{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:VCXIC7GSKVJ65BUBDPIDI6KJJO","short_pith_number":"pith:VCXIC7GS","canonical_record":{"source":{"id":"q-alg/9608022","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1996-08-26T20:02:22Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"d249846fa6d81eeb8287bab76f3f86d8ff3be0fd4c167c5001fb15755f0f9aa2","abstract_canon_sha256":"504833aba3c783143fb8725d72c6ff026c699f507c2cb3c56bc5448b62569298"},"schema_version":"1.0"},"canonical_sha256":"a8ae817cd25553ee86811bd03479494b97015421aa283d2f817328e47d828175","source":{"kind":"arxiv","id":"q-alg/9608022","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9608022","created_at":"2026-07-04T15:09:09Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9608022v1","created_at":"2026-07-04T15:09:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9608022","created_at":"2026-07-04T15:09:09Z"},{"alias_kind":"pith_short_12","alias_value":"VCXIC7GSKVJ6","created_at":"2026-07-04T15:09:09Z"},{"alias_kind":"pith_short_16","alias_value":"VCXIC7GSKVJ65BUB","created_at":"2026-07-04T15:09:09Z"},{"alias_kind":"pith_short_8","alias_value":"VCXIC7GS","created_at":"2026-07-04T15:09:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:VCXIC7GSKVJ65BUBDPIDI6KJJO","target":"record","payload":{"canonical_record":{"source":{"id":"q-alg/9608022","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-alg","submitted_at":"1996-08-26T20:02:22Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"d249846fa6d81eeb8287bab76f3f86d8ff3be0fd4c167c5001fb15755f0f9aa2","abstract_canon_sha256":"504833aba3c783143fb8725d72c6ff026c699f507c2cb3c56bc5448b62569298"},"schema_version":"1.0"},"canonical_sha256":"a8ae817cd25553ee86811bd03479494b97015421aa283d2f817328e47d828175","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T15:09:09.363819Z","signature_b64":"7uInrNmZPIZciprdEZIrQfcFLhVpbGevSd9P7m6/fneC2SjOEV+mUPftjWEjyQtoc0niXsnrI46HSY6WgNVcBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a8ae817cd25553ee86811bd03479494b97015421aa283d2f817328e47d828175","last_reissued_at":"2026-07-04T15:09:09.363472Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T15:09:09.363472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"q-alg/9608022","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":"2026-07-04T15:09:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ETZoFHl+NphCq0fDLrwPUle5rx+NntCIPxVDdFDDRyGQAuHkEfiXtX7Ly5eTSWSjnAp4k3wY//0OxCNpRdggCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T07:04:43.062166Z"},"content_sha256":"38c9f68fbad4341112810360574507d5818db90230ce2774459db481f322fe87","schema_version":"1.0","event_id":"sha256:38c9f68fbad4341112810360574507d5818db90230ce2774459db481f322fe87"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:VCXIC7GSKVJ65BUBDPIDI6KJJO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The radical of a vertex operator algebra","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"q-alg","authors_text":"C. Dong, G. Mason, H. Li, P. Montague","submitted_at":"1996-08-26T20:02:22Z","abstract_excerpt":"The radical $J(V)$ of a vertex operator algebra $V$ is defined to be the subspace of $V$ consisting of vectors $v$ such that the zero mode $o(v)=0$ on $V$ where $o(v)=v_{wt v-1}$ if $v$ is homogeneous. We establish various facts about $o(v),$ including the determination of $J(V)$ which is shown to be essentially equal to $(L(0)+L(-1))V.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9608022","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/q-alg/9608022/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":"2026-07-04T15:09:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"duAw2KMnjV28bt/fO9kzupy7GcBG9oVtPggh5fIZqmlyoc+lk7fLWLI9ec8oWFEJ/QeyDnEK1qHuOsbP11ScDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-12T07:04:43.062554Z"},"content_sha256":"9d17ef38df2a3ac48cb1ab254d0733758ce1cbf03225ea2179a5e9652184d458","schema_version":"1.0","event_id":"sha256:9d17ef38df2a3ac48cb1ab254d0733758ce1cbf03225ea2179a5e9652184d458"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VCXIC7GSKVJ65BUBDPIDI6KJJO/bundle.json","state_url":"https://pith.science/pith/VCXIC7GSKVJ65BUBDPIDI6KJJO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VCXIC7GSKVJ65BUBDPIDI6KJJO/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":"2026-07-12T07:04:43Z","links":{"resolver":"https://pith.science/pith/VCXIC7GSKVJ65BUBDPIDI6KJJO","bundle":"https://pith.science/pith/VCXIC7GSKVJ65BUBDPIDI6KJJO/bundle.json","state":"https://pith.science/pith/VCXIC7GSKVJ65BUBDPIDI6KJJO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VCXIC7GSKVJ65BUBDPIDI6KJJO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:VCXIC7GSKVJ65BUBDPIDI6KJJO","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":"504833aba3c783143fb8725d72c6ff026c699f507c2cb3c56bc5448b62569298","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1996-08-26T20:02:22Z","title_canon_sha256":"d249846fa6d81eeb8287bab76f3f86d8ff3be0fd4c167c5001fb15755f0f9aa2"},"schema_version":"1.0","source":{"id":"q-alg/9608022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-alg/9608022","created_at":"2026-07-04T15:09:09Z"},{"alias_kind":"arxiv_version","alias_value":"q-alg/9608022v1","created_at":"2026-07-04T15:09:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-alg/9608022","created_at":"2026-07-04T15:09:09Z"},{"alias_kind":"pith_short_12","alias_value":"VCXIC7GSKVJ6","created_at":"2026-07-04T15:09:09Z"},{"alias_kind":"pith_short_16","alias_value":"VCXIC7GSKVJ65BUB","created_at":"2026-07-04T15:09:09Z"},{"alias_kind":"pith_short_8","alias_value":"VCXIC7GS","created_at":"2026-07-04T15:09:09Z"}],"graph_snapshots":[{"event_id":"sha256:9d17ef38df2a3ac48cb1ab254d0733758ce1cbf03225ea2179a5e9652184d458","target":"graph","created_at":"2026-07-04T15:09:09Z","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/q-alg/9608022/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The radical $J(V)$ of a vertex operator algebra $V$ is defined to be the subspace of $V$ consisting of vectors $v$ such that the zero mode $o(v)=0$ on $V$ where $o(v)=v_{wt v-1}$ if $v$ is homogeneous. We establish various facts about $o(v),$ including the determination of $J(V)$ which is shown to be essentially equal to $(L(0)+L(-1))V.$","authors_text":"C. Dong, G. Mason, H. Li, P. Montague","cross_cats":["math.QA"],"headline":"","license":"","primary_cat":"q-alg","submitted_at":"1996-08-26T20:02:22Z","title":"The radical of a vertex operator algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-alg/9608022","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":"sha256:38c9f68fbad4341112810360574507d5818db90230ce2774459db481f322fe87","target":"record","created_at":"2026-07-04T15:09:09Z","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":"504833aba3c783143fb8725d72c6ff026c699f507c2cb3c56bc5448b62569298","cross_cats_sorted":["math.QA"],"license":"","primary_cat":"q-alg","submitted_at":"1996-08-26T20:02:22Z","title_canon_sha256":"d249846fa6d81eeb8287bab76f3f86d8ff3be0fd4c167c5001fb15755f0f9aa2"},"schema_version":"1.0","source":{"id":"q-alg/9608022","kind":"arxiv","version":1}},"canonical_sha256":"a8ae817cd25553ee86811bd03479494b97015421aa283d2f817328e47d828175","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a8ae817cd25553ee86811bd03479494b97015421aa283d2f817328e47d828175","first_computed_at":"2026-07-04T15:09:09.363472Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:09:09.363472Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7uInrNmZPIZciprdEZIrQfcFLhVpbGevSd9P7m6/fneC2SjOEV+mUPftjWEjyQtoc0niXsnrI46HSY6WgNVcBA==","signature_status":"signed_v1","signed_at":"2026-07-04T15:09:09.363819Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-alg/9608022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:38c9f68fbad4341112810360574507d5818db90230ce2774459db481f322fe87","sha256:9d17ef38df2a3ac48cb1ab254d0733758ce1cbf03225ea2179a5e9652184d458"],"state_sha256":"cbbabbee4f93b1f0f2c23ba1181ea36a934d748b379d4b0954c15d61aac768ca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5RgEz76IIsM/wd8/ZZwm1krUK5us/9OVuau+Uqt7QO/EowF0ndvTsKusc2wT5FEg3WoKCgXi3ea69icEhHXXCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-12T07:04:43.064904Z","bundle_sha256":"b73ed031d09e8c379634e1ca97bb62b5a818b96500db008a37b43b5b99965f59"}}