{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:B4CLNVMDUMU6RPGO72CUEZTQLY","short_pith_number":"pith:B4CLNVMD","canonical_record":{"source":{"id":"1604.06702","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-22T15:16:14Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"118775fbe725832d8767f0b073643c881cf82d9823c000b3676cfd9ed4d7558f","abstract_canon_sha256":"7101c20925c440a472b542132eb4f276385129777c276053df8f028422e88898"},"schema_version":"1.0"},"canonical_sha256":"0f04b6d583a329e8bccefe854266705e2cb5053848e740d0e29fabe546946613","source":{"kind":"arxiv","id":"1604.06702","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06702","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06702v2","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06702","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"B4CLNVMDUMU6","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"B4CLNVMDUMU6RPGO","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"B4CLNVMD","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:B4CLNVMDUMU6RPGO72CUEZTQLY","target":"record","payload":{"canonical_record":{"source":{"id":"1604.06702","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-22T15:16:14Z","cross_cats_sorted":["math.FA","math.MP"],"title_canon_sha256":"118775fbe725832d8767f0b073643c881cf82d9823c000b3676cfd9ed4d7558f","abstract_canon_sha256":"7101c20925c440a472b542132eb4f276385129777c276053df8f028422e88898"},"schema_version":"1.0"},"canonical_sha256":"0f04b6d583a329e8bccefe854266705e2cb5053848e740d0e29fabe546946613","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:35.775279Z","signature_b64":"Enl4C4xFQQ9FD/2SP9uQFb1gkhfIGTf6kIOPgWpuFvt4rZ7TEK7z3E6iicHjICBTof2Gmhlz+UQXKeS3Ec22BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f04b6d583a329e8bccefe854266705e2cb5053848e740d0e29fabe546946613","last_reissued_at":"2026-05-18T00:12:35.774627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:35.774627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1604.06702","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":"2026-05-18T00:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lfRWZ6jHWkn0MrMqffCgskTzVvAmQazdHwyiC+XvkdMCjG5JnlUxDZWOoQFaE9k2rnnV6W8jNfpXmh2R8c3NDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:59:08.315710Z"},"content_sha256":"7ec00f09d2b86aa21228200def19d913c6515a2b43a7cb81b7668caa1d56d6c9","schema_version":"1.0","event_id":"sha256:7ec00f09d2b86aa21228200def19d913c6515a2b43a7cb81b7668caa1d56d6c9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:B4CLNVMDUMU6RPGO72CUEZTQLY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uncertainty relations on nilpotent Lie groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Durvudkhan Suragan, Michael Ruzhansky","submitted_at":"2016-04-22T15:16:14Z","abstract_excerpt":"We give relations between main operators of quantum mechanics on one of most general classes of nilpotent Lie groups. Namely, we show relations between momentum and position operators as well as Euler and Coulomb potential operators on homogeneous groups. Homogeneous group analogues of some well-known inequalities such as Hardy's inequality, Heisenberg-Kennard type and Heisenberg-Pauli-Weyl type uncertainty inequalities, as well as Caffarelli-Kohn-Nirenberg inequality are derived, with best constants. The obtained relations yield new results already in the setting of both isotropic and anisotr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06702","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":"2026-05-18T00:12:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zXCiYm2Vz7CnflaTgb9CiArY3yApGnUy5NnCGJfCvPk3lRno8Pk4VZ/oL2fvl37QUD5j4G3tXKdoG8o5p5xqAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:59:08.316480Z"},"content_sha256":"9bbef46e2e05667325c822b916eb8b77f3416051841482fe53d5e89275e222a1","schema_version":"1.0","event_id":"sha256:9bbef46e2e05667325c822b916eb8b77f3416051841482fe53d5e89275e222a1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B4CLNVMDUMU6RPGO72CUEZTQLY/bundle.json","state_url":"https://pith.science/pith/B4CLNVMDUMU6RPGO72CUEZTQLY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B4CLNVMDUMU6RPGO72CUEZTQLY/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":"2026-06-10T00:59:08Z","links":{"resolver":"https://pith.science/pith/B4CLNVMDUMU6RPGO72CUEZTQLY","bundle":"https://pith.science/pith/B4CLNVMDUMU6RPGO72CUEZTQLY/bundle.json","state":"https://pith.science/pith/B4CLNVMDUMU6RPGO72CUEZTQLY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B4CLNVMDUMU6RPGO72CUEZTQLY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:B4CLNVMDUMU6RPGO72CUEZTQLY","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":"7101c20925c440a472b542132eb4f276385129777c276053df8f028422e88898","cross_cats_sorted":["math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-22T15:16:14Z","title_canon_sha256":"118775fbe725832d8767f0b073643c881cf82d9823c000b3676cfd9ed4d7558f"},"schema_version":"1.0","source":{"id":"1604.06702","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.06702","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"arxiv_version","alias_value":"1604.06702v2","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.06702","created_at":"2026-05-18T00:12:35Z"},{"alias_kind":"pith_short_12","alias_value":"B4CLNVMDUMU6","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"B4CLNVMDUMU6RPGO","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"B4CLNVMD","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:9bbef46e2e05667325c822b916eb8b77f3416051841482fe53d5e89275e222a1","target":"graph","created_at":"2026-05-18T00:12:35Z","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 give relations between main operators of quantum mechanics on one of most general classes of nilpotent Lie groups. Namely, we show relations between momentum and position operators as well as Euler and Coulomb potential operators on homogeneous groups. Homogeneous group analogues of some well-known inequalities such as Hardy's inequality, Heisenberg-Kennard type and Heisenberg-Pauli-Weyl type uncertainty inequalities, as well as Caffarelli-Kohn-Nirenberg inequality are derived, with best constants. The obtained relations yield new results already in the setting of both isotropic and anisotr","authors_text":"Durvudkhan Suragan, Michael Ruzhansky","cross_cats":["math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-22T15:16:14Z","title":"Uncertainty relations on nilpotent Lie groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06702","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":"sha256:7ec00f09d2b86aa21228200def19d913c6515a2b43a7cb81b7668caa1d56d6c9","target":"record","created_at":"2026-05-18T00:12:35Z","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":"7101c20925c440a472b542132eb4f276385129777c276053df8f028422e88898","cross_cats_sorted":["math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-22T15:16:14Z","title_canon_sha256":"118775fbe725832d8767f0b073643c881cf82d9823c000b3676cfd9ed4d7558f"},"schema_version":"1.0","source":{"id":"1604.06702","kind":"arxiv","version":2}},"canonical_sha256":"0f04b6d583a329e8bccefe854266705e2cb5053848e740d0e29fabe546946613","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f04b6d583a329e8bccefe854266705e2cb5053848e740d0e29fabe546946613","first_computed_at":"2026-05-18T00:12:35.774627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:12:35.774627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Enl4C4xFQQ9FD/2SP9uQFb1gkhfIGTf6kIOPgWpuFvt4rZ7TEK7z3E6iicHjICBTof2Gmhlz+UQXKeS3Ec22BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:12:35.775279Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.06702","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ec00f09d2b86aa21228200def19d913c6515a2b43a7cb81b7668caa1d56d6c9","sha256:9bbef46e2e05667325c822b916eb8b77f3416051841482fe53d5e89275e222a1"],"state_sha256":"1fc26ee5b8a9e559b8377c82837d0dccc243af3ca13647654f14fb0824a2e286"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+zhPzii9yYfgpf74BOzzt8v8p+g2hjO5BC1GDkjPCZLj1naeM52Yqe70WmQbAnlXBOIexgyz8AKdtyqybzYTDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T00:59:08.320859Z","bundle_sha256":"ce69b76b8ebfac7db5fd342b6fa1e679c12f9bb5977397227031e13dd7cd60d9"}}