{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ACM6DYZD6FYK3YT5DOYXDEWOPW","short_pith_number":"pith:ACM6DYZD","canonical_record":{"source":{"id":"1301.1665","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-01-08T20:33:48Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"3b2e65bf52b3a1c86cd8638a5905ae77be4e17000b81353a491138102c220616","abstract_canon_sha256":"619190bdc855b19b02ad2a1edc9a23ad87e1733c8737e4be32e8bf1139fa34df"},"schema_version":"1.0"},"canonical_sha256":"0099e1e323f170ade27d1bb17192ce7dab286fa24bfe4d46d7afcc96567b9848","source":{"kind":"arxiv","id":"1301.1665","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1665","created_at":"2026-05-18T03:06:51Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1665v2","created_at":"2026-05-18T03:06:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1665","created_at":"2026-05-18T03:06:51Z"},{"alias_kind":"pith_short_12","alias_value":"ACM6DYZD6FYK","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ACM6DYZD6FYK3YT5","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ACM6DYZD","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ACM6DYZD6FYK3YT5DOYXDEWOPW","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1665","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-01-08T20:33:48Z","cross_cats_sorted":["math.RT"],"title_canon_sha256":"3b2e65bf52b3a1c86cd8638a5905ae77be4e17000b81353a491138102c220616","abstract_canon_sha256":"619190bdc855b19b02ad2a1edc9a23ad87e1733c8737e4be32e8bf1139fa34df"},"schema_version":"1.0"},"canonical_sha256":"0099e1e323f170ade27d1bb17192ce7dab286fa24bfe4d46d7afcc96567b9848","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:51.662596Z","signature_b64":"mJ/KgpkpqQ5r+9VfeTFJEH61EEDl/qmCo1hFDubfvR22Bb5B0rhV+3NPkPjoQdVhnzuN1F97iv6lJIpEVpyOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0099e1e323f170ade27d1bb17192ce7dab286fa24bfe4d46d7afcc96567b9848","last_reissued_at":"2026-05-18T03:06:51.661843Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:51.661843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1665","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":"2026-05-18T03:06:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YYP3nbQ8agqsCGbdqmPOAFK7x1lT94nUDdVvVk/5Jd9+GaOuv/oans2pAX1A5TEdSiuoGzYN0cw/6YGknaiSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:39:14.242702Z"},"content_sha256":"22bfbfef7b5e92bcc53b5ec3b1b81d1fa7987832abd77ee9ad79d6b2e95b0463","schema_version":"1.0","event_id":"sha256:22bfbfef7b5e92bcc53b5ec3b1b81d1fa7987832abd77ee9ad79d6b2e95b0463"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ACM6DYZD6FYK3YT5DOYXDEWOPW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Supergroups I. Foundations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"David Hill, Sean Clark, Weiqiang Wang","submitted_at":"2013-01-08T20:33:48Z","abstract_excerpt":"In this part one of a series of papers, we introduce a new version of quantum covering and super groups with no isotropic odd simple root, which is suitable for the studies of integrable modules, integral forms and bar-involution. A quantum covering group involves a quantum parameter q and a sign parameter pi squaring to 1, and it specializes to a quantum supergroup when pi=-1. Following Lusztig, we formulate and establish various structural results of the quantum covering groups, including bilinear form, quasi-R-matrix, Casimir, character formulas for integrable modules, and higher Serre rela"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1665","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":"2026-05-18T03:06:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xL2m6U1QN5qfkwKLp90v7to1EviXul69iomj1duR9GzyEZU3Uad0YZ4BuF4mLzDHbPqC4FrBtgFOEHa3RuqDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:39:14.243043Z"},"content_sha256":"93b11175aacd41a0417dbaf22ce1a3af600f848bc9e54502b7160dfdaa8252be","schema_version":"1.0","event_id":"sha256:93b11175aacd41a0417dbaf22ce1a3af600f848bc9e54502b7160dfdaa8252be"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ACM6DYZD6FYK3YT5DOYXDEWOPW/bundle.json","state_url":"https://pith.science/pith/ACM6DYZD6FYK3YT5DOYXDEWOPW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ACM6DYZD6FYK3YT5DOYXDEWOPW/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":"2026-06-21T19:39:14Z","links":{"resolver":"https://pith.science/pith/ACM6DYZD6FYK3YT5DOYXDEWOPW","bundle":"https://pith.science/pith/ACM6DYZD6FYK3YT5DOYXDEWOPW/bundle.json","state":"https://pith.science/pith/ACM6DYZD6FYK3YT5DOYXDEWOPW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ACM6DYZD6FYK3YT5DOYXDEWOPW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ACM6DYZD6FYK3YT5DOYXDEWOPW","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":"619190bdc855b19b02ad2a1edc9a23ad87e1733c8737e4be32e8bf1139fa34df","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-01-08T20:33:48Z","title_canon_sha256":"3b2e65bf52b3a1c86cd8638a5905ae77be4e17000b81353a491138102c220616"},"schema_version":"1.0","source":{"id":"1301.1665","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1665","created_at":"2026-05-18T03:06:51Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1665v2","created_at":"2026-05-18T03:06:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1665","created_at":"2026-05-18T03:06:51Z"},{"alias_kind":"pith_short_12","alias_value":"ACM6DYZD6FYK","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"ACM6DYZD6FYK3YT5","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"ACM6DYZD","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:93b11175aacd41a0417dbaf22ce1a3af600f848bc9e54502b7160dfdaa8252be","target":"graph","created_at":"2026-05-18T03:06:51Z","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":"In this part one of a series of papers, we introduce a new version of quantum covering and super groups with no isotropic odd simple root, which is suitable for the studies of integrable modules, integral forms and bar-involution. A quantum covering group involves a quantum parameter q and a sign parameter pi squaring to 1, and it specializes to a quantum supergroup when pi=-1. Following Lusztig, we formulate and establish various structural results of the quantum covering groups, including bilinear form, quasi-R-matrix, Casimir, character formulas for integrable modules, and higher Serre rela","authors_text":"David Hill, Sean Clark, Weiqiang Wang","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-01-08T20:33:48Z","title":"Quantum Supergroups I. Foundations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1665","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":"sha256:22bfbfef7b5e92bcc53b5ec3b1b81d1fa7987832abd77ee9ad79d6b2e95b0463","target":"record","created_at":"2026-05-18T03:06:51Z","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":"619190bdc855b19b02ad2a1edc9a23ad87e1733c8737e4be32e8bf1139fa34df","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2013-01-08T20:33:48Z","title_canon_sha256":"3b2e65bf52b3a1c86cd8638a5905ae77be4e17000b81353a491138102c220616"},"schema_version":"1.0","source":{"id":"1301.1665","kind":"arxiv","version":2}},"canonical_sha256":"0099e1e323f170ade27d1bb17192ce7dab286fa24bfe4d46d7afcc96567b9848","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0099e1e323f170ade27d1bb17192ce7dab286fa24bfe4d46d7afcc96567b9848","first_computed_at":"2026-05-18T03:06:51.661843Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:51.661843Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mJ/KgpkpqQ5r+9VfeTFJEH61EEDl/qmCo1hFDubfvR22Bb5B0rhV+3NPkPjoQdVhnzuN1F97iv6lJIpEVpyOBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:51.662596Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1665","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22bfbfef7b5e92bcc53b5ec3b1b81d1fa7987832abd77ee9ad79d6b2e95b0463","sha256:93b11175aacd41a0417dbaf22ce1a3af600f848bc9e54502b7160dfdaa8252be"],"state_sha256":"b0ed9b4c0a21d2396dce7ff9a5229ca59d2ff3f4c4d20325f423a8f31cf55ee2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0fkd2KzmcVABvWFeUXDXee9HPLJxo2+b4ZKdQ+X8q0iNUul2yx/q9OrNaWn1tv8m0cS52lwTKHA95jecqIoBCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T19:39:14.244937Z","bundle_sha256":"fb6edfd8533a6e7c5cc753cf14653e664b5a96cf73ed689c44f0a93108b3ba79"}}