{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:6BXLIG55Q7Z6OUIRMUSIEVX3P5","short_pith_number":"pith:6BXLIG55","canonical_record":{"source":{"id":"1507.06098","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-07-22T08:27:16Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"baca8e22a0e0b315faad80f2d69cb8856e8de6e892646645372d0e4da576355c","abstract_canon_sha256":"15826c137334a2f621a479c200593c1eb9d2665f8154238196e6b5e2efb29dee"},"schema_version":"1.0"},"canonical_sha256":"f06eb41bbd87f3e7511165248256fb7f538d886fb6426a25f4ab451d8229c124","source":{"kind":"arxiv","id":"1507.06098","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06098","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06098v2","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06098","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"pith_short_12","alias_value":"6BXLIG55Q7Z6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6BXLIG55Q7Z6OUIR","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6BXLIG55","created_at":"2026-05-18T12:29:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:6BXLIG55Q7Z6OUIRMUSIEVX3P5","target":"record","payload":{"canonical_record":{"source":{"id":"1507.06098","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-07-22T08:27:16Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"baca8e22a0e0b315faad80f2d69cb8856e8de6e892646645372d0e4da576355c","abstract_canon_sha256":"15826c137334a2f621a479c200593c1eb9d2665f8154238196e6b5e2efb29dee"},"schema_version":"1.0"},"canonical_sha256":"f06eb41bbd87f3e7511165248256fb7f538d886fb6426a25f4ab451d8229c124","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:40.535876Z","signature_b64":"Hd7/WX67lzlgUMR5YWh00qEVoWb3CsYJsw8GNweKxwdxObcC3JOI/HVhiVv9eT954nl4mV4gXYoaTU/WRuTtAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f06eb41bbd87f3e7511165248256fb7f538d886fb6426a25f4ab451d8229c124","last_reissued_at":"2026-05-18T01:12:40.535544Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:40.535544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.06098","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yhucsZxQiQ5hAO4x3r16Svv+K8BG7ntaqfn2mERSJNrZU0fQJyTSwfPAuxrXQaCdfSHmGPlyNeUjwKOL0Jm2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:56:08.039607Z"},"content_sha256":"ca4174334a3295f61c10c7d9c4bd54ad88b78c9842bfa7600791d4eb6a415b1e","schema_version":"1.0","event_id":"sha256:ca4174334a3295f61c10c7d9c4bd54ad88b78c9842bfa7600791d4eb6a415b1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:6BXLIG55Q7Z6OUIRMUSIEVX3P5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Two constructions of grading-restricted vertex (super)algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"math.QA","authors_text":"Yi-Zhi Huang","submitted_at":"2015-07-22T08:27:16Z","abstract_excerpt":"We give two constructions of grading-restricted vertex (super)algebras. We first give a new construction of a class of grading-restricted vertex (super)algebras originally obtained by Meurman and Primc using a different method. This construction is based on a new definition of vertex operators and a new method. Our second construction is a generalization of the author's construction of the moonshine module vertex operator algebra and a related vertex operator superalgebra. This construction needs properties of intertwining operators formulated and proved by the author."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06098","kind":"arxiv","version":2},"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":"2026-05-18T01:12:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"g2Da8BhlEaF7oCUGDetO5NjHZLJFFkT9yUosS2e7I2ZR4G35zsyJjwG5XRyUE/rVr1EEKW6xWiaqQCi98w9ZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T12:56:08.040137Z"},"content_sha256":"d71ac89aa9ab09b5cf57d6de6050fa91f364ce6c20b4753085c3941e5f6346b4","schema_version":"1.0","event_id":"sha256:d71ac89aa9ab09b5cf57d6de6050fa91f364ce6c20b4753085c3941e5f6346b4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6BXLIG55Q7Z6OUIRMUSIEVX3P5/bundle.json","state_url":"https://pith.science/pith/6BXLIG55Q7Z6OUIRMUSIEVX3P5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6BXLIG55Q7Z6OUIRMUSIEVX3P5/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":"2026-06-27T12:56:08Z","links":{"resolver":"https://pith.science/pith/6BXLIG55Q7Z6OUIRMUSIEVX3P5","bundle":"https://pith.science/pith/6BXLIG55Q7Z6OUIRMUSIEVX3P5/bundle.json","state":"https://pith.science/pith/6BXLIG55Q7Z6OUIRMUSIEVX3P5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6BXLIG55Q7Z6OUIRMUSIEVX3P5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:6BXLIG55Q7Z6OUIRMUSIEVX3P5","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":"15826c137334a2f621a479c200593c1eb9d2665f8154238196e6b5e2efb29dee","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-07-22T08:27:16Z","title_canon_sha256":"baca8e22a0e0b315faad80f2d69cb8856e8de6e892646645372d0e4da576355c"},"schema_version":"1.0","source":{"id":"1507.06098","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.06098","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"arxiv_version","alias_value":"1507.06098v2","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.06098","created_at":"2026-05-18T01:12:40Z"},{"alias_kind":"pith_short_12","alias_value":"6BXLIG55Q7Z6","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_16","alias_value":"6BXLIG55Q7Z6OUIR","created_at":"2026-05-18T12:29:07Z"},{"alias_kind":"pith_short_8","alias_value":"6BXLIG55","created_at":"2026-05-18T12:29:07Z"}],"graph_snapshots":[{"event_id":"sha256:d71ac89aa9ab09b5cf57d6de6050fa91f364ce6c20b4753085c3941e5f6346b4","target":"graph","created_at":"2026-05-18T01:12:40Z","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 give two constructions of grading-restricted vertex (super)algebras. We first give a new construction of a class of grading-restricted vertex (super)algebras originally obtained by Meurman and Primc using a different method. This construction is based on a new definition of vertex operators and a new method. Our second construction is a generalization of the author's construction of the moonshine module vertex operator algebra and a related vertex operator superalgebra. This construction needs properties of intertwining operators formulated and proved by the author.","authors_text":"Yi-Zhi Huang","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-07-22T08:27:16Z","title":"Two constructions of grading-restricted vertex (super)algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06098","kind":"arxiv","version":2},"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:ca4174334a3295f61c10c7d9c4bd54ad88b78c9842bfa7600791d4eb6a415b1e","target":"record","created_at":"2026-05-18T01:12:40Z","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":"15826c137334a2f621a479c200593c1eb9d2665f8154238196e6b5e2efb29dee","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-07-22T08:27:16Z","title_canon_sha256":"baca8e22a0e0b315faad80f2d69cb8856e8de6e892646645372d0e4da576355c"},"schema_version":"1.0","source":{"id":"1507.06098","kind":"arxiv","version":2}},"canonical_sha256":"f06eb41bbd87f3e7511165248256fb7f538d886fb6426a25f4ab451d8229c124","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f06eb41bbd87f3e7511165248256fb7f538d886fb6426a25f4ab451d8229c124","first_computed_at":"2026-05-18T01:12:40.535544Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:40.535544Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Hd7/WX67lzlgUMR5YWh00qEVoWb3CsYJsw8GNweKxwdxObcC3JOI/HVhiVv9eT954nl4mV4gXYoaTU/WRuTtAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:40.535876Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.06098","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca4174334a3295f61c10c7d9c4bd54ad88b78c9842bfa7600791d4eb6a415b1e","sha256:d71ac89aa9ab09b5cf57d6de6050fa91f364ce6c20b4753085c3941e5f6346b4"],"state_sha256":"ce250b7cde662fe62e7518ade959ee2ff85728ff4f33826be047139485bb0d2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"weNTQTbnU+yTs/mr6UhKeTXriQOF7EokDtYXFVRBqfQGabO5Su1B3IugtF/4GqvDTSZFqCY2BAwe7lzdaFWeAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T12:56:08.042086Z","bundle_sha256":"cdd1bb0323260d29a40ace45be8878d8f6d01a6c8e77f90782399cb7dbfbaaff"}}