{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:V2LSAOYOFXG7SAPTKG7YRQIE4O","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":"6ea7b08b70c1a4a445d0f2e778fa8e896338b86d37227424a457c4988b20e646","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2000-12-03T19:03:31Z","title_canon_sha256":"0d74f45ed643bc7dbf6778db73ed2b3dd8bdc5a668f07782a99a1b8411e88f0a"},"schema_version":"1.0","source":{"id":"math/0012013","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0012013","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"arxiv_version","alias_value":"math/0012013v1","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0012013","created_at":"2026-05-18T01:38:30Z"},{"alias_kind":"pith_short_12","alias_value":"V2LSAOYOFXG7","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"V2LSAOYOFXG7SAPT","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"V2LSAOYO","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:de45e619ca41689c4496354080b7578165a081dabdd8d3ffd34f3014f978dcc3","target":"graph","created_at":"2026-05-18T01:38:30Z","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":"It is proved that an indecomposable Harish-Chandra module over the Virasoro algebra must be (i) a uniformly bounded module, or (ii) a module in Category $\\cal O$, or (iii) a module in Category ${\\cal O}^-$, or (iv) a module which contains the trivial module as one of its composition factors.","authors_text":"Yucai Su","cross_cats":["math-ph","math.MP"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2000-12-03T19:03:31Z","title":"On indecomposable modules over the Virasoro algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0012013","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:a298d7aa19912d16714f52ddabf3588ea1713ea75add297a1f0051d4e2cba428","target":"record","created_at":"2026-05-18T01:38:30Z","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":"6ea7b08b70c1a4a445d0f2e778fa8e896338b86d37227424a457c4988b20e646","cross_cats_sorted":["math-ph","math.MP"],"license":"","primary_cat":"math.QA","submitted_at":"2000-12-03T19:03:31Z","title_canon_sha256":"0d74f45ed643bc7dbf6778db73ed2b3dd8bdc5a668f07782a99a1b8411e88f0a"},"schema_version":"1.0","source":{"id":"math/0012013","kind":"arxiv","version":1}},"canonical_sha256":"ae97203b0e2dcdf901f351bf88c104e3bc6c66a862c3eb012f496c2884f73258","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae97203b0e2dcdf901f351bf88c104e3bc6c66a862c3eb012f496c2884f73258","first_computed_at":"2026-05-18T01:38:30.104226Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:30.104226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qRYL8BitjzfraU4BnbgwuyKBk/Rn1X81IRbeVELLbeswT60RJ4uP13IShHCpfKkqg58eeD8sbRW1HX8KWSsQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:30.104721Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0012013","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a298d7aa19912d16714f52ddabf3588ea1713ea75add297a1f0051d4e2cba428","sha256:de45e619ca41689c4496354080b7578165a081dabdd8d3ffd34f3014f978dcc3"],"state_sha256":"0b3f4ca12b666df2c7942d9a96afb8d77d2abe507db0fe3276b855d18ce7e296"}