{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:CJH5NFTQ2JZO7CODZURHQE4GPS","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":"4eb40b83dcd6143a82d9cb1b02ae88d93a019942a93023cf4a2333a16f59448e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-08-05T14:51:48Z","title_canon_sha256":"dae7299d593562818826a97dc5fd2521e25352cf324568a62870f6787a2b6581"},"schema_version":"1.0","source":{"id":"1908.01658","kind":"arxiv","version":7}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01658","created_at":"2026-07-05T01:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01658v7","created_at":"2026-07-05T01:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01658","created_at":"2026-07-05T01:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"CJH5NFTQ2JZO","created_at":"2026-07-05T01:48:06Z"},{"alias_kind":"pith_short_16","alias_value":"CJH5NFTQ2JZO7COD","created_at":"2026-07-05T01:48:06Z"},{"alias_kind":"pith_short_8","alias_value":"CJH5NFTQ","created_at":"2026-07-05T01:48:06Z"}],"graph_snapshots":[{"event_id":"sha256:2b585af0c6a4e2c4e9be227742c3a11873ea35fee762e9ddf8ed0ecb181f3c37","target":"graph","created_at":"2026-07-05T01:48:06Z","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/1908.01658/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce a notion of an integral along a bimonoid homomorphism as a simultaneous generalization of the integral and cointegral of bimonoids. The purpose of this paper is to characterize an existence of a specific integral, called a normalized generator integral, along a bimonoid homomorphism in terms of the kernel and cokernel of the homomorphism. We introduce a notion of a volume on an abelian category as a generalization of the dimension of vector spaces and the order of abelian groups. In applications, we show that there exists a nontrivial volume partially defined on a category of bico","authors_text":"Minkyu Kim","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-08-05T14:51:48Z","title":"Integrals along bimonoid homomorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01658","kind":"arxiv","version":7},"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":"sha256:3f33fbf2629e779a3a14547127b273dc3cf6fde9cbe96b7e29b69c4a06d3bbc8","target":"record","created_at":"2026-07-05T01:48:06Z","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":"4eb40b83dcd6143a82d9cb1b02ae88d93a019942a93023cf4a2333a16f59448e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2019-08-05T14:51:48Z","title_canon_sha256":"dae7299d593562818826a97dc5fd2521e25352cf324568a62870f6787a2b6581"},"schema_version":"1.0","source":{"id":"1908.01658","kind":"arxiv","version":7}},"canonical_sha256":"124fd69670d272ef89c3cd227813867c9c40871b4aea56fa611cdf801ce79903","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"124fd69670d272ef89c3cd227813867c9c40871b4aea56fa611cdf801ce79903","first_computed_at":"2026-07-05T01:48:06.219584Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:48:06.219584Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wMAK/x55Wbq94Sc3vO8sHEFILEFlTll57C67LxjAehKYcXpk6F3FcH5wB4bLk/+Z0TmwHaCzhkxlgg7UKst5Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T01:48:06.219978Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01658","source_kind":"arxiv","source_version":7}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f33fbf2629e779a3a14547127b273dc3cf6fde9cbe96b7e29b69c4a06d3bbc8","sha256:2b585af0c6a4e2c4e9be227742c3a11873ea35fee762e9ddf8ed0ecb181f3c37"],"state_sha256":"10c7e908fbe66ecac9422aee18727bdf21844274c1c674c5e8d9bef4998e4c4c"}