{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Q4R6X7EEC2MPGYBJZ5VGZQ63BD","short_pith_number":"pith:Q4R6X7EE","canonical_record":{"source":{"id":"1205.0296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-05-02T00:40:36Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"dacbd6659c53be536be419c112e6a63586f15c5f6eb9ee6065c1572de817645c","abstract_canon_sha256":"aa3c38629ef3aa3da92dfb95507c695740de0fdaa32c9b429377989a67b45fc7"},"schema_version":"1.0"},"canonical_sha256":"8723ebfc841698f36029cf6a6cc3db08daabd4636b299a7b8d33b9e8f7b7cb2d","source":{"kind":"arxiv","id":"1205.0296","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0296","created_at":"2026-05-18T01:57:39Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0296v1","created_at":"2026-05-18T01:57:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0296","created_at":"2026-05-18T01:57:39Z"},{"alias_kind":"pith_short_12","alias_value":"Q4R6X7EEC2MP","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q4R6X7EEC2MPGYBJ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q4R6X7EE","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Q4R6X7EEC2MPGYBJZ5VGZQ63BD","target":"record","payload":{"canonical_record":{"source":{"id":"1205.0296","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-05-02T00:40:36Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"dacbd6659c53be536be419c112e6a63586f15c5f6eb9ee6065c1572de817645c","abstract_canon_sha256":"aa3c38629ef3aa3da92dfb95507c695740de0fdaa32c9b429377989a67b45fc7"},"schema_version":"1.0"},"canonical_sha256":"8723ebfc841698f36029cf6a6cc3db08daabd4636b299a7b8d33b9e8f7b7cb2d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:39.165746Z","signature_b64":"87z9uMd5OxPSdXzsJ4T005wmYTBFkz6Fq4ot8uEv/q+Z9U67GdW+MNx3Wm1q6HwccQObo7Dd0ZnbCSU8es0sDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8723ebfc841698f36029cf6a6cc3db08daabd4636b299a7b8d33b9e8f7b7cb2d","last_reissued_at":"2026-05-18T01:57:39.165199Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:39.165199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.0296","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":"2026-05-18T01:57:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"63VJEpDBxfdLCRWYXjRV9IeCWvjDiQQw6iYkpZuD9X3WgryEcvoOYivdcAsKbOd30QXz3IMhRoP8Bpq8AyhxBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:06:41.960486Z"},"content_sha256":"de0cd833eaef02f75c69ed81025cc50161d57e29fae1eeb6356f76ac21865972","schema_version":"1.0","event_id":"sha256:de0cd833eaef02f75c69ed81025cc50161d57e29fae1eeb6356f76ac21865972"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Q4R6X7EEC2MPGYBJZ5VGZQ63BD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dephasing by a Continuous-Time Random Walk Process","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.chem-ph","authors_text":"Daniel M Packwood, Yoshitaka Tanimura","submitted_at":"2012-05-02T00:40:36Z","abstract_excerpt":"Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions like <exp(i int_0^t Q(s)ds)>, where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets denote ensemble averaging. This paper gives an exact evaluation of these functions for the case where Q is a continuous-time random walk process. The continuous time random walk describes an environment that undergoes slow, step-like changes in time. It also has a well-defined Gaussian limit, and so allows for non-Gaussian and Gaussian stochastic dynamics to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0296","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":"2026-05-18T01:57:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"phLxSIdh2jxsr7O0W64TQg2SUqPMitIV9RP3NRaKaIVj8KhMRhZdCftki1MLtit5i8HLx9QTx/ROtAFvur79Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T06:06:41.960813Z"},"content_sha256":"38d0083804d467efe8b4277fdc81710eba6343ace0ca1aeda7e3504237771695","schema_version":"1.0","event_id":"sha256:38d0083804d467efe8b4277fdc81710eba6343ace0ca1aeda7e3504237771695"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q4R6X7EEC2MPGYBJZ5VGZQ63BD/bundle.json","state_url":"https://pith.science/pith/Q4R6X7EEC2MPGYBJZ5VGZQ63BD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q4R6X7EEC2MPGYBJZ5VGZQ63BD/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":"2026-06-21T06:06:41Z","links":{"resolver":"https://pith.science/pith/Q4R6X7EEC2MPGYBJZ5VGZQ63BD","bundle":"https://pith.science/pith/Q4R6X7EEC2MPGYBJZ5VGZQ63BD/bundle.json","state":"https://pith.science/pith/Q4R6X7EEC2MPGYBJZ5VGZQ63BD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q4R6X7EEC2MPGYBJZ5VGZQ63BD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Q4R6X7EEC2MPGYBJZ5VGZQ63BD","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":"aa3c38629ef3aa3da92dfb95507c695740de0fdaa32c9b429377989a67b45fc7","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-05-02T00:40:36Z","title_canon_sha256":"dacbd6659c53be536be419c112e6a63586f15c5f6eb9ee6065c1572de817645c"},"schema_version":"1.0","source":{"id":"1205.0296","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.0296","created_at":"2026-05-18T01:57:39Z"},{"alias_kind":"arxiv_version","alias_value":"1205.0296v1","created_at":"2026-05-18T01:57:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.0296","created_at":"2026-05-18T01:57:39Z"},{"alias_kind":"pith_short_12","alias_value":"Q4R6X7EEC2MP","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"Q4R6X7EEC2MPGYBJ","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"Q4R6X7EE","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:38d0083804d467efe8b4277fdc81710eba6343ace0ca1aeda7e3504237771695","target":"graph","created_at":"2026-05-18T01:57:39Z","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":"Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions like <exp(i int_0^t Q(s)ds)>, where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets denote ensemble averaging. This paper gives an exact evaluation of these functions for the case where Q is a continuous-time random walk process. The continuous time random walk describes an environment that undergoes slow, step-like changes in time. It also has a well-defined Gaussian limit, and so allows for non-Gaussian and Gaussian stochastic dynamics to","authors_text":"Daniel M Packwood, Yoshitaka Tanimura","cross_cats":["quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-05-02T00:40:36Z","title":"Dephasing by a Continuous-Time Random Walk Process"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.0296","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:de0cd833eaef02f75c69ed81025cc50161d57e29fae1eeb6356f76ac21865972","target":"record","created_at":"2026-05-18T01:57:39Z","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":"aa3c38629ef3aa3da92dfb95507c695740de0fdaa32c9b429377989a67b45fc7","cross_cats_sorted":["quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2012-05-02T00:40:36Z","title_canon_sha256":"dacbd6659c53be536be419c112e6a63586f15c5f6eb9ee6065c1572de817645c"},"schema_version":"1.0","source":{"id":"1205.0296","kind":"arxiv","version":1}},"canonical_sha256":"8723ebfc841698f36029cf6a6cc3db08daabd4636b299a7b8d33b9e8f7b7cb2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8723ebfc841698f36029cf6a6cc3db08daabd4636b299a7b8d33b9e8f7b7cb2d","first_computed_at":"2026-05-18T01:57:39.165199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:39.165199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"87z9uMd5OxPSdXzsJ4T005wmYTBFkz6Fq4ot8uEv/q+Z9U67GdW+MNx3Wm1q6HwccQObo7Dd0ZnbCSU8es0sDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:39.165746Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.0296","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:de0cd833eaef02f75c69ed81025cc50161d57e29fae1eeb6356f76ac21865972","sha256:38d0083804d467efe8b4277fdc81710eba6343ace0ca1aeda7e3504237771695"],"state_sha256":"823e305b4a98edfcd21223a35b179fc35722a1d80e136d159bfbca0d9cd62a8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XWmsIJ6oXJqacaZ8egKSwbMb+AxvKnJl13Hc9j6QmnYcxQ2Y0JJ78W0ejYUAEGhooG5MHX2nhIye3MZgYxFECQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T06:06:41.962614Z","bundle_sha256":"71a46868094c443b26b79c57ba4c951695442cc928c22c31b60f9e2bf85b3043"}}