{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:MIP7JWY664TLDCQAPDDSXMPXP7","short_pith_number":"pith:MIP7JWY6","canonical_record":{"source":{"id":"1612.05942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-12-18T16:29:13Z","cross_cats_sorted":["hep-ph","math-ph","math.MP","quant-ph"],"title_canon_sha256":"05feadd83998b040ce59edee6e46c57d306134955ef5b8933f67413e04e6ce59","abstract_canon_sha256":"47c9e93b85a68a080ede8e8ae7d3ad5968eabf793de629ac067896a79cbee412"},"schema_version":"1.0"},"canonical_sha256":"621ff4db1ef726b18a0078c72bb1f77fd746af95f51484c67b44f94256dddc19","source":{"kind":"arxiv","id":"1612.05942","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05942","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05942v1","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05942","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"MIP7JWY664TL","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MIP7JWY664TLDCQA","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MIP7JWY6","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:MIP7JWY664TLDCQAPDDSXMPXP7","target":"record","payload":{"canonical_record":{"source":{"id":"1612.05942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-12-18T16:29:13Z","cross_cats_sorted":["hep-ph","math-ph","math.MP","quant-ph"],"title_canon_sha256":"05feadd83998b040ce59edee6e46c57d306134955ef5b8933f67413e04e6ce59","abstract_canon_sha256":"47c9e93b85a68a080ede8e8ae7d3ad5968eabf793de629ac067896a79cbee412"},"schema_version":"1.0"},"canonical_sha256":"621ff4db1ef726b18a0078c72bb1f77fd746af95f51484c67b44f94256dddc19","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:07.768995Z","signature_b64":"PlJ6UOcRZ1V2n6bmos7bVqTGd+x1BXntQnLqU2JOK/VMNV8I63DDdsNe89OZ00tvyVVX944iFmW2jcgDNCgnAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"621ff4db1ef726b18a0078c72bb1f77fd746af95f51484c67b44f94256dddc19","last_reissued_at":"2026-05-18T00:46:07.768392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:07.768392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.05942","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":"2026-05-18T00:46:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"REFXKAXH0f/WG38bFRVYTvMZnmRtOBcwzOanbOlKbZPfqZP+9VRdaxNf6rEjUWZNWS4hx3Mat8nB2EYbYeK2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:06:24.569907Z"},"content_sha256":"3707426a15ce2b96e509038fc68ad18f50b491d33142d390c95152bfe59700bc","schema_version":"1.0","event_id":"sha256:3707426a15ce2b96e509038fc68ad18f50b491d33142d390c95152bfe59700bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:MIP7JWY664TLDCQAPDDSXMPXP7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirac equation, hydrogen atom spectrum and the Lamb shift in dynamical noncommutative spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-ph","math-ph","math.MP","quant-ph"],"primary_cat":"hep-th","authors_text":"N. Rezaei, S. A. Alavi","submitted_at":"2016-12-18T16:29:13Z","abstract_excerpt":"We derive the relativistic Hamiltonian of hydrogen atom in dynamical noncommutative spaces (DNCS or {\\tau}-space). Using this Hamiltonian we calculate the energy shift of the ground state and as well the [2P]_(1/2), [2S]_(1/2) levels. In all cases the energy shift depend on the dynamical noncommutative parameter {\\tau}. Using the accuracy of the energy measurement we obtain an upper bound for {\\tau}. We also study the lamb shift in DNCS. Both the levels [2P]_(1/2) and [2S]_(1/2) receive corrections due to dynamical noncommutativity of space which is in contrast to the non-dynamical noncommutat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05942","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":"2026-05-18T00:46:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RwVfUn7yKS7ktU5PsAMLpQZBdynRNKtHeZVkHzWmSHUxz9RqezhZD4gfer1MucwHTQx2ttjGfekgln0x+EnoBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-21T19:06:24.570254Z"},"content_sha256":"75daf77337f5affe36b3dbc81d97e6451b0c0e2bfcc9f77fce6596021a1bc9fa","schema_version":"1.0","event_id":"sha256:75daf77337f5affe36b3dbc81d97e6451b0c0e2bfcc9f77fce6596021a1bc9fa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MIP7JWY664TLDCQAPDDSXMPXP7/bundle.json","state_url":"https://pith.science/pith/MIP7JWY664TLDCQAPDDSXMPXP7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MIP7JWY664TLDCQAPDDSXMPXP7/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":"2026-06-21T19:06:24Z","links":{"resolver":"https://pith.science/pith/MIP7JWY664TLDCQAPDDSXMPXP7","bundle":"https://pith.science/pith/MIP7JWY664TLDCQAPDDSXMPXP7/bundle.json","state":"https://pith.science/pith/MIP7JWY664TLDCQAPDDSXMPXP7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MIP7JWY664TLDCQAPDDSXMPXP7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:MIP7JWY664TLDCQAPDDSXMPXP7","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":"47c9e93b85a68a080ede8e8ae7d3ad5968eabf793de629ac067896a79cbee412","cross_cats_sorted":["hep-ph","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-12-18T16:29:13Z","title_canon_sha256":"05feadd83998b040ce59edee6e46c57d306134955ef5b8933f67413e04e6ce59"},"schema_version":"1.0","source":{"id":"1612.05942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05942","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05942v1","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05942","created_at":"2026-05-18T00:46:07Z"},{"alias_kind":"pith_short_12","alias_value":"MIP7JWY664TL","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"MIP7JWY664TLDCQA","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"MIP7JWY6","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:75daf77337f5affe36b3dbc81d97e6451b0c0e2bfcc9f77fce6596021a1bc9fa","target":"graph","created_at":"2026-05-18T00:46:07Z","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 derive the relativistic Hamiltonian of hydrogen atom in dynamical noncommutative spaces (DNCS or {\\tau}-space). Using this Hamiltonian we calculate the energy shift of the ground state and as well the [2P]_(1/2), [2S]_(1/2) levels. In all cases the energy shift depend on the dynamical noncommutative parameter {\\tau}. Using the accuracy of the energy measurement we obtain an upper bound for {\\tau}. We also study the lamb shift in DNCS. Both the levels [2P]_(1/2) and [2S]_(1/2) receive corrections due to dynamical noncommutativity of space which is in contrast to the non-dynamical noncommutat","authors_text":"N. Rezaei, S. A. Alavi","cross_cats":["hep-ph","math-ph","math.MP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-12-18T16:29:13Z","title":"Dirac equation, hydrogen atom spectrum and the Lamb shift in dynamical noncommutative spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05942","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":"sha256:3707426a15ce2b96e509038fc68ad18f50b491d33142d390c95152bfe59700bc","target":"record","created_at":"2026-05-18T00:46:07Z","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":"47c9e93b85a68a080ede8e8ae7d3ad5968eabf793de629ac067896a79cbee412","cross_cats_sorted":["hep-ph","math-ph","math.MP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2016-12-18T16:29:13Z","title_canon_sha256":"05feadd83998b040ce59edee6e46c57d306134955ef5b8933f67413e04e6ce59"},"schema_version":"1.0","source":{"id":"1612.05942","kind":"arxiv","version":1}},"canonical_sha256":"621ff4db1ef726b18a0078c72bb1f77fd746af95f51484c67b44f94256dddc19","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"621ff4db1ef726b18a0078c72bb1f77fd746af95f51484c67b44f94256dddc19","first_computed_at":"2026-05-18T00:46:07.768392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:07.768392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PlJ6UOcRZ1V2n6bmos7bVqTGd+x1BXntQnLqU2JOK/VMNV8I63DDdsNe89OZ00tvyVVX944iFmW2jcgDNCgnAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:07.768995Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3707426a15ce2b96e509038fc68ad18f50b491d33142d390c95152bfe59700bc","sha256:75daf77337f5affe36b3dbc81d97e6451b0c0e2bfcc9f77fce6596021a1bc9fa"],"state_sha256":"b9e999b6b7ae28406cf28c704ce50ac0bbba0bcd898c95fe94d227e47e20d8c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kNqhSKr3lfPaP6yogXgKaTtx/WMFCe5W/bKIosijH/dl2QXfpUHXXUEB/BlkZzLXphcHk6IVAQpgSHkqQFTTBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-21T19:06:24.572281Z","bundle_sha256":"fe78d4a5019d18222ee1d2416a34bdbb43733b023279f8593df5e1f7d82cbb4f"}}