{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CAMMDELT4WBVMMLOECVGIUOHMS","short_pith_number":"pith:CAMMDELT","canonical_record":{"source":{"id":"1707.01824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-07-06T14:50:24Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"be413cccea2d3d10d3c5978506d6305fc384eaa6c515680210154d2999906994","abstract_canon_sha256":"6a90b5aed7c1cea095154fddd8f9c42444286b5af940b223b3220a3cc83c1e46"},"schema_version":"1.0"},"canonical_sha256":"1018c19173e58356316e20aa6451c764ac0f9f830a7c87f9c1297e1a952e8fa3","source":{"kind":"arxiv","id":"1707.01824","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01824","created_at":"2026-05-18T00:25:56Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01824v1","created_at":"2026-05-18T00:25:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01824","created_at":"2026-05-18T00:25:56Z"},{"alias_kind":"pith_short_12","alias_value":"CAMMDELT4WBV","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CAMMDELT4WBVMMLO","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CAMMDELT","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CAMMDELT4WBVMMLOECVGIUOHMS","target":"record","payload":{"canonical_record":{"source":{"id":"1707.01824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-07-06T14:50:24Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"be413cccea2d3d10d3c5978506d6305fc384eaa6c515680210154d2999906994","abstract_canon_sha256":"6a90b5aed7c1cea095154fddd8f9c42444286b5af940b223b3220a3cc83c1e46"},"schema_version":"1.0"},"canonical_sha256":"1018c19173e58356316e20aa6451c764ac0f9f830a7c87f9c1297e1a952e8fa3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:56.756135Z","signature_b64":"iZA0LAizGJ1LId9M5k2sv45u7jNktE318CGy+9N5DcJnqcS9KOB7kfmYdTHOCVrysgpW+cUlIAB9YXsj/q2wCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1018c19173e58356316e20aa6451c764ac0f9f830a7c87f9c1297e1a952e8fa3","last_reissued_at":"2026-05-18T00:25:56.755445Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:56.755445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.01824","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":"2026-05-18T00:25:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NU2rstVSdcq49jZJ6LhAbg5m4iQUHwRIoeFWmy5KTnaDydlC+A4tXtNRalD9NKF2r2z5wsW2/cL9IU76kGEaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:06:31.559639Z"},"content_sha256":"7456cbdf993a530e29f439f4bfe575ee8bbf2666f2b6a99c000267fe87871aca","schema_version":"1.0","event_id":"sha256:7456cbdf993a530e29f439f4bfe575ee8bbf2666f2b6a99c000267fe87871aca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CAMMDELT4WBVMMLOECVGIUOHMS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Computation of unitary group for the Rashba spin-orbit coupled operator, with application to point-interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Rytis Jursenas","submitted_at":"2017-07-06T14:50:24Z","abstract_excerpt":"We compute an explicit formula for the one-parameter unitary group of the single-particle Rashba spin-orbit coupled operator in dimension three. As an application, we derive the formula for the Green function for the two-particle operator, and then prove that the spin-dependent point-interaction is of class $\\mathcal{H}_{-4}$. The latter is thus the example of a supersingular perturbation for which no self-adjoint operator can be constructed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01824","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":"2026-05-18T00:25:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lUmwWoNYkVjlfk+bCnITkcge68k624ixZuifx1ROghXDFMRX+Hy0UeZkgjoxKN3W3X/vHZbdG8ZoxUulo3bBDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:06:31.560411Z"},"content_sha256":"fe931db2ac4e81103882bbcc80a16691461c36c0524aad7a7cfb66e56ce37417","schema_version":"1.0","event_id":"sha256:fe931db2ac4e81103882bbcc80a16691461c36c0524aad7a7cfb66e56ce37417"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CAMMDELT4WBVMMLOECVGIUOHMS/bundle.json","state_url":"https://pith.science/pith/CAMMDELT4WBVMMLOECVGIUOHMS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CAMMDELT4WBVMMLOECVGIUOHMS/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":"2026-06-10T08:06:31Z","links":{"resolver":"https://pith.science/pith/CAMMDELT4WBVMMLOECVGIUOHMS","bundle":"https://pith.science/pith/CAMMDELT4WBVMMLOECVGIUOHMS/bundle.json","state":"https://pith.science/pith/CAMMDELT4WBVMMLOECVGIUOHMS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CAMMDELT4WBVMMLOECVGIUOHMS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CAMMDELT4WBVMMLOECVGIUOHMS","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":"6a90b5aed7c1cea095154fddd8f9c42444286b5af940b223b3220a3cc83c1e46","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-07-06T14:50:24Z","title_canon_sha256":"be413cccea2d3d10d3c5978506d6305fc384eaa6c515680210154d2999906994"},"schema_version":"1.0","source":{"id":"1707.01824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.01824","created_at":"2026-05-18T00:25:56Z"},{"alias_kind":"arxiv_version","alias_value":"1707.01824v1","created_at":"2026-05-18T00:25:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.01824","created_at":"2026-05-18T00:25:56Z"},{"alias_kind":"pith_short_12","alias_value":"CAMMDELT4WBV","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CAMMDELT4WBVMMLO","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CAMMDELT","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:fe931db2ac4e81103882bbcc80a16691461c36c0524aad7a7cfb66e56ce37417","target":"graph","created_at":"2026-05-18T00:25:56Z","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 compute an explicit formula for the one-parameter unitary group of the single-particle Rashba spin-orbit coupled operator in dimension three. As an application, we derive the formula for the Green function for the two-particle operator, and then prove that the spin-dependent point-interaction is of class $\\mathcal{H}_{-4}$. The latter is thus the example of a supersingular perturbation for which no self-adjoint operator can be constructed.","authors_text":"Rytis Jursenas","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-07-06T14:50:24Z","title":"Computation of unitary group for the Rashba spin-orbit coupled operator, with application to point-interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.01824","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":"sha256:7456cbdf993a530e29f439f4bfe575ee8bbf2666f2b6a99c000267fe87871aca","target":"record","created_at":"2026-05-18T00:25:56Z","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":"6a90b5aed7c1cea095154fddd8f9c42444286b5af940b223b3220a3cc83c1e46","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-07-06T14:50:24Z","title_canon_sha256":"be413cccea2d3d10d3c5978506d6305fc384eaa6c515680210154d2999906994"},"schema_version":"1.0","source":{"id":"1707.01824","kind":"arxiv","version":1}},"canonical_sha256":"1018c19173e58356316e20aa6451c764ac0f9f830a7c87f9c1297e1a952e8fa3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1018c19173e58356316e20aa6451c764ac0f9f830a7c87f9c1297e1a952e8fa3","first_computed_at":"2026-05-18T00:25:56.755445Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:25:56.755445Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iZA0LAizGJ1LId9M5k2sv45u7jNktE318CGy+9N5DcJnqcS9KOB7kfmYdTHOCVrysgpW+cUlIAB9YXsj/q2wCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:25:56.756135Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.01824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7456cbdf993a530e29f439f4bfe575ee8bbf2666f2b6a99c000267fe87871aca","sha256:fe931db2ac4e81103882bbcc80a16691461c36c0524aad7a7cfb66e56ce37417"],"state_sha256":"5193b1d0a4c4a4fb44d2f7600a81b7ed7c401e5ead79131e9a0ff694b0245c2d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sE/KwO0TqxCqKHuYMyrW2AJIMTW+YXXsZbqtQt5N0fYNpZexNayq8mgfeg5mkraa3tpVhC4oTduZO4sYbZTJCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T08:06:31.564522Z","bundle_sha256":"260352aa92120b8683f8088eeaa3ca46c06e8544190aea2366167e6092aaefa4"}}