{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:ULVF6EHH7YL627WRKDXDKLSD4J","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":"126540a4e69fd9b4714e108e0628aa48578b3c5a5df93114de4cbd04e04da4d9","cross_cats_sorted":["math.CT"],"license":"","primary_cat":"math.AT","submitted_at":"2001-01-11T15:56:18Z","title_canon_sha256":"1cb08efde815469bd47c379cf78e78eaa4b62f489e23be523e8ccdaa3f06ccf6"},"schema_version":"1.0","source":{"id":"math/0101102","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0101102","created_at":"2026-07-04T14:35:01Z"},{"alias_kind":"arxiv_version","alias_value":"math/0101102v1","created_at":"2026-07-04T14:35:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0101102","created_at":"2026-07-04T14:35:01Z"},{"alias_kind":"pith_short_12","alias_value":"ULVF6EHH7YL6","created_at":"2026-07-04T14:35:01Z"},{"alias_kind":"pith_short_16","alias_value":"ULVF6EHH7YL627WR","created_at":"2026-07-04T14:35:01Z"},{"alias_kind":"pith_short_8","alias_value":"ULVF6EHH","created_at":"2026-07-04T14:35:01Z"}],"graph_snapshots":[{"event_id":"sha256:bef2e0030bad7731222efe72aa716114044619dd6f407a869dace652411e56df","target":"graph","created_at":"2026-07-04T14:35:01Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0101102/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we develop the theory of operads, algebras and modules in cofibrantly generated symmetric monoidal model categories. We give J-semi model strucures, which are a slightly weaker version of model structures, for operads and algebras and model structures for modules. In a second part we develop the thoery of S-modules of [EKMM]., which allows a general homotopy theory for commutative algebras and pseudo unital symmetric monoidal categories of modules over them. Finally we prove a base change and projection formula.","authors_text":"Markus Spitzweck","cross_cats":["math.CT"],"headline":"","license":"","primary_cat":"math.AT","submitted_at":"2001-01-11T15:56:18Z","title":"Operads, Algebras and Modules in General Model Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0101102","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":"sha256:6b9885e9b866476bde0f9ce643738f2fe78052220477b720841eeaa2dfd44046","target":"record","created_at":"2026-07-04T14:35:01Z","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":"126540a4e69fd9b4714e108e0628aa48578b3c5a5df93114de4cbd04e04da4d9","cross_cats_sorted":["math.CT"],"license":"","primary_cat":"math.AT","submitted_at":"2001-01-11T15:56:18Z","title_canon_sha256":"1cb08efde815469bd47c379cf78e78eaa4b62f489e23be523e8ccdaa3f06ccf6"},"schema_version":"1.0","source":{"id":"math/0101102","kind":"arxiv","version":1}},"canonical_sha256":"a2ea5f10e7fe17ed7ed150ee352e43e251642fa69cdd0ce886edcd98ecc48e30","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2ea5f10e7fe17ed7ed150ee352e43e251642fa69cdd0ce886edcd98ecc48e30","first_computed_at":"2026-07-04T14:35:01.453150Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:35:01.453150Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PfZNi7RvgNfjZ0Xd/VFdG4YqcNL5b3n4afMEnsn9c3KulFRh/EDNU3+HVhs4tOiAxJDlweWdJbciWsW3lzEmDA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:35:01.453619Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0101102","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b9885e9b866476bde0f9ce643738f2fe78052220477b720841eeaa2dfd44046","sha256:bef2e0030bad7731222efe72aa716114044619dd6f407a869dace652411e56df"],"state_sha256":"bc20e149c773753b80fd9778478e49ad8e974bed6483f5305a7ca8f4251b40f8"}