{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:LR4KKNGN6CCHYQNZ32JWO6GDIA","short_pith_number":"pith:LR4KKNGN","canonical_record":{"source":{"id":"0805.4096","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-05-27T18:32:39Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1ca09d8220b46b3e62ef874819c223f2cf5c2fc26ba6dd0d856ebfa32b2961b1","abstract_canon_sha256":"250dc62db3a9f836d362090d9f973fecabad19d502b8f4f4297fa23c466fc5a7"},"schema_version":"1.0"},"canonical_sha256":"5c78a534cdf0847c41b9de936778c34032fd0870dc8f61812a05f62391d94903","source":{"kind":"arxiv","id":"0805.4096","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.4096","created_at":"2026-07-04T15:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"0805.4096v2","created_at":"2026-07-04T15:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.4096","created_at":"2026-07-04T15:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"LR4KKNGN6CCH","created_at":"2026-07-04T15:15:03Z"},{"alias_kind":"pith_short_16","alias_value":"LR4KKNGN6CCHYQNZ","created_at":"2026-07-04T15:15:03Z"},{"alias_kind":"pith_short_8","alias_value":"LR4KKNGN","created_at":"2026-07-04T15:15:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:LR4KKNGN6CCHYQNZ32JWO6GDIA","target":"record","payload":{"canonical_record":{"source":{"id":"0805.4096","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-05-27T18:32:39Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"1ca09d8220b46b3e62ef874819c223f2cf5c2fc26ba6dd0d856ebfa32b2961b1","abstract_canon_sha256":"250dc62db3a9f836d362090d9f973fecabad19d502b8f4f4297fa23c466fc5a7"},"schema_version":"1.0"},"canonical_sha256":"5c78a534cdf0847c41b9de936778c34032fd0870dc8f61812a05f62391d94903","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:15:03.760736Z","signature_b64":"gSal2VVSnvHMp2OwMRpaa2GitHMFh7YX4e5FUMBxsRW0ddjf9VV+yxhsQKoEXyApeuobH1ula2FMb8cIh/EBAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5c78a534cdf0847c41b9de936778c34032fd0870dc8f61812a05f62391d94903","last_reissued_at":"2026-07-04T15:15:03.760249Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:15:03.760249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0805.4096","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":"2026-07-04T15:15:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X9VcwU9BK6kbNjgTnx0TTVf0/6UBACVYdgMqxaTJnEx9WYghto/NxvCV15EUENkHaRwyeNy/rZazGhuW/mHKCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:28:35.124682Z"},"content_sha256":"57c795a30587941ac3eabea5af4c8d5a96272589094077533184884f60074751","schema_version":"1.0","event_id":"sha256:57c795a30587941ac3eabea5af4c8d5a96272589094077533184884f60074751"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:LR4KKNGN6CCHYQNZ32JWO6GDIA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characters of coinvariants in (1,p) logarithmic models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"B.L. Feigin, I.Yu. Tipunin","submitted_at":"2008-05-27T18:32:39Z","abstract_excerpt":"We investigate induced modules of doublet algebra in (1,p) logarithmic models. We give fermionic formulas for the characters of induced modules and coinvariants with respect to different subalgebras calculated in the irreducible modules. The characters of coinvariants give multiplicities of projective modules in fusion of induced modules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.4096","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/0805.4096/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":"2026-07-04T15:15:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y/nFfC9NWHaJPrNVSBV67EsPit8Ir93MsgB2AfocnQcHRROR2nO817dOmzNwxNUMOJO6PThGeyxNWSAIqQFcBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:28:35.125649Z"},"content_sha256":"79300924ac2c6323f23edc7c7315ca653de053fa6a2ad8fe2b39d342f24e3c22","schema_version":"1.0","event_id":"sha256:79300924ac2c6323f23edc7c7315ca653de053fa6a2ad8fe2b39d342f24e3c22"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LR4KKNGN6CCHYQNZ32JWO6GDIA/bundle.json","state_url":"https://pith.science/pith/LR4KKNGN6CCHYQNZ32JWO6GDIA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LR4KKNGN6CCHYQNZ32JWO6GDIA/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":"2026-08-04T19:28:35Z","links":{"resolver":"https://pith.science/pith/LR4KKNGN6CCHYQNZ32JWO6GDIA","bundle":"https://pith.science/pith/LR4KKNGN6CCHYQNZ32JWO6GDIA/bundle.json","state":"https://pith.science/pith/LR4KKNGN6CCHYQNZ32JWO6GDIA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LR4KKNGN6CCHYQNZ32JWO6GDIA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:LR4KKNGN6CCHYQNZ32JWO6GDIA","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":"250dc62db3a9f836d362090d9f973fecabad19d502b8f4f4297fa23c466fc5a7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-05-27T18:32:39Z","title_canon_sha256":"1ca09d8220b46b3e62ef874819c223f2cf5c2fc26ba6dd0d856ebfa32b2961b1"},"schema_version":"1.0","source":{"id":"0805.4096","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0805.4096","created_at":"2026-07-04T15:15:03Z"},{"alias_kind":"arxiv_version","alias_value":"0805.4096v2","created_at":"2026-07-04T15:15:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0805.4096","created_at":"2026-07-04T15:15:03Z"},{"alias_kind":"pith_short_12","alias_value":"LR4KKNGN6CCH","created_at":"2026-07-04T15:15:03Z"},{"alias_kind":"pith_short_16","alias_value":"LR4KKNGN6CCHYQNZ","created_at":"2026-07-04T15:15:03Z"},{"alias_kind":"pith_short_8","alias_value":"LR4KKNGN","created_at":"2026-07-04T15:15:03Z"}],"graph_snapshots":[{"event_id":"sha256:79300924ac2c6323f23edc7c7315ca653de053fa6a2ad8fe2b39d342f24e3c22","target":"graph","created_at":"2026-07-04T15:15:03Z","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/0805.4096/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We investigate induced modules of doublet algebra in (1,p) logarithmic models. We give fermionic formulas for the characters of induced modules and coinvariants with respect to different subalgebras calculated in the irreducible modules. The characters of coinvariants give multiplicities of projective modules in fusion of induced modules.","authors_text":"B.L. Feigin, I.Yu. Tipunin","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-05-27T18:32:39Z","title":"Characters of coinvariants in (1,p) logarithmic models"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.4096","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":"sha256:57c795a30587941ac3eabea5af4c8d5a96272589094077533184884f60074751","target":"record","created_at":"2026-07-04T15:15:03Z","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":"250dc62db3a9f836d362090d9f973fecabad19d502b8f4f4297fa23c466fc5a7","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2008-05-27T18:32:39Z","title_canon_sha256":"1ca09d8220b46b3e62ef874819c223f2cf5c2fc26ba6dd0d856ebfa32b2961b1"},"schema_version":"1.0","source":{"id":"0805.4096","kind":"arxiv","version":2}},"canonical_sha256":"5c78a534cdf0847c41b9de936778c34032fd0870dc8f61812a05f62391d94903","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5c78a534cdf0847c41b9de936778c34032fd0870dc8f61812a05f62391d94903","first_computed_at":"2026-07-04T15:15:03.760249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:15:03.760249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gSal2VVSnvHMp2OwMRpaa2GitHMFh7YX4e5FUMBxsRW0ddjf9VV+yxhsQKoEXyApeuobH1ula2FMb8cIh/EBAg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:15:03.760736Z","signed_message":"canonical_sha256_bytes"},"source_id":"0805.4096","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:57c795a30587941ac3eabea5af4c8d5a96272589094077533184884f60074751","sha256:79300924ac2c6323f23edc7c7315ca653de053fa6a2ad8fe2b39d342f24e3c22"],"state_sha256":"e5755976a7f824551c6350585993fd74f26e055187fdff6e823a12a02df9dc6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gEajTNAnyt15q9knmAphoujaX1hXWla1P5l6BHT2SSAgeP6D5bhyi3rF1I8AMDPdyvWifXqJ0M1IOQS5yIdeCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:28:35.190931Z","bundle_sha256":"213b0fa4d1fcdecfaf5c842fc96ea73f1da025c62efec21aa5e0cf11575da7a5"}}