{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7E5XTL73JECA6I5T5LUP5RY3LE","short_pith_number":"pith:7E5XTL73","canonical_record":{"source":{"id":"1204.5842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-26T06:44:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"dd4d59c5d7cfb33226721187e20954a828bd62969a6d3299ccaf299c5f021299","abstract_canon_sha256":"d33bcafb50d1faf4588a342637695ed20bae6f581f6f864b317b90e75d1237f9"},"schema_version":"1.0"},"canonical_sha256":"f93b79affb49040f23b3eae8fec71b5915f004a835ee56db23964e2af08addd4","source":{"kind":"arxiv","id":"1204.5842","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5842","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5842v1","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5842","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"7E5XTL73JECA","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7E5XTL73JECA6I5T","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7E5XTL73","created_at":"2026-05-18T12:26:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7E5XTL73JECA6I5T5LUP5RY3LE","target":"record","payload":{"canonical_record":{"source":{"id":"1204.5842","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-26T06:44:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"dd4d59c5d7cfb33226721187e20954a828bd62969a6d3299ccaf299c5f021299","abstract_canon_sha256":"d33bcafb50d1faf4588a342637695ed20bae6f581f6f864b317b90e75d1237f9"},"schema_version":"1.0"},"canonical_sha256":"f93b79affb49040f23b3eae8fec71b5915f004a835ee56db23964e2af08addd4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:59.302951Z","signature_b64":"2dGqBvf8xw19/wJ7Q5TFkvIekmTpXqltwiKwAV9+DWisv7cLjL7+TmPsd6VfD4gUrOoN0tDuectX8mYmrzy7BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f93b79affb49040f23b3eae8fec71b5915f004a835ee56db23964e2af08addd4","last_reissued_at":"2026-05-18T03:56:59.302125Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:59.302125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.5842","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":"2026-05-18T03:56:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C0ma0Jwg0ZaEPP3BNNse11/1eisK7lcmw38zX/PSRdYDckRnIaH9UyYMES6Sm92tNKf++qnN/rs/Ld/q5DucBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:54:06.085452Z"},"content_sha256":"736a4c96dba8323d0d4b656d32a143870f2caad5b9f1b9f2793da5e5b8958256","schema_version":"1.0","event_id":"sha256:736a4c96dba8323d0d4b656d32a143870f2caad5b9f1b9f2793da5e5b8958256"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7E5XTL73JECA6I5T5LUP5RY3LE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bicrossproduct construction versus Weyl-Heisenberg algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"A. Borowiec, A. Pacho{\\l}","submitted_at":"2012-04-26T06:44:37Z","abstract_excerpt":"We are focused on detailed analysis of the Weyl-Heisenberg algebra in the framework of bicrossproduct construction. We argue that however it is not possible to introduce full bialgebra structure in this case, it is possible to introduce non-counital bialgebra counterpart of this construction. Some remarks concerning bicrossproduct basis for kappa-Poincare Hopf algebra are also presented."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5842","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":"2026-05-18T03:56:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"to7inEmH6W34Yfje9gwrzS8BC3HwCKF0knl5j3UplXCRMSHlRKkCBfqoWwMOr1k8f1C8+2IIOJsDgU7Hwj3hAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T12:54:06.086091Z"},"content_sha256":"435430892d3954e1ffcd4dd8b5c0069c5d89919aae73140d559233bab468d838","schema_version":"1.0","event_id":"sha256:435430892d3954e1ffcd4dd8b5c0069c5d89919aae73140d559233bab468d838"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7E5XTL73JECA6I5T5LUP5RY3LE/bundle.json","state_url":"https://pith.science/pith/7E5XTL73JECA6I5T5LUP5RY3LE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7E5XTL73JECA6I5T5LUP5RY3LE/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":"2026-05-31T12:54:06Z","links":{"resolver":"https://pith.science/pith/7E5XTL73JECA6I5T5LUP5RY3LE","bundle":"https://pith.science/pith/7E5XTL73JECA6I5T5LUP5RY3LE/bundle.json","state":"https://pith.science/pith/7E5XTL73JECA6I5T5LUP5RY3LE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7E5XTL73JECA6I5T5LUP5RY3LE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7E5XTL73JECA6I5T5LUP5RY3LE","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":"d33bcafb50d1faf4588a342637695ed20bae6f581f6f864b317b90e75d1237f9","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-26T06:44:37Z","title_canon_sha256":"dd4d59c5d7cfb33226721187e20954a828bd62969a6d3299ccaf299c5f021299"},"schema_version":"1.0","source":{"id":"1204.5842","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.5842","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"arxiv_version","alias_value":"1204.5842v1","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.5842","created_at":"2026-05-18T03:56:59Z"},{"alias_kind":"pith_short_12","alias_value":"7E5XTL73JECA","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"7E5XTL73JECA6I5T","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"7E5XTL73","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:435430892d3954e1ffcd4dd8b5c0069c5d89919aae73140d559233bab468d838","target":"graph","created_at":"2026-05-18T03:56:59Z","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 are focused on detailed analysis of the Weyl-Heisenberg algebra in the framework of bicrossproduct construction. We argue that however it is not possible to introduce full bialgebra structure in this case, it is possible to introduce non-counital bialgebra counterpart of this construction. Some remarks concerning bicrossproduct basis for kappa-Poincare Hopf algebra are also presented.","authors_text":"A. Borowiec, A. Pacho{\\l}","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-26T06:44:37Z","title":"Bicrossproduct construction versus Weyl-Heisenberg algebra"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.5842","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":"sha256:736a4c96dba8323d0d4b656d32a143870f2caad5b9f1b9f2793da5e5b8958256","target":"record","created_at":"2026-05-18T03:56:59Z","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":"d33bcafb50d1faf4588a342637695ed20bae6f581f6f864b317b90e75d1237f9","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-04-26T06:44:37Z","title_canon_sha256":"dd4d59c5d7cfb33226721187e20954a828bd62969a6d3299ccaf299c5f021299"},"schema_version":"1.0","source":{"id":"1204.5842","kind":"arxiv","version":1}},"canonical_sha256":"f93b79affb49040f23b3eae8fec71b5915f004a835ee56db23964e2af08addd4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f93b79affb49040f23b3eae8fec71b5915f004a835ee56db23964e2af08addd4","first_computed_at":"2026-05-18T03:56:59.302125Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:59.302125Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2dGqBvf8xw19/wJ7Q5TFkvIekmTpXqltwiKwAV9+DWisv7cLjL7+TmPsd6VfD4gUrOoN0tDuectX8mYmrzy7BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:59.302951Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.5842","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:736a4c96dba8323d0d4b656d32a143870f2caad5b9f1b9f2793da5e5b8958256","sha256:435430892d3954e1ffcd4dd8b5c0069c5d89919aae73140d559233bab468d838"],"state_sha256":"927a02a812c8fbbef92fa1c840498d411c99078563493a6873a0fd871315c69d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+18+VKE2lVIW6SUE6+UNhiiHhfUN0CooQPFEeh7r+JaYgdSJGDICNuwcNe7gvy8Spcc+ct8+F4k8NHAEQzzeDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T12:54:06.089659Z","bundle_sha256":"7502ec9a480d6886b89a789fc8b8dadaca5b400d651e466169ef7fc9a21c2459"}}