{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:E7YTSAZ6B42Y6LTBPYKOMPVKWO","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":"5cdb86894a5a73ea522f87c23a05301f6b4f86e04197a3dc3231de188792b3a9","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-07-03T18:50:46Z","title_canon_sha256":"17dc369708e73d643aa8a5202286d84837a4e7167d904a91ff43e8f53c5e43a7"},"schema_version":"1.0","source":{"id":"1607.00668","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00668","created_at":"2026-07-05T01:37:38Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00668v4","created_at":"2026-07-05T01:37:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00668","created_at":"2026-07-05T01:37:38Z"},{"alias_kind":"pith_short_12","alias_value":"E7YTSAZ6B42Y","created_at":"2026-07-05T01:37:38Z"},{"alias_kind":"pith_short_16","alias_value":"E7YTSAZ6B42Y6LTB","created_at":"2026-07-05T01:37:38Z"},{"alias_kind":"pith_short_8","alias_value":"E7YTSAZ6","created_at":"2026-07-05T01:37:38Z"}],"graph_snapshots":[{"event_id":"sha256:31268c78b8f1ffef79bd79a9637be6c3197bb5db3cffa41f02293f899bf5063c","target":"graph","created_at":"2026-07-05T01:37:38Z","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/1607.00668/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The goal of this paper is to develop a theory of join and slices for strict $\\infty$-categories. To any pair of strict $\\infty$-categories, we associate a third one that we call their join. This operation is compatible with the usual join of categories up to truncation. We show that the join defines a monoidal category structure on the category of strict $\\infty$-categories and that it respects connected inductive limits in each variable. In particular, we obtain the existence of some right adjoints; these adjoints define $\\infty$-categorical slices, in a generalized sense. We state some conje","authors_text":"Dimitri Ara, Georges Maltsiniotis","cross_cats":["math.AT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-07-03T18:50:46Z","title":"Join and slices for strict $\\infty$-categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00668","kind":"arxiv","version":4},"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":"sha256:0e5aac824ade5d221d4d6d79029ed15a39e14b8ff2e2354603c71863072afba9","target":"record","created_at":"2026-07-05T01:37:38Z","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":"5cdb86894a5a73ea522f87c23a05301f6b4f86e04197a3dc3231de188792b3a9","cross_cats_sorted":["math.AT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2016-07-03T18:50:46Z","title_canon_sha256":"17dc369708e73d643aa8a5202286d84837a4e7167d904a91ff43e8f53c5e43a7"},"schema_version":"1.0","source":{"id":"1607.00668","kind":"arxiv","version":4}},"canonical_sha256":"27f139033e0f358f2e617e14e63eaab3acd79d712bba8c76da4248d73eb33afa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27f139033e0f358f2e617e14e63eaab3acd79d712bba8c76da4248d73eb33afa","first_computed_at":"2026-07-05T01:37:38.288973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:37:38.288973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BKwi2JIlgdvKYmZYCuxvYyCP7AZn2MHK7c6/ksRSqTMqztDzqXszGPFOpIDmpbK/gIL66dJZl6gdHXEyEpryDw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:37:38.289444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00668","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0e5aac824ade5d221d4d6d79029ed15a39e14b8ff2e2354603c71863072afba9","sha256:31268c78b8f1ffef79bd79a9637be6c3197bb5db3cffa41f02293f899bf5063c"],"state_sha256":"e88f0a8a49482d66580e80771b473871f3f2fb729171ec5a7035b56c055d34d4"}