{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:SHRD2YAUIU632HX2LFWHRF75TC","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":"e11581b91fd5bae0d7f3b551be20ee3f45bfc8fa472ec07cc2deaa94e78e6664","cross_cats_sorted":["math.QA","q-alg"],"license":"","primary_cat":"hep-th","submitted_at":"1996-10-11T17:48:16Z","title_canon_sha256":"b1ec6d63db0b07ba577cf1b99080e2355763196287c0da5142c1c1144009c371"},"schema_version":"1.0","source":{"id":"hep-th/9610087","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/9610087","created_at":"2026-05-18T01:06:00Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/9610087v1","created_at":"2026-05-18T01:06:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/9610087","created_at":"2026-05-18T01:06:00Z"},{"alias_kind":"pith_short_12","alias_value":"SHRD2YAUIU63","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_16","alias_value":"SHRD2YAUIU632HX2","created_at":"2026-05-18T12:25:48Z"},{"alias_kind":"pith_short_8","alias_value":"SHRD2YAU","created_at":"2026-05-18T12:25:48Z"}],"graph_snapshots":[{"event_id":"sha256:30166095ad256b5d71a01663445dc66e3d4febe8dac01aa592c3f94971862a21","target":"graph","created_at":"2026-05-18T01:06:00Z","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 deformed $q$-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra of a $q$-deformed boson. The limit of this algebra when $q$ is a $n$-th root of unity is also studied in detail. By means of a chain rule expansion, the left and right derivatives are identified with the charge $Q$ and covariant derivative $D$ encountered in ordinary/fractional supersymmetry and this leads to new results for these operators. A generalized Be","authors_text":"A.J. Macfarlane, J.A. de Azc\\'arraga, J.C. P\\'erez Bueno, R.S. Dunne","cross_cats":["math.QA","q-alg"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"1996-10-11T17:48:16Z","title":"Geometrical foundations of fractional supersymmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/9610087","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:e474692aaded99d726e3a02f97116f9e22c39b8a7eb25539f292aee12fd902fe","target":"record","created_at":"2026-05-18T01:06:00Z","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":"e11581b91fd5bae0d7f3b551be20ee3f45bfc8fa472ec07cc2deaa94e78e6664","cross_cats_sorted":["math.QA","q-alg"],"license":"","primary_cat":"hep-th","submitted_at":"1996-10-11T17:48:16Z","title_canon_sha256":"b1ec6d63db0b07ba577cf1b99080e2355763196287c0da5142c1c1144009c371"},"schema_version":"1.0","source":{"id":"hep-th/9610087","kind":"arxiv","version":1}},"canonical_sha256":"91e23d6014453dbd1efa596c7897fd98be9d5ffa32be47d9df82e3e3999c8b5a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91e23d6014453dbd1efa596c7897fd98be9d5ffa32be47d9df82e3e3999c8b5a","first_computed_at":"2026-05-18T01:06:00.473651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:00.473651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c+/yBtMcrIQ9IvjJNIz2YGoqpRI1aK9eI//nHD/LEY8lJuEgTnab+fZ72CkoXHlvf8YHXgPZouvmrVK9w0EgBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:00.474105Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/9610087","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e474692aaded99d726e3a02f97116f9e22c39b8a7eb25539f292aee12fd902fe","sha256:30166095ad256b5d71a01663445dc66e3d4febe8dac01aa592c3f94971862a21"],"state_sha256":"09c3bf1de1017701dc8e5b1b007169ec63b1866881e628734bb2b31b96a66d51"}