{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:UIIC6FT4PAKS6YBVKXLWQXDRKP","short_pith_number":"pith:UIIC6FT4","canonical_record":{"source":{"id":"1607.00362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-01T19:34:34Z","cross_cats_sorted":["math.MP","math.NA"],"title_canon_sha256":"6250d39551ace2aacab80b09040a4601cef443e133129b82d2a46e9e7186ba92","abstract_canon_sha256":"1327e4a6e0154693a6204c0f2ea99545488b22aaba09f4455ec199dbf4ef3c03"},"schema_version":"1.0"},"canonical_sha256":"a2102f167c78152f603555d7685c7153ecb84bce5bd76d685c08ea79ba790908","source":{"kind":"arxiv","id":"1607.00362","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00362","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00362v2","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00362","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"UIIC6FT4PAKS","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UIIC6FT4PAKS6YBV","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UIIC6FT4","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:UIIC6FT4PAKS6YBVKXLWQXDRKP","target":"record","payload":{"canonical_record":{"source":{"id":"1607.00362","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-01T19:34:34Z","cross_cats_sorted":["math.MP","math.NA"],"title_canon_sha256":"6250d39551ace2aacab80b09040a4601cef443e133129b82d2a46e9e7186ba92","abstract_canon_sha256":"1327e4a6e0154693a6204c0f2ea99545488b22aaba09f4455ec199dbf4ef3c03"},"schema_version":"1.0"},"canonical_sha256":"a2102f167c78152f603555d7685c7153ecb84bce5bd76d685c08ea79ba790908","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:17:13.654102Z","signature_b64":"ZftPNJmin/BYJEGpiavYDG3CDmzCbh66Wa0xb+BztBT1+krUqc9yWundF3BTdmi0Cr7qT8VansifpFoRDWomDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2102f167c78152f603555d7685c7153ecb84bce5bd76d685c08ea79ba790908","last_reissued_at":"2026-05-18T00:17:13.653421Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:17:13.653421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.00362","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":"2026-05-18T00:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+/at5nLCMv7TVThrFeSdqBkRHBhc30i74iyBE57o9U0dOqjc0BS0CYvOcAM3E1csIUuLWD2Qy/j3J3TFQ4HGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T06:40:48.455705Z"},"content_sha256":"af0575f543b3ad656af7866366351815331780807760118abd59f715788447e7","schema_version":"1.0","event_id":"sha256:af0575f543b3ad656af7866366351815331780807760118abd59f715788447e7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:UIIC6FT4PAKS6YBVKXLWQXDRKP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The spectrogram expansion of Wigner functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.NA"],"primary_cat":"math-ph","authors_text":"Johannes Keller","submitted_at":"2016-07-01T19:34:34Z","abstract_excerpt":"Wigner functions generically attain negative values and hence are not probability densities. We prove an asymptotic expansion of Wigner functions in terms of Hermite spectrograms, which are probability densities. The expansion provides exact formulas for the quantum expectations of polynomial observables. In the high frequency regime it allows to approximate quantum expectation values up to any order of accuracy in the high frequency parameter. We present a Markov Chain Monte Carlo method to sample from the new densities and illustrate our findings by numerical experiments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00362","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":"2026-05-18T00:17:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YKIej881zM9NE9KPCklxCxfBAGCvTKqNqbpZ9YdB0NSziNzKo4hUXbchs/q5caB2YFgGXnhJYS2uyu8cIeJaDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T06:40:48.456044Z"},"content_sha256":"6fb5ff6851254e7abb8a861f1d8272689af9ecfc4771303ed33d008bf69e4088","schema_version":"1.0","event_id":"sha256:6fb5ff6851254e7abb8a861f1d8272689af9ecfc4771303ed33d008bf69e4088"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UIIC6FT4PAKS6YBVKXLWQXDRKP/bundle.json","state_url":"https://pith.science/pith/UIIC6FT4PAKS6YBVKXLWQXDRKP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UIIC6FT4PAKS6YBVKXLWQXDRKP/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":"2026-06-30T06:40:48Z","links":{"resolver":"https://pith.science/pith/UIIC6FT4PAKS6YBVKXLWQXDRKP","bundle":"https://pith.science/pith/UIIC6FT4PAKS6YBVKXLWQXDRKP/bundle.json","state":"https://pith.science/pith/UIIC6FT4PAKS6YBVKXLWQXDRKP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UIIC6FT4PAKS6YBVKXLWQXDRKP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:UIIC6FT4PAKS6YBVKXLWQXDRKP","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":"1327e4a6e0154693a6204c0f2ea99545488b22aaba09f4455ec199dbf4ef3c03","cross_cats_sorted":["math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-01T19:34:34Z","title_canon_sha256":"6250d39551ace2aacab80b09040a4601cef443e133129b82d2a46e9e7186ba92"},"schema_version":"1.0","source":{"id":"1607.00362","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.00362","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"arxiv_version","alias_value":"1607.00362v2","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.00362","created_at":"2026-05-18T00:17:13Z"},{"alias_kind":"pith_short_12","alias_value":"UIIC6FT4PAKS","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"UIIC6FT4PAKS6YBV","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"UIIC6FT4","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:6fb5ff6851254e7abb8a861f1d8272689af9ecfc4771303ed33d008bf69e4088","target":"graph","created_at":"2026-05-18T00:17:13Z","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":"Wigner functions generically attain negative values and hence are not probability densities. We prove an asymptotic expansion of Wigner functions in terms of Hermite spectrograms, which are probability densities. The expansion provides exact formulas for the quantum expectations of polynomial observables. In the high frequency regime it allows to approximate quantum expectation values up to any order of accuracy in the high frequency parameter. We present a Markov Chain Monte Carlo method to sample from the new densities and illustrate our findings by numerical experiments.","authors_text":"Johannes Keller","cross_cats":["math.MP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-01T19:34:34Z","title":"The spectrogram expansion of Wigner functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.00362","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:af0575f543b3ad656af7866366351815331780807760118abd59f715788447e7","target":"record","created_at":"2026-05-18T00:17:13Z","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":"1327e4a6e0154693a6204c0f2ea99545488b22aaba09f4455ec199dbf4ef3c03","cross_cats_sorted":["math.MP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-07-01T19:34:34Z","title_canon_sha256":"6250d39551ace2aacab80b09040a4601cef443e133129b82d2a46e9e7186ba92"},"schema_version":"1.0","source":{"id":"1607.00362","kind":"arxiv","version":2}},"canonical_sha256":"a2102f167c78152f603555d7685c7153ecb84bce5bd76d685c08ea79ba790908","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2102f167c78152f603555d7685c7153ecb84bce5bd76d685c08ea79ba790908","first_computed_at":"2026-05-18T00:17:13.653421Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:17:13.653421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZftPNJmin/BYJEGpiavYDG3CDmzCbh66Wa0xb+BztBT1+krUqc9yWundF3BTdmi0Cr7qT8VansifpFoRDWomDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:17:13.654102Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.00362","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af0575f543b3ad656af7866366351815331780807760118abd59f715788447e7","sha256:6fb5ff6851254e7abb8a861f1d8272689af9ecfc4771303ed33d008bf69e4088"],"state_sha256":"a782468543cfbd69683d63f35638cc6cdf811254291c0801d43b7483c96a6480"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pQ8K9Nk64HJgq6j6FNgey7Pt0Y1iH40zOtuj9Q3XrOjtrdKgAvAclS9M0P5Ku++HRdfBNUvw5tibMhXmKUmuCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T06:40:48.457908Z","bundle_sha256":"967565f0c9581bf185527e47dde7300fbae324536c92174af8f095d7e62782ab"}}