{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:N4MTUDGMFJH7GEX3O4YHRI2O5S","short_pith_number":"pith:N4MTUDGM","canonical_record":{"source":{"id":"1302.1030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-05T13:34:53Z","cross_cats_sorted":[],"title_canon_sha256":"a1b8178d955d33c3bde290a9ff42562b9a034d312d1608165c265690107fc8db","abstract_canon_sha256":"7370860bc717eac7fb29e1c9ed730a65d60876c2ab952ace658c7c06cfaf38ac"},"schema_version":"1.0"},"canonical_sha256":"6f193a0ccc2a4ff312fb773078a34eec812359d1ab6173bfbafca66d6eea8f65","source":{"kind":"arxiv","id":"1302.1030","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1030","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1030v1","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1030","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"N4MTUDGMFJH7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N4MTUDGMFJH7GEX3","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N4MTUDGM","created_at":"2026-05-18T12:27:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:N4MTUDGMFJH7GEX3O4YHRI2O5S","target":"record","payload":{"canonical_record":{"source":{"id":"1302.1030","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-05T13:34:53Z","cross_cats_sorted":[],"title_canon_sha256":"a1b8178d955d33c3bde290a9ff42562b9a034d312d1608165c265690107fc8db","abstract_canon_sha256":"7370860bc717eac7fb29e1c9ed730a65d60876c2ab952ace658c7c06cfaf38ac"},"schema_version":"1.0"},"canonical_sha256":"6f193a0ccc2a4ff312fb773078a34eec812359d1ab6173bfbafca66d6eea8f65","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:43.322902Z","signature_b64":"ORtNyOcc0BIsbbFvoWn1fwQp/BOmIiTfnHhqv/WfGWL+5xkG4QoWzLb9VdwZJKbYVBfQYlJDRwOmRTEiznYZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f193a0ccc2a4ff312fb773078a34eec812359d1ab6173bfbafca66d6eea8f65","last_reissued_at":"2026-05-18T03:21:43.322196Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:43.322196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.1030","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":"2026-05-18T03:21:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tCyyzjxYdKPZNRdjLkJEzZ2rvKN3wpNQHWrlTbj935asODxCeh7XLQbeYZjEobvMXSylfoJIRlAbwA5rPXHwBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:12:20.016787Z"},"content_sha256":"c7c4aabf4dcf671800e8d8da673859140d0742f7332a36414db6d0ab4d7918c3","schema_version":"1.0","event_id":"sha256:c7c4aabf4dcf671800e8d8da673859140d0742f7332a36414db6d0ab4d7918c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:N4MTUDGMFJH7GEX3O4YHRI2O5S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tunneling through a parabolic barrier viewed from Wigner phase space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"D. M. Heim, J. P. Dahl, P. M. Alsing, S. Varro, W. P. Schleich","submitted_at":"2013-02-05T13:34:53Z","abstract_excerpt":"We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients $R$ or $T$ are then given by the total weight of all classical phase space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1030","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":"2026-05-18T03:21:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6kn3SyXAe/vP17pL0PNgBOCqtVyQJuLtmWIF+vgqpmgzgg5u4upCnAiesbZsO0xoZk8lK+nspULjE5duMXMIAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T22:12:20.017124Z"},"content_sha256":"e489fed36176dcd60d8a8e34cca06349189af7c44f0b0cc5e81ed388da8bb66e","schema_version":"1.0","event_id":"sha256:e489fed36176dcd60d8a8e34cca06349189af7c44f0b0cc5e81ed388da8bb66e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N4MTUDGMFJH7GEX3O4YHRI2O5S/bundle.json","state_url":"https://pith.science/pith/N4MTUDGMFJH7GEX3O4YHRI2O5S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N4MTUDGMFJH7GEX3O4YHRI2O5S/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":"2026-06-08T22:12:20Z","links":{"resolver":"https://pith.science/pith/N4MTUDGMFJH7GEX3O4YHRI2O5S","bundle":"https://pith.science/pith/N4MTUDGMFJH7GEX3O4YHRI2O5S/bundle.json","state":"https://pith.science/pith/N4MTUDGMFJH7GEX3O4YHRI2O5S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N4MTUDGMFJH7GEX3O4YHRI2O5S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:N4MTUDGMFJH7GEX3O4YHRI2O5S","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":"7370860bc717eac7fb29e1c9ed730a65d60876c2ab952ace658c7c06cfaf38ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-05T13:34:53Z","title_canon_sha256":"a1b8178d955d33c3bde290a9ff42562b9a034d312d1608165c265690107fc8db"},"schema_version":"1.0","source":{"id":"1302.1030","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.1030","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"arxiv_version","alias_value":"1302.1030v1","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.1030","created_at":"2026-05-18T03:21:43Z"},{"alias_kind":"pith_short_12","alias_value":"N4MTUDGMFJH7","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"N4MTUDGMFJH7GEX3","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"N4MTUDGM","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:e489fed36176dcd60d8a8e34cca06349189af7c44f0b0cc5e81ed388da8bb66e","target":"graph","created_at":"2026-05-18T03:21:43Z","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 analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients $R$ or $T$ are then given by the total weight of all classical phase space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function.","authors_text":"D. M. Heim, J. P. Dahl, P. M. Alsing, S. Varro, W. P. Schleich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-05T13:34:53Z","title":"Tunneling through a parabolic barrier viewed from Wigner phase space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.1030","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:c7c4aabf4dcf671800e8d8da673859140d0742f7332a36414db6d0ab4d7918c3","target":"record","created_at":"2026-05-18T03:21:43Z","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":"7370860bc717eac7fb29e1c9ed730a65d60876c2ab952ace658c7c06cfaf38ac","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2013-02-05T13:34:53Z","title_canon_sha256":"a1b8178d955d33c3bde290a9ff42562b9a034d312d1608165c265690107fc8db"},"schema_version":"1.0","source":{"id":"1302.1030","kind":"arxiv","version":1}},"canonical_sha256":"6f193a0ccc2a4ff312fb773078a34eec812359d1ab6173bfbafca66d6eea8f65","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f193a0ccc2a4ff312fb773078a34eec812359d1ab6173bfbafca66d6eea8f65","first_computed_at":"2026-05-18T03:21:43.322196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:43.322196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ORtNyOcc0BIsbbFvoWn1fwQp/BOmIiTfnHhqv/WfGWL+5xkG4QoWzLb9VdwZJKbYVBfQYlJDRwOmRTEiznYZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:43.322902Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.1030","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7c4aabf4dcf671800e8d8da673859140d0742f7332a36414db6d0ab4d7918c3","sha256:e489fed36176dcd60d8a8e34cca06349189af7c44f0b0cc5e81ed388da8bb66e"],"state_sha256":"89a16b88829d86b98b515ada0ed9f139a618ba848e55c8a652eedccd9e92e596"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zg/Tm5Tg7dRb52WT+7JbnR+O2FBd5bnjO99Yih2yeUpjWsCmfmiatJ3EZfQJBdMEeb6CwIdN1iOPYJ6tSgtABg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T22:12:20.018952Z","bundle_sha256":"2d9540ee20323b474a55c5a2df8a39d6e655e0214f85c066158ff8b66580506a"}}