{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:N6VB5OH5ZSE37MXN37TPNLIY74","short_pith_number":"pith:N6VB5OH5","canonical_record":{"source":{"id":"1006.3987","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-21T05:12:50Z","cross_cats_sorted":[],"title_canon_sha256":"fd3d09bb87232326d66a631a2b9fab4e22247f17af81803eb9b4f3db3ee86ee1","abstract_canon_sha256":"9f87d0b5884327e3caaa6e13052eeaefbd4d8f203671c532581cc59ee837bbc1"},"schema_version":"1.0"},"canonical_sha256":"6faa1eb8fdcc89bfb2eddfe6f6ad18ff32d1680defd5529f9bdbd1d19be729f7","source":{"kind":"arxiv","id":"1006.3987","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3987","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3987v4","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3987","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"N6VB5OH5ZSE3","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"N6VB5OH5ZSE37MXN","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"N6VB5OH5","created_at":"2026-05-18T12:26:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:N6VB5OH5ZSE37MXN37TPNLIY74","target":"record","payload":{"canonical_record":{"source":{"id":"1006.3987","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-21T05:12:50Z","cross_cats_sorted":[],"title_canon_sha256":"fd3d09bb87232326d66a631a2b9fab4e22247f17af81803eb9b4f3db3ee86ee1","abstract_canon_sha256":"9f87d0b5884327e3caaa6e13052eeaefbd4d8f203671c532581cc59ee837bbc1"},"schema_version":"1.0"},"canonical_sha256":"6faa1eb8fdcc89bfb2eddfe6f6ad18ff32d1680defd5529f9bdbd1d19be729f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:22.302640Z","signature_b64":"5QDIaMtEj7nX8am12AOCkcOQeD7+/uDMP+bdUQe+iZtpg/w1nhOo3icql4r1Hj0QgZ+wG4bmG7SqXeUPt2xKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6faa1eb8fdcc89bfb2eddfe6f6ad18ff32d1680defd5529f9bdbd1d19be729f7","last_reissued_at":"2026-05-18T01:29:22.301912Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:22.301912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.3987","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/Sgpgb/fGADOI8IIY/FwnrMS4lbzkGaVZ6h/MHR9PKHjnQ8a5s7GjEsoXtBUOLBG/h2yT3Xs10Ue8BXUGjb8AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T09:29:04.822301Z"},"content_sha256":"8ed3fb21bddd6625a2399a3072c5c58ef8f6ad3054304443d079f907f0bd7f29","schema_version":"1.0","event_id":"sha256:8ed3fb21bddd6625a2399a3072c5c58ef8f6ad3054304443d079f907f0bd7f29"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:N6VB5OH5ZSE37MXN37TPNLIY74","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on entropic uncertainty relations of position and momentum","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Thomas Sch\\\"urmann","submitted_at":"2010-06-21T05:12:50Z","abstract_excerpt":"We consider two entropic uncertainty relations of position and momentum recently discussed in literature. By a suitable rescaling of one of them, we obtain a smooth interpolation of both for high-resolution and low-resolution measurements respectively. Because our interpolation has never been mentioned in literature before, we propose it as a candidate for an improved entropic uncertainty relation of position and momentum. Up to now, the author has neither been able to falsify nor prove the new inequality. In our opinion it is a challenge to do either one."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3987","kind":"arxiv","version":4},"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":"2026-05-18T01:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J6hJKa17Q2bLuoP7w/qVuN3EIbFDNL7N1rAcPUMSYDooy9uGGyLsDIEghj3ab3iz0/6HngPKhmcyalPmfWRcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T09:29:04.822669Z"},"content_sha256":"835e5b4683eecbd8ae1c2f54753010052b49490d2ddd71d831c44215eeee883d","schema_version":"1.0","event_id":"sha256:835e5b4683eecbd8ae1c2f54753010052b49490d2ddd71d831c44215eeee883d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N6VB5OH5ZSE37MXN37TPNLIY74/bundle.json","state_url":"https://pith.science/pith/N6VB5OH5ZSE37MXN37TPNLIY74/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N6VB5OH5ZSE37MXN37TPNLIY74/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":"2026-07-02T09:29:04Z","links":{"resolver":"https://pith.science/pith/N6VB5OH5ZSE37MXN37TPNLIY74","bundle":"https://pith.science/pith/N6VB5OH5ZSE37MXN37TPNLIY74/bundle.json","state":"https://pith.science/pith/N6VB5OH5ZSE37MXN37TPNLIY74/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N6VB5OH5ZSE37MXN37TPNLIY74/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:N6VB5OH5ZSE37MXN37TPNLIY74","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":"9f87d0b5884327e3caaa6e13052eeaefbd4d8f203671c532581cc59ee837bbc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-21T05:12:50Z","title_canon_sha256":"fd3d09bb87232326d66a631a2b9fab4e22247f17af81803eb9b4f3db3ee86ee1"},"schema_version":"1.0","source":{"id":"1006.3987","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.3987","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1006.3987v4","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.3987","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"N6VB5OH5ZSE3","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"N6VB5OH5ZSE37MXN","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"N6VB5OH5","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:835e5b4683eecbd8ae1c2f54753010052b49490d2ddd71d831c44215eeee883d","target":"graph","created_at":"2026-05-18T01:29:22Z","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 consider two entropic uncertainty relations of position and momentum recently discussed in literature. By a suitable rescaling of one of them, we obtain a smooth interpolation of both for high-resolution and low-resolution measurements respectively. Because our interpolation has never been mentioned in literature before, we propose it as a candidate for an improved entropic uncertainty relation of position and momentum. Up to now, the author has neither been able to falsify nor prove the new inequality. In our opinion it is a challenge to do either one.","authors_text":"Thomas Sch\\\"urmann","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-21T05:12:50Z","title":"A note on entropic uncertainty relations of position and momentum"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.3987","kind":"arxiv","version":4},"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":"sha256:8ed3fb21bddd6625a2399a3072c5c58ef8f6ad3054304443d079f907f0bd7f29","target":"record","created_at":"2026-05-18T01:29:22Z","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":"9f87d0b5884327e3caaa6e13052eeaefbd4d8f203671c532581cc59ee837bbc1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-06-21T05:12:50Z","title_canon_sha256":"fd3d09bb87232326d66a631a2b9fab4e22247f17af81803eb9b4f3db3ee86ee1"},"schema_version":"1.0","source":{"id":"1006.3987","kind":"arxiv","version":4}},"canonical_sha256":"6faa1eb8fdcc89bfb2eddfe6f6ad18ff32d1680defd5529f9bdbd1d19be729f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6faa1eb8fdcc89bfb2eddfe6f6ad18ff32d1680defd5529f9bdbd1d19be729f7","first_computed_at":"2026-05-18T01:29:22.301912Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:22.301912Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5QDIaMtEj7nX8am12AOCkcOQeD7+/uDMP+bdUQe+iZtpg/w1nhOo3icql4r1Hj0QgZ+wG4bmG7SqXeUPt2xKCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:22.302640Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.3987","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8ed3fb21bddd6625a2399a3072c5c58ef8f6ad3054304443d079f907f0bd7f29","sha256:835e5b4683eecbd8ae1c2f54753010052b49490d2ddd71d831c44215eeee883d"],"state_sha256":"b638772efe400fa7b4771b4c89654fe0b8e77d23d620894752d6621bb07cdb22"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DQ5wEp3NIDjPYaOxwrZ7J+VRdBtMCfJDqLBMglBoKfgG3fvScUbnf0Gr5itej4CU1NW53tg14cdrkQFnsW6ZDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T09:29:04.825987Z","bundle_sha256":"0c2bec467e03a0838fec156431dd687a0419478df9c8bce60a40185ea8e1d3e7"}}