{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:OATGTZA3KGVRL6LMX4AQIB6DZG","short_pith_number":"pith:OATGTZA3","canonical_record":{"source":{"id":"1102.2486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-12T07:55:24Z","cross_cats_sorted":[],"title_canon_sha256":"eb3febf867b31d7d5afd77999fb9eb3a8d00eddd0cf355b3ad18ffa6c4e23b74","abstract_canon_sha256":"b049766a5ae6160b582b5fcef04cd242b36ecbf335af716407a3c32b8de3b4f8"},"schema_version":"1.0"},"canonical_sha256":"702669e41b51ab15f96cbf010407c3c99c730a70b74418d2b0eafe00be1ebcf7","source":{"kind":"arxiv","id":"1102.2486","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2486","created_at":"2026-05-18T04:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2486v1","created_at":"2026-05-18T04:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2486","created_at":"2026-05-18T04:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"OATGTZA3KGVR","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OATGTZA3KGVRL6LM","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OATGTZA3","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:OATGTZA3KGVRL6LMX4AQIB6DZG","target":"record","payload":{"canonical_record":{"source":{"id":"1102.2486","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-12T07:55:24Z","cross_cats_sorted":[],"title_canon_sha256":"eb3febf867b31d7d5afd77999fb9eb3a8d00eddd0cf355b3ad18ffa6c4e23b74","abstract_canon_sha256":"b049766a5ae6160b582b5fcef04cd242b36ecbf335af716407a3c32b8de3b4f8"},"schema_version":"1.0"},"canonical_sha256":"702669e41b51ab15f96cbf010407c3c99c730a70b74418d2b0eafe00be1ebcf7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:28:47.271690Z","signature_b64":"u3lt/Bde2crFUuoYAg8pw1WaVE3g7l3QCPt8Sj/FU/ztzNhYJYzyh+m/u5fzjWiZ43sie5F5M74rYhZt443pBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"702669e41b51ab15f96cbf010407c3c99c730a70b74418d2b0eafe00be1ebcf7","last_reissued_at":"2026-05-18T04:28:47.271067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:28:47.271067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.2486","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":"2026-05-18T04:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9YEDhz3VPQCi04mmBfomIgJBjxigg5WsW+ts94h8mBCy674xXBh30lZ7672016HWPRNMzKBJHQJNgljk5CjsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:12:14.182228Z"},"content_sha256":"f9d077c46c563345581db80de32a965aef64653076cbdd0ac9cd5d0999af5f78","schema_version":"1.0","event_id":"sha256:f9d077c46c563345581db80de32a965aef64653076cbdd0ac9cd5d0999af5f78"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:OATGTZA3KGVRL6LMX4AQIB6DZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Maupertuis Principle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Antonia Karamatskou, Hagen Kleinert","submitted_at":"2011-02-12T07:55:24Z","abstract_excerpt":"According to the Maupertuis principle, the movement of a classical particle in an external potential $V(x)$ can be understood as the movement in a curved space with the metric $g_{\\mu\\nu}(x)=2M[V(x)-E]\\delta_{\\mu\\nu}$. We show that the principle can be extended to the quantum regime, i.e., we show that the wave function of the particle follows a Schr\\\"odinger equation in curved space where the kinetic operator is formed with the {\\it Weyl--invariant Laplace-Beltrami} operator. As an application, we use DeWitt's recursive semiclassical expansion of the time-evolution operator in curved space to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2486","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":"2026-05-18T04:28:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AH0jxpz5PEECm6St6mDQm69yuerfG3yAYRKopr4GHFjuLdz0Hr7ufZ+U6QPnJ70NYpj5jDRDBLKduWQxcVDfBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T16:12:14.182570Z"},"content_sha256":"4ed97bb087e163f5cb8476b3f603b084e1c08abd830e8fd93d2e0407fde03bb9","schema_version":"1.0","event_id":"sha256:4ed97bb087e163f5cb8476b3f603b084e1c08abd830e8fd93d2e0407fde03bb9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OATGTZA3KGVRL6LMX4AQIB6DZG/bundle.json","state_url":"https://pith.science/pith/OATGTZA3KGVRL6LMX4AQIB6DZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OATGTZA3KGVRL6LMX4AQIB6DZG/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":"2026-06-03T16:12:14Z","links":{"resolver":"https://pith.science/pith/OATGTZA3KGVRL6LMX4AQIB6DZG","bundle":"https://pith.science/pith/OATGTZA3KGVRL6LMX4AQIB6DZG/bundle.json","state":"https://pith.science/pith/OATGTZA3KGVRL6LMX4AQIB6DZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OATGTZA3KGVRL6LMX4AQIB6DZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OATGTZA3KGVRL6LMX4AQIB6DZG","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":"b049766a5ae6160b582b5fcef04cd242b36ecbf335af716407a3c32b8de3b4f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-12T07:55:24Z","title_canon_sha256":"eb3febf867b31d7d5afd77999fb9eb3a8d00eddd0cf355b3ad18ffa6c4e23b74"},"schema_version":"1.0","source":{"id":"1102.2486","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.2486","created_at":"2026-05-18T04:28:47Z"},{"alias_kind":"arxiv_version","alias_value":"1102.2486v1","created_at":"2026-05-18T04:28:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.2486","created_at":"2026-05-18T04:28:47Z"},{"alias_kind":"pith_short_12","alias_value":"OATGTZA3KGVR","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OATGTZA3KGVRL6LM","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OATGTZA3","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:4ed97bb087e163f5cb8476b3f603b084e1c08abd830e8fd93d2e0407fde03bb9","target":"graph","created_at":"2026-05-18T04:28:47Z","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":"According to the Maupertuis principle, the movement of a classical particle in an external potential $V(x)$ can be understood as the movement in a curved space with the metric $g_{\\mu\\nu}(x)=2M[V(x)-E]\\delta_{\\mu\\nu}$. We show that the principle can be extended to the quantum regime, i.e., we show that the wave function of the particle follows a Schr\\\"odinger equation in curved space where the kinetic operator is formed with the {\\it Weyl--invariant Laplace-Beltrami} operator. As an application, we use DeWitt's recursive semiclassical expansion of the time-evolution operator in curved space to","authors_text":"Antonia Karamatskou, Hagen Kleinert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-12T07:55:24Z","title":"Quantum Maupertuis Principle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.2486","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:f9d077c46c563345581db80de32a965aef64653076cbdd0ac9cd5d0999af5f78","target":"record","created_at":"2026-05-18T04:28:47Z","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":"b049766a5ae6160b582b5fcef04cd242b36ecbf335af716407a3c32b8de3b4f8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2011-02-12T07:55:24Z","title_canon_sha256":"eb3febf867b31d7d5afd77999fb9eb3a8d00eddd0cf355b3ad18ffa6c4e23b74"},"schema_version":"1.0","source":{"id":"1102.2486","kind":"arxiv","version":1}},"canonical_sha256":"702669e41b51ab15f96cbf010407c3c99c730a70b74418d2b0eafe00be1ebcf7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"702669e41b51ab15f96cbf010407c3c99c730a70b74418d2b0eafe00be1ebcf7","first_computed_at":"2026-05-18T04:28:47.271067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:47.271067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u3lt/Bde2crFUuoYAg8pw1WaVE3g7l3QCPt8Sj/FU/ztzNhYJYzyh+m/u5fzjWiZ43sie5F5M74rYhZt443pBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:47.271690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.2486","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9d077c46c563345581db80de32a965aef64653076cbdd0ac9cd5d0999af5f78","sha256:4ed97bb087e163f5cb8476b3f603b084e1c08abd830e8fd93d2e0407fde03bb9"],"state_sha256":"6da13b1fbe5f7f3143e311155c74b87eba80f21ca302590522db1946a5774956"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nyV7rt/88t9BmHnx8mLYOzWOivJmjiN92XXBekQmmwgaK56oxFa+4MNf9132gwpG7sRyFBnavTFlcEXYHM6TBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T16:12:14.184312Z","bundle_sha256":"ffe81f8e2d2dcbc6c5281577f3c5b61f9e09d56fe69a24edf506c5751c8b7830"}}