algebraic. We also prove that for a noetherian semi-separated formal scheme X, its derived category of sheaves of modules with quasi-coherent torsion homologies D_qct(X) is a stable homotopy category. It is algebraic but if the formal scheme is not a usual scheme, it "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0493","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":"2026-05-18T00:45:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NE5VG1/NPbdibhsJsT5zkAAuw0OocFlLZT+K+iUsmJrVDPql0ILvSg/eW0agukOnaK+9q8xBNn5OrD3/W09pCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T22:20:23.989961Z"},"content_sha256":"89f39427ba091dfc444edf44c1ba54cb616e8be42e399aadc373563cb4381cba","schema_version":"1.0","event_id":"sha256:89f39427ba091dfc444edf44c1ba54cb616e8be42e399aadc373563cb4381cba"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PR4YLZ4TO7H7KQ2MBAV2WNPVEM/bundle.json","state_url":"https://pith.science/pith/PR4YLZ4TO7H7KQ2MBAV2WNPVEM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PR4YLZ4TO7H7KQ2MBAV2WNPVEM/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":"2026-06-04T22:20:23Z","links":{"resolver":"https://pith.science/pith/PR4YLZ4TO7H7KQ2MBAV2WNPVEM","bundle":"https://pith.science/pith/PR4YLZ4TO7H7KQ2MBAV2WNPVEM/bundle.json","state":"https://pith.science/pith/PR4YLZ4TO7H7KQ2MBAV2WNPVEM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PR4YLZ4TO7H7KQ2MBAV2WNPVEM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:PR4YLZ4TO7H7KQ2MBAV2WNPVEM","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":"0ab665c8a750e8ebff38f2ee9a7791c544b133605cced2864b9a0f199a54c8ef","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.AG","submitted_at":"2007-06-04T18:32:28Z","title_canon_sha256":"11cd2c2a4cd734db63d053779be4ab8569360cfc8c4334ccdc5d9c0299d5c79a"},"schema_version":"1.0","source":{"id":"0706.0493","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.0493","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"arxiv_version","alias_value":"0706.0493v3","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.0493","created_at":"2026-05-18T00:45:35Z"},{"alias_kind":"pith_short_12","alias_value":"PR4YLZ4TO7H7","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"PR4YLZ4TO7H7KQ2M","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"PR4YLZ4T","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:89f39427ba091dfc444edf44c1ba54cb616e8be42e399aadc373563cb4381cba","target":"graph","created_at":"2026-05-18T00:45:35Z","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 prove in this paper that for a quasi-compact and semi-separated (non necessarily noetherian) scheme X, the derived category of quasi-coherent sheaves over X, D(A_qc(X)), is a stable homotopy category in the sense of Hovey, Palmieri and Strickland, answering a question posed by Strickland. Moreover we show that it is unital and algebraic. We also prove that for a noetherian semi-separated formal scheme X, its derived category of sheaves of modules with quasi-coherent torsion homologies D_qct(X) is a stable homotopy category. It is algebraic but if the formal scheme is not a usual scheme, it ","authors_text":"Ana Jeremias, Leovigildo Alonso, Maria J. Vale, Marta Perez","cross_cats":["math.AT"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2007-06-04T18:32:28Z","title":"The derived category of quasi-coherent sheaves and axiomatic stable homotopy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0493","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:f78890f54e7c35550dc5c3fe6bd6659ea3d9554e478b91c8d6d4ec1472499871","target":"record","created_at":"2026-05-18T00:45:35Z","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":"0ab665c8a750e8ebff38f2ee9a7791c544b133605cced2864b9a0f199a54c8ef","cross_cats_sorted":["math.AT"],"license":"","primary_cat":"math.AG","submitted_at":"2007-06-04T18:32:28Z","title_canon_sha256":"11cd2c2a4cd734db63d053779be4ab8569360cfc8c4334ccdc5d9c0299d5c79a"},"schema_version":"1.0","source":{"id":"0706.0493","kind":"arxiv","version":3}},"canonical_sha256":"7c7985e79377cff5434c082bab35f52329256f4445e6984c6059fb80185f77b4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c7985e79377cff5434c082bab35f52329256f4445e6984c6059fb80185f77b4","first_computed_at":"2026-05-18T00:45:35.542992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:35.542992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pHQEYR+ajg6wFfvXtGW3AfCBL6IRyTr6bdarFG4utg8iRhjIHDTmXoFKbz+R+dik+ZCyTdYYg1+wZ4SsnHK1BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:35.544401Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.0493","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f78890f54e7c35550dc5c3fe6bd6659ea3d9554e478b91c8d6d4ec1472499871","sha256:89f39427ba091dfc444edf44c1ba54cb616e8be42e399aadc373563cb4381cba"],"state_sha256":"d789f11f8c16a6c4806897fce44b30fc37de9dffcda2303de221a0b0915f9e19"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Cb+OUvHQjRrv02b96eeAvnXAsgQhyn+pv9pjDhKWw0/GZxk4ekX+LdXgKwyshNFQoepHU5mWzk3Ourj8HxoDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T22:20:23.992237Z","bundle_sha256":"2b528f868a793bb5a53e88d9ba4f9e719d1eee5ae672b2b40d55031e75222af7"}}