{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PQ2GR527NJ2ODDKLO3WNUCJUPF","short_pith_number":"pith:PQ2GR527","canonical_record":{"source":{"id":"1410.5199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-20T09:02:03Z","cross_cats_sorted":["cond-mat.quant-gas","math.MP"],"title_canon_sha256":"dc3f2ee709c54e44d42229cd13d0b6a2307a85b2007da89af441cf738ab2d8b5","abstract_canon_sha256":"1d342b7ccc9784e1e701087e24b642ff3584e44dc79072b6f4caaeaef4011451"},"schema_version":"1.0"},"canonical_sha256":"7c3468f75f6a74e18d4b76ecda093479779cd0ba01190d6b109d09ffd6064cb1","source":{"kind":"arxiv","id":"1410.5199","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5199","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5199v1","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5199","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"pith_short_12","alias_value":"PQ2GR527NJ2O","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PQ2GR527NJ2ODDKL","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PQ2GR527","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PQ2GR527NJ2ODDKLO3WNUCJUPF","target":"record","payload":{"canonical_record":{"source":{"id":"1410.5199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-20T09:02:03Z","cross_cats_sorted":["cond-mat.quant-gas","math.MP"],"title_canon_sha256":"dc3f2ee709c54e44d42229cd13d0b6a2307a85b2007da89af441cf738ab2d8b5","abstract_canon_sha256":"1d342b7ccc9784e1e701087e24b642ff3584e44dc79072b6f4caaeaef4011451"},"schema_version":"1.0"},"canonical_sha256":"7c3468f75f6a74e18d4b76ecda093479779cd0ba01190d6b109d09ffd6064cb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:39:46.619412Z","signature_b64":"nWJNz8Zto3dZKQ7Ure1NITtNuo7YeUa6jwLlk4fPWteA+Q+U4peqqNYuoE6Hc8Zr25KJzJBp6Hp49tzl7K6BAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c3468f75f6a74e18d4b76ecda093479779cd0ba01190d6b109d09ffd6064cb1","last_reissued_at":"2026-05-18T02:39:46.618902Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:39:46.618902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1410.5199","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":"2026-05-18T02:39:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DtVdqT2XNHQMQlIddot97YQNof1eXt8LFfRSJ3yO50r0RLDD1uQYwCDcplPbcZmc3OQc+OEyrQIeKJyrXZFOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:07:06.808955Z"},"content_sha256":"31c315804e2b0c2d086c3bb82ae660831b08274d073d5edf3549ba7d1b7b6e76","schema_version":"1.0","event_id":"sha256:31c315804e2b0c2d086c3bb82ae660831b08274d073d5edf3549ba7d1b7b6e76"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PQ2GR527NJ2ODDKLO3WNUCJUPF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Series expansion for the Fourier transform of a rational function in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.quant-gas","math.MP"],"primary_cat":"math-ph","authors_text":"Rytis Jursenas","submitted_at":"2014-10-20T09:02:03Z","abstract_excerpt":"In Rashba-Dresselhaus spin-orbit coupled systems, the calculation of Green's function requires the knowledge of the inverse Fourier transform of rational function $P(p)/Q(p)$, where $P(p)$ takes the values $1$ and $p^{2}$, and where \\[ Q(p)=(p^{2}-\\zeta)^{2}- \\alpha^{2}(p_{1}^{2}+p_{2}^{2})-\\beta^{2} \\] with suitable parameters $\\alpha$, $\\beta\\geq0$, $\\zeta\\in\\mathbb{C}$. While a two-dimensional problem, with $p=(p_{1},p_{2})$, has been recently solved [J. Br\\\"{u}ning et al, J. Phys. A: Math. Theor. 40 (2007)], its three-dimensional analogue, with $p=(p_{1},p_{2},p_{3})$, remains open. In thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5199","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":"2026-05-18T02:39:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6bv1IeWbVezeHVYDuiBjXEsl09TKro0hWlvviwXTJKufJ1UcStgAU7GkHkALD7ePa67mfOl+mtHHigGaR+o9Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T00:07:06.809703Z"},"content_sha256":"1671a433e167c73d0cb422bdebb22aa568e87eb8bcf94bcf608b9a016c2fb473","schema_version":"1.0","event_id":"sha256:1671a433e167c73d0cb422bdebb22aa568e87eb8bcf94bcf608b9a016c2fb473"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQ2GR527NJ2ODDKLO3WNUCJUPF/bundle.json","state_url":"https://pith.science/pith/PQ2GR527NJ2ODDKLO3WNUCJUPF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQ2GR527NJ2ODDKLO3WNUCJUPF/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":"2026-06-10T00:07:06Z","links":{"resolver":"https://pith.science/pith/PQ2GR527NJ2ODDKLO3WNUCJUPF","bundle":"https://pith.science/pith/PQ2GR527NJ2ODDKLO3WNUCJUPF/bundle.json","state":"https://pith.science/pith/PQ2GR527NJ2ODDKLO3WNUCJUPF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQ2GR527NJ2ODDKLO3WNUCJUPF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PQ2GR527NJ2ODDKLO3WNUCJUPF","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":"1d342b7ccc9784e1e701087e24b642ff3584e44dc79072b6f4caaeaef4011451","cross_cats_sorted":["cond-mat.quant-gas","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-20T09:02:03Z","title_canon_sha256":"dc3f2ee709c54e44d42229cd13d0b6a2307a85b2007da89af441cf738ab2d8b5"},"schema_version":"1.0","source":{"id":"1410.5199","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.5199","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"arxiv_version","alias_value":"1410.5199v1","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.5199","created_at":"2026-05-18T02:39:46Z"},{"alias_kind":"pith_short_12","alias_value":"PQ2GR527NJ2O","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PQ2GR527NJ2ODDKL","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PQ2GR527","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:1671a433e167c73d0cb422bdebb22aa568e87eb8bcf94bcf608b9a016c2fb473","target":"graph","created_at":"2026-05-18T02:39:46Z","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 Rashba-Dresselhaus spin-orbit coupled systems, the calculation of Green's function requires the knowledge of the inverse Fourier transform of rational function $P(p)/Q(p)$, where $P(p)$ takes the values $1$ and $p^{2}$, and where \\[ Q(p)=(p^{2}-\\zeta)^{2}- \\alpha^{2}(p_{1}^{2}+p_{2}^{2})-\\beta^{2} \\] with suitable parameters $\\alpha$, $\\beta\\geq0$, $\\zeta\\in\\mathbb{C}$. While a two-dimensional problem, with $p=(p_{1},p_{2})$, has been recently solved [J. Br\\\"{u}ning et al, J. Phys. A: Math. Theor. 40 (2007)], its three-dimensional analogue, with $p=(p_{1},p_{2},p_{3})$, remains open. In thi","authors_text":"Rytis Jursenas","cross_cats":["cond-mat.quant-gas","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-20T09:02:03Z","title":"Series expansion for the Fourier transform of a rational function in three dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.5199","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":"sha256:31c315804e2b0c2d086c3bb82ae660831b08274d073d5edf3549ba7d1b7b6e76","target":"record","created_at":"2026-05-18T02:39:46Z","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":"1d342b7ccc9784e1e701087e24b642ff3584e44dc79072b6f4caaeaef4011451","cross_cats_sorted":["cond-mat.quant-gas","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2014-10-20T09:02:03Z","title_canon_sha256":"dc3f2ee709c54e44d42229cd13d0b6a2307a85b2007da89af441cf738ab2d8b5"},"schema_version":"1.0","source":{"id":"1410.5199","kind":"arxiv","version":1}},"canonical_sha256":"7c3468f75f6a74e18d4b76ecda093479779cd0ba01190d6b109d09ffd6064cb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c3468f75f6a74e18d4b76ecda093479779cd0ba01190d6b109d09ffd6064cb1","first_computed_at":"2026-05-18T02:39:46.618902Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:39:46.618902Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nWJNz8Zto3dZKQ7Ure1NITtNuo7YeUa6jwLlk4fPWteA+Q+U4peqqNYuoE6Hc8Zr25KJzJBp6Hp49tzl7K6BAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:39:46.619412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.5199","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31c315804e2b0c2d086c3bb82ae660831b08274d073d5edf3549ba7d1b7b6e76","sha256:1671a433e167c73d0cb422bdebb22aa568e87eb8bcf94bcf608b9a016c2fb473"],"state_sha256":"abebc53577d20dca4f124b9183bc2ef3d34c88991573d00b68ace38a7bd29cf0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H65BLb5ZtQ42bdTLDv933oMAQtZsaBCmYI2dz/Zy74HGR8IaxA/1kDZrDwItkw/5e6i8gB8HWOwK56NFyvd3DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T00:07:06.813543Z","bundle_sha256":"203820fc9a8164a1d9fad87d7804093322097617d5586e741117e322dd3a147d"}}