{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:O63NQ4NYJZGQETRVJXLMKM6KKK","short_pith_number":"pith:O63NQ4NY","canonical_record":{"source":{"id":"1702.05282","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-02-17T09:54:20Z","cross_cats_sorted":[],"title_canon_sha256":"6b9cd6e906773ff684e57b23a616c2fae62b1357a3a1d1bb6609692d7df88ec4","abstract_canon_sha256":"dfce94928eea474e81b319fa7ba43ec66592933c484d3b968459eae5dddd2bde"},"schema_version":"1.0"},"canonical_sha256":"77b6d871b84e4d024e354dd6c533ca52a1ae0fed9391c3f9e6ee3fa074b07886","source":{"kind":"arxiv","id":"1702.05282","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05282","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05282v1","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05282","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"pith_short_12","alias_value":"O63NQ4NYJZGQ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O63NQ4NYJZGQETRV","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O63NQ4NY","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:O63NQ4NYJZGQETRVJXLMKM6KKK","target":"record","payload":{"canonical_record":{"source":{"id":"1702.05282","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-02-17T09:54:20Z","cross_cats_sorted":[],"title_canon_sha256":"6b9cd6e906773ff684e57b23a616c2fae62b1357a3a1d1bb6609692d7df88ec4","abstract_canon_sha256":"dfce94928eea474e81b319fa7ba43ec66592933c484d3b968459eae5dddd2bde"},"schema_version":"1.0"},"canonical_sha256":"77b6d871b84e4d024e354dd6c533ca52a1ae0fed9391c3f9e6ee3fa074b07886","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:21.065943Z","signature_b64":"n8kDaqGXzPJcIeJvT8zCAorgNvGgMUg2Hxpd+OZopfsbg58nvld5xRmKfXig8evPobtiHFMsa6hk7Iglm94JDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77b6d871b84e4d024e354dd6c533ca52a1ae0fed9391c3f9e6ee3fa074b07886","last_reissued_at":"2026-05-18T00:25:21.065255Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:21.065255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.05282","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":"2026-05-18T00:25:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+kTQeMo2qMD9ZeFPOZHXa/QY32t78yYrozvK6qkWg6Rf3I5r14CjJ3gRJi5wxhynUtaIvoAZSHsX+/WfNPZMAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:22:27.985419Z"},"content_sha256":"9d9bd2198e6e8f9af0851dc437139b58bc769b69e7acecc25b546c158c084b0f","schema_version":"1.0","event_id":"sha256:9d9bd2198e6e8f9af0851dc437139b58bc769b69e7acecc25b546c158c084b0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:O63NQ4NYJZGQETRVJXLMKM6KKK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Time Wave Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Matthias Lienert, Roderich Tumulka, S\\\"oren Petrat","submitted_at":"2017-02-17T09:54:20Z","abstract_excerpt":"In non-relativistic quantum mechanics of $N$ particles in three spatial dimensions, the wave function $\\psi(q_1,\\ldots,q_N,t)$ is a function of $3N$ position coordinates and one time coordinate. It is an obvious idea that in a relativistic setting, such functions should be replaced by $\\phi((t_1,q_1),\\ldots,(t_N,q_N))$, a function of $N$ space-time points called a multi-time wave function because it involves $N$ time variables. Its evolution is determined by $N$ Schr\\\"odinger equations, one for each time variable; to ensure that simultaneous solutions to these $N$ equations exist, the $N$ Hami"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05282","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":"2026-05-18T00:25:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1wERS7TpLIlgDckt2piqYBsYgv2AyYfkiM20PKmlQZLtFuH1eaZhyr3Dv9gtlM0oSvZ6GgU2pwc6NUC8OquGBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T17:22:27.985773Z"},"content_sha256":"c9b9556255878c840984ed483c8aa3ebe313747c5759f0727d681c9a0b72a208","schema_version":"1.0","event_id":"sha256:c9b9556255878c840984ed483c8aa3ebe313747c5759f0727d681c9a0b72a208"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O63NQ4NYJZGQETRVJXLMKM6KKK/bundle.json","state_url":"https://pith.science/pith/O63NQ4NYJZGQETRVJXLMKM6KKK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O63NQ4NYJZGQETRVJXLMKM6KKK/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":"2026-06-22T17:22:27Z","links":{"resolver":"https://pith.science/pith/O63NQ4NYJZGQETRVJXLMKM6KKK","bundle":"https://pith.science/pith/O63NQ4NYJZGQETRVJXLMKM6KKK/bundle.json","state":"https://pith.science/pith/O63NQ4NYJZGQETRVJXLMKM6KKK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O63NQ4NYJZGQETRVJXLMKM6KKK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:O63NQ4NYJZGQETRVJXLMKM6KKK","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":"dfce94928eea474e81b319fa7ba43ec66592933c484d3b968459eae5dddd2bde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-02-17T09:54:20Z","title_canon_sha256":"6b9cd6e906773ff684e57b23a616c2fae62b1357a3a1d1bb6609692d7df88ec4"},"schema_version":"1.0","source":{"id":"1702.05282","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.05282","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"arxiv_version","alias_value":"1702.05282v1","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.05282","created_at":"2026-05-18T00:25:21Z"},{"alias_kind":"pith_short_12","alias_value":"O63NQ4NYJZGQ","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O63NQ4NYJZGQETRV","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O63NQ4NY","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:c9b9556255878c840984ed483c8aa3ebe313747c5759f0727d681c9a0b72a208","target":"graph","created_at":"2026-05-18T00:25:21Z","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":"In non-relativistic quantum mechanics of $N$ particles in three spatial dimensions, the wave function $\\psi(q_1,\\ldots,q_N,t)$ is a function of $3N$ position coordinates and one time coordinate. It is an obvious idea that in a relativistic setting, such functions should be replaced by $\\phi((t_1,q_1),\\ldots,(t_N,q_N))$, a function of $N$ space-time points called a multi-time wave function because it involves $N$ time variables. Its evolution is determined by $N$ Schr\\\"odinger equations, one for each time variable; to ensure that simultaneous solutions to these $N$ equations exist, the $N$ Hami","authors_text":"Matthias Lienert, Roderich Tumulka, S\\\"oren Petrat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-02-17T09:54:20Z","title":"Multi-Time Wave Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05282","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":"sha256:9d9bd2198e6e8f9af0851dc437139b58bc769b69e7acecc25b546c158c084b0f","target":"record","created_at":"2026-05-18T00:25:21Z","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":"dfce94928eea474e81b319fa7ba43ec66592933c484d3b968459eae5dddd2bde","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2017-02-17T09:54:20Z","title_canon_sha256":"6b9cd6e906773ff684e57b23a616c2fae62b1357a3a1d1bb6609692d7df88ec4"},"schema_version":"1.0","source":{"id":"1702.05282","kind":"arxiv","version":1}},"canonical_sha256":"77b6d871b84e4d024e354dd6c533ca52a1ae0fed9391c3f9e6ee3fa074b07886","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77b6d871b84e4d024e354dd6c533ca52a1ae0fed9391c3f9e6ee3fa074b07886","first_computed_at":"2026-05-18T00:25:21.065255Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:21.065255Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n8kDaqGXzPJcIeJvT8zCAorgNvGgMUg2Hxpd+OZopfsbg58nvld5xRmKfXig8evPobtiHFMsa6hk7Iglm94JDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:21.065943Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.05282","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9d9bd2198e6e8f9af0851dc437139b58bc769b69e7acecc25b546c158c084b0f","sha256:c9b9556255878c840984ed483c8aa3ebe313747c5759f0727d681c9a0b72a208"],"state_sha256":"34d279fc933c9c4cbb594e12344154bf3b23fc1b401549dfef3e93f06167b29b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xRMjsgtEBw0hAvaSdXC8cOblYVC67dA7I0gyW4FNr1/u1zJAAwL+CyA/O1goyrfiPKx92HDGm16svJ6DxWk5Bw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T17:22:27.987790Z","bundle_sha256":"c46c165db51f892f87c12dc286b2f85eda5752864f33a8856f2b526a70e835d4"}}