{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:RCLPLCHDZD5V2BQBBULY2HBRKJ","short_pith_number":"pith:RCLPLCHD","canonical_record":{"source":{"id":"1612.09391","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-30T05:41:35Z","cross_cats_sorted":[],"title_canon_sha256":"9b449cd9e32519cd58d399ede8d33bc1f230c24e94d299ae3f0cecff152760f7","abstract_canon_sha256":"ae318e2a6fa0009765c9e697b5867a5aff4efacb9a5be41f48193cb41a045227"},"schema_version":"1.0"},"canonical_sha256":"8896f588e3c8fb5d06010d178d1c31527108675a537dfd354cf48698dc8dba11","source":{"kind":"arxiv","id":"1612.09391","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09391","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09391v1","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09391","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"RCLPLCHDZD5V","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RCLPLCHDZD5V2BQB","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RCLPLCHD","created_at":"2026-05-18T12:30:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:RCLPLCHDZD5V2BQBBULY2HBRKJ","target":"record","payload":{"canonical_record":{"source":{"id":"1612.09391","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-30T05:41:35Z","cross_cats_sorted":[],"title_canon_sha256":"9b449cd9e32519cd58d399ede8d33bc1f230c24e94d299ae3f0cecff152760f7","abstract_canon_sha256":"ae318e2a6fa0009765c9e697b5867a5aff4efacb9a5be41f48193cb41a045227"},"schema_version":"1.0"},"canonical_sha256":"8896f588e3c8fb5d06010d178d1c31527108675a537dfd354cf48698dc8dba11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:41.633781Z","signature_b64":"wjBuDhNc3ZKYhow8XPuog5nepboz1vcfccOFLu5ZQCT2Sj+s8+s1xrGjEoS+t36JXnk0rBvWBiRxFX9BOO15AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8896f588e3c8fb5d06010d178d1c31527108675a537dfd354cf48698dc8dba11","last_reissued_at":"2026-05-18T00:53:41.633402Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:41.633402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.09391","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":"2026-05-18T00:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ucheyedJLSiAeyeINIrEtkhzRPH1YX/15toZ8aUlWUtEsRMeVSUjw40P/RsJfqRJq8Rn3zUxO3pKOUbFSMUbDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:30:02.432822Z"},"content_sha256":"ba34a20bec5eada786eb8ecda70d54052515c15131d25dd10b7d16a0118b18c0","schema_version":"1.0","event_id":"sha256:ba34a20bec5eada786eb8ecda70d54052515c15131d25dd10b7d16a0118b18c0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:RCLPLCHDZD5V2BQBBULY2HBRKJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Indecomposable generalized weight modules over the algebra of polynomial integro-differential operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Victor Bekkert, Vladimir Bavula, Vyacheslav Futorny","submitted_at":"2016-12-30T05:41:35Z","abstract_excerpt":"For the algebra L= K <x, d/dx, \\int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an infinite dimensional uniserial module. Ext-groups are found between indecomposable generalized weight modules, it is proven that they are finite dimensional vector spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09391","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":""},"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":"2026-05-18T00:53:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H64FjvyHI/QmA0hbNcvmqSEccCtYPAQTalyRZvr/ejbbi80KZBpgBsm6QStmVJfZ94cuNShcjb09gqLiSUlMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T08:30:02.433170Z"},"content_sha256":"6497025d70863b9beae6c38da93973415e9502c605b7eafa8719cd6af06f3c6c","schema_version":"1.0","event_id":"sha256:6497025d70863b9beae6c38da93973415e9502c605b7eafa8719cd6af06f3c6c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RCLPLCHDZD5V2BQBBULY2HBRKJ/bundle.json","state_url":"https://pith.science/pith/RCLPLCHDZD5V2BQBBULY2HBRKJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RCLPLCHDZD5V2BQBBULY2HBRKJ/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":"2026-06-01T08:30:02Z","links":{"resolver":"https://pith.science/pith/RCLPLCHDZD5V2BQBBULY2HBRKJ","bundle":"https://pith.science/pith/RCLPLCHDZD5V2BQBBULY2HBRKJ/bundle.json","state":"https://pith.science/pith/RCLPLCHDZD5V2BQBBULY2HBRKJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RCLPLCHDZD5V2BQBBULY2HBRKJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:RCLPLCHDZD5V2BQBBULY2HBRKJ","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":"ae318e2a6fa0009765c9e697b5867a5aff4efacb9a5be41f48193cb41a045227","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-30T05:41:35Z","title_canon_sha256":"9b449cd9e32519cd58d399ede8d33bc1f230c24e94d299ae3f0cecff152760f7"},"schema_version":"1.0","source":{"id":"1612.09391","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09391","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09391v1","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09391","created_at":"2026-05-18T00:53:41Z"},{"alias_kind":"pith_short_12","alias_value":"RCLPLCHDZD5V","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_16","alias_value":"RCLPLCHDZD5V2BQB","created_at":"2026-05-18T12:30:41Z"},{"alias_kind":"pith_short_8","alias_value":"RCLPLCHD","created_at":"2026-05-18T12:30:41Z"}],"graph_snapshots":[{"event_id":"sha256:6497025d70863b9beae6c38da93973415e9502c605b7eafa8719cd6af06f3c6c","target":"graph","created_at":"2026-05-18T00:53:41Z","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 the algebra L= K <x, d/dx, \\int> of polynomial integro-differential operators over a field K of characteristic zero, a classification of indecomposable, generalized weight L-modules of finite length is given. Each such module is an infinite dimensional uniserial module. Ext-groups are found between indecomposable generalized weight modules, it is proven that they are finite dimensional vector spaces.","authors_text":"Victor Bekkert, Vladimir Bavula, Vyacheslav Futorny","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-30T05:41:35Z","title":"Indecomposable generalized weight modules over the algebra of polynomial integro-differential operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09391","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:ba34a20bec5eada786eb8ecda70d54052515c15131d25dd10b7d16a0118b18c0","target":"record","created_at":"2026-05-18T00:53:41Z","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":"ae318e2a6fa0009765c9e697b5867a5aff4efacb9a5be41f48193cb41a045227","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2016-12-30T05:41:35Z","title_canon_sha256":"9b449cd9e32519cd58d399ede8d33bc1f230c24e94d299ae3f0cecff152760f7"},"schema_version":"1.0","source":{"id":"1612.09391","kind":"arxiv","version":1}},"canonical_sha256":"8896f588e3c8fb5d06010d178d1c31527108675a537dfd354cf48698dc8dba11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8896f588e3c8fb5d06010d178d1c31527108675a537dfd354cf48698dc8dba11","first_computed_at":"2026-05-18T00:53:41.633402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:41.633402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wjBuDhNc3ZKYhow8XPuog5nepboz1vcfccOFLu5ZQCT2Sj+s8+s1xrGjEoS+t36JXnk0rBvWBiRxFX9BOO15AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:41.633781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09391","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba34a20bec5eada786eb8ecda70d54052515c15131d25dd10b7d16a0118b18c0","sha256:6497025d70863b9beae6c38da93973415e9502c605b7eafa8719cd6af06f3c6c"],"state_sha256":"69b3ca882e966cfd1308bf66311a838fcc068c4e3334eec98bebecd4c20fd573"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M4LwSexF/XOKpwBnMSi7Rsgg4Hh1EqmeZJs/0aJ7n4ByyTY43KxQQt88N3a8adklIc67H253w4Qu1amQE+qlAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T08:30:02.435109Z","bundle_sha256":"fa3c5f424b42fcb416c6f4ecc17e8966190e18fd212ab51782d706219f3d3eca"}}