{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Z6FD5YJELIEK7NJF7N6247RFGZ","short_pith_number":"pith:Z6FD5YJE","canonical_record":{"source":{"id":"1105.1997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-05-10T16:58:32Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"0452fe3dfd2b1856cc21d935f5583a4e49a65e6dd783c49968cc42b7f2207d59","abstract_canon_sha256":"9914a97836fe6d58dea2d27ca392680cfda5a03c80a9179fd7746546a862ca84"},"schema_version":"1.0"},"canonical_sha256":"cf8a3ee1245a08afb525fb7dae7e253664f2a36695f5e885f8011982a22741cb","source":{"kind":"arxiv","id":"1105.1997","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1997","created_at":"2026-05-18T02:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1997v1","created_at":"2026-05-18T02:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1997","created_at":"2026-05-18T02:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"Z6FD5YJELIEK","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z6FD5YJELIEK7NJF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z6FD5YJE","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Z6FD5YJELIEK7NJF7N6247RFGZ","target":"record","payload":{"canonical_record":{"source":{"id":"1105.1997","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-05-10T16:58:32Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"0452fe3dfd2b1856cc21d935f5583a4e49a65e6dd783c49968cc42b7f2207d59","abstract_canon_sha256":"9914a97836fe6d58dea2d27ca392680cfda5a03c80a9179fd7746546a862ca84"},"schema_version":"1.0"},"canonical_sha256":"cf8a3ee1245a08afb525fb7dae7e253664f2a36695f5e885f8011982a22741cb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:02:01.812390Z","signature_b64":"gU1kNBF9dOWyPka0UQRLfqW/7krujJU9ohawhVbunK6pVtBtduN2NZuKkQgFY1zJuuwvtgqq6hubyfjsyxdWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf8a3ee1245a08afb525fb7dae7e253664f2a36695f5e885f8011982a22741cb","last_reissued_at":"2026-05-18T02:02:01.811520Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:02:01.811520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1105.1997","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":"2026-05-18T02:02:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XGeqxzb3+UksMfOIRUMP1xghEnZqYNItnNy1CPTzKApPtNEHc7Apl1lMPZLna9+L9+NdyY/cEWVhFv1cb5+ABA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:12:33.764752Z"},"content_sha256":"2375880915b95df48d3db176709e2e9d6df2c6c0370a5b267b2e78f1de4822f6","schema_version":"1.0","event_id":"sha256:2375880915b95df48d3db176709e2e9d6df2c6c0370a5b267b2e78f1de4822f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Z6FD5YJELIEK7NJF7N6247RFGZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cellularization of structures in stable homotopy categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Javier J. Guti\\'errez","submitted_at":"2011-05-10T16:58:32Z","abstract_excerpt":"We describe the formal properties of cellularization functors in triangulated categories and study the preservation of ring and module structures under these functors in stable homotopy categories in the sense of Hovey, Palmieri and Strickland, such as the homotopy category of spectra or the derived category of a commutative ring. We prove that cellularization functors preserve modules over connective rings but they do not preserve rings in general (even if the ring is connective or the cellularization functor is triangulated). As an application of these results, we describe the cellularizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1997","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":"2026-05-18T02:02:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vO97X03OSZL+uGJjaD4AJBq/kweo26zEul6uculXH7LzO/R7tXe6PGdtIIhFG9mUmRzPyDICwb5DqSXVH+NIBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:12:33.765108Z"},"content_sha256":"550310c5482a5d4148bf237d777c5b9bf7ea9548354777ca5dd3be3e2aa71e9b","schema_version":"1.0","event_id":"sha256:550310c5482a5d4148bf237d777c5b9bf7ea9548354777ca5dd3be3e2aa71e9b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z6FD5YJELIEK7NJF7N6247RFGZ/bundle.json","state_url":"https://pith.science/pith/Z6FD5YJELIEK7NJF7N6247RFGZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z6FD5YJELIEK7NJF7N6247RFGZ/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":"2026-05-28T23:12:33Z","links":{"resolver":"https://pith.science/pith/Z6FD5YJELIEK7NJF7N6247RFGZ","bundle":"https://pith.science/pith/Z6FD5YJELIEK7NJF7N6247RFGZ/bundle.json","state":"https://pith.science/pith/Z6FD5YJELIEK7NJF7N6247RFGZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z6FD5YJELIEK7NJF7N6247RFGZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z6FD5YJELIEK7NJF7N6247RFGZ","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":"9914a97836fe6d58dea2d27ca392680cfda5a03c80a9179fd7746546a862ca84","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-05-10T16:58:32Z","title_canon_sha256":"0452fe3dfd2b1856cc21d935f5583a4e49a65e6dd783c49968cc42b7f2207d59"},"schema_version":"1.0","source":{"id":"1105.1997","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1105.1997","created_at":"2026-05-18T02:02:01Z"},{"alias_kind":"arxiv_version","alias_value":"1105.1997v1","created_at":"2026-05-18T02:02:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1105.1997","created_at":"2026-05-18T02:02:01Z"},{"alias_kind":"pith_short_12","alias_value":"Z6FD5YJELIEK","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z6FD5YJELIEK7NJF","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z6FD5YJE","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:550310c5482a5d4148bf237d777c5b9bf7ea9548354777ca5dd3be3e2aa71e9b","target":"graph","created_at":"2026-05-18T02:02:01Z","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 describe the formal properties of cellularization functors in triangulated categories and study the preservation of ring and module structures under these functors in stable homotopy categories in the sense of Hovey, Palmieri and Strickland, such as the homotopy category of spectra or the derived category of a commutative ring. We prove that cellularization functors preserve modules over connective rings but they do not preserve rings in general (even if the ring is connective or the cellularization functor is triangulated). As an application of these results, we describe the cellularizatio","authors_text":"Javier J. Guti\\'errez","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-05-10T16:58:32Z","title":"Cellularization of structures in stable homotopy categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.1997","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":"sha256:2375880915b95df48d3db176709e2e9d6df2c6c0370a5b267b2e78f1de4822f6","target":"record","created_at":"2026-05-18T02:02:01Z","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":"9914a97836fe6d58dea2d27ca392680cfda5a03c80a9179fd7746546a862ca84","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2011-05-10T16:58:32Z","title_canon_sha256":"0452fe3dfd2b1856cc21d935f5583a4e49a65e6dd783c49968cc42b7f2207d59"},"schema_version":"1.0","source":{"id":"1105.1997","kind":"arxiv","version":1}},"canonical_sha256":"cf8a3ee1245a08afb525fb7dae7e253664f2a36695f5e885f8011982a22741cb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf8a3ee1245a08afb525fb7dae7e253664f2a36695f5e885f8011982a22741cb","first_computed_at":"2026-05-18T02:02:01.811520Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:02:01.811520Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gU1kNBF9dOWyPka0UQRLfqW/7krujJU9ohawhVbunK6pVtBtduN2NZuKkQgFY1zJuuwvtgqq6hubyfjsyxdWAg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:02:01.812390Z","signed_message":"canonical_sha256_bytes"},"source_id":"1105.1997","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2375880915b95df48d3db176709e2e9d6df2c6c0370a5b267b2e78f1de4822f6","sha256:550310c5482a5d4148bf237d777c5b9bf7ea9548354777ca5dd3be3e2aa71e9b"],"state_sha256":"d22e247d800e4a42f9db56a39a946cb34aebc38af5491755314a8503b357a6f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i6pQ/gUkkf0qyfHzHXOPOmyMwQ1NMyUKSB69ax3lsG+Ad7XOmzUUvogMTYTIedAa9bloIGqLZB46d+iPY6VzDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:12:33.767047Z","bundle_sha256":"f62c5190c88df65b37c09d8659ebe1bb47d63dd72d6434f9086008c44019e9f4"}}