{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:DQYDEIBVNHTU5GUZCLSAHGNINT","short_pith_number":"pith:DQYDEIBV","canonical_record":{"source":{"id":"1612.07149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2016-12-17T08:05:38Z","cross_cats_sorted":[],"title_canon_sha256":"d419f3be5b2d89fce9c368d86eb93457f9bad3a445eafced965f71f4a2118739","abstract_canon_sha256":"acf62eccdfaf9942dce186c9fea3d002d5ef7849eaf0fa6b70d4658cde12a80d"},"schema_version":"1.0"},"canonical_sha256":"1c3032203569e74e9a9912e40399a86cc868ed24ee963fac92a689bdb3c10338","source":{"kind":"arxiv","id":"1612.07149","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07149","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07149v1","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07149","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"pith_short_12","alias_value":"DQYDEIBVNHTU","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DQYDEIBVNHTU5GUZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DQYDEIBV","created_at":"2026-05-18T12:30:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:DQYDEIBVNHTU5GUZCLSAHGNINT","target":"record","payload":{"canonical_record":{"source":{"id":"1612.07149","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2016-12-17T08:05:38Z","cross_cats_sorted":[],"title_canon_sha256":"d419f3be5b2d89fce9c368d86eb93457f9bad3a445eafced965f71f4a2118739","abstract_canon_sha256":"acf62eccdfaf9942dce186c9fea3d002d5ef7849eaf0fa6b70d4658cde12a80d"},"schema_version":"1.0"},"canonical_sha256":"1c3032203569e74e9a9912e40399a86cc868ed24ee963fac92a689bdb3c10338","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:54:14.571869Z","signature_b64":"SBJczjWDvXC76chbcXp3MWOcq327zLRuDVMhFKYzkSclhS0IPIHgv4PH9c+n+0EpouiJnbupHeXQzpifEh4hBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1c3032203569e74e9a9912e40399a86cc868ed24ee963fac92a689bdb3c10338","last_reissued_at":"2026-05-18T00:54:14.571463Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:54:14.571463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.07149","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":"2026-05-18T00:54:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ABytO1zIro/KPBYmCF+fPQeOQdLvq3HRtjLbQGAq/7pTxUVzqfDjae2tMdut/afjz8eusTrn1rUeByipiiJ6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T11:01:26.212422Z"},"content_sha256":"18041141ca80f8339ac00011cbeea93b8198f80f337e128f5f89512d779a602b","schema_version":"1.0","event_id":"sha256:18041141ca80f8339ac00011cbeea93b8198f80f337e128f5f89512d779a602b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:DQYDEIBVNHTU5GUZCLSAHGNINT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topologically nontrivial solution in Einstein-Dirac gravity on the Hopf bundle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.gen-ph","authors_text":"Vladimir Dzhunushaliev","submitted_at":"2016-12-17T08:05:38Z","abstract_excerpt":"The topologically nontrivial solution in Einstein-Dirac gravity with cosmological constant is obtained. The spacetime has the Hopf bundle as a spatial section. It is shown that the Hopf invariant is related to the spinor current density. Two Dirac spinors are used for obtaining a diagonal energy-momentum tensor. The solutions for the nongravitating Dirac equation on the background of Lorentzian spacetime with the Hopf bundle as a spatial section are also obtained. Nongravitating solutions of the Dirac equation are defined by two quantum half-integer numbers $m, n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07149","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":"2026-05-18T00:54:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fa31LWAkx77W/M5p7FKRO3JeDuHGy3Mam9UXUDz86sCIA+kXjt5SZryBDB5weedvkTPeedXXBa9dL8cnYhX6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T11:01:26.212755Z"},"content_sha256":"36a5e9b60f9d4b7329cc9681317559e3bd815d32d24721e143b77c1bbcaed381","schema_version":"1.0","event_id":"sha256:36a5e9b60f9d4b7329cc9681317559e3bd815d32d24721e143b77c1bbcaed381"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DQYDEIBVNHTU5GUZCLSAHGNINT/bundle.json","state_url":"https://pith.science/pith/DQYDEIBVNHTU5GUZCLSAHGNINT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DQYDEIBVNHTU5GUZCLSAHGNINT/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":"2026-07-04T11:01:26Z","links":{"resolver":"https://pith.science/pith/DQYDEIBVNHTU5GUZCLSAHGNINT","bundle":"https://pith.science/pith/DQYDEIBVNHTU5GUZCLSAHGNINT/bundle.json","state":"https://pith.science/pith/DQYDEIBVNHTU5GUZCLSAHGNINT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DQYDEIBVNHTU5GUZCLSAHGNINT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DQYDEIBVNHTU5GUZCLSAHGNINT","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":"acf62eccdfaf9942dce186c9fea3d002d5ef7849eaf0fa6b70d4658cde12a80d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2016-12-17T08:05:38Z","title_canon_sha256":"d419f3be5b2d89fce9c368d86eb93457f9bad3a445eafced965f71f4a2118739"},"schema_version":"1.0","source":{"id":"1612.07149","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.07149","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"arxiv_version","alias_value":"1612.07149v1","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.07149","created_at":"2026-05-18T00:54:14Z"},{"alias_kind":"pith_short_12","alias_value":"DQYDEIBVNHTU","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DQYDEIBVNHTU5GUZ","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DQYDEIBV","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:36a5e9b60f9d4b7329cc9681317559e3bd815d32d24721e143b77c1bbcaed381","target":"graph","created_at":"2026-05-18T00:54:14Z","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":"The topologically nontrivial solution in Einstein-Dirac gravity with cosmological constant is obtained. The spacetime has the Hopf bundle as a spatial section. It is shown that the Hopf invariant is related to the spinor current density. Two Dirac spinors are used for obtaining a diagonal energy-momentum tensor. The solutions for the nongravitating Dirac equation on the background of Lorentzian spacetime with the Hopf bundle as a spatial section are also obtained. Nongravitating solutions of the Dirac equation are defined by two quantum half-integer numbers $m, n$.","authors_text":"Vladimir Dzhunushaliev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2016-12-17T08:05:38Z","title":"Topologically nontrivial solution in Einstein-Dirac gravity on the Hopf bundle"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.07149","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":"sha256:18041141ca80f8339ac00011cbeea93b8198f80f337e128f5f89512d779a602b","target":"record","created_at":"2026-05-18T00:54:14Z","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":"acf62eccdfaf9942dce186c9fea3d002d5ef7849eaf0fa6b70d4658cde12a80d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.gen-ph","submitted_at":"2016-12-17T08:05:38Z","title_canon_sha256":"d419f3be5b2d89fce9c368d86eb93457f9bad3a445eafced965f71f4a2118739"},"schema_version":"1.0","source":{"id":"1612.07149","kind":"arxiv","version":1}},"canonical_sha256":"1c3032203569e74e9a9912e40399a86cc868ed24ee963fac92a689bdb3c10338","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1c3032203569e74e9a9912e40399a86cc868ed24ee963fac92a689bdb3c10338","first_computed_at":"2026-05-18T00:54:14.571463Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:14.571463Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SBJczjWDvXC76chbcXp3MWOcq327zLRuDVMhFKYzkSclhS0IPIHgv4PH9c+n+0EpouiJnbupHeXQzpifEh4hBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:14.571869Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.07149","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18041141ca80f8339ac00011cbeea93b8198f80f337e128f5f89512d779a602b","sha256:36a5e9b60f9d4b7329cc9681317559e3bd815d32d24721e143b77c1bbcaed381"],"state_sha256":"987577b82b0472042a1c1216d9c97d5c1f0fd7c9b38014bb85eac3c7833e1c2a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2WMXfXIeSGrD8XI4qMNOjy8ui5q7e9JRPhHUFp3OqSj0ZvSt3X/3+BDaDh88/z98wDu6skHqNipC85eUhDjECw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T11:01:26.214546Z","bundle_sha256":"67536ba72670c3a3b59015dd99cf5199f29c6f2e48e89e9f4f647ff6eee6eb2a"}}