{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:FIZ5L3QVZ5QWTBXAXOUBRSCMN5","short_pith_number":"pith:FIZ5L3QV","schema_version":"1.0","canonical_sha256":"2a33d5ee15cf616986e0bba818c84c6f7087bd7d097464212e6a0315d5553067","source":{"kind":"arxiv","id":"1701.07538","version":1},"attestation_state":"computed","paper":{"title":"The join construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CT","authors_text":"Egbert Rijke","submitted_at":"2017-01-26T01:31:53Z","abstract_excerpt":"In homotopy type theory we can define the join of maps as a binary operation on maps with a common co-domain. This operation is commutative, associative, and the unique map from the empty type into the common codomain is a neutral element. Moreover, we show that the idempotents of the join of maps are precisely the embeddings, and we prove the `join connectivity theorem', which states that the connectivity of the join of maps equals the join of the connectivities of the individual maps.\n  We define the image of a map $f:A\\to X$ in $U$ via the join construction, as the colimit of the finite joi"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1701.07538","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-01-26T01:31:53Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"2a2ed78464962c612afbb5eb3ef11950062a2ba368091b7c166295646639e5dc","abstract_canon_sha256":"807e4ba88f77e68effda9ed6f86fee1299d2de9358d2d5dd08d78638697afcb5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:03.210307Z","signature_b64":"7Z9kV15f6LUk1RS4jRb66hzmmyjOq+HXr5eCgJiOjbZESdi8O5gPqjM/j0JgUwMd87iWPtu140kKbXd4iHj/Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a33d5ee15cf616986e0bba818c84c6f7087bd7d097464212e6a0315d5553067","last_reissued_at":"2026-05-18T00:52:03.209754Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:03.209754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The join construction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.CT","authors_text":"Egbert Rijke","submitted_at":"2017-01-26T01:31:53Z","abstract_excerpt":"In homotopy type theory we can define the join of maps as a binary operation on maps with a common co-domain. This operation is commutative, associative, and the unique map from the empty type into the common codomain is a neutral element. Moreover, we show that the idempotents of the join of maps are precisely the embeddings, and we prove the `join connectivity theorem', which states that the connectivity of the join of maps equals the join of the connectivities of the individual maps.\n  We define the image of a map $f:A\\to X$ in $U$ via the join construction, as the colimit of the finite joi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.07538","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1701.07538","created_at":"2026-05-18T00:52:03.209848+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.07538v1","created_at":"2026-05-18T00:52:03.209848+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.07538","created_at":"2026-05-18T00:52:03.209848+00:00"},{"alias_kind":"pith_short_12","alias_value":"FIZ5L3QVZ5QW","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"FIZ5L3QVZ5QWTBXA","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"FIZ5L3QV","created_at":"2026-05-18T12:31:15.632608+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.15126","citing_title":"Constructive higher sheaf models with applications to synthetic mathematics","ref_index":33,"is_internal_anchor":true},{"citing_arxiv_id":"2605.15126","citing_title":"Constructive higher sheaf models with applications to synthetic mathematics","ref_index":33,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FIZ5L3QVZ5QWTBXAXOUBRSCMN5","json":"https://pith.science/pith/FIZ5L3QVZ5QWTBXAXOUBRSCMN5.json","graph_json":"https://pith.science/api/pith-number/FIZ5L3QVZ5QWTBXAXOUBRSCMN5/graph.json","events_json":"https://pith.science/api/pith-number/FIZ5L3QVZ5QWTBXAXOUBRSCMN5/events.json","paper":"https://pith.science/paper/FIZ5L3QV"},"agent_actions":{"view_html":"https://pith.science/pith/FIZ5L3QVZ5QWTBXAXOUBRSCMN5","download_json":"https://pith.science/pith/FIZ5L3QVZ5QWTBXAXOUBRSCMN5.json","view_paper":"https://pith.science/paper/FIZ5L3QV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.07538&json=true","fetch_graph":"https://pith.science/api/pith-number/FIZ5L3QVZ5QWTBXAXOUBRSCMN5/graph.json","fetch_events":"https://pith.science/api/pith-number/FIZ5L3QVZ5QWTBXAXOUBRSCMN5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FIZ5L3QVZ5QWTBXAXOUBRSCMN5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FIZ5L3QVZ5QWTBXAXOUBRSCMN5/action/storage_attestation","attest_author":"https://pith.science/pith/FIZ5L3QVZ5QWTBXAXOUBRSCMN5/action/author_attestation","sign_citation":"https://pith.science/pith/FIZ5L3QVZ5QWTBXAXOUBRSCMN5/action/citation_signature","submit_replication":"https://pith.science/pith/FIZ5L3QVZ5QWTBXAXOUBRSCMN5/action/replication_record"}},"created_at":"2026-05-18T00:52:03.209848+00:00","updated_at":"2026-05-18T00:52:03.209848+00:00"}