{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PEL77KYNGSNTTDRCYKANKE5S4A","short_pith_number":"pith:PEL77KYN","canonical_record":{"source":{"id":"1406.3757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-06-14T17:13:52Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6df9cb1af4b43b387cd4e4feaaae680031c25b10cef803894fa1a115cd2e72b6","abstract_canon_sha256":"3d65a63529f33eec075b9d367ff833b4e4c8961cff0809b1833d8acf6a12a55d"},"schema_version":"1.0"},"canonical_sha256":"7917ffab0d349b398e22c280d513b2e01032c72c24f1c0ed10aa628fade65d22","source":{"kind":"arxiv","id":"1406.3757","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3757","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3757v1","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3757","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"PEL77KYNGSNT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PEL77KYNGSNTTDRC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PEL77KYN","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PEL77KYNGSNTTDRCYKANKE5S4A","target":"record","payload":{"canonical_record":{"source":{"id":"1406.3757","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-06-14T17:13:52Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"6df9cb1af4b43b387cd4e4feaaae680031c25b10cef803894fa1a115cd2e72b6","abstract_canon_sha256":"3d65a63529f33eec075b9d367ff833b4e4c8961cff0809b1833d8acf6a12a55d"},"schema_version":"1.0"},"canonical_sha256":"7917ffab0d349b398e22c280d513b2e01032c72c24f1c0ed10aa628fade65d22","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:45.095432Z","signature_b64":"v8JxigW5fO29T6xBBVtyF80eLVJwZnEo9KJw2QPDFxB7d3pfZnsrl7ZT5s3dBoxoE7BOO9vpjX6pcC9g4IVMAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7917ffab0d349b398e22c280d513b2e01032c72c24f1c0ed10aa628fade65d22","last_reissued_at":"2026-05-18T02:49:45.095060Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:45.095060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.3757","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":"2026-05-18T02:49:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1JUaWiUHTULc0JbMX3w48K8Y6e7jbs4auudyUvr/wzW49ypPV8MryzM/8qfkZ9iiDgbmx1qSq5q4pPoKp52lCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T16:07:57.462672Z"},"content_sha256":"9727d3dc09f5d24dc99d272115c8123d72ade0400d4bb188e176156fa972d7aa","schema_version":"1.0","event_id":"sha256:9727d3dc09f5d24dc99d272115c8123d72ade0400d4bb188e176156fa972d7aa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PEL77KYNGSNTTDRCYKANKE5S4A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"$GL(m|n)$-supermodules with good and Weyl filtrations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.RA","authors_text":"Alexandr N. Zubkov","submitted_at":"2014-06-14T17:13:52Z","abstract_excerpt":"The purpose of this paper is to prove necessary and sufficient criteria for a $GL(m|n)$-supermodule to have a good or Weryl filtration. We also introduce the notion of a Steinberg supermodule analogous to the classical notion of Steinberg module. We prove that the Steinberg supermodule inherits some properties of the Steinberg module. Some new series of finite-dimensional tilting supermodules are found."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3757","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":"2026-05-18T02:49:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MKvJZgRoKoq9ZgA5wXDjA7Jx+IHju7ja6PGA681i1ofXn66ycB9utxFsrEika/EvB1ECzvIELq+1ph+z9wGXBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T16:07:57.463018Z"},"content_sha256":"6e3578d754ee39bbfca3b7e24437c33e4e85947d4095cf8ab584a166c8f3ca12","schema_version":"1.0","event_id":"sha256:6e3578d754ee39bbfca3b7e24437c33e4e85947d4095cf8ab584a166c8f3ca12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PEL77KYNGSNTTDRCYKANKE5S4A/bundle.json","state_url":"https://pith.science/pith/PEL77KYNGSNTTDRCYKANKE5S4A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PEL77KYNGSNTTDRCYKANKE5S4A/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":"2026-06-30T16:07:57Z","links":{"resolver":"https://pith.science/pith/PEL77KYNGSNTTDRCYKANKE5S4A","bundle":"https://pith.science/pith/PEL77KYNGSNTTDRCYKANKE5S4A/bundle.json","state":"https://pith.science/pith/PEL77KYNGSNTTDRCYKANKE5S4A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PEL77KYNGSNTTDRCYKANKE5S4A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PEL77KYNGSNTTDRCYKANKE5S4A","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":"3d65a63529f33eec075b9d367ff833b4e4c8961cff0809b1833d8acf6a12a55d","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-06-14T17:13:52Z","title_canon_sha256":"6df9cb1af4b43b387cd4e4feaaae680031c25b10cef803894fa1a115cd2e72b6"},"schema_version":"1.0","source":{"id":"1406.3757","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.3757","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"arxiv_version","alias_value":"1406.3757v1","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.3757","created_at":"2026-05-18T02:49:45Z"},{"alias_kind":"pith_short_12","alias_value":"PEL77KYNGSNT","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PEL77KYNGSNTTDRC","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PEL77KYN","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:6e3578d754ee39bbfca3b7e24437c33e4e85947d4095cf8ab584a166c8f3ca12","target":"graph","created_at":"2026-05-18T02:49:45Z","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":"The purpose of this paper is to prove necessary and sufficient criteria for a $GL(m|n)$-supermodule to have a good or Weryl filtration. We also introduce the notion of a Steinberg supermodule analogous to the classical notion of Steinberg module. We prove that the Steinberg supermodule inherits some properties of the Steinberg module. Some new series of finite-dimensional tilting supermodules are found.","authors_text":"Alexandr N. Zubkov","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-06-14T17:13:52Z","title":"$GL(m|n)$-supermodules with good and Weyl filtrations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3757","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":"sha256:9727d3dc09f5d24dc99d272115c8123d72ade0400d4bb188e176156fa972d7aa","target":"record","created_at":"2026-05-18T02:49:45Z","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":"3d65a63529f33eec075b9d367ff833b4e4c8961cff0809b1833d8acf6a12a55d","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2014-06-14T17:13:52Z","title_canon_sha256":"6df9cb1af4b43b387cd4e4feaaae680031c25b10cef803894fa1a115cd2e72b6"},"schema_version":"1.0","source":{"id":"1406.3757","kind":"arxiv","version":1}},"canonical_sha256":"7917ffab0d349b398e22c280d513b2e01032c72c24f1c0ed10aa628fade65d22","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7917ffab0d349b398e22c280d513b2e01032c72c24f1c0ed10aa628fade65d22","first_computed_at":"2026-05-18T02:49:45.095060Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:45.095060Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v8JxigW5fO29T6xBBVtyF80eLVJwZnEo9KJw2QPDFxB7d3pfZnsrl7ZT5s3dBoxoE7BOO9vpjX6pcC9g4IVMAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:45.095432Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.3757","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9727d3dc09f5d24dc99d272115c8123d72ade0400d4bb188e176156fa972d7aa","sha256:6e3578d754ee39bbfca3b7e24437c33e4e85947d4095cf8ab584a166c8f3ca12"],"state_sha256":"a88a16204c56b1324fb8cb3a5f2363b20a481613622aecddada28a4296746ec0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UvF6Ul+Bk01/3XCY+Qk85vNUmgR7B5jg4LThBxOSuLaJRpB9hM01OF9dL0C+xce8Q0HgldS/peCkMsPCZmycBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T16:07:57.464970Z","bundle_sha256":"9614c84571994e3a1584334b5be0d6039f158a21dd2886a041514b31af5cac6c"}}