{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2001:KNIVEYYPD2UHDGA3NN4BEZVCED","short_pith_number":"pith:KNIVEYYP","canonical_record":{"source":{"id":"math/0112248","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2001-12-21T16:11:41Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"537373518f7f601ac7532921c34f49303c69eb1c78ef3c99fc8b79e0c023fee7","abstract_canon_sha256":"00f17d4214f0c79d9eec9c16ec26f64d72fe36134c1e59783aacb7912ca50882"},"schema_version":"1.0"},"canonical_sha256":"535152630f1ea871981b6b781266a220dd5d4525298fbdd80c38f2a1f11dcb2e","source":{"kind":"arxiv","id":"math/0112248","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0112248","created_at":"2026-05-18T00:37:07Z"},{"alias_kind":"arxiv_version","alias_value":"math/0112248v1","created_at":"2026-05-18T00:37:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0112248","created_at":"2026-05-18T00:37:07Z"},{"alias_kind":"pith_short_12","alias_value":"KNIVEYYPD2UH","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"KNIVEYYPD2UHDGA3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"KNIVEYYP","created_at":"2026-05-18T12:25:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2001:KNIVEYYPD2UHDGA3NN4BEZVCED","target":"record","payload":{"canonical_record":{"source":{"id":"math/0112248","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.QA","submitted_at":"2001-12-21T16:11:41Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"537373518f7f601ac7532921c34f49303c69eb1c78ef3c99fc8b79e0c023fee7","abstract_canon_sha256":"00f17d4214f0c79d9eec9c16ec26f64d72fe36134c1e59783aacb7912ca50882"},"schema_version":"1.0"},"canonical_sha256":"535152630f1ea871981b6b781266a220dd5d4525298fbdd80c38f2a1f11dcb2e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:37:07.967489Z","signature_b64":"R/EzuBnUjBTsWroMchVSIFy3NsCheRnAzWO0FMgFPO+dQCDQ/wLsiaBghoUJ6CJckaPQ1BzKsaM2OaugrYysBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"535152630f1ea871981b6b781266a220dd5d4525298fbdd80c38f2a1f11dcb2e","last_reissued_at":"2026-05-18T00:37:07.966804Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:37:07.966804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0112248","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":"2026-05-18T00:37:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sIaJMZ37DM47KkBh5/ufGYhfTh1kS9BrsjxCyK2SAt/r7o8s6+9CQw0b9eHXhr+ZhcfPeK3TbWr6EP3g7Lx7AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:49:20.144173Z"},"content_sha256":"e8d5b5fc808a5ae5f0de964077a6cbdfc805b46a22996980c91b2afa6fa25bd5","schema_version":"1.0","event_id":"sha256:e8d5b5fc808a5ae5f0de964077a6cbdfc805b46a22996980c91b2afa6fa25bd5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2001:KNIVEYYPD2UHDGA3NN4BEZVCED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decoupling of Translations from Homogeneous Transformations in Inhomogeneous Quantum Groups","license":"","headline":"","cross_cats":["math.GR"],"primary_cat":"math.QA","authors_text":"Gaetano Fiore","submitted_at":"2001-12-21T16:11:41Z","abstract_excerpt":"We briefly report on our result that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then their cross-product is equal to the product of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$. We illustrate its application to the Euclidean quantum groups in $N\\ge 3$ dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0112248","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":""},"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":"2026-05-18T00:37:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1QXFntu/Xl884IAD7QnI4cXrCaa2dzXpP09/FlxUIgIDKjeJ+GnONTM5CATTu+I/nnFLTTmdYCnhCSfrersMDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T04:49:20.144888Z"},"content_sha256":"cbb30b4214815af33ced6dc4d4ecc580238302eff4a7011853f9535d3143c5d9","schema_version":"1.0","event_id":"sha256:cbb30b4214815af33ced6dc4d4ecc580238302eff4a7011853f9535d3143c5d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KNIVEYYPD2UHDGA3NN4BEZVCED/bundle.json","state_url":"https://pith.science/pith/KNIVEYYPD2UHDGA3NN4BEZVCED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KNIVEYYPD2UHDGA3NN4BEZVCED/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":"2026-06-09T04:49:20Z","links":{"resolver":"https://pith.science/pith/KNIVEYYPD2UHDGA3NN4BEZVCED","bundle":"https://pith.science/pith/KNIVEYYPD2UHDGA3NN4BEZVCED/bundle.json","state":"https://pith.science/pith/KNIVEYYPD2UHDGA3NN4BEZVCED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KNIVEYYPD2UHDGA3NN4BEZVCED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2001:KNIVEYYPD2UHDGA3NN4BEZVCED","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":"00f17d4214f0c79d9eec9c16ec26f64d72fe36134c1e59783aacb7912ca50882","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.QA","submitted_at":"2001-12-21T16:11:41Z","title_canon_sha256":"537373518f7f601ac7532921c34f49303c69eb1c78ef3c99fc8b79e0c023fee7"},"schema_version":"1.0","source":{"id":"math/0112248","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0112248","created_at":"2026-05-18T00:37:07Z"},{"alias_kind":"arxiv_version","alias_value":"math/0112248v1","created_at":"2026-05-18T00:37:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0112248","created_at":"2026-05-18T00:37:07Z"},{"alias_kind":"pith_short_12","alias_value":"KNIVEYYPD2UH","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_16","alias_value":"KNIVEYYPD2UHDGA3","created_at":"2026-05-18T12:25:50Z"},{"alias_kind":"pith_short_8","alias_value":"KNIVEYYP","created_at":"2026-05-18T12:25:50Z"}],"graph_snapshots":[{"event_id":"sha256:cbb30b4214815af33ced6dc4d4ecc580238302eff4a7011853f9535d3143c5d9","target":"graph","created_at":"2026-05-18T00:37:07Z","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":"We briefly report on our result that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then their cross-product is equal to the product of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$. We illustrate its application to the Euclidean quantum groups in $N\\ge 3$ dimensions.","authors_text":"Gaetano Fiore","cross_cats":["math.GR"],"headline":"","license":"","primary_cat":"math.QA","submitted_at":"2001-12-21T16:11:41Z","title":"Decoupling of Translations from Homogeneous Transformations in Inhomogeneous Quantum Groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0112248","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:e8d5b5fc808a5ae5f0de964077a6cbdfc805b46a22996980c91b2afa6fa25bd5","target":"record","created_at":"2026-05-18T00:37:07Z","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":"00f17d4214f0c79d9eec9c16ec26f64d72fe36134c1e59783aacb7912ca50882","cross_cats_sorted":["math.GR"],"license":"","primary_cat":"math.QA","submitted_at":"2001-12-21T16:11:41Z","title_canon_sha256":"537373518f7f601ac7532921c34f49303c69eb1c78ef3c99fc8b79e0c023fee7"},"schema_version":"1.0","source":{"id":"math/0112248","kind":"arxiv","version":1}},"canonical_sha256":"535152630f1ea871981b6b781266a220dd5d4525298fbdd80c38f2a1f11dcb2e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"535152630f1ea871981b6b781266a220dd5d4525298fbdd80c38f2a1f11dcb2e","first_computed_at":"2026-05-18T00:37:07.966804Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:07.966804Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R/EzuBnUjBTsWroMchVSIFy3NsCheRnAzWO0FMgFPO+dQCDQ/wLsiaBghoUJ6CJckaPQ1BzKsaM2OaugrYysBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:07.967489Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0112248","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e8d5b5fc808a5ae5f0de964077a6cbdfc805b46a22996980c91b2afa6fa25bd5","sha256:cbb30b4214815af33ced6dc4d4ecc580238302eff4a7011853f9535d3143c5d9"],"state_sha256":"b383ec7b4e3b86fbdbf91a6fc8bfa4f123ef630011132ccbb189f24788b157df"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q3ddmJGH3H9tOGeP4Neev/ENbM3GH1c2fz3Dh6tkV4iDvlCmGiawWQGiMhGQGqVKlEe/e/Ch/K/opnBSy8aQDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T04:49:20.149384Z","bundle_sha256":"54b68f51aedf4f527f4645d0c7e43bd31588075cf9ba7bcd0f1ab2116b294745"}}