{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:45VTJNBEYVNMT2FVPSJZXJH3PY","short_pith_number":"pith:45VTJNBE","canonical_record":{"source":{"id":"math-ph/0212009","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-12-03T01:38:11Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"df0b465c56bb365472268131eda4c6a8f3a246547174dcf3e1d43dac26a3bcbe","abstract_canon_sha256":"d7344af8bc9cfc16ab2543dd090fb3dbe40e395c29c01f4f087a8fb3de22e64a"},"schema_version":"1.0"},"canonical_sha256":"e76b34b424c55ac9e8b57c939ba4fb7e156f926035f9e31f0dd39e20e0ba81f1","source":{"kind":"arxiv","id":"math-ph/0212009","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0212009","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0212009v1","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0212009","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"45VTJNBEYVNM","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"45VTJNBEYVNMT2FV","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"45VTJNBE","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:45VTJNBEYVNMT2FVPSJZXJH3PY","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0212009","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-12-03T01:38:11Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"df0b465c56bb365472268131eda4c6a8f3a246547174dcf3e1d43dac26a3bcbe","abstract_canon_sha256":"d7344af8bc9cfc16ab2543dd090fb3dbe40e395c29c01f4f087a8fb3de22e64a"},"schema_version":"1.0"},"canonical_sha256":"e76b34b424c55ac9e8b57c939ba4fb7e156f926035f9e31f0dd39e20e0ba81f1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:30:14.962886Z","signature_b64":"Xg6KyARf/oX758CDwTsX8ucveH9qxeujjwd66izphQAfg9Yf4efynvWPKTz4IHYxqaW+AZ6kdD3+SSjU9rf6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e76b34b424c55ac9e8b57c939ba4fb7e156f926035f9e31f0dd39e20e0ba81f1","last_reissued_at":"2026-05-18T04:30:14.962249Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:30:14.962249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0212009","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":"2026-05-18T04:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W8ezBpHh/5ZMQoerFcB1fkdgFFEe2+o9sfs7ak29WErCvVWGr3jswZrEhkTQ3A1J5pDoYBFRFrMHav4rwA2/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:00:50.347126Z"},"content_sha256":"452e961da3074e5d82cc4f153c8fcb5f4a1662f3ff638d9022efb892e5e4364d","schema_version":"1.0","event_id":"sha256:452e961da3074e5d82cc4f153c8fcb5f4a1662f3ff638d9022efb892e5e4364d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:45VTJNBEYVNMT2FVPSJZXJH3PY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Graded Lie Algebra Generating of Parastatistical Algebraic Structure","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Si Cong Jing, Wei Min Yang","submitted_at":"2002-12-03T01:38:11Z","abstract_excerpt":"A new kind of graded Lie algebra (we call it $Z_{2,2}$ graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable bose subspace of the $Z_{2,2}$ graded Lie algebra and using relevant generalized Jacobi identities, we generate the whole algebraic structure of parastatistics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0212009","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":"2026-05-18T04:30:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Owm/kn3mWWzlUOITsG6rvGz9eoOGnyANnv+xeVGvpkzISBBTeSnVCfIShriWD0aH9CvIrOlMaY7Ad3Q/l4MYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T20:00:50.347800Z"},"content_sha256":"908db74ee8b6423497e2431d91e29128724104bdab1c35d44ea95231246bdd4d","schema_version":"1.0","event_id":"sha256:908db74ee8b6423497e2431d91e29128724104bdab1c35d44ea95231246bdd4d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/45VTJNBEYVNMT2FVPSJZXJH3PY/bundle.json","state_url":"https://pith.science/pith/45VTJNBEYVNMT2FVPSJZXJH3PY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/45VTJNBEYVNMT2FVPSJZXJH3PY/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":"2026-05-30T20:00:50Z","links":{"resolver":"https://pith.science/pith/45VTJNBEYVNMT2FVPSJZXJH3PY","bundle":"https://pith.science/pith/45VTJNBEYVNMT2FVPSJZXJH3PY/bundle.json","state":"https://pith.science/pith/45VTJNBEYVNMT2FVPSJZXJH3PY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/45VTJNBEYVNMT2FVPSJZXJH3PY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:45VTJNBEYVNMT2FVPSJZXJH3PY","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":"d7344af8bc9cfc16ab2543dd090fb3dbe40e395c29c01f4f087a8fb3de22e64a","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-12-03T01:38:11Z","title_canon_sha256":"df0b465c56bb365472268131eda4c6a8f3a246547174dcf3e1d43dac26a3bcbe"},"schema_version":"1.0","source":{"id":"math-ph/0212009","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0212009","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0212009v1","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0212009","created_at":"2026-05-18T04:30:14Z"},{"alias_kind":"pith_short_12","alias_value":"45VTJNBEYVNM","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"45VTJNBEYVNMT2FV","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"45VTJNBE","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:908db74ee8b6423497e2431d91e29128724104bdab1c35d44ea95231246bdd4d","target":"graph","created_at":"2026-05-18T04:30:14Z","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":"A new kind of graded Lie algebra (we call it $Z_{2,2}$ graded Lie algebra) is introduced as a framework for formulating parasupersymmetric theories. By choosing suitable bose subspace of the $Z_{2,2}$ graded Lie algebra and using relevant generalized Jacobi identities, we generate the whole algebraic structure of parastatistics.","authors_text":"Si Cong Jing, Wei Min Yang","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-12-03T01:38:11Z","title":"Graded Lie Algebra Generating of Parastatistical Algebraic Structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0212009","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":"sha256:452e961da3074e5d82cc4f153c8fcb5f4a1662f3ff638d9022efb892e5e4364d","target":"record","created_at":"2026-05-18T04:30:14Z","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":"d7344af8bc9cfc16ab2543dd090fb3dbe40e395c29c01f4f087a8fb3de22e64a","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-12-03T01:38:11Z","title_canon_sha256":"df0b465c56bb365472268131eda4c6a8f3a246547174dcf3e1d43dac26a3bcbe"},"schema_version":"1.0","source":{"id":"math-ph/0212009","kind":"arxiv","version":1}},"canonical_sha256":"e76b34b424c55ac9e8b57c939ba4fb7e156f926035f9e31f0dd39e20e0ba81f1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e76b34b424c55ac9e8b57c939ba4fb7e156f926035f9e31f0dd39e20e0ba81f1","first_computed_at":"2026-05-18T04:30:14.962249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:30:14.962249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xg6KyARf/oX758CDwTsX8ucveH9qxeujjwd66izphQAfg9Yf4efynvWPKTz4IHYxqaW+AZ6kdD3+SSjU9rf6Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:30:14.962886Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0212009","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:452e961da3074e5d82cc4f153c8fcb5f4a1662f3ff638d9022efb892e5e4364d","sha256:908db74ee8b6423497e2431d91e29128724104bdab1c35d44ea95231246bdd4d"],"state_sha256":"eefa1b498130c653395cf34ffadcf55b91ce2f8ec459c16d64af38fe97a81346"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M2JcFdJf6fBjVxRt/sMbtXRHBxYOeC+aT5knHXqVPtuTJQe3gjYQkMncVJG9Lccgxq3WLSpHqFTY+9ryjR0oBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T20:00:50.351202Z","bundle_sha256":"4e43754e21bd0aa46ea5647f25e52e77b01489d4949701128e85a7573ba6aeac"}}