{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2003:JBJTHUPLNYGR2R3DTO2PZ464AC","short_pith_number":"pith:JBJTHUPL","canonical_record":{"source":{"id":"quant-ph/0302148","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2003-02-20T07:41:00Z","cross_cats_sorted":[],"title_canon_sha256":"ed81a098c4080c71fa72093e304f63c6489117bd8a03eea4c828af9336e523c4","abstract_canon_sha256":"eb51fec60922005b3bdde92fea89f01e6e9f7ff504f8ca9991e31fe667ab6cc9"},"schema_version":"1.0"},"canonical_sha256":"485333d1eb6e0d1d47639bb4fcf3dc009830ea6ce3bd82b6ff5ff9a8cab5a8b8","source":{"kind":"arxiv","id":"quant-ph/0302148","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0302148","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0302148v1","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0302148","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"JBJTHUPLNYGR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"JBJTHUPLNYGR2R3D","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"JBJTHUPL","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2003:JBJTHUPLNYGR2R3DTO2PZ464AC","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0302148","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2003-02-20T07:41:00Z","cross_cats_sorted":[],"title_canon_sha256":"ed81a098c4080c71fa72093e304f63c6489117bd8a03eea4c828af9336e523c4","abstract_canon_sha256":"eb51fec60922005b3bdde92fea89f01e6e9f7ff504f8ca9991e31fe667ab6cc9"},"schema_version":"1.0"},"canonical_sha256":"485333d1eb6e0d1d47639bb4fcf3dc009830ea6ce3bd82b6ff5ff9a8cab5a8b8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:59.547369Z","signature_b64":"yoxTo7sa084p59HX41BB311tDTzPWQV4Lmog7/whMDc267QbcCywr+RHXq1apM5BEiT7f4GrTcCxzK948aJrCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"485333d1eb6e0d1d47639bb4fcf3dc009830ea6ce3bd82b6ff5ff9a8cab5a8b8","last_reissued_at":"2026-05-18T01:37:59.546814Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:59.546814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0302148","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":"2026-05-18T01:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qeNMQD8EshFGKL1Hzk3M/YlkdYSkJMiApS7zi6QrsMjH0H8iGJI9DPSMVS2Uz3zGRJNrC7e2WUs3EgO/wjqMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:21:28.278311Z"},"content_sha256":"4dcdf333aef5107e822749172e42f925acc4fd84cda9f99a599f2bae5d50c349","schema_version":"1.0","event_id":"sha256:4dcdf333aef5107e822749172e42f925acc4fd84cda9f99a599f2bae5d50c349"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2003:JBJTHUPLNYGR2R3DTO2PZ464AC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Zero-Energy Flows and Vortex Patterns in Quantum Mechanics","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Tsunehiro Kobayashi","submitted_at":"2003-02-20T07:41:00Z","abstract_excerpt":"We show that zero-energy flows appear in many particle systems as same as in single particle cases in 2-dimensions. Vortex patterns constructed from the zero-energy flows can be investigated in terms of the eigenstates in conjugate spaces of Gel'fand triplets. Stable patterns are written by the superposition of zero-energy eigenstates. On the other hand vortex creations and annihilations are described by the insertions of unstable eigenstates with complex-energy eigenvalues into the stable patterns. Some concrete examples are presented in the 2-dimensional parabolic potential barrier case. %, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0302148","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":"2026-05-18T01:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W369jF0TGfLpZhTahM1DNqENUyEBmEbentkYWo47kXe7knfxDWVzSH5/i2kehBpZEEIiFRsk/GjmaXaUsZG2BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T05:21:28.278679Z"},"content_sha256":"e01e831caf3f1d0d64adbfd31106cc5d7ad4882084602e4ad77ec3eb5d8e177a","schema_version":"1.0","event_id":"sha256:e01e831caf3f1d0d64adbfd31106cc5d7ad4882084602e4ad77ec3eb5d8e177a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JBJTHUPLNYGR2R3DTO2PZ464AC/bundle.json","state_url":"https://pith.science/pith/JBJTHUPLNYGR2R3DTO2PZ464AC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JBJTHUPLNYGR2R3DTO2PZ464AC/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":"2026-06-03T05:21:28Z","links":{"resolver":"https://pith.science/pith/JBJTHUPLNYGR2R3DTO2PZ464AC","bundle":"https://pith.science/pith/JBJTHUPLNYGR2R3DTO2PZ464AC/bundle.json","state":"https://pith.science/pith/JBJTHUPLNYGR2R3DTO2PZ464AC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JBJTHUPLNYGR2R3DTO2PZ464AC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2003:JBJTHUPLNYGR2R3DTO2PZ464AC","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":"eb51fec60922005b3bdde92fea89f01e6e9f7ff504f8ca9991e31fe667ab6cc9","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2003-02-20T07:41:00Z","title_canon_sha256":"ed81a098c4080c71fa72093e304f63c6489117bd8a03eea4c828af9336e523c4"},"schema_version":"1.0","source":{"id":"quant-ph/0302148","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0302148","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0302148v1","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0302148","created_at":"2026-05-18T01:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"JBJTHUPLNYGR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"JBJTHUPLNYGR2R3D","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"JBJTHUPL","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:e01e831caf3f1d0d64adbfd31106cc5d7ad4882084602e4ad77ec3eb5d8e177a","target":"graph","created_at":"2026-05-18T01:37:59Z","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 show that zero-energy flows appear in many particle systems as same as in single particle cases in 2-dimensions. Vortex patterns constructed from the zero-energy flows can be investigated in terms of the eigenstates in conjugate spaces of Gel'fand triplets. Stable patterns are written by the superposition of zero-energy eigenstates. On the other hand vortex creations and annihilations are described by the insertions of unstable eigenstates with complex-energy eigenvalues into the stable patterns. Some concrete examples are presented in the 2-dimensional parabolic potential barrier case. %, ","authors_text":"Tsunehiro Kobayashi","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2003-02-20T07:41:00Z","title":"Zero-Energy Flows and Vortex Patterns in Quantum Mechanics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0302148","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":"sha256:4dcdf333aef5107e822749172e42f925acc4fd84cda9f99a599f2bae5d50c349","target":"record","created_at":"2026-05-18T01:37:59Z","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":"eb51fec60922005b3bdde92fea89f01e6e9f7ff504f8ca9991e31fe667ab6cc9","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2003-02-20T07:41:00Z","title_canon_sha256":"ed81a098c4080c71fa72093e304f63c6489117bd8a03eea4c828af9336e523c4"},"schema_version":"1.0","source":{"id":"quant-ph/0302148","kind":"arxiv","version":1}},"canonical_sha256":"485333d1eb6e0d1d47639bb4fcf3dc009830ea6ce3bd82b6ff5ff9a8cab5a8b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"485333d1eb6e0d1d47639bb4fcf3dc009830ea6ce3bd82b6ff5ff9a8cab5a8b8","first_computed_at":"2026-05-18T01:37:59.546814Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:59.546814Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yoxTo7sa084p59HX41BB311tDTzPWQV4Lmog7/whMDc267QbcCywr+RHXq1apM5BEiT7f4GrTcCxzK948aJrCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:59.547369Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0302148","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4dcdf333aef5107e822749172e42f925acc4fd84cda9f99a599f2bae5d50c349","sha256:e01e831caf3f1d0d64adbfd31106cc5d7ad4882084602e4ad77ec3eb5d8e177a"],"state_sha256":"d861eac5a4432fb3e1aec7fc36638865f75076b86b8b2fcbcf24abce2d23757a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SAujb1ij3n5zxaZaqoSqFKc93+mo/0E2iKlR8u3imltKQIKJ5RXdN+FNRDYhHP2X0IreyQDL5dlUu2aKlbWfAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T05:21:28.280788Z","bundle_sha256":"e1e943b54293fb496319c3ddc5efba457756a85b14f093e991a10e5af3f0cc9f"}}