{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:V4DM2DTPBJ52Z53E2T3MFFNXZL","short_pith_number":"pith:V4DM2DTP","canonical_record":{"source":{"id":"1705.03863","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-10T17:27:43Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"e9a47df495c2b63fd5c631173843627c1f5351cdbf1db523ec9bcd51628d0266","abstract_canon_sha256":"81779d3cda0b3305ae280fd1a61b4ee00d38fa47c39859140862a99e71466763"},"schema_version":"1.0"},"canonical_sha256":"af06cd0e6f0a7bacf764d4f6c295b7caf407382ecb6c836bd0d750c0c831565d","source":{"kind":"arxiv","id":"1705.03863","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03863","created_at":"2026-05-18T00:32:25Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03863v3","created_at":"2026-05-18T00:32:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03863","created_at":"2026-05-18T00:32:25Z"},{"alias_kind":"pith_short_12","alias_value":"V4DM2DTPBJ52","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V4DM2DTPBJ52Z53E","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V4DM2DTP","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:V4DM2DTPBJ52Z53E2T3MFFNXZL","target":"record","payload":{"canonical_record":{"source":{"id":"1705.03863","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-10T17:27:43Z","cross_cats_sorted":["math.CT"],"title_canon_sha256":"e9a47df495c2b63fd5c631173843627c1f5351cdbf1db523ec9bcd51628d0266","abstract_canon_sha256":"81779d3cda0b3305ae280fd1a61b4ee00d38fa47c39859140862a99e71466763"},"schema_version":"1.0"},"canonical_sha256":"af06cd0e6f0a7bacf764d4f6c295b7caf407382ecb6c836bd0d750c0c831565d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:25.726549Z","signature_b64":"DMUfuyxjniqJzdkpDvD2UPpxKUmODr54K0g3mb5Fsc8MU2b2kJ2W+NccCsF+Dnj5sax/vc+Ikh1jBWQX/5grCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af06cd0e6f0a7bacf764d4f6c295b7caf407382ecb6c836bd0d750c0c831565d","last_reissued_at":"2026-05-18T00:32:25.725898Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:25.725898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1705.03863","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":"2026-05-18T00:32:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bLOv20TkXkB0apD8zm4SZRmOB/xHYlIid/pENpWyq5r0w2sr8L3GxEjo66Ej37VkgcVY755ByQMUh1ZmdVmpCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:37:30.913650Z"},"content_sha256":"35c2d104c48217bf82185c864a4b3a8ea3066786076ce9d9bfcf9f453b92ba1a","schema_version":"1.0","event_id":"sha256:35c2d104c48217bf82185c864a4b3a8ea3066786076ce9d9bfcf9f453b92ba1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:V4DM2DTPBJ52Z53E2T3MFFNXZL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Gabriel-Morita theory for excisive model categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT"],"primary_cat":"math.AT","authors_text":"Clemens Berger, Kruna Ratkovic","submitted_at":"2017-05-10T17:27:43Z","abstract_excerpt":"We develop a Gabriel-Morita theory for strong monads on pointed monoidal model categories. Assuming that the model category is excisive, i.e. the derived suspension functor is conservative, we show that if the monad T preserves cofibre sequences up to homotopy and has a weakly invertible strength, then the category of T-algebras is Quillen equivalent to the category of T(I)-modules where I is the monoidal unit. This recovers Schwede's theorem on connective stable homotopy over a pointed Lawvere theory as special case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03863","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":"2026-05-18T00:32:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hp4inOE+SbhNnMVyQeKNCLOgo00a+NP/p+WSO0xQo2tN0W6YyRclPpRacNlHZbk6V/X0Tmc/1I1XbzwZb2bnAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:37:30.913998Z"},"content_sha256":"775c50241ea9f29b3e4b8194ef61a6e1f0bb3b91f94b8c09932a0c7c3d2041c8","schema_version":"1.0","event_id":"sha256:775c50241ea9f29b3e4b8194ef61a6e1f0bb3b91f94b8c09932a0c7c3d2041c8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL/bundle.json","state_url":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL/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":"2026-06-03T05:37:30Z","links":{"resolver":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL","bundle":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL/bundle.json","state":"https://pith.science/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V4DM2DTPBJ52Z53E2T3MFFNXZL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:V4DM2DTPBJ52Z53E2T3MFFNXZL","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":"81779d3cda0b3305ae280fd1a61b4ee00d38fa47c39859140862a99e71466763","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-10T17:27:43Z","title_canon_sha256":"e9a47df495c2b63fd5c631173843627c1f5351cdbf1db523ec9bcd51628d0266"},"schema_version":"1.0","source":{"id":"1705.03863","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.03863","created_at":"2026-05-18T00:32:25Z"},{"alias_kind":"arxiv_version","alias_value":"1705.03863v3","created_at":"2026-05-18T00:32:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.03863","created_at":"2026-05-18T00:32:25Z"},{"alias_kind":"pith_short_12","alias_value":"V4DM2DTPBJ52","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"V4DM2DTPBJ52Z53E","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"V4DM2DTP","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:775c50241ea9f29b3e4b8194ef61a6e1f0bb3b91f94b8c09932a0c7c3d2041c8","target":"graph","created_at":"2026-05-18T00:32:25Z","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 develop a Gabriel-Morita theory for strong monads on pointed monoidal model categories. Assuming that the model category is excisive, i.e. the derived suspension functor is conservative, we show that if the monad T preserves cofibre sequences up to homotopy and has a weakly invertible strength, then the category of T-algebras is Quillen equivalent to the category of T(I)-modules where I is the monoidal unit. This recovers Schwede's theorem on connective stable homotopy over a pointed Lawvere theory as special case.","authors_text":"Clemens Berger, Kruna Ratkovic","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-10T17:27:43Z","title":"Gabriel-Morita theory for excisive model categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.03863","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":"sha256:35c2d104c48217bf82185c864a4b3a8ea3066786076ce9d9bfcf9f453b92ba1a","target":"record","created_at":"2026-05-18T00:32:25Z","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":"81779d3cda0b3305ae280fd1a61b4ee00d38fa47c39859140862a99e71466763","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AT","submitted_at":"2017-05-10T17:27:43Z","title_canon_sha256":"e9a47df495c2b63fd5c631173843627c1f5351cdbf1db523ec9bcd51628d0266"},"schema_version":"1.0","source":{"id":"1705.03863","kind":"arxiv","version":3}},"canonical_sha256":"af06cd0e6f0a7bacf764d4f6c295b7caf407382ecb6c836bd0d750c0c831565d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af06cd0e6f0a7bacf764d4f6c295b7caf407382ecb6c836bd0d750c0c831565d","first_computed_at":"2026-05-18T00:32:25.725898Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:25.725898Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DMUfuyxjniqJzdkpDvD2UPpxKUmODr54K0g3mb5Fsc8MU2b2kJ2W+NccCsF+Dnj5sax/vc+Ikh1jBWQX/5grCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:25.726549Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.03863","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35c2d104c48217bf82185c864a4b3a8ea3066786076ce9d9bfcf9f453b92ba1a","sha256:775c50241ea9f29b3e4b8194ef61a6e1f0bb3b91f94b8c09932a0c7c3d2041c8"],"state_sha256":"6afe7b25c5aa05cfa27520e6ff5003e381e3252f61ebcf18b54bed8fe794afbb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gm+5GDa3Qfpe6mWTsvSKZHX1cJfdVxGvyuj83zulK5IPS9sM/v9H3fFnnEKV8G5MdDfiOdUvK5JYaX0X5G6SAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:37:30.916117Z","bundle_sha256":"5eed4a5227bd35c25b55556df8ae39c014c4b27d912e5bb43676db4d58cac0f5"}}