{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2W6LCT77JRWOQGI2TQTQBNTNI5","short_pith_number":"pith:2W6LCT77","canonical_record":{"source":{"id":"2405.16468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-05-26T07:31:08Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"29ccb936f8642cb5473276cba105ce66438a00132b812db7a4b00b52c9386da2","abstract_canon_sha256":"ada85b7ac9988610811dccb71b1a5d6c6f955da71e10e7535ba85d9e8ee17164"},"schema_version":"1.0"},"canonical_sha256":"d5bcb14fff4c6ce8191a9c2700b66d475671884c9ad1e310b74714f4760b928d","source":{"kind":"arxiv","id":"2405.16468","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.16468","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"arxiv_version","alias_value":"2405.16468v1","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.16468","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_12","alias_value":"2W6LCT77JRWO","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_16","alias_value":"2W6LCT77JRWOQGI2","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_8","alias_value":"2W6LCT77","created_at":"2026-07-05T08:23:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2W6LCT77JRWOQGI2TQTQBNTNI5","target":"record","payload":{"canonical_record":{"source":{"id":"2405.16468","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-05-26T07:31:08Z","cross_cats_sorted":["math.RA","math.RT"],"title_canon_sha256":"29ccb936f8642cb5473276cba105ce66438a00132b812db7a4b00b52c9386da2","abstract_canon_sha256":"ada85b7ac9988610811dccb71b1a5d6c6f955da71e10e7535ba85d9e8ee17164"},"schema_version":"1.0"},"canonical_sha256":"d5bcb14fff4c6ce8191a9c2700b66d475671884c9ad1e310b74714f4760b928d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:23:30.891837Z","signature_b64":"Zm6c2HJ9RqOYUk/+jOLv4dL/bdWSGBwjZKUF83GUU2UL3r6/tcOK2bU+zhPlYmh9gOb/PRpJfUIgMkZz9XGWBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5bcb14fff4c6ce8191a9c2700b66d475671884c9ad1e310b74714f4760b928d","last_reissued_at":"2026-07-05T08:23:30.891366Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:23:30.891366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.16468","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":"2026-07-05T08:23:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LXh0TnwkVnjmCIIZlerB0gz+10uMg/qz4iScSnkDJVvNYkc5ozkEjXH/VG22gvl1qKDzB6egrEVdc8NKgHjYAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:54:01.002266Z"},"content_sha256":"4503a5d23066b5ff43ab7f0b3ce0bb9f1bdd849f509166f5e7ab1e9a95f9889f","schema_version":"1.0","event_id":"sha256:4503a5d23066b5ff43ab7f0b3ce0bb9f1bdd849f509166f5e7ab1e9a95f9889f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2W6LCT77JRWOQGI2TQTQBNTNI5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Module-theoretic approach to dualizable Grothendieck categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.CT","authors_text":"Ryo Kanda","submitted_at":"2024-05-26T07:31:08Z","abstract_excerpt":"We prove that every dualizable Grothendieck category whose dual is again a Grothendieck category satisfies Grothendieck's conditions Ab6 and Ab4*, by taking a module-theoretic approach based on the Gabriel-Popescu embedding. Combining this with a result by Stefanich, we conclude that the class of dualizable linear cocomplete categories is precisely the class of linear Grothendieck category satisfying Ab6 and Ab4*. This provides a complete answer to a modified conjecture on the dualizability, originally posed by Brandenburg, Chirvasitu, and Johnson-Freyd."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.16468","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/2405.16468/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":"2026-07-05T08:23:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mpEkkoMNDah1lyNtpuv6nhxXSGysCIjiB2Tg55TW7nSHYcggj5+Q2TlZxLIHjuSr3LR8PkqIf4268G0ma5tXBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T07:54:01.002870Z"},"content_sha256":"7ecba7407131f91e9cc0d1d9b2172821d40d1c1fbe874142300daf781b43c9a9","schema_version":"1.0","event_id":"sha256:7ecba7407131f91e9cc0d1d9b2172821d40d1c1fbe874142300daf781b43c9a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2W6LCT77JRWOQGI2TQTQBNTNI5/bundle.json","state_url":"https://pith.science/pith/2W6LCT77JRWOQGI2TQTQBNTNI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2W6LCT77JRWOQGI2TQTQBNTNI5/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":"2026-08-09T07:54:01Z","links":{"resolver":"https://pith.science/pith/2W6LCT77JRWOQGI2TQTQBNTNI5","bundle":"https://pith.science/pith/2W6LCT77JRWOQGI2TQTQBNTNI5/bundle.json","state":"https://pith.science/pith/2W6LCT77JRWOQGI2TQTQBNTNI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2W6LCT77JRWOQGI2TQTQBNTNI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2W6LCT77JRWOQGI2TQTQBNTNI5","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":"ada85b7ac9988610811dccb71b1a5d6c6f955da71e10e7535ba85d9e8ee17164","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-05-26T07:31:08Z","title_canon_sha256":"29ccb936f8642cb5473276cba105ce66438a00132b812db7a4b00b52c9386da2"},"schema_version":"1.0","source":{"id":"2405.16468","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.16468","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"arxiv_version","alias_value":"2405.16468v1","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.16468","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_12","alias_value":"2W6LCT77JRWO","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_16","alias_value":"2W6LCT77JRWOQGI2","created_at":"2026-07-05T08:23:30Z"},{"alias_kind":"pith_short_8","alias_value":"2W6LCT77","created_at":"2026-07-05T08:23:30Z"}],"graph_snapshots":[{"event_id":"sha256:7ecba7407131f91e9cc0d1d9b2172821d40d1c1fbe874142300daf781b43c9a9","target":"graph","created_at":"2026-07-05T08:23:30Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.16468/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that every dualizable Grothendieck category whose dual is again a Grothendieck category satisfies Grothendieck's conditions Ab6 and Ab4*, by taking a module-theoretic approach based on the Gabriel-Popescu embedding. Combining this with a result by Stefanich, we conclude that the class of dualizable linear cocomplete categories is precisely the class of linear Grothendieck category satisfying Ab6 and Ab4*. This provides a complete answer to a modified conjecture on the dualizability, originally posed by Brandenburg, Chirvasitu, and Johnson-Freyd.","authors_text":"Ryo Kanda","cross_cats":["math.RA","math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-05-26T07:31:08Z","title":"Module-theoretic approach to dualizable Grothendieck categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.16468","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":"sha256:4503a5d23066b5ff43ab7f0b3ce0bb9f1bdd849f509166f5e7ab1e9a95f9889f","target":"record","created_at":"2026-07-05T08:23:30Z","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":"ada85b7ac9988610811dccb71b1a5d6c6f955da71e10e7535ba85d9e8ee17164","cross_cats_sorted":["math.RA","math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2024-05-26T07:31:08Z","title_canon_sha256":"29ccb936f8642cb5473276cba105ce66438a00132b812db7a4b00b52c9386da2"},"schema_version":"1.0","source":{"id":"2405.16468","kind":"arxiv","version":1}},"canonical_sha256":"d5bcb14fff4c6ce8191a9c2700b66d475671884c9ad1e310b74714f4760b928d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d5bcb14fff4c6ce8191a9c2700b66d475671884c9ad1e310b74714f4760b928d","first_computed_at":"2026-07-05T08:23:30.891366Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:23:30.891366Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Zm6c2HJ9RqOYUk/+jOLv4dL/bdWSGBwjZKUF83GUU2UL3r6/tcOK2bU+zhPlYmh9gOb/PRpJfUIgMkZz9XGWBg==","signature_status":"signed_v1","signed_at":"2026-07-05T08:23:30.891837Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.16468","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4503a5d23066b5ff43ab7f0b3ce0bb9f1bdd849f509166f5e7ab1e9a95f9889f","sha256:7ecba7407131f91e9cc0d1d9b2172821d40d1c1fbe874142300daf781b43c9a9"],"state_sha256":"fc8a33855d45bde75876dd35f56984e577b4c57a2be95b053ef49908c9e8d1d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jjG+yCMOLNseUJa7/PWpLPKC8a50KNVdioC2cglVgyszU6sysGbiHR9V8F1/VZF0sysfCZP3oH8Ulfd9949pBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T07:54:01.009414Z","bundle_sha256":"86d17edabdc9f8f39783cc3d17164f3d6f193c6a1d3494266e3c4eafb906064e"}}