{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:7JR5LG3ZCXB2DOQWQQC4JR5RV2","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":"945843c4c5a96b4ecd2545a0d4ca30707416a4e498022c0b549067aff04c517c","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-08-17T18:41:26Z","title_canon_sha256":"9d226844bf38247e35d485ae420fe25fa18eee2bfdc70e990ef195c534e51c5d"},"schema_version":"1.0","source":{"id":"2308.09148","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2308.09148","created_at":"2026-07-05T06:44:20Z"},{"alias_kind":"arxiv_version","alias_value":"2308.09148v1","created_at":"2026-07-05T06:44:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2308.09148","created_at":"2026-07-05T06:44:20Z"},{"alias_kind":"pith_short_12","alias_value":"7JR5LG3ZCXB2","created_at":"2026-07-05T06:44:20Z"},{"alias_kind":"pith_short_16","alias_value":"7JR5LG3ZCXB2DOQW","created_at":"2026-07-05T06:44:20Z"},{"alias_kind":"pith_short_8","alias_value":"7JR5LG3Z","created_at":"2026-07-05T06:44:20Z"}],"graph_snapshots":[{"event_id":"sha256:568cb408cfe5f1e8b297ba5f4cd5f2e770dbb1ee6446a4283e45666fe625370c","target":"graph","created_at":"2026-07-05T06:44:20Z","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/2308.09148/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The framework of templicial objects was put forth in arXiv:2302.02484v1 in order to develop higher categorical concepts in the presence of enrichment. In particular, quasi-categories in modules constitute a subclass of templicial modules which may be considered as a kind of \"weak dg-categories (concentrated in homologically positive degrees)\" according to arXiv:2005.04778v3. The main goal of the present paper is to initiate the deformation theory of templicial modules. In particular, we show that quasi-categories in modules are preserved under levelwise flat infinitesimal deformation.","authors_text":"Arne Mertens, Violeta Borges Marques, Wendy Lowen","cross_cats":["math.AT","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-08-17T18:41:26Z","title":"Deformations of quasi-categories in modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2308.09148","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:bf273690c8db3a16b3b5ed8dca92f002124329c50b3ccaea604f5c941a44cd39","target":"record","created_at":"2026-07-05T06:44:20Z","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":"945843c4c5a96b4ecd2545a0d4ca30707416a4e498022c0b549067aff04c517c","cross_cats_sorted":["math.AT","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2023-08-17T18:41:26Z","title_canon_sha256":"9d226844bf38247e35d485ae420fe25fa18eee2bfdc70e990ef195c534e51c5d"},"schema_version":"1.0","source":{"id":"2308.09148","kind":"arxiv","version":1}},"canonical_sha256":"fa63d59b7915c3a1ba168405c4c7b1aea76752ac5132c08061186b2101d0fb44","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fa63d59b7915c3a1ba168405c4c7b1aea76752ac5132c08061186b2101d0fb44","first_computed_at":"2026-07-05T06:44:20.403252Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:44:20.403252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"45USpgZCriaeXepAEPwZ9v/CSlt1Mp+ujaUirWzo7nCUb88AkxViPaIPLJqIdDBp7EX8sCUEH0GiFe8QdNpBDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:44:20.403805Z","signed_message":"canonical_sha256_bytes"},"source_id":"2308.09148","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf273690c8db3a16b3b5ed8dca92f002124329c50b3ccaea604f5c941a44cd39","sha256:568cb408cfe5f1e8b297ba5f4cd5f2e770dbb1ee6446a4283e45666fe625370c"],"state_sha256":"b8cdaa24b4d54eb75ab3baa42e045e72a4fd9f944e42abed32fd6d8a6d7a055d"}