{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:RCBZ7LNCTKS3APP4DWVL7IYSBT","short_pith_number":"pith:RCBZ7LNC","canonical_record":{"source":{"id":"1908.05248","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-08-14T17:18:55Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"f749423a303c5baf98afc59ee593292d334f8d4dfc500981c48ba6990be78078","abstract_canon_sha256":"497a32660fd3a537c7dc3966e34172205d1f6216e32680cc3cb91c6bd8f64cb8"},"schema_version":"1.0"},"canonical_sha256":"88839fada29aa5b03dfc1daabfa3120ce9c22b677eb5f8d16a2a0ac6abab4019","source":{"kind":"arxiv","id":"1908.05248","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05248","created_at":"2026-07-05T00:54:12Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05248v1","created_at":"2026-07-05T00:54:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05248","created_at":"2026-07-05T00:54:12Z"},{"alias_kind":"pith_short_12","alias_value":"RCBZ7LNCTKS3","created_at":"2026-07-05T00:54:12Z"},{"alias_kind":"pith_short_16","alias_value":"RCBZ7LNCTKS3APP4","created_at":"2026-07-05T00:54:12Z"},{"alias_kind":"pith_short_8","alias_value":"RCBZ7LNC","created_at":"2026-07-05T00:54:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:RCBZ7LNCTKS3APP4DWVL7IYSBT","target":"record","payload":{"canonical_record":{"source":{"id":"1908.05248","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-08-14T17:18:55Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"f749423a303c5baf98afc59ee593292d334f8d4dfc500981c48ba6990be78078","abstract_canon_sha256":"497a32660fd3a537c7dc3966e34172205d1f6216e32680cc3cb91c6bd8f64cb8"},"schema_version":"1.0"},"canonical_sha256":"88839fada29aa5b03dfc1daabfa3120ce9c22b677eb5f8d16a2a0ac6abab4019","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:54:12.136844Z","signature_b64":"3xLrGJMChkjZDGEheFSpfT4yJU+4DCbOWCrMn5aXeb0wQ28NiJLQ3Vpwo1oAoryb4N+qvzKK5KO+9Yx/0EO5Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"88839fada29aa5b03dfc1daabfa3120ce9c22b677eb5f8d16a2a0ac6abab4019","last_reissued_at":"2026-07-05T00:54:12.136471Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:54:12.136471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.05248","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":"2026-07-05T00:54:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wpxX0Q4vWJgmyMY/bKb+NZcec18fYhwAdTfW/WArwW99ndG0LmELCCuxjg8bH8bl8yL8FxDz6RnOoolujYSRDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:18:50.164232Z"},"content_sha256":"5c78fb19002ee8ebf18d8622d124b44677e1cf543ca90724ff9f6d41b1061458","schema_version":"1.0","event_id":"sha256:5c78fb19002ee8ebf18d8622d124b44677e1cf543ca90724ff9f6d41b1061458"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:RCBZ7LNCTKS3APP4DWVL7IYSBT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Actions of quantum linear spaces on quantum algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RA","authors_text":"Jason Gaddis, Zachary Cline","submitted_at":"2019-08-14T17:18:55Z","abstract_excerpt":"We study actions of bosonizations of quantum linear spaces on quantum algebras. Under mild conditions, we classify actions on quantum affine spaces and quantum matrix algebras. In the former case, it is shown that all actions of generalized Taft algebras are trivial extensions of actions on quantum planes. In both cases we achieve bounds on the rank of the bosonization acting on the algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05248","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/1908.05248/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":"2026-07-05T00:54:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GXu6Xq4XRiv2g5PFpRR4c+2H9KPNN/4LRfxOATZDVtbfo2rC/wDWgST+14IIlfTn4IgN0h8HjiZNq/00aeZBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-07T08:18:50.164638Z"},"content_sha256":"72a4ed229f770a22882cb5d3b62b25d465986f3fdb38f1df79e811785f3a2d73","schema_version":"1.0","event_id":"sha256:72a4ed229f770a22882cb5d3b62b25d465986f3fdb38f1df79e811785f3a2d73"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RCBZ7LNCTKS3APP4DWVL7IYSBT/bundle.json","state_url":"https://pith.science/pith/RCBZ7LNCTKS3APP4DWVL7IYSBT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RCBZ7LNCTKS3APP4DWVL7IYSBT/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":"2026-07-07T08:18:50Z","links":{"resolver":"https://pith.science/pith/RCBZ7LNCTKS3APP4DWVL7IYSBT","bundle":"https://pith.science/pith/RCBZ7LNCTKS3APP4DWVL7IYSBT/bundle.json","state":"https://pith.science/pith/RCBZ7LNCTKS3APP4DWVL7IYSBT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RCBZ7LNCTKS3APP4DWVL7IYSBT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:RCBZ7LNCTKS3APP4DWVL7IYSBT","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":"497a32660fd3a537c7dc3966e34172205d1f6216e32680cc3cb91c6bd8f64cb8","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-08-14T17:18:55Z","title_canon_sha256":"f749423a303c5baf98afc59ee593292d334f8d4dfc500981c48ba6990be78078"},"schema_version":"1.0","source":{"id":"1908.05248","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.05248","created_at":"2026-07-05T00:54:12Z"},{"alias_kind":"arxiv_version","alias_value":"1908.05248v1","created_at":"2026-07-05T00:54:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.05248","created_at":"2026-07-05T00:54:12Z"},{"alias_kind":"pith_short_12","alias_value":"RCBZ7LNCTKS3","created_at":"2026-07-05T00:54:12Z"},{"alias_kind":"pith_short_16","alias_value":"RCBZ7LNCTKS3APP4","created_at":"2026-07-05T00:54:12Z"},{"alias_kind":"pith_short_8","alias_value":"RCBZ7LNC","created_at":"2026-07-05T00:54:12Z"}],"graph_snapshots":[{"event_id":"sha256:72a4ed229f770a22882cb5d3b62b25d465986f3fdb38f1df79e811785f3a2d73","target":"graph","created_at":"2026-07-05T00:54:12Z","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/1908.05248/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study actions of bosonizations of quantum linear spaces on quantum algebras. Under mild conditions, we classify actions on quantum affine spaces and quantum matrix algebras. In the former case, it is shown that all actions of generalized Taft algebras are trivial extensions of actions on quantum planes. In both cases we achieve bounds on the rank of the bosonization acting on the algebra.","authors_text":"Jason Gaddis, Zachary Cline","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-08-14T17:18:55Z","title":"Actions of quantum linear spaces on quantum algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.05248","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":"sha256:5c78fb19002ee8ebf18d8622d124b44677e1cf543ca90724ff9f6d41b1061458","target":"record","created_at":"2026-07-05T00:54:12Z","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":"497a32660fd3a537c7dc3966e34172205d1f6216e32680cc3cb91c6bd8f64cb8","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2019-08-14T17:18:55Z","title_canon_sha256":"f749423a303c5baf98afc59ee593292d334f8d4dfc500981c48ba6990be78078"},"schema_version":"1.0","source":{"id":"1908.05248","kind":"arxiv","version":1}},"canonical_sha256":"88839fada29aa5b03dfc1daabfa3120ce9c22b677eb5f8d16a2a0ac6abab4019","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"88839fada29aa5b03dfc1daabfa3120ce9c22b677eb5f8d16a2a0ac6abab4019","first_computed_at":"2026-07-05T00:54:12.136471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:54:12.136471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3xLrGJMChkjZDGEheFSpfT4yJU+4DCbOWCrMn5aXeb0wQ28NiJLQ3Vpwo1oAoryb4N+qvzKK5KO+9Yx/0EO5Dw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:54:12.136844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.05248","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5c78fb19002ee8ebf18d8622d124b44677e1cf543ca90724ff9f6d41b1061458","sha256:72a4ed229f770a22882cb5d3b62b25d465986f3fdb38f1df79e811785f3a2d73"],"state_sha256":"e48c3950d759b9ae2a8d2271995d78bef9fd5b29f7c342158beed2c29587a370"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuaHsFFymacgMg2csEUi1d7/ZNzIr7tf/S43tcx5EBkjix+/7ZzHpU/Gf6nylClL6436+KmU8AyUHbaLEJGTDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-07T08:18:50.166756Z","bundle_sha256":"c45547577ecc1498c043b3fcc6c53d18d7557cd5a4e4ffab81218250a584cc86"}}