{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:N7HTYMBVPH37K6TOUUQ52ACEMK","short_pith_number":"pith:N7HTYMBV","canonical_record":{"source":{"id":"hep-th/0212134","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2002-12-11T18:47:01Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"c4025a575e07cf5ae90e0485d6f35c0d619728cf6b9fc926e75dcdc7bf48aac9","abstract_canon_sha256":"cb55f9fd151aa2d0c44c5ed67e143221e32b5656ad065ef81b2e61c27340a22f"},"schema_version":"1.0"},"canonical_sha256":"6fcf3c303579f7f57a6ea521dd0044628c40c24db4a67f6a8ba35700fb2e8848","source":{"kind":"arxiv","id":"hep-th/0212134","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0212134","created_at":"2026-07-04T14:31:54Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0212134v1","created_at":"2026-07-04T14:31:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0212134","created_at":"2026-07-04T14:31:54Z"},{"alias_kind":"pith_short_12","alias_value":"N7HTYMBVPH37","created_at":"2026-07-04T14:31:54Z"},{"alias_kind":"pith_short_16","alias_value":"N7HTYMBVPH37K6TO","created_at":"2026-07-04T14:31:54Z"},{"alias_kind":"pith_short_8","alias_value":"N7HTYMBV","created_at":"2026-07-04T14:31:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:N7HTYMBVPH37K6TOUUQ52ACEMK","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0212134","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2002-12-11T18:47:01Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"c4025a575e07cf5ae90e0485d6f35c0d619728cf6b9fc926e75dcdc7bf48aac9","abstract_canon_sha256":"cb55f9fd151aa2d0c44c5ed67e143221e32b5656ad065ef81b2e61c27340a22f"},"schema_version":"1.0"},"canonical_sha256":"6fcf3c303579f7f57a6ea521dd0044628c40c24db4a67f6a8ba35700fb2e8848","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:31:54.178959Z","signature_b64":"hPbYjWvq9jYf26c5bd6qMJgTdHBA/qiGRtm89Xoqv6O3xeh4YXS0+rzi7GMkv/UDay1mA9CuTBhLCUCB4BSEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6fcf3c303579f7f57a6ea521dd0044628c40c24db4a67f6a8ba35700fb2e8848","last_reissued_at":"2026-07-04T14:31:54.178591Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:31:54.178591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0212134","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":"2026-07-04T14:31:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TYnz/z0Q0paXWq9BYCqhu/bj8hFs7EcJZwQ+VCKGMWl9nUwMh1cQRfqOi1bPRiTZ7k88zS8x8Dv1/lDHFXb4AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:37:06.691354Z"},"content_sha256":"a03490d63a62d2a44e2974f00640bc5ccea8fbc1d6d1f8c6c6abae854cc46ed4","schema_version":"1.0","event_id":"sha256:a03490d63a62d2a44e2974f00640bc5ccea8fbc1d6d1f8c6c6abae854cc46ed4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:N7HTYMBVPH37K6TOUUQ52ACEMK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirac operator on the Riemann sphere","license":"","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"A. A. Abrikosov Jr","submitted_at":"2002-12-11T18:47:01Z","abstract_excerpt":"We solve for spectrum, obtain explicitly and study group properties of eigenfunctions of Dirac operator on the Riemann sphere $S^2$. The eigenvalues $\\lambda$ are nonzero integers. The eigenfunctions are two-component spinors that belong to representations of SU(2)-group with half-integer angular momenta $l = |\\lambda| - \\half$. They form on the sphere a complete orthonormal functional set alternative to conventional spherical spinors. The difference and relationship between the spherical spinors in question and the standard ones are explained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0212134","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/hep-th/0212134/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:31:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AMop2BIBamuDhZWr/FEuQql3q1uhP2fjZSHQfyAlmNgto+Kpd2+W63G30sh2A+XTs82SR7I5CR6eWOlYmueGCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:37:06.691909Z"},"content_sha256":"cec2edf19c09bf2e19e058837f840438c08bc0a75cf8ff233f2a4176534b9f3f","schema_version":"1.0","event_id":"sha256:cec2edf19c09bf2e19e058837f840438c08bc0a75cf8ff233f2a4176534b9f3f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7HTYMBVPH37K6TOUUQ52ACEMK/bundle.json","state_url":"https://pith.science/pith/N7HTYMBVPH37K6TOUUQ52ACEMK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7HTYMBVPH37K6TOUUQ52ACEMK/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":"2026-08-09T15:37:06Z","links":{"resolver":"https://pith.science/pith/N7HTYMBVPH37K6TOUUQ52ACEMK","bundle":"https://pith.science/pith/N7HTYMBVPH37K6TOUUQ52ACEMK/bundle.json","state":"https://pith.science/pith/N7HTYMBVPH37K6TOUUQ52ACEMK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7HTYMBVPH37K6TOUUQ52ACEMK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:N7HTYMBVPH37K6TOUUQ52ACEMK","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":"cb55f9fd151aa2d0c44c5ed67e143221e32b5656ad065ef81b2e61c27340a22f","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2002-12-11T18:47:01Z","title_canon_sha256":"c4025a575e07cf5ae90e0485d6f35c0d619728cf6b9fc926e75dcdc7bf48aac9"},"schema_version":"1.0","source":{"id":"hep-th/0212134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0212134","created_at":"2026-07-04T14:31:54Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0212134v1","created_at":"2026-07-04T14:31:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0212134","created_at":"2026-07-04T14:31:54Z"},{"alias_kind":"pith_short_12","alias_value":"N7HTYMBVPH37","created_at":"2026-07-04T14:31:54Z"},{"alias_kind":"pith_short_16","alias_value":"N7HTYMBVPH37K6TO","created_at":"2026-07-04T14:31:54Z"},{"alias_kind":"pith_short_8","alias_value":"N7HTYMBV","created_at":"2026-07-04T14:31:54Z"}],"graph_snapshots":[{"event_id":"sha256:cec2edf19c09bf2e19e058837f840438c08bc0a75cf8ff233f2a4176534b9f3f","target":"graph","created_at":"2026-07-04T14:31:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/0212134/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We solve for spectrum, obtain explicitly and study group properties of eigenfunctions of Dirac operator on the Riemann sphere $S^2$. The eigenvalues $\\lambda$ are nonzero integers. The eigenfunctions are two-component spinors that belong to representations of SU(2)-group with half-integer angular momenta $l = |\\lambda| - \\half$. They form on the sphere a complete orthonormal functional set alternative to conventional spherical spinors. The difference and relationship between the spherical spinors in question and the standard ones are explained.","authors_text":"A. A. Abrikosov Jr","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2002-12-11T18:47:01Z","title":"Dirac operator on the Riemann sphere"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0212134","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:a03490d63a62d2a44e2974f00640bc5ccea8fbc1d6d1f8c6c6abae854cc46ed4","target":"record","created_at":"2026-07-04T14:31:54Z","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":"cb55f9fd151aa2d0c44c5ed67e143221e32b5656ad065ef81b2e61c27340a22f","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"","primary_cat":"hep-th","submitted_at":"2002-12-11T18:47:01Z","title_canon_sha256":"c4025a575e07cf5ae90e0485d6f35c0d619728cf6b9fc926e75dcdc7bf48aac9"},"schema_version":"1.0","source":{"id":"hep-th/0212134","kind":"arxiv","version":1}},"canonical_sha256":"6fcf3c303579f7f57a6ea521dd0044628c40c24db4a67f6a8ba35700fb2e8848","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fcf3c303579f7f57a6ea521dd0044628c40c24db4a67f6a8ba35700fb2e8848","first_computed_at":"2026-07-04T14:31:54.178591Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:31:54.178591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hPbYjWvq9jYf26c5bd6qMJgTdHBA/qiGRtm89Xoqv6O3xeh4YXS0+rzi7GMkv/UDay1mA9CuTBhLCUCB4BSEDg==","signature_status":"signed_v1","signed_at":"2026-07-04T14:31:54.178959Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0212134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a03490d63a62d2a44e2974f00640bc5ccea8fbc1d6d1f8c6c6abae854cc46ed4","sha256:cec2edf19c09bf2e19e058837f840438c08bc0a75cf8ff233f2a4176534b9f3f"],"state_sha256":"5391e8cb169f68e1b7ad5667bc87197e7c40d593c0644cd3e696108d61318d6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HhsGO+HV9KXprM+jpc79IpQ4CGRAdTH/+I60mOeBBso3MFA7GS0X3Yj9Om62m9SKsx7+zVoztDVgVEucLe0PBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T15:37:06.697032Z","bundle_sha256":"a68157bf7f7da945070a1513bef02ca4fad62f016ddc23b7d7a9dfa9cf39bc8b"}}