{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:C3RGKM4D7LNLLXMWFGRMSYIG2A","short_pith_number":"pith:C3RGKM4D","canonical_record":{"source":{"id":"1604.00199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-04-01T10:50:24Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9693e45667c3c3ef2e269fd18e31b19a72bacca31a3a7d33bfc85daa540a5e2b","abstract_canon_sha256":"dccee8748abde65dc628ec17c5096aa546b15d71c79dadf0f83144249e313132"},"schema_version":"1.0"},"canonical_sha256":"16e2653383fadab5dd9629a2c96106d0239cb01856125ff13aca3afb3d2604b0","source":{"kind":"arxiv","id":"1604.00199","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00199","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00199v2","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00199","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"pith_short_12","alias_value":"C3RGKM4D7LNL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C3RGKM4D7LNLLXMW","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C3RGKM4D","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:C3RGKM4D7LNLLXMWFGRMSYIG2A","target":"record","payload":{"canonical_record":{"source":{"id":"1604.00199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-04-01T10:50:24Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9693e45667c3c3ef2e269fd18e31b19a72bacca31a3a7d33bfc85daa540a5e2b","abstract_canon_sha256":"dccee8748abde65dc628ec17c5096aa546b15d71c79dadf0f83144249e313132"},"schema_version":"1.0"},"canonical_sha256":"16e2653383fadab5dd9629a2c96106d0239cb01856125ff13aca3afb3d2604b0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:07:50.812443Z","signature_b64":"ypD1kRCrigGLd0/Ud4jVfHiYJ0WwFp95rraZRLnHxAOFPUCkkvBbcXjVe6wGdJq5ezI1yWPivOSnbCR1h3K/CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16e2653383fadab5dd9629a2c96106d0239cb01856125ff13aca3afb3d2604b0","last_reissued_at":"2026-05-18T01:07:50.812029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:07:50.812029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.00199","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":"2026-05-18T01:07:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d0b8nJCd1gfk1qKUwlmCv0A14PaG42+HKHVOFJ8ALB2Oyrt39eoRd0r/9faPPaTM8QB1KUw74mpA2TFiWOLaCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:21:57.425791Z"},"content_sha256":"969eca27e9556dd8c23e6b53f0a3d5e7b09bfe7302c2c063cbc31475342912f6","schema_version":"1.0","event_id":"sha256:969eca27e9556dd8c23e6b53f0a3d5e7b09bfe7302c2c063cbc31475342912f6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:C3RGKM4D7LNLLXMWFGRMSYIG2A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Nodal Cubic is a Quantum Homogeneous Space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.QA","authors_text":"Angela Tabiri, Ulrich Kraehmer","submitted_at":"2016-04-01T10:50:24Z","abstract_excerpt":"The cusp was recently shown to admit the structure of a quantum homogeneous space, that is, its coordinate ring $B$ can be embedded as a right coideal subalgebra into a Hopf algebra $A$ such that $A$ is faithfully flat as a $B$-module. In the present article such a Hopf algebra $A$ is constructed for the coordinate ring $B$ of the nodal cubic, thus further motivating the question which affine varieties are quantum homogeneous spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00199","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":"2026-05-18T01:07:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yl1k5QQZ9AL15B8UiKD94nW2xcuibuwWYWdH8aNnghxUIjWclxHVPYVOPptL+s6K29ylBm45SUkeKzfV1XnaBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:21:57.426135Z"},"content_sha256":"909187598a3e2a8207bc2350ac34c204ae54758f4ea5c5933104b38bcd5b513b","schema_version":"1.0","event_id":"sha256:909187598a3e2a8207bc2350ac34c204ae54758f4ea5c5933104b38bcd5b513b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C3RGKM4D7LNLLXMWFGRMSYIG2A/bundle.json","state_url":"https://pith.science/pith/C3RGKM4D7LNLLXMWFGRMSYIG2A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C3RGKM4D7LNLLXMWFGRMSYIG2A/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":"2026-05-28T03:21:57Z","links":{"resolver":"https://pith.science/pith/C3RGKM4D7LNLLXMWFGRMSYIG2A","bundle":"https://pith.science/pith/C3RGKM4D7LNLLXMWFGRMSYIG2A/bundle.json","state":"https://pith.science/pith/C3RGKM4D7LNLLXMWFGRMSYIG2A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C3RGKM4D7LNLLXMWFGRMSYIG2A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:C3RGKM4D7LNLLXMWFGRMSYIG2A","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":"dccee8748abde65dc628ec17c5096aa546b15d71c79dadf0f83144249e313132","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-04-01T10:50:24Z","title_canon_sha256":"9693e45667c3c3ef2e269fd18e31b19a72bacca31a3a7d33bfc85daa540a5e2b"},"schema_version":"1.0","source":{"id":"1604.00199","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.00199","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"arxiv_version","alias_value":"1604.00199v2","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.00199","created_at":"2026-05-18T01:07:50Z"},{"alias_kind":"pith_short_12","alias_value":"C3RGKM4D7LNL","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"C3RGKM4D7LNLLXMW","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"C3RGKM4D","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:909187598a3e2a8207bc2350ac34c204ae54758f4ea5c5933104b38bcd5b513b","target":"graph","created_at":"2026-05-18T01:07:50Z","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":"The cusp was recently shown to admit the structure of a quantum homogeneous space, that is, its coordinate ring $B$ can be embedded as a right coideal subalgebra into a Hopf algebra $A$ such that $A$ is faithfully flat as a $B$-module. In the present article such a Hopf algebra $A$ is constructed for the coordinate ring $B$ of the nodal cubic, thus further motivating the question which affine varieties are quantum homogeneous spaces.","authors_text":"Angela Tabiri, Ulrich Kraehmer","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-04-01T10:50:24Z","title":"The Nodal Cubic is a Quantum Homogeneous Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.00199","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":"sha256:969eca27e9556dd8c23e6b53f0a3d5e7b09bfe7302c2c063cbc31475342912f6","target":"record","created_at":"2026-05-18T01:07:50Z","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":"dccee8748abde65dc628ec17c5096aa546b15d71c79dadf0f83144249e313132","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2016-04-01T10:50:24Z","title_canon_sha256":"9693e45667c3c3ef2e269fd18e31b19a72bacca31a3a7d33bfc85daa540a5e2b"},"schema_version":"1.0","source":{"id":"1604.00199","kind":"arxiv","version":2}},"canonical_sha256":"16e2653383fadab5dd9629a2c96106d0239cb01856125ff13aca3afb3d2604b0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16e2653383fadab5dd9629a2c96106d0239cb01856125ff13aca3afb3d2604b0","first_computed_at":"2026-05-18T01:07:50.812029Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:50.812029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ypD1kRCrigGLd0/Ud4jVfHiYJ0WwFp95rraZRLnHxAOFPUCkkvBbcXjVe6wGdJq5ezI1yWPivOSnbCR1h3K/CA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:50.812443Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.00199","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:969eca27e9556dd8c23e6b53f0a3d5e7b09bfe7302c2c063cbc31475342912f6","sha256:909187598a3e2a8207bc2350ac34c204ae54758f4ea5c5933104b38bcd5b513b"],"state_sha256":"edc0de98fc72f4077664e03edd7b4a87362cac5a8bd69c7b258fddab929c8d42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/4mLveBOuTrs6NRVJQq23KCAfc7qTNi8hz5/AL38BxFHsiqF8IOi8hXL/dLeqp0hGH0FFEIzuEECJMQNT4VKAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:21:57.428091Z","bundle_sha256":"40e1273fd1b7adfce0b11f0008b253f4a6b9b3cc7b519bef9c06abc617413f29"}}