{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:NRU75IJCYGUBR6EPLSGTD3BARL","short_pith_number":"pith:NRU75IJC","canonical_record":{"source":{"id":"1111.0788","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-03T10:55:50Z","cross_cats_sorted":[],"title_canon_sha256":"722122a58f652a53e788b843a871c8cd3c81306f425e4cd29e91c93f110041b3","abstract_canon_sha256":"9496762e65f1acf5894767a82d05b721a21e01efbaeec8e518e03cbc77a00ece"},"schema_version":"1.0"},"canonical_sha256":"6c69fea122c1a818f88f5c8d31ec208af43794312b6e533eb17157187a11d598","source":{"kind":"arxiv","id":"1111.0788","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0788","created_at":"2026-05-18T01:59:47Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0788v3","created_at":"2026-05-18T01:59:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0788","created_at":"2026-05-18T01:59:47Z"},{"alias_kind":"pith_short_12","alias_value":"NRU75IJCYGUB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NRU75IJCYGUBR6EP","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NRU75IJC","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:NRU75IJCYGUBR6EPLSGTD3BARL","target":"record","payload":{"canonical_record":{"source":{"id":"1111.0788","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-03T10:55:50Z","cross_cats_sorted":[],"title_canon_sha256":"722122a58f652a53e788b843a871c8cd3c81306f425e4cd29e91c93f110041b3","abstract_canon_sha256":"9496762e65f1acf5894767a82d05b721a21e01efbaeec8e518e03cbc77a00ece"},"schema_version":"1.0"},"canonical_sha256":"6c69fea122c1a818f88f5c8d31ec208af43794312b6e533eb17157187a11d598","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:59:47.904857Z","signature_b64":"GVG+4pFy7PTGzHOhEhYpS8X7NH7gm4d8unJt/m/43RR8dgOEXntvFOuYA+0KAxk3NEHm17R/kylfwPf/ozJXDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c69fea122c1a818f88f5c8d31ec208af43794312b6e533eb17157187a11d598","last_reissued_at":"2026-05-18T01:59:47.904168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:59:47.904168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.0788","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:59:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tjnp1mHwIU6fN4Qq4iw8oox9jdt/kOQOEH62/bGnOR4p6fBqrSAoFaxEhPW1CnZA3r9ikadHNYcxhvzbWvGUCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:16:52.312220Z"},"content_sha256":"1409832bb94393445cf6e3c4518e3a80f696a4633181b7774f95f275d6d40497","schema_version":"1.0","event_id":"sha256:1409832bb94393445cf6e3c4518e3a80f696a4633181b7774f95f275d6d40497"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:NRU75IJCYGUBR6EPLSGTD3BARL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Universality of the Heisenberg limit for estimates of random phase shifts","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Dominic W. Berry, Howard M. Wiseman, Marcin Zwierz, Michael J. W. Hall","submitted_at":"2011-11-03T10:55:50Z","abstract_excerpt":"The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as 1/<N>, where <N> is the mean number of photons in the probe. However, this limit has a number of loopholes which potentially might be exploited, to achieve measurements with even greater accuracy. Here we close these loopholes by proving a completely rigorous form of the Heisenberg limit for the average error over all phase shifts. Our result gives the first completely general, constraint-free and non-asymptotic statement of the Heisenberg limit. It holds for all phase estimation schemes, including mu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0788","kind":"arxiv","version":3},"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":"2026-05-18T01:59:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MlYVoDOmBJHIn4PY7857NJ/fVpCvOCAYE1IzCt6IIm+GUd27c4BcJT3D+/bvo3EcsiEtkUtH4ahwuKXh+gwJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T01:16:52.312578Z"},"content_sha256":"3d87b32f779733d2920b5b7d775f5bf386c227349b2e8ce79de8a3ec1ebaf131","schema_version":"1.0","event_id":"sha256:3d87b32f779733d2920b5b7d775f5bf386c227349b2e8ce79de8a3ec1ebaf131"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL/bundle.json","state_url":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NRU75IJCYGUBR6EPLSGTD3BARL/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":"2026-05-28T01:16:52Z","links":{"resolver":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL","bundle":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL/bundle.json","state":"https://pith.science/pith/NRU75IJCYGUBR6EPLSGTD3BARL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NRU75IJCYGUBR6EPLSGTD3BARL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:NRU75IJCYGUBR6EPLSGTD3BARL","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":"9496762e65f1acf5894767a82d05b721a21e01efbaeec8e518e03cbc77a00ece","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-03T10:55:50Z","title_canon_sha256":"722122a58f652a53e788b843a871c8cd3c81306f425e4cd29e91c93f110041b3"},"schema_version":"1.0","source":{"id":"1111.0788","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.0788","created_at":"2026-05-18T01:59:47Z"},{"alias_kind":"arxiv_version","alias_value":"1111.0788v3","created_at":"2026-05-18T01:59:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.0788","created_at":"2026-05-18T01:59:47Z"},{"alias_kind":"pith_short_12","alias_value":"NRU75IJCYGUB","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"NRU75IJCYGUBR6EP","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"NRU75IJC","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:3d87b32f779733d2920b5b7d775f5bf386c227349b2e8ce79de8a3ec1ebaf131","target":"graph","created_at":"2026-05-18T01:59:47Z","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":"The Heisenberg limit traditionally provides a lower bound on the phase uncertainty scaling as 1/<N>, where <N> is the mean number of photons in the probe. However, this limit has a number of loopholes which potentially might be exploited, to achieve measurements with even greater accuracy. Here we close these loopholes by proving a completely rigorous form of the Heisenberg limit for the average error over all phase shifts. Our result gives the first completely general, constraint-free and non-asymptotic statement of the Heisenberg limit. It holds for all phase estimation schemes, including mu","authors_text":"Dominic W. Berry, Howard M. Wiseman, Marcin Zwierz, Michael J. W. Hall","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-03T10:55:50Z","title":"Universality of the Heisenberg limit for estimates of random phase shifts"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0788","kind":"arxiv","version":3},"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":"sha256:1409832bb94393445cf6e3c4518e3a80f696a4633181b7774f95f275d6d40497","target":"record","created_at":"2026-05-18T01:59:47Z","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":"9496762e65f1acf5894767a82d05b721a21e01efbaeec8e518e03cbc77a00ece","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-11-03T10:55:50Z","title_canon_sha256":"722122a58f652a53e788b843a871c8cd3c81306f425e4cd29e91c93f110041b3"},"schema_version":"1.0","source":{"id":"1111.0788","kind":"arxiv","version":3}},"canonical_sha256":"6c69fea122c1a818f88f5c8d31ec208af43794312b6e533eb17157187a11d598","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c69fea122c1a818f88f5c8d31ec208af43794312b6e533eb17157187a11d598","first_computed_at":"2026-05-18T01:59:47.904168Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:59:47.904168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GVG+4pFy7PTGzHOhEhYpS8X7NH7gm4d8unJt/m/43RR8dgOEXntvFOuYA+0KAxk3NEHm17R/kylfwPf/ozJXDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:59:47.904857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.0788","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1409832bb94393445cf6e3c4518e3a80f696a4633181b7774f95f275d6d40497","sha256:3d87b32f779733d2920b5b7d775f5bf386c227349b2e8ce79de8a3ec1ebaf131"],"state_sha256":"ae228fbfe52f29c8f830645ebbd730717f0dd42acef46221bcda15a79d4d2925"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i9a2LZvAB1StCJpq/9eGo4zgcMPdzU5SXhw5vVV9F6uNDH39f+dFMwRvLIPfA+Acsmn9t0Rh77JnXqyyR/gyCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T01:16:52.314447Z","bundle_sha256":"401ff29f33dc4f74a81cb4a66ad69d7461994b12fd109ce5cbda92d11c8020a1"}}