{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:ZUMAIP2GGTL5GITU2KXYGRUBE4","short_pith_number":"pith:ZUMAIP2G","canonical_record":{"source":{"id":"1011.2852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-11-12T09:09:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"145d9549bbe6d3dc7e5c2d105720914d1ffa2154093751124d13b549741345df","abstract_canon_sha256":"b37c5500642c296cd08b9182648f202a457fc0af359e24f491dff891322b1800"},"schema_version":"1.0"},"canonical_sha256":"cd18043f4634d7d32274d2af8346812712e43e69ccbf780d4e2c4c2460951209","source":{"kind":"arxiv","id":"1011.2852","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2852","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2852v1","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2852","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZUMAIP2GGTL5","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZUMAIP2GGTL5GITU","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZUMAIP2G","created_at":"2026-05-18T12:26:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:ZUMAIP2GGTL5GITU2KXYGRUBE4","target":"record","payload":{"canonical_record":{"source":{"id":"1011.2852","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-11-12T09:09:51Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"145d9549bbe6d3dc7e5c2d105720914d1ffa2154093751124d13b549741345df","abstract_canon_sha256":"b37c5500642c296cd08b9182648f202a457fc0af359e24f491dff891322b1800"},"schema_version":"1.0"},"canonical_sha256":"cd18043f4634d7d32274d2af8346812712e43e69ccbf780d4e2c4c2460951209","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:08.038251Z","signature_b64":"gBa9YxLtUOOAz+h4x5Br8IP9K1GDxlAWib1VAXwtEq55lP8MZZJO5ELJgTi7bNkMY3wTsR7PIdX2TAfs18ZlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd18043f4634d7d32274d2af8346812712e43e69ccbf780d4e2c4c2460951209","last_reissued_at":"2026-05-18T04:36:08.037553Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:08.037553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.2852","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":"2026-05-18T04:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2/WXuPh4WKgckVxg5Mt7y9fR1/dkTeHFuYY5MKsQzJc4GbsYbJLMd1f6xIQxD/fMq0MHPKsyuogaUVx2FsAzDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:52:52.433253Z"},"content_sha256":"8994cb34bc1f2805a35e7f7c642ed1215bf0d6a8e1cdd6469f64708793258314","schema_version":"1.0","event_id":"sha256:8994cb34bc1f2805a35e7f7c642ed1215bf0d6a8e1cdd6469f64708793258314"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:ZUMAIP2GGTL5GITU2KXYGRUBE4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-differentiable Bohmian trajectories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Gebhard Gruebl, Markus Penz","submitted_at":"2010-11-12T09:09:51Z","abstract_excerpt":"A solution $\\psi $ to Schr\\\"odinger's equation needs some degree of regularity in order to allow the construction of a Bohmian mechanics from the integral curves of the velocity field $\\hbar \\Im \\left( \\bigtriangledown \\psi /m\\psi \\right) .$ In the case of one specific non-differentiable weak solution $\\Psi $ we show how Bohmian trajectories can be obtained for $\\Psi $ from the trajectories of a sequence $\\Psi_{n}\\rightarrow \\Psi.$ (For any real $t$ the sequence $\\Psi_{n}\\left( t,\\cdot \\right) $ converges strongly.) The limiting trajectories no longer need to be differentiable. This suggests a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2852","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":"2026-05-18T04:36:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pIPi6VMu2vffwoXizJgLMfvrb5vIRtSaj7Kt+4FSGGeUDxjxNIb9LLGU/Tlcit1+4zN2DYN1/v+gobFm9RQZAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T21:52:52.433627Z"},"content_sha256":"24f11cea15563d05a6092330d1a05893a77aad9141af9f33506ed372ba4a0c5f","schema_version":"1.0","event_id":"sha256:24f11cea15563d05a6092330d1a05893a77aad9141af9f33506ed372ba4a0c5f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZUMAIP2GGTL5GITU2KXYGRUBE4/bundle.json","state_url":"https://pith.science/pith/ZUMAIP2GGTL5GITU2KXYGRUBE4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZUMAIP2GGTL5GITU2KXYGRUBE4/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":"2026-06-22T21:52:52Z","links":{"resolver":"https://pith.science/pith/ZUMAIP2GGTL5GITU2KXYGRUBE4","bundle":"https://pith.science/pith/ZUMAIP2GGTL5GITU2KXYGRUBE4/bundle.json","state":"https://pith.science/pith/ZUMAIP2GGTL5GITU2KXYGRUBE4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZUMAIP2GGTL5GITU2KXYGRUBE4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:ZUMAIP2GGTL5GITU2KXYGRUBE4","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":"b37c5500642c296cd08b9182648f202a457fc0af359e24f491dff891322b1800","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-11-12T09:09:51Z","title_canon_sha256":"145d9549bbe6d3dc7e5c2d105720914d1ffa2154093751124d13b549741345df"},"schema_version":"1.0","source":{"id":"1011.2852","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.2852","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"1011.2852v1","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.2852","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"ZUMAIP2GGTL5","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"ZUMAIP2GGTL5GITU","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"ZUMAIP2G","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:24f11cea15563d05a6092330d1a05893a77aad9141af9f33506ed372ba4a0c5f","target":"graph","created_at":"2026-05-18T04:36:08Z","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":"A solution $\\psi $ to Schr\\\"odinger's equation needs some degree of regularity in order to allow the construction of a Bohmian mechanics from the integral curves of the velocity field $\\hbar \\Im \\left( \\bigtriangledown \\psi /m\\psi \\right) .$ In the case of one specific non-differentiable weak solution $\\Psi $ we show how Bohmian trajectories can be obtained for $\\Psi $ from the trajectories of a sequence $\\Psi_{n}\\rightarrow \\Psi.$ (For any real $t$ the sequence $\\Psi_{n}\\left( t,\\cdot \\right) $ converges strongly.) The limiting trajectories no longer need to be differentiable. This suggests a","authors_text":"Gebhard Gruebl, Markus Penz","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-11-12T09:09:51Z","title":"Non-differentiable Bohmian trajectories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2852","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":"sha256:8994cb34bc1f2805a35e7f7c642ed1215bf0d6a8e1cdd6469f64708793258314","target":"record","created_at":"2026-05-18T04:36:08Z","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":"b37c5500642c296cd08b9182648f202a457fc0af359e24f491dff891322b1800","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2010-11-12T09:09:51Z","title_canon_sha256":"145d9549bbe6d3dc7e5c2d105720914d1ffa2154093751124d13b549741345df"},"schema_version":"1.0","source":{"id":"1011.2852","kind":"arxiv","version":1}},"canonical_sha256":"cd18043f4634d7d32274d2af8346812712e43e69ccbf780d4e2c4c2460951209","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd18043f4634d7d32274d2af8346812712e43e69ccbf780d4e2c4c2460951209","first_computed_at":"2026-05-18T04:36:08.037553Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:08.037553Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gBa9YxLtUOOAz+h4x5Br8IP9K1GDxlAWib1VAXwtEq55lP8MZZJO5ELJgTi7bNkMY3wTsR7PIdX2TAfs18ZlAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:08.038251Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.2852","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8994cb34bc1f2805a35e7f7c642ed1215bf0d6a8e1cdd6469f64708793258314","sha256:24f11cea15563d05a6092330d1a05893a77aad9141af9f33506ed372ba4a0c5f"],"state_sha256":"25030a43c51fb8c6cc3ec008b09eb1fce99565a2b82fddc3a70507a0bd6fb2f3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tf3+G1RNSTJzlbST0X3okIgpXYC7eerYnqH/BTPpwXS7MAYsQ1GLmcXJoYY9VdEmfYB1plqUsqeT503npmssBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T21:52:52.435557Z","bundle_sha256":"e91eaa4f988ee8c2f374b9c1e747d6518117d09abde523d89e60619d17baee39"}}