{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:E77FYVZFEJYJSMM3YGGZV6CN2S","short_pith_number":"pith:E77FYVZF","canonical_record":{"source":{"id":"math/0303019","kind":"arxiv","version":9},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2003-03-03T11:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"faac96aeadc205704cd870134bef014cb61786b37758605c9c5df539659cdbdf","abstract_canon_sha256":"2793044058def94199519e8a9fe56c65d09990a28e5d3def6405512669a8158c"},"schema_version":"1.0"},"canonical_sha256":"27fe5c5725227099319bc18d9af84dd482537ab6299740717dc92f11b684f0f8","source":{"kind":"arxiv","id":"math/0303019","version":9},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0303019","created_at":"2026-05-18T03:43:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0303019v9","created_at":"2026-05-18T03:43:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0303019","created_at":"2026-05-18T03:43:53Z"},{"alias_kind":"pith_short_12","alias_value":"E77FYVZFEJYJ","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"E77FYVZFEJYJSMM3","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"E77FYVZF","created_at":"2026-05-18T12:25:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:E77FYVZFEJYJSMM3YGGZV6CN2S","target":"record","payload":{"canonical_record":{"source":{"id":"math/0303019","kind":"arxiv","version":9},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2003-03-03T11:00:31Z","cross_cats_sorted":[],"title_canon_sha256":"faac96aeadc205704cd870134bef014cb61786b37758605c9c5df539659cdbdf","abstract_canon_sha256":"2793044058def94199519e8a9fe56c65d09990a28e5d3def6405512669a8158c"},"schema_version":"1.0"},"canonical_sha256":"27fe5c5725227099319bc18d9af84dd482537ab6299740717dc92f11b684f0f8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:43:53.208327Z","signature_b64":"A7HfmzJaBqSif4+Mf/77fbQmScbbMKa3KvMzz2HRKdC15ELn2JCayJ7mAi315AqKfw88/knX5Y85qxHMxrcUAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"27fe5c5725227099319bc18d9af84dd482537ab6299740717dc92f11b684f0f8","last_reissued_at":"2026-05-18T03:43:53.207773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:43:53.207773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0303019","source_version":9,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:43:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QLEH2W3LO2fnHfdAxQzs6XkxlREsiTdqvvuRgLkTl8pjJ6nl9vJ40WtrheT+oDSlvE1G9DOvFX3dFQe3m94MBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T13:43:39.386374Z"},"content_sha256":"7bab03be6e1593c817dda1da5da852d0cfa1e32b36295a5bf1383354a9291997","schema_version":"1.0","event_id":"sha256:7bab03be6e1593c817dda1da5da852d0cfa1e32b36295a5bf1383354a9291997"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:E77FYVZFEJYJSMM3YGGZV6CN2S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The global quantum duality principle: theory, examples, and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Fabio Gavarini (Universita` di Roma \"Tor Vergata\")","submitted_at":"2003-03-03T11:00:31Z","abstract_excerpt":"Let R be an integral domain, h non-zero in R such that R/hR is a field, and HA the category of torsionless (or flat) Hopf algebras over R. We call any H in HA \"quantized function algebra\" (=QFA), resp. \"quantized (restricted) universal enveloping algebra\" (=QrUEA), at h if H/hH is the function algebra of a connected Poisson group, resp. the (restricted, if R/hR has positive characteristic) universal enveloping algebra of a (restricted) Lie bialgebra.\n  We establish an \"inner\" Galois' correspondence on HA, via the definition of two endofunctors, ()^\\vee and ()', of HA such that:\n  (a) the image"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303019","kind":"arxiv","version":9},"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":"2026-05-18T03:43:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OKdOYiR/Tv19jilTod/PWWIfPjrcgfLDJA7D9Z/VIThPqBL+J4T43KCWE9xATrmvH3DByRlTIoXxJeE0aiAeAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T13:43:39.387265Z"},"content_sha256":"1a63a374fed99ea36987cdc51950091d9a17750b414bb788f929f8afa787b103","schema_version":"1.0","event_id":"sha256:1a63a374fed99ea36987cdc51950091d9a17750b414bb788f929f8afa787b103"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E77FYVZFEJYJSMM3YGGZV6CN2S/bundle.json","state_url":"https://pith.science/pith/E77FYVZFEJYJSMM3YGGZV6CN2S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E77FYVZFEJYJSMM3YGGZV6CN2S/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":"2026-08-04T13:43:39Z","links":{"resolver":"https://pith.science/pith/E77FYVZFEJYJSMM3YGGZV6CN2S","bundle":"https://pith.science/pith/E77FYVZFEJYJSMM3YGGZV6CN2S/bundle.json","state":"https://pith.science/pith/E77FYVZFEJYJSMM3YGGZV6CN2S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E77FYVZFEJYJSMM3YGGZV6CN2S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:E77FYVZFEJYJSMM3YGGZV6CN2S","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":"2793044058def94199519e8a9fe56c65d09990a28e5d3def6405512669a8158c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2003-03-03T11:00:31Z","title_canon_sha256":"faac96aeadc205704cd870134bef014cb61786b37758605c9c5df539659cdbdf"},"schema_version":"1.0","source":{"id":"math/0303019","kind":"arxiv","version":9}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0303019","created_at":"2026-05-18T03:43:53Z"},{"alias_kind":"arxiv_version","alias_value":"math/0303019v9","created_at":"2026-05-18T03:43:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0303019","created_at":"2026-05-18T03:43:53Z"},{"alias_kind":"pith_short_12","alias_value":"E77FYVZFEJYJ","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"E77FYVZFEJYJSMM3","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"E77FYVZF","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:1a63a374fed99ea36987cdc51950091d9a17750b414bb788f929f8afa787b103","target":"graph","created_at":"2026-05-18T03:43:53Z","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":"Let R be an integral domain, h non-zero in R such that R/hR is a field, and HA the category of torsionless (or flat) Hopf algebras over R. We call any H in HA \"quantized function algebra\" (=QFA), resp. \"quantized (restricted) universal enveloping algebra\" (=QrUEA), at h if H/hH is the function algebra of a connected Poisson group, resp. the (restricted, if R/hR has positive characteristic) universal enveloping algebra of a (restricted) Lie bialgebra.\n  We establish an \"inner\" Galois' correspondence on HA, via the definition of two endofunctors, ()^\\vee and ()', of HA such that:\n  (a) the image","authors_text":"Fabio Gavarini (Universita` di Roma \"Tor Vergata\")","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2003-03-03T11:00:31Z","title":"The global quantum duality principle: theory, examples, and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0303019","kind":"arxiv","version":9},"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":"sha256:7bab03be6e1593c817dda1da5da852d0cfa1e32b36295a5bf1383354a9291997","target":"record","created_at":"2026-05-18T03:43:53Z","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":"2793044058def94199519e8a9fe56c65d09990a28e5d3def6405512669a8158c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2003-03-03T11:00:31Z","title_canon_sha256":"faac96aeadc205704cd870134bef014cb61786b37758605c9c5df539659cdbdf"},"schema_version":"1.0","source":{"id":"math/0303019","kind":"arxiv","version":9}},"canonical_sha256":"27fe5c5725227099319bc18d9af84dd482537ab6299740717dc92f11b684f0f8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27fe5c5725227099319bc18d9af84dd482537ab6299740717dc92f11b684f0f8","first_computed_at":"2026-05-18T03:43:53.207773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:43:53.207773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A7HfmzJaBqSif4+Mf/77fbQmScbbMKa3KvMzz2HRKdC15ELn2JCayJ7mAi315AqKfw88/knX5Y85qxHMxrcUAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:43:53.208327Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0303019","source_kind":"arxiv","source_version":9}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bab03be6e1593c817dda1da5da852d0cfa1e32b36295a5bf1383354a9291997","sha256:1a63a374fed99ea36987cdc51950091d9a17750b414bb788f929f8afa787b103"],"state_sha256":"3c11a04130a0857dbbf7b17726cb280a6bc0be5246160b3aeb891f5897aea584"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"35PZBGG6jQ2yLO7uvSD9C4OEuIJoGjXATVNNrCic3glg4jUODbWVPVhaMzgP90Seieb9SnfpZJrQAu2hwKWsDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T13:43:39.394713Z","bundle_sha256":"ae9f031d23e44540476099942fc7cac5adf188ee2ed52ed1348167ed34a70a22"}}