{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:XBEBFDIDJMHYENSXSTZXVOIIMC","short_pith_number":"pith:XBEBFDID","canonical_record":{"source":{"id":"1612.05182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-15T18:28:25Z","cross_cats_sorted":[],"title_canon_sha256":"42de811f7f0c622b43202d76ac7fe53300c8369991a46fb13cc3a97a486553b8","abstract_canon_sha256":"db9e55206106c59be0db20d6cd7b64fac465322560380dacfb802ee8a6f304a0"},"schema_version":"1.0"},"canonical_sha256":"b848128d034b0f82365794f37ab908609365c602f03a2398c540ea250ed9c188","source":{"kind":"arxiv","id":"1612.05182","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05182","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05182v2","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05182","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"XBEBFDIDJMHY","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XBEBFDIDJMHYENSX","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XBEBFDID","created_at":"2026-05-18T12:30:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:XBEBFDIDJMHYENSXSTZXVOIIMC","target":"record","payload":{"canonical_record":{"source":{"id":"1612.05182","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-15T18:28:25Z","cross_cats_sorted":[],"title_canon_sha256":"42de811f7f0c622b43202d76ac7fe53300c8369991a46fb13cc3a97a486553b8","abstract_canon_sha256":"db9e55206106c59be0db20d6cd7b64fac465322560380dacfb802ee8a6f304a0"},"schema_version":"1.0"},"canonical_sha256":"b848128d034b0f82365794f37ab908609365c602f03a2398c540ea250ed9c188","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:05.561413Z","signature_b64":"xVUdMMFu07z0zrCBopNOV4bNhuY8PshcjAmN2rSDFGcFnyco72GcPtWQPlcqg7Q2349tIZW3MjDMkHo5reaHDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b848128d034b0f82365794f37ab908609365c602f03a2398c540ea250ed9c188","last_reissued_at":"2026-05-18T00:51:05.561007Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:05.561007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.05182","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bqM/uUVCb+w0qjbJ+gaFBCO0t7/PKc5+UH+qPGnqLe64bgKyd9obGWzzZ8JCL4/ZegiFFJBpfLZ6erXz55rEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:36:41.846589Z"},"content_sha256":"d81e79dab06c7050128f5899fb3992476e1ba737037b362e01a95b3cb81be3fe","schema_version":"1.0","event_id":"sha256:d81e79dab06c7050128f5899fb3992476e1ba737037b362e01a95b3cb81be3fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:XBEBFDIDJMHYENSXSTZXVOIIMC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Jellyfish partition categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Jonathan Comes","submitted_at":"2016-12-15T18:28:25Z","abstract_excerpt":"For each positive integer $n$, we introduce a monoidal category $\\mathcal{JP}(n)$ using a generalization of partition diagrams. When the characteristic of the ground field is either 0 or at least $n$, we show $\\mathcal{JP}(n)$ is monoidally equivalent to the full subcategory of $\\operatorname{Rep}(A_n)$ whose objects are tensor powers of the natural $n$-dimensional permutation representation of the alternating group $A_n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05182","kind":"arxiv","version":2},"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":"2026-05-18T00:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CtXYmlKHemUuyRIJ0G7aLcR5opabZMAea7K/MtcAkvN659C6q13Jl3DkWaqGq8ToWChJ213DpqcutAvQ3KX7Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:36:41.847252Z"},"content_sha256":"031e38474e7735b85a91486ddd150d8286cc52b402f3ead188954de2f117d76a","schema_version":"1.0","event_id":"sha256:031e38474e7735b85a91486ddd150d8286cc52b402f3ead188954de2f117d76a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC/bundle.json","state_url":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XBEBFDIDJMHYENSXSTZXVOIIMC/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":"2026-06-11T06:36:41Z","links":{"resolver":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC","bundle":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC/bundle.json","state":"https://pith.science/pith/XBEBFDIDJMHYENSXSTZXVOIIMC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XBEBFDIDJMHYENSXSTZXVOIIMC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:XBEBFDIDJMHYENSXSTZXVOIIMC","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":"db9e55206106c59be0db20d6cd7b64fac465322560380dacfb802ee8a6f304a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-15T18:28:25Z","title_canon_sha256":"42de811f7f0c622b43202d76ac7fe53300c8369991a46fb13cc3a97a486553b8"},"schema_version":"1.0","source":{"id":"1612.05182","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05182","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05182v2","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05182","created_at":"2026-05-18T00:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"XBEBFDIDJMHY","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_16","alias_value":"XBEBFDIDJMHYENSX","created_at":"2026-05-18T12:30:51Z"},{"alias_kind":"pith_short_8","alias_value":"XBEBFDID","created_at":"2026-05-18T12:30:51Z"}],"graph_snapshots":[{"event_id":"sha256:031e38474e7735b85a91486ddd150d8286cc52b402f3ead188954de2f117d76a","target":"graph","created_at":"2026-05-18T00:51:05Z","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":"For each positive integer $n$, we introduce a monoidal category $\\mathcal{JP}(n)$ using a generalization of partition diagrams. When the characteristic of the ground field is either 0 or at least $n$, we show $\\mathcal{JP}(n)$ is monoidally equivalent to the full subcategory of $\\operatorname{Rep}(A_n)$ whose objects are tensor powers of the natural $n$-dimensional permutation representation of the alternating group $A_n$.","authors_text":"Jonathan Comes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-15T18:28:25Z","title":"Jellyfish partition categories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05182","kind":"arxiv","version":2},"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:d81e79dab06c7050128f5899fb3992476e1ba737037b362e01a95b3cb81be3fe","target":"record","created_at":"2026-05-18T00:51:05Z","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":"db9e55206106c59be0db20d6cd7b64fac465322560380dacfb802ee8a6f304a0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-15T18:28:25Z","title_canon_sha256":"42de811f7f0c622b43202d76ac7fe53300c8369991a46fb13cc3a97a486553b8"},"schema_version":"1.0","source":{"id":"1612.05182","kind":"arxiv","version":2}},"canonical_sha256":"b848128d034b0f82365794f37ab908609365c602f03a2398c540ea250ed9c188","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b848128d034b0f82365794f37ab908609365c602f03a2398c540ea250ed9c188","first_computed_at":"2026-05-18T00:51:05.561007Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:05.561007Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xVUdMMFu07z0zrCBopNOV4bNhuY8PshcjAmN2rSDFGcFnyco72GcPtWQPlcqg7Q2349tIZW3MjDMkHo5reaHDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:05.561413Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05182","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d81e79dab06c7050128f5899fb3992476e1ba737037b362e01a95b3cb81be3fe","sha256:031e38474e7735b85a91486ddd150d8286cc52b402f3ead188954de2f117d76a"],"state_sha256":"86c618d59770097f0f76bb51b5fc23e218f459384e67fda21ceeba8d1c3aa9e1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WgskkAQNyvyrtOSbw3QVdumANXB/hcZExghXcjYmqncujrtu4wm0bgryaxaDD/AsrYEtMnq134ny0ZH0QTQYCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T06:36:41.851075Z","bundle_sha256":"e343a43b3a5f0eee86508ec5db57e3483131c8991222e13421025f8430c90291"}}