{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:LUQXKERC3OXAR7GIIU2V63K7R2","short_pith_number":"pith:LUQXKERC","canonical_record":{"source":{"id":"1406.2064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-06-09T03:45:29Z","cross_cats_sorted":["cs.PL","math.CT"],"title_canon_sha256":"ee7a2bb7ca6899c6b2e03b3fc814042b49b2d01134f1090bc3fe0e938a220544","abstract_canon_sha256":"4fbabeaaa1001498a0ed6a818e46fdf41e1122e38905b845665be62286daa412"},"schema_version":"1.0"},"canonical_sha256":"5d21751222dbae08fcc845355f6d5f8ea7012bdabdf98380153dc826f886a70b","source":{"kind":"arxiv","id":"1406.2064","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2064","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2064v1","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2064","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"LUQXKERC3OXA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LUQXKERC3OXAR7GI","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LUQXKERC","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:LUQXKERC3OXAR7GIIU2V63K7R2","target":"record","payload":{"canonical_record":{"source":{"id":"1406.2064","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-06-09T03:45:29Z","cross_cats_sorted":["cs.PL","math.CT"],"title_canon_sha256":"ee7a2bb7ca6899c6b2e03b3fc814042b49b2d01134f1090bc3fe0e938a220544","abstract_canon_sha256":"4fbabeaaa1001498a0ed6a818e46fdf41e1122e38905b845665be62286daa412"},"schema_version":"1.0"},"canonical_sha256":"5d21751222dbae08fcc845355f6d5f8ea7012bdabdf98380153dc826f886a70b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:30.623526Z","signature_b64":"j1KTOcffq2PyLeZZb5HbjDFMhwQjsmYyOk9GtEepRlac1OYmdeM4KFicbTBzAoXKbKfR83jqtzVpHL8j6mouDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d21751222dbae08fcc845355f6d5f8ea7012bdabdf98380153dc826f886a70b","last_reissued_at":"2026-05-18T02:44:30.622852Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:30.622852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.2064","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PgAzBLr12/hivorM7DcNAZ9HsqwPVyGCVcw1xjw4x6wcwGl+WnrH832Yxh2HKm4P7aSTXHmUhdJ94ciQ8W8JCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:48:13.682818Z"},"content_sha256":"ee43bc604cf04e96bfab74fa66c86b35c21d6e127b7815f8443a6deed0d89ad6","schema_version":"1.0","event_id":"sha256:ee43bc604cf04e96bfab74fa66c86b35c21d6e127b7815f8443a6deed0d89ad6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:LUQXKERC3OXAR7GIIU2V63K7R2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coherence for Skew-Monoidal Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.PL","math.CT"],"primary_cat":"cs.LO","authors_text":"Tarmo Uustalu","submitted_at":"2014-06-09T03:45:29Z","abstract_excerpt":"I motivate a variation (due to K. Szlach\\'{a}nyi) of monoidal categories called skew-monoidal categories where the unital and associativity laws are not required to be isomorphisms, only natural transformations. Coherence has to be formulated differently than in the well-known monoidal case. In my (to my knowledge new) version, it becomes a statement of uniqueness of normalizing rewrites. I present a proof of this coherence theorem and also formalize it fully in the dependently typed programming language Agda."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2064","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uCTtYC88UNL/ptn9/scCK5xH0rqH+NjAV7AF2aHMCEBPW3hAODMOvRHPRw0foTOvZTYdS6fPCX33x6/RRkq9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T12:48:13.683159Z"},"content_sha256":"0c240c71da86d47eb3351be727192391351fa74aefe003aa904956c74f7e1810","schema_version":"1.0","event_id":"sha256:0c240c71da86d47eb3351be727192391351fa74aefe003aa904956c74f7e1810"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LUQXKERC3OXAR7GIIU2V63K7R2/bundle.json","state_url":"https://pith.science/pith/LUQXKERC3OXAR7GIIU2V63K7R2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LUQXKERC3OXAR7GIIU2V63K7R2/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":"2026-06-22T12:48:13Z","links":{"resolver":"https://pith.science/pith/LUQXKERC3OXAR7GIIU2V63K7R2","bundle":"https://pith.science/pith/LUQXKERC3OXAR7GIIU2V63K7R2/bundle.json","state":"https://pith.science/pith/LUQXKERC3OXAR7GIIU2V63K7R2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LUQXKERC3OXAR7GIIU2V63K7R2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:LUQXKERC3OXAR7GIIU2V63K7R2","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":"4fbabeaaa1001498a0ed6a818e46fdf41e1122e38905b845665be62286daa412","cross_cats_sorted":["cs.PL","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-06-09T03:45:29Z","title_canon_sha256":"ee7a2bb7ca6899c6b2e03b3fc814042b49b2d01134f1090bc3fe0e938a220544"},"schema_version":"1.0","source":{"id":"1406.2064","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.2064","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"arxiv_version","alias_value":"1406.2064v1","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.2064","created_at":"2026-05-18T02:44:30Z"},{"alias_kind":"pith_short_12","alias_value":"LUQXKERC3OXA","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"LUQXKERC3OXAR7GI","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"LUQXKERC","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:0c240c71da86d47eb3351be727192391351fa74aefe003aa904956c74f7e1810","target":"graph","created_at":"2026-05-18T02:44:30Z","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":"I motivate a variation (due to K. Szlach\\'{a}nyi) of monoidal categories called skew-monoidal categories where the unital and associativity laws are not required to be isomorphisms, only natural transformations. Coherence has to be formulated differently than in the well-known monoidal case. In my (to my knowledge new) version, it becomes a statement of uniqueness of normalizing rewrites. I present a proof of this coherence theorem and also formalize it fully in the dependently typed programming language Agda.","authors_text":"Tarmo Uustalu","cross_cats":["cs.PL","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-06-09T03:45:29Z","title":"Coherence for Skew-Monoidal Categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.2064","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:ee43bc604cf04e96bfab74fa66c86b35c21d6e127b7815f8443a6deed0d89ad6","target":"record","created_at":"2026-05-18T02:44:30Z","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":"4fbabeaaa1001498a0ed6a818e46fdf41e1122e38905b845665be62286daa412","cross_cats_sorted":["cs.PL","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2014-06-09T03:45:29Z","title_canon_sha256":"ee7a2bb7ca6899c6b2e03b3fc814042b49b2d01134f1090bc3fe0e938a220544"},"schema_version":"1.0","source":{"id":"1406.2064","kind":"arxiv","version":1}},"canonical_sha256":"5d21751222dbae08fcc845355f6d5f8ea7012bdabdf98380153dc826f886a70b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5d21751222dbae08fcc845355f6d5f8ea7012bdabdf98380153dc826f886a70b","first_computed_at":"2026-05-18T02:44:30.622852Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:30.622852Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"j1KTOcffq2PyLeZZb5HbjDFMhwQjsmYyOk9GtEepRlac1OYmdeM4KFicbTBzAoXKbKfR83jqtzVpHL8j6mouDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:30.623526Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.2064","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee43bc604cf04e96bfab74fa66c86b35c21d6e127b7815f8443a6deed0d89ad6","sha256:0c240c71da86d47eb3351be727192391351fa74aefe003aa904956c74f7e1810"],"state_sha256":"0d358d5b695e1f8cc6e3d606791c384a435528ae8f117b861149fced85304296"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UV6a0n/V/TKxXrQQ7VQsc+xbRfCnY9MRH4hly9G/IRnc2BmjEgt4x5ozBiPqcuQoZyHpzv3EDL3FLp+vHyEmBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T12:48:13.685141Z","bundle_sha256":"6dcd916a15a51a01374d4d1bc50e8cbd57b056578e739c1fa719b00794ac8f76"}}