{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:PBMT3OB5MIGY3STKBZZLLLYPXI","short_pith_number":"pith:PBMT3OB5","canonical_record":{"source":{"id":"2605.19167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-18T22:42:46Z","cross_cats_sorted":[],"title_canon_sha256":"5e95ff65faf6010e7c60f86e96cf45783879b0e9ceaa8a37dfb3b7e7350861de","abstract_canon_sha256":"bac29bb26ea85d1a56517490cedfd2661049adbbfa5696945126497784994482"},"schema_version":"1.0"},"canonical_sha256":"78593db83d620d8dca6a0e72b5af0fba044562a1dec3ec0360af9ebd51383620","source":{"kind":"arxiv","id":"2605.19167","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19167","created_at":"2026-05-20T01:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19167v1","created_at":"2026-05-20T01:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19167","created_at":"2026-05-20T01:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"PBMT3OB5MIGY","created_at":"2026-05-20T01:05:31Z"},{"alias_kind":"pith_short_16","alias_value":"PBMT3OB5MIGY3STK","created_at":"2026-05-20T01:05:31Z"},{"alias_kind":"pith_short_8","alias_value":"PBMT3OB5","created_at":"2026-05-20T01:05:31Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:PBMT3OB5MIGY3STKBZZLLLYPXI","target":"record","payload":{"canonical_record":{"source":{"id":"2605.19167","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-18T22:42:46Z","cross_cats_sorted":[],"title_canon_sha256":"5e95ff65faf6010e7c60f86e96cf45783879b0e9ceaa8a37dfb3b7e7350861de","abstract_canon_sha256":"bac29bb26ea85d1a56517490cedfd2661049adbbfa5696945126497784994482"},"schema_version":"1.0"},"canonical_sha256":"78593db83d620d8dca6a0e72b5af0fba044562a1dec3ec0360af9ebd51383620","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-20T01:05:31.264543Z","signature_b64":"CF7ptO+D/7LaBsA2UTBvSboBnxhxtK/AnNk8+WuBTc/W/whvzf7MIXh74Bd1vbwhiyw8kmoZ0neC5CB/ozSXCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"78593db83d620d8dca6a0e72b5af0fba044562a1dec3ec0360af9ebd51383620","last_reissued_at":"2026-05-20T01:05:31.263787Z","signature_status":"signed_v1","first_computed_at":"2026-05-20T01:05:31.263787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.19167","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":"2026-05-20T01:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7f+hmsGGcCxsvra9Newp6NPFLxMh1vcTDqeb6WrM3dLYJK8EwHQ4b+sf6r2Z5ALIVeRCdW5BnXwQVI5+JGIHBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:08:37.938379Z"},"content_sha256":"884f9ed657d65be64c427baaeb665110f03b87517c061cb533fb7e8ffba8b0b0","schema_version":"1.0","event_id":"sha256:884f9ed657d65be64c427baaeb665110f03b87517c061cb533fb7e8ffba8b0b0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:PBMT3OB5MIGY3STKBZZLLLYPXI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On geometrically reductive tensor categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Kevin Coulembier","submitted_at":"2026-05-18T22:42:46Z","abstract_excerpt":"We prove the conjecture that higher Verlinde categories are geometrically reductive. This is one of the two properties required in order for recent results on algebraic geometry in tensor categories to apply to these categories. We also reduce two further conjectures concerning geometric reductivity for tensor categories to other conjectures appearing in the literature."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19167","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/2605.19167/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":"2026-05-20T01:05:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uPC6TABugSsCnObK2kkMHUgSJERuYcspB5mjK8n2wl45jKeHKLbkH6q8ssHKrBP9j025qRWMhLEDwIuaz+emAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T23:08:37.938764Z"},"content_sha256":"ad5d495c2d0c3e6309799d3de521cd8680c79dab91c855cf5018ab3dbca52c8e","schema_version":"1.0","event_id":"sha256:ad5d495c2d0c3e6309799d3de521cd8680c79dab91c855cf5018ab3dbca52c8e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PBMT3OB5MIGY3STKBZZLLLYPXI/bundle.json","state_url":"https://pith.science/pith/PBMT3OB5MIGY3STKBZZLLLYPXI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PBMT3OB5MIGY3STKBZZLLLYPXI/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":"2026-06-02T23:08:37Z","links":{"resolver":"https://pith.science/pith/PBMT3OB5MIGY3STKBZZLLLYPXI","bundle":"https://pith.science/pith/PBMT3OB5MIGY3STKBZZLLLYPXI/bundle.json","state":"https://pith.science/pith/PBMT3OB5MIGY3STKBZZLLLYPXI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PBMT3OB5MIGY3STKBZZLLLYPXI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:PBMT3OB5MIGY3STKBZZLLLYPXI","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":"bac29bb26ea85d1a56517490cedfd2661049adbbfa5696945126497784994482","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-18T22:42:46Z","title_canon_sha256":"5e95ff65faf6010e7c60f86e96cf45783879b0e9ceaa8a37dfb3b7e7350861de"},"schema_version":"1.0","source":{"id":"2605.19167","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.19167","created_at":"2026-05-20T01:05:31Z"},{"alias_kind":"arxiv_version","alias_value":"2605.19167v1","created_at":"2026-05-20T01:05:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.19167","created_at":"2026-05-20T01:05:31Z"},{"alias_kind":"pith_short_12","alias_value":"PBMT3OB5MIGY","created_at":"2026-05-20T01:05:31Z"},{"alias_kind":"pith_short_16","alias_value":"PBMT3OB5MIGY3STK","created_at":"2026-05-20T01:05:31Z"},{"alias_kind":"pith_short_8","alias_value":"PBMT3OB5","created_at":"2026-05-20T01:05:31Z"}],"graph_snapshots":[{"event_id":"sha256:ad5d495c2d0c3e6309799d3de521cd8680c79dab91c855cf5018ab3dbca52c8e","target":"graph","created_at":"2026-05-20T01:05:31Z","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/2605.19167/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove the conjecture that higher Verlinde categories are geometrically reductive. This is one of the two properties required in order for recent results on algebraic geometry in tensor categories to apply to these categories. We also reduce two further conjectures concerning geometric reductivity for tensor categories to other conjectures appearing in the literature.","authors_text":"Kevin Coulembier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-18T22:42:46Z","title":"On geometrically reductive tensor categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.19167","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":"sha256:884f9ed657d65be64c427baaeb665110f03b87517c061cb533fb7e8ffba8b0b0","target":"record","created_at":"2026-05-20T01:05:31Z","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":"bac29bb26ea85d1a56517490cedfd2661049adbbfa5696945126497784994482","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2026-05-18T22:42:46Z","title_canon_sha256":"5e95ff65faf6010e7c60f86e96cf45783879b0e9ceaa8a37dfb3b7e7350861de"},"schema_version":"1.0","source":{"id":"2605.19167","kind":"arxiv","version":1}},"canonical_sha256":"78593db83d620d8dca6a0e72b5af0fba044562a1dec3ec0360af9ebd51383620","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"78593db83d620d8dca6a0e72b5af0fba044562a1dec3ec0360af9ebd51383620","first_computed_at":"2026-05-20T01:05:31.263787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T01:05:31.263787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CF7ptO+D/7LaBsA2UTBvSboBnxhxtK/AnNk8+WuBTc/W/whvzf7MIXh74Bd1vbwhiyw8kmoZ0neC5CB/ozSXCQ==","signature_status":"signed_v1","signed_at":"2026-05-20T01:05:31.264543Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.19167","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:884f9ed657d65be64c427baaeb665110f03b87517c061cb533fb7e8ffba8b0b0","sha256:ad5d495c2d0c3e6309799d3de521cd8680c79dab91c855cf5018ab3dbca52c8e"],"state_sha256":"9c87f1fa65280a15639c5e27e2f362edab7a1208dbc2223a9bb59a23878594be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5bdLTh2aNj6JuMUcsouGpawp792or27eIwSWtRIQcGGOZkE4jNvFqT/mF6LOH4DIwI9CvebMyuLYNtjwdrFaCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T23:08:37.940846Z","bundle_sha256":"a2623c4ed3c784cb4d6858bca13de8d663967db5a339e81d0f6f173e31204ec8"}}