{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:QOV7AKHRNCLGZLH47TJCMDYHXY","short_pith_number":"pith:QOV7AKHR","canonical_record":{"source":{"id":"2607.23144","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2026-07-25T10:51:26Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"fd2ae820dfc03adc153c0735226ab0d4fb29fffd6102835e6f1bd154e8080490","abstract_canon_sha256":"fb253615f02dfa357fbcd645979291df0d06ee917c1a3cd6dff8869bd3f18e8e"},"schema_version":"1.0"},"canonical_sha256":"83abf028f168966cacfcfcd2260f07be1405a6239f46dff90a09655b431b9f8c","source":{"kind":"arxiv","id":"2607.23144","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23144","created_at":"2026-07-28T01:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23144v1","created_at":"2026-07-28T01:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23144","created_at":"2026-07-28T01:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"QOV7AKHRNCLG","created_at":"2026-07-28T01:22:09Z"},{"alias_kind":"pith_short_16","alias_value":"QOV7AKHRNCLGZLH4","created_at":"2026-07-28T01:22:09Z"},{"alias_kind":"pith_short_8","alias_value":"QOV7AKHR","created_at":"2026-07-28T01:22:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:QOV7AKHRNCLGZLH47TJCMDYHXY","target":"record","payload":{"canonical_record":{"source":{"id":"2607.23144","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2026-07-25T10:51:26Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"fd2ae820dfc03adc153c0735226ab0d4fb29fffd6102835e6f1bd154e8080490","abstract_canon_sha256":"fb253615f02dfa357fbcd645979291df0d06ee917c1a3cd6dff8869bd3f18e8e"},"schema_version":"1.0"},"canonical_sha256":"83abf028f168966cacfcfcd2260f07be1405a6239f46dff90a09655b431b9f8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-28T01:22:09.336764Z","signature_b64":"PDaIjBr3Ku6mXDHSLf098JEsUqidYgOw9AxgirTIyUCYo3NRYbdO7aIQxZryCA36wxAlOdzoZbLVjBmr0vJLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"83abf028f168966cacfcfcd2260f07be1405a6239f46dff90a09655b431b9f8c","last_reissued_at":"2026-07-28T01:22:09.335992Z","signature_status":"signed_v1","first_computed_at":"2026-07-28T01:22:09.335992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.23144","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":"2026-07-28T01:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H9b7H0w1f3mS0UdpfnwYzbEcO6w+RUxUxAQU3tcWpQILKjHvTfqXBjNn/PmkmagKnBetU6FHLxbn6oVi+YNhBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T03:57:31.812534Z"},"content_sha256":"38392464f814b0843d5f5e987328fff8c4bac40bcd59705e49f5e685a6337fb6","schema_version":"1.0","event_id":"sha256:38392464f814b0843d5f5e987328fff8c4bac40bcd59705e49f5e685a6337fb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:QOV7AKHRNCLGZLH47TJCMDYHXY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Categorical Algebra of Atomic Monoids: Presentability, Regularity, and Pretorsion Theories","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.CT","authors_text":"Federico Campanini, Laura Cossu","submitted_at":"2026-07-25T10:51:26Z","abstract_excerpt":"We study the category $\\mathsf{AtoMon}$ of atomic monoids and atom-preserving homomorphisms. We prove that $\\mathsf{AtoMon}$ is locally finitely presentable by exhibiting a strong generator consisting of compact objects. We show that $\\mathsf{AtoMon}$ admits (regular epi, mono)-factorizations but that it is not a regular category: we construct a regular epimorphism which is not pullback-stable. We also establish adjunctions for the group of units and explicitly construct the ``cofree atomic monoid'' over an arbitrary monoid. Finally, we exhibit a way to lift torsion theories of $\\mathsf{Grp}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23144","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.23144/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-28T01:22:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rzg3v2/ftMTc5s4T6ygjxxore8uRRHdRQiiwsACCTJjcqHBTy/GSHuGjPUaY1/WeiSn30aRUZgDlA7hYSV6MDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T03:57:31.813032Z"},"content_sha256":"46d19c2b6987e959c1f1e0d81ecce83d3ba85c80ae07407818896c5d33c4b75a","schema_version":"1.0","event_id":"sha256:46d19c2b6987e959c1f1e0d81ecce83d3ba85c80ae07407818896c5d33c4b75a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QOV7AKHRNCLGZLH47TJCMDYHXY/bundle.json","state_url":"https://pith.science/pith/QOV7AKHRNCLGZLH47TJCMDYHXY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QOV7AKHRNCLGZLH47TJCMDYHXY/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":"2026-08-15T03:57:31Z","links":{"resolver":"https://pith.science/pith/QOV7AKHRNCLGZLH47TJCMDYHXY","bundle":"https://pith.science/pith/QOV7AKHRNCLGZLH47TJCMDYHXY/bundle.json","state":"https://pith.science/pith/QOV7AKHRNCLGZLH47TJCMDYHXY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QOV7AKHRNCLGZLH47TJCMDYHXY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:QOV7AKHRNCLGZLH47TJCMDYHXY","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":"fb253615f02dfa357fbcd645979291df0d06ee917c1a3cd6dff8869bd3f18e8e","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2026-07-25T10:51:26Z","title_canon_sha256":"fd2ae820dfc03adc153c0735226ab0d4fb29fffd6102835e6f1bd154e8080490"},"schema_version":"1.0","source":{"id":"2607.23144","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.23144","created_at":"2026-07-28T01:22:09Z"},{"alias_kind":"arxiv_version","alias_value":"2607.23144v1","created_at":"2026-07-28T01:22:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.23144","created_at":"2026-07-28T01:22:09Z"},{"alias_kind":"pith_short_12","alias_value":"QOV7AKHRNCLG","created_at":"2026-07-28T01:22:09Z"},{"alias_kind":"pith_short_16","alias_value":"QOV7AKHRNCLGZLH4","created_at":"2026-07-28T01:22:09Z"},{"alias_kind":"pith_short_8","alias_value":"QOV7AKHR","created_at":"2026-07-28T01:22:09Z"}],"graph_snapshots":[{"event_id":"sha256:46d19c2b6987e959c1f1e0d81ecce83d3ba85c80ae07407818896c5d33c4b75a","target":"graph","created_at":"2026-07-28T01:22:09Z","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/2607.23144/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the category $\\mathsf{AtoMon}$ of atomic monoids and atom-preserving homomorphisms. We prove that $\\mathsf{AtoMon}$ is locally finitely presentable by exhibiting a strong generator consisting of compact objects. We show that $\\mathsf{AtoMon}$ admits (regular epi, mono)-factorizations but that it is not a regular category: we construct a regular epimorphism which is not pullback-stable. We also establish adjunctions for the group of units and explicitly construct the ``cofree atomic monoid'' over an arbitrary monoid. Finally, we exhibit a way to lift torsion theories of $\\mathsf{Grp}$ ","authors_text":"Federico Campanini, Laura Cossu","cross_cats":["math.RA"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2026-07-25T10:51:26Z","title":"Categorical Algebra of Atomic Monoids: Presentability, Regularity, and Pretorsion Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.23144","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":"sha256:38392464f814b0843d5f5e987328fff8c4bac40bcd59705e49f5e685a6337fb6","target":"record","created_at":"2026-07-28T01:22:09Z","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":"fb253615f02dfa357fbcd645979291df0d06ee917c1a3cd6dff8869bd3f18e8e","cross_cats_sorted":["math.RA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CT","submitted_at":"2026-07-25T10:51:26Z","title_canon_sha256":"fd2ae820dfc03adc153c0735226ab0d4fb29fffd6102835e6f1bd154e8080490"},"schema_version":"1.0","source":{"id":"2607.23144","kind":"arxiv","version":1}},"canonical_sha256":"83abf028f168966cacfcfcd2260f07be1405a6239f46dff90a09655b431b9f8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83abf028f168966cacfcfcd2260f07be1405a6239f46dff90a09655b431b9f8c","first_computed_at":"2026-07-28T01:22:09.335992Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-28T01:22:09.335992Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PDaIjBr3Ku6mXDHSLf098JEsUqidYgOw9AxgirTIyUCYo3NRYbdO7aIQxZryCA36wxAlOdzoZbLVjBmr0vJLBA==","signature_status":"signed_v1","signed_at":"2026-07-28T01:22:09.336764Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.23144","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38392464f814b0843d5f5e987328fff8c4bac40bcd59705e49f5e685a6337fb6","sha256:46d19c2b6987e959c1f1e0d81ecce83d3ba85c80ae07407818896c5d33c4b75a"],"state_sha256":"b2c311c7a917f2e66ee0c9cbf0df982b2518c528f60ac8155ab8e7d1f8e77261"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eer0bAFPDFjO6w/IR2+DOnYdjmT7qVCJZLoLSED1sERSFsckkGh5BgdZCNtjRlwghokrgJVkvIuocowSMbMAAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T03:57:31.817486Z","bundle_sha256":"42992f330719044d472d64dfee424fd5eca84cad748cd59e8352d2af1083f685"}}