{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:VMTXHTENEXTDN6B64HEVWHDS7W","short_pith_number":"pith:VMTXHTEN","schema_version":"1.0","canonical_sha256":"ab2773cc8d25e636f83ee1c95b1c72fd8348b459960cf525141044db91601a3b","source":{"kind":"arxiv","id":"1907.02695","version":1},"attestation_state":"computed","paper":{"title":"Span composition using fake pullbacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Ross Street","submitted_at":"2019-07-05T06:52:50Z","abstract_excerpt":"The construction of a category of spans can be made in some categories $\\CC$ which do not have pullbacks in the traditional sense. The PROP for monoids is a good example of such a $\\CC$. The 2012 book concerning homological algebra by Marco Grandis gives the proof of associativity of relations in a Puppe-exact category based on a 1967 paper of M.\\v{S}. Calenko. The proof here is a restructuring of that proof in the spirit of the first sentence of this Abstract. We observe that these relations are spans of EM-spans and that EM-spans admit fake pullbacks so that spans of EM-spans compose. Our se"},"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":"1907.02695","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2019-07-05T06:52:50Z","cross_cats_sorted":[],"title_canon_sha256":"27bb3ff244556bee1e9c9aef13ae319fd4e3a551af7a4d038506c61cd06af36b","abstract_canon_sha256":"b6b0a78694b68a037c5236c56a4ca31fc8236c9a7c9eabb06ca575a173edf384"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:23.461960Z","signature_b64":"ZAaDpX2zxdpy3onOXH/eV6oQGF2/Zmvh7O5UmT10c2fkmBrCAlBh/jpXXSSbEktrwHAqUiyYTDNt7sUgZJXNBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ab2773cc8d25e636f83ee1c95b1c72fd8348b459960cf525141044db91601a3b","last_reissued_at":"2026-05-17T23:41:23.461359Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:23.461359Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Span composition using fake pullbacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Ross Street","submitted_at":"2019-07-05T06:52:50Z","abstract_excerpt":"The construction of a category of spans can be made in some categories $\\CC$ which do not have pullbacks in the traditional sense. The PROP for monoids is a good example of such a $\\CC$. The 2012 book concerning homological algebra by Marco Grandis gives the proof of associativity of relations in a Puppe-exact category based on a 1967 paper of M.\\v{S}. Calenko. The proof here is a restructuring of that proof in the spirit of the first sentence of this Abstract. We observe that these relations are spans of EM-spans and that EM-spans admit fake pullbacks so that spans of EM-spans compose. Our se"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02695","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":"1907.02695","created_at":"2026-05-17T23:41:23.461444+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.02695v1","created_at":"2026-05-17T23:41:23.461444+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02695","created_at":"2026-05-17T23:41:23.461444+00:00"},{"alias_kind":"pith_short_12","alias_value":"VMTXHTENEXTD","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"VMTXHTENEXTDN6B6","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"VMTXHTEN","created_at":"2026-05-18T12:33:30.264802+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VMTXHTENEXTDN6B64HEVWHDS7W","json":"https://pith.science/pith/VMTXHTENEXTDN6B64HEVWHDS7W.json","graph_json":"https://pith.science/api/pith-number/VMTXHTENEXTDN6B64HEVWHDS7W/graph.json","events_json":"https://pith.science/api/pith-number/VMTXHTENEXTDN6B64HEVWHDS7W/events.json","paper":"https://pith.science/paper/VMTXHTEN"},"agent_actions":{"view_html":"https://pith.science/pith/VMTXHTENEXTDN6B64HEVWHDS7W","download_json":"https://pith.science/pith/VMTXHTENEXTDN6B64HEVWHDS7W.json","view_paper":"https://pith.science/paper/VMTXHTEN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.02695&json=true","fetch_graph":"https://pith.science/api/pith-number/VMTXHTENEXTDN6B64HEVWHDS7W/graph.json","fetch_events":"https://pith.science/api/pith-number/VMTXHTENEXTDN6B64HEVWHDS7W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VMTXHTENEXTDN6B64HEVWHDS7W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VMTXHTENEXTDN6B64HEVWHDS7W/action/storage_attestation","attest_author":"https://pith.science/pith/VMTXHTENEXTDN6B64HEVWHDS7W/action/author_attestation","sign_citation":"https://pith.science/pith/VMTXHTENEXTDN6B64HEVWHDS7W/action/citation_signature","submit_replication":"https://pith.science/pith/VMTXHTENEXTDN6B64HEVWHDS7W/action/replication_record"}},"created_at":"2026-05-17T23:41:23.461444+00:00","updated_at":"2026-05-17T23:41:23.461444+00:00"}