{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:XECCPCFGIXC6NEASWXBXRAA7R7","short_pith_number":"pith:XECCPCFG","canonical_record":{"source":{"id":"math/0309016","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2003-09-01T07:50:56Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"970ddbe64f5854869d15b169feb2cf82a0e1111bd3b83a1502549c74a1a572d8","abstract_canon_sha256":"14db4301b74e28d101e39a16b69e3acd3966c5b8dc2bec671980d0706b460af0"},"schema_version":"1.0"},"canonical_sha256":"b9042788a645c5e69012b5c378801f8fc7a2634ac923ae0c1274f2c18afc30c5","source":{"kind":"arxiv","id":"math/0309016","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0309016","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"arxiv_version","alias_value":"math/0309016v1","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0309016","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"pith_short_12","alias_value":"XECCPCFGIXC6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XECCPCFGIXC6NEAS","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XECCPCFG","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:XECCPCFGIXC6NEASWXBXRAA7R7","target":"record","payload":{"canonical_record":{"source":{"id":"math/0309016","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2003-09-01T07:50:56Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"970ddbe64f5854869d15b169feb2cf82a0e1111bd3b83a1502549c74a1a572d8","abstract_canon_sha256":"14db4301b74e28d101e39a16b69e3acd3966c5b8dc2bec671980d0706b460af0"},"schema_version":"1.0"},"canonical_sha256":"b9042788a645c5e69012b5c378801f8fc7a2634ac923ae0c1274f2c18afc30c5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:17.235581Z","signature_b64":"9vKtM6bIpFTuSCpsZK6JGzapOBJZH5alO8IakZIkjSPCaQt+ZVAyNuA1hxzn6LzZ4z8pqSDysa3g3lYXrxqkAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9042788a645c5e69012b5c378801f8fc7a2634ac923ae0c1274f2c18afc30c5","last_reissued_at":"2026-05-18T03:46:17.234542Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:17.234542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0309016","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":"2026-05-18T03:46:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mEyX4EBUsX04nQ6Xw//W0ZSy9smH/a9gKIe33lUf1rUgKoCEFeEPUzjK5Thf0W3Z9RGGrYHtDPRq4Ok/4u3JBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:46:13.810734Z"},"content_sha256":"5c57336fd9756efa4b19063d79d412e866fee1b123419863b2732ac4245d7ab8","schema_version":"1.0","event_id":"sha256:5c57336fd9756efa4b19063d79d412e866fee1b123419863b2732ac4245d7ab8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:XECCPCFGIXC6NEASWXBXRAA7R7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Filtrations and completions of certain positive level modules of affine algebras","license":"","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Jacob Greenstein, Vyjayanthi Chari","submitted_at":"2003-09-01T07:50:56Z","abstract_excerpt":"We define a filtration indexed by the integers on the tensor product of an integrable highest weight module and a loop module for a quantum affine algebra. We prove that the filtration is either trivial or strictly decreasing and give sufficient conditions for this to happen. In the first case we prove that the module is irreducible and in the second case we prove that the intersection of all the modules is zero, thus allowing us to define the completed tensor product. In certain special cases, we identify the subsequent quotients of filtration. These are certain highest weight integrable modu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309016","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":"2026-05-18T03:46:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2U8VpKaocaohB0iFcIYErLaQauCmyGKVgxZprswll25/ztwM79xTISFyuZJYiZQV60sJVeKxSxGqGvsXoSP0BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T16:46:13.811075Z"},"content_sha256":"6172466624a7780d50d9af583af2673c8a5e0de8313ab1d3884f51e7f96ce6d7","schema_version":"1.0","event_id":"sha256:6172466624a7780d50d9af583af2673c8a5e0de8313ab1d3884f51e7f96ce6d7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XECCPCFGIXC6NEASWXBXRAA7R7/bundle.json","state_url":"https://pith.science/pith/XECCPCFGIXC6NEASWXBXRAA7R7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XECCPCFGIXC6NEASWXBXRAA7R7/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":"2026-06-01T16:46:13Z","links":{"resolver":"https://pith.science/pith/XECCPCFGIXC6NEASWXBXRAA7R7","bundle":"https://pith.science/pith/XECCPCFGIXC6NEASWXBXRAA7R7/bundle.json","state":"https://pith.science/pith/XECCPCFGIXC6NEASWXBXRAA7R7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XECCPCFGIXC6NEASWXBXRAA7R7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:XECCPCFGIXC6NEASWXBXRAA7R7","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":"14db4301b74e28d101e39a16b69e3acd3966c5b8dc2bec671980d0706b460af0","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.QA","submitted_at":"2003-09-01T07:50:56Z","title_canon_sha256":"970ddbe64f5854869d15b169feb2cf82a0e1111bd3b83a1502549c74a1a572d8"},"schema_version":"1.0","source":{"id":"math/0309016","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0309016","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"arxiv_version","alias_value":"math/0309016v1","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0309016","created_at":"2026-05-18T03:46:17Z"},{"alias_kind":"pith_short_12","alias_value":"XECCPCFGIXC6","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"XECCPCFGIXC6NEAS","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"XECCPCFG","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:6172466624a7780d50d9af583af2673c8a5e0de8313ab1d3884f51e7f96ce6d7","target":"graph","created_at":"2026-05-18T03:46:17Z","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":"We define a filtration indexed by the integers on the tensor product of an integrable highest weight module and a loop module for a quantum affine algebra. We prove that the filtration is either trivial or strictly decreasing and give sufficient conditions for this to happen. In the first case we prove that the module is irreducible and in the second case we prove that the intersection of all the modules is zero, thus allowing us to define the completed tensor product. In certain special cases, we identify the subsequent quotients of filtration. These are certain highest weight integrable modu","authors_text":"Jacob Greenstein, Vyjayanthi Chari","cross_cats":["math.RT"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2003-09-01T07:50:56Z","title":"Filtrations and completions of certain positive level modules of affine algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0309016","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":"sha256:5c57336fd9756efa4b19063d79d412e866fee1b123419863b2732ac4245d7ab8","target":"record","created_at":"2026-05-18T03:46:17Z","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":"14db4301b74e28d101e39a16b69e3acd3966c5b8dc2bec671980d0706b460af0","cross_cats_sorted":["math.RT"],"license":"","primary_cat":"math.QA","submitted_at":"2003-09-01T07:50:56Z","title_canon_sha256":"970ddbe64f5854869d15b169feb2cf82a0e1111bd3b83a1502549c74a1a572d8"},"schema_version":"1.0","source":{"id":"math/0309016","kind":"arxiv","version":1}},"canonical_sha256":"b9042788a645c5e69012b5c378801f8fc7a2634ac923ae0c1274f2c18afc30c5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b9042788a645c5e69012b5c378801f8fc7a2634ac923ae0c1274f2c18afc30c5","first_computed_at":"2026-05-18T03:46:17.234542Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:46:17.234542Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9vKtM6bIpFTuSCpsZK6JGzapOBJZH5alO8IakZIkjSPCaQt+ZVAyNuA1hxzn6LzZ4z8pqSDysa3g3lYXrxqkAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:46:17.235581Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0309016","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c57336fd9756efa4b19063d79d412e866fee1b123419863b2732ac4245d7ab8","sha256:6172466624a7780d50d9af583af2673c8a5e0de8313ab1d3884f51e7f96ce6d7"],"state_sha256":"1e3e8e862a95309231221f22d23cfda4a43ff2d49ba5fdd39fa054dacd95284d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"28ZqNVJul0PxBhvKkblBtEJ/tJSBGgWF4sLBWPBRY6Ke5EmZ+gc1gwDkTxfuHSZLc2hMNL9Hu47KALEUki86Bg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T16:46:13.813069Z","bundle_sha256":"5be4b39d50a746e6df12388a9287a908414b71f4de2dbf7e136f90bed10428ba"}}