{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:P22DPKUFQICZ2AZENGDQJS3POE","short_pith_number":"pith:P22DPKUF","canonical_record":{"source":{"id":"0708.2962","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2007-08-22T13:40:02Z","cross_cats_sorted":[],"title_canon_sha256":"abe79964461a133d286dd8c7987f57796fbe3e4896d524c4a4c7a4de2c4e077f","abstract_canon_sha256":"8f8b05643a757747b6a0ab375d7568ecd1a3692ac93f6a72510f69173bcd4a84"},"schema_version":"1.0"},"canonical_sha256":"7eb437aa8582059d0324698704cb6f7107f81a7637975964bdfa35b0e862dee3","source":{"kind":"arxiv","id":"0708.2962","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.2962","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"arxiv_version","alias_value":"0708.2962v5","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2962","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"pith_short_12","alias_value":"P22DPKUFQICZ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"P22DPKUFQICZ2AZE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"P22DPKUF","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:P22DPKUFQICZ2AZENGDQJS3POE","target":"record","payload":{"canonical_record":{"source":{"id":"0708.2962","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2007-08-22T13:40:02Z","cross_cats_sorted":[],"title_canon_sha256":"abe79964461a133d286dd8c7987f57796fbe3e4896d524c4a4c7a4de2c4e077f","abstract_canon_sha256":"8f8b05643a757747b6a0ab375d7568ecd1a3692ac93f6a72510f69173bcd4a84"},"schema_version":"1.0"},"canonical_sha256":"7eb437aa8582059d0324698704cb6f7107f81a7637975964bdfa35b0e862dee3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:38.417071Z","signature_b64":"v53zdSsLm/1yRwuQMnpXCWtVNeqIbS+pfENILAZp/9ApPX9BRhI88CKvqGWcbGj9taycuB6revYC61DV03KBBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7eb437aa8582059d0324698704cb6f7107f81a7637975964bdfa35b0e862dee3","last_reissued_at":"2026-05-18T00:28:38.416416Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:38.416416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0708.2962","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:28:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+WBncRrtT/S1oxGXfZsQhdBLA04FVP8UyWluSrEdN0A2rZID8Qx1TmzffPVt2YTlk4sgoR3mHdwf/KbOfmFEDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:05:10.102710Z"},"content_sha256":"eeed92cab296584a8ed44d7e812ca25b873b49d6b512f269a0e56f9b36b16e5b","schema_version":"1.0","event_id":"sha256:eeed92cab296584a8ed44d7e812ca25b873b49d6b512f269a0e56f9b36b16e5b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:P22DPKUFQICZ2AZENGDQJS3POE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Procedure to Solve the Eigen Solution to Dirac Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Ying-Qiu Gu","submitted_at":"2007-08-22T13:40:02Z","abstract_excerpt":"In this paper, we provide a procedure to solve the eigen solutions of Dirac equation with complicated potential approximately. At first, we solve the eigen solutions of a linear Dirac equation with complete eigen system, which approximately equals to the original equation. Take the eigen functions as base of Hilbert space, and expand the spinor on the bases, we convert the original problem into solution of extremum of an algebraic function on the unit sphere of the coefficients. Then the problem can be easily solved. This is a standard finite element method with strict theory for convergence a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2962","kind":"arxiv","version":5},"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":"2026-05-18T00:28:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i27mSiZDRrXeZTC4ZuhYwMY7gXZdE8FMm03+yWLMwVzB5Jl8mjWB/xIbkICP6zpymkWej6IijpvU5HmOkwG4Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:05:10.103394Z"},"content_sha256":"5a52b5a94ec916982d11473e9e4644a32e27ef4cae1cec53323834acec429f81","schema_version":"1.0","event_id":"sha256:5a52b5a94ec916982d11473e9e4644a32e27ef4cae1cec53323834acec429f81"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P22DPKUFQICZ2AZENGDQJS3POE/bundle.json","state_url":"https://pith.science/pith/P22DPKUFQICZ2AZENGDQJS3POE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P22DPKUFQICZ2AZENGDQJS3POE/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":"2026-05-31T20:05:10Z","links":{"resolver":"https://pith.science/pith/P22DPKUFQICZ2AZENGDQJS3POE","bundle":"https://pith.science/pith/P22DPKUFQICZ2AZENGDQJS3POE/bundle.json","state":"https://pith.science/pith/P22DPKUFQICZ2AZENGDQJS3POE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P22DPKUFQICZ2AZENGDQJS3POE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:P22DPKUFQICZ2AZENGDQJS3POE","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":"8f8b05643a757747b6a0ab375d7568ecd1a3692ac93f6a72510f69173bcd4a84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2007-08-22T13:40:02Z","title_canon_sha256":"abe79964461a133d286dd8c7987f57796fbe3e4896d524c4a4c7a4de2c4e077f"},"schema_version":"1.0","source":{"id":"0708.2962","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0708.2962","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"arxiv_version","alias_value":"0708.2962v5","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0708.2962","created_at":"2026-05-18T00:28:38Z"},{"alias_kind":"pith_short_12","alias_value":"P22DPKUFQICZ","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"P22DPKUFQICZ2AZE","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"P22DPKUF","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:5a52b5a94ec916982d11473e9e4644a32e27ef4cae1cec53323834acec429f81","target":"graph","created_at":"2026-05-18T00:28:38Z","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 this paper, we provide a procedure to solve the eigen solutions of Dirac equation with complicated potential approximately. At first, we solve the eigen solutions of a linear Dirac equation with complete eigen system, which approximately equals to the original equation. Take the eigen functions as base of Hilbert space, and expand the spinor on the bases, we convert the original problem into solution of extremum of an algebraic function on the unit sphere of the coefficients. Then the problem can be easily solved. This is a standard finite element method with strict theory for convergence a","authors_text":"Ying-Qiu Gu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2007-08-22T13:40:02Z","title":"A Procedure to Solve the Eigen Solution to Dirac Equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0708.2962","kind":"arxiv","version":5},"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:eeed92cab296584a8ed44d7e812ca25b873b49d6b512f269a0e56f9b36b16e5b","target":"record","created_at":"2026-05-18T00:28:38Z","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":"8f8b05643a757747b6a0ab375d7568ecd1a3692ac93f6a72510f69173bcd4a84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2007-08-22T13:40:02Z","title_canon_sha256":"abe79964461a133d286dd8c7987f57796fbe3e4896d524c4a4c7a4de2c4e077f"},"schema_version":"1.0","source":{"id":"0708.2962","kind":"arxiv","version":5}},"canonical_sha256":"7eb437aa8582059d0324698704cb6f7107f81a7637975964bdfa35b0e862dee3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7eb437aa8582059d0324698704cb6f7107f81a7637975964bdfa35b0e862dee3","first_computed_at":"2026-05-18T00:28:38.416416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:38.416416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v53zdSsLm/1yRwuQMnpXCWtVNeqIbS+pfENILAZp/9ApPX9BRhI88CKvqGWcbGj9taycuB6revYC61DV03KBBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:38.417071Z","signed_message":"canonical_sha256_bytes"},"source_id":"0708.2962","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eeed92cab296584a8ed44d7e812ca25b873b49d6b512f269a0e56f9b36b16e5b","sha256:5a52b5a94ec916982d11473e9e4644a32e27ef4cae1cec53323834acec429f81"],"state_sha256":"da2d424c5e37bf44f6bb4779176add7913a0ed275ef0520b13f4d6918d3ae927"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4h8ioP2WMFrS7fleftIdElkEnMLeSsavtGvFY+WHfWBKp1UdRBTIGzwP1flvsCTkn3zZ2p8aY3sJOVyhsZ8/Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:05:10.106818Z","bundle_sha256":"1c300a0b8e6f3eaebf0ce8e2313d3c561c5c3bc15d477542b354542fa48c1fb1"}}