{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:ZUJ5V2DFOD3QJUZE5CLVU7UDEV","short_pith_number":"pith:ZUJ5V2DF","canonical_record":{"source":{"id":"nucl-th/0612003","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nucl-th","submitted_at":"2006-12-02T07:05:58Z","cross_cats_sorted":[],"title_canon_sha256":"cc6c0bced11067b85ab1ccea293c60165900b11e5862080ee5ef8735a120d590","abstract_canon_sha256":"d03e5d4fac45e3776170cb2cabaa8b97222d36257f08bd8e7552077267747fab"},"schema_version":"1.0"},"canonical_sha256":"cd13dae86570f704d324e8975a7e832554c46aec441abbb4225efba12ac110ff","source":{"kind":"arxiv","id":"nucl-th/0612003","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nucl-th/0612003","created_at":"2026-05-18T01:38:12Z"},{"alias_kind":"arxiv_version","alias_value":"nucl-th/0612003v2","created_at":"2026-05-18T01:38:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nucl-th/0612003","created_at":"2026-05-18T01:38:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZUJ5V2DFOD3Q","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZUJ5V2DFOD3QJUZE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZUJ5V2DF","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:ZUJ5V2DFOD3QJUZE5CLVU7UDEV","target":"record","payload":{"canonical_record":{"source":{"id":"nucl-th/0612003","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"nucl-th","submitted_at":"2006-12-02T07:05:58Z","cross_cats_sorted":[],"title_canon_sha256":"cc6c0bced11067b85ab1ccea293c60165900b11e5862080ee5ef8735a120d590","abstract_canon_sha256":"d03e5d4fac45e3776170cb2cabaa8b97222d36257f08bd8e7552077267747fab"},"schema_version":"1.0"},"canonical_sha256":"cd13dae86570f704d324e8975a7e832554c46aec441abbb4225efba12ac110ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:38:12.952998Z","signature_b64":"4vU7tUmK18rzK9BwAawRUpOE6L48CXWEb1Wneu3IeJ0p2Xk4ZKebCRAWtuj7Kp2VuRRheJfoDYA4qjrGniQUCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd13dae86570f704d324e8975a7e832554c46aec441abbb4225efba12ac110ff","last_reissued_at":"2026-05-18T01:38:12.952347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:38:12.952347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"nucl-th/0612003","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:38:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8cj7eMN/6WXatrtYCFgy1hOUjptHQnGJ4pR3BGcJpoJh7n+8WAz+ocTNJk12AAAUQmHBUpMi9TfChYhd9l+3Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:27:46.511123Z"},"content_sha256":"391043d7b9eee6c4a1a4a659d7bc2343ca5e1f278b06ad6d64a5e677388bded3","schema_version":"1.0","event_id":"sha256:391043d7b9eee6c4a1a4a659d7bc2343ca5e1f278b06ad6d64a5e677388bded3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:ZUJ5V2DFOD3QJUZE5CLVU7UDEV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Empirical formula for the excitation energies of the first $2^+$ and $3^-$ states in even-even nuclei","license":"","headline":"","cross_cats":[],"primary_cat":"nucl-th","authors_text":"Dongwoo Cha, Eunja Ha","submitted_at":"2006-12-02T07:05:58Z","abstract_excerpt":"We report empirical findings that a simple formula in terms of the mass number $A$, the valence proton number $N_p$, and the valence neutron number $N_n$ can describe the essential trends of excitation energies $E_x$ of the first $2^+$ and $3^-$ states in even-even nuclei throughout the periodic table. The formula reads as $E_x = \\alpha A^{-\\beta} + \\exp (- \\lambda N_p) + \\exp (- \\lambda N_n)$. The parameter $\\beta$ in the first term is determined by the mass number $A$ dependence of the bottom contour line of the excitation energy systematics. The other two parameters $\\alpha$ and $\\lambda$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nucl-th/0612003","kind":"arxiv","version":2},"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":"2026-05-18T01:38:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8SKePPQsiJ6ycNcojA6L4G0Rl2nXWEqZrrikx8fzVfP4TwrL/qMZi5ladXSePbNScxDj+LySfTlsgGsNpPYbAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T19:27:46.511476Z"},"content_sha256":"bac4e04599417342ff03415ebfc39e05365d5869d382d063b07eb723a585be37","schema_version":"1.0","event_id":"sha256:bac4e04599417342ff03415ebfc39e05365d5869d382d063b07eb723a585be37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/bundle.json","state_url":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/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":"2026-07-06T19:27:46Z","links":{"resolver":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV","bundle":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/bundle.json","state":"https://pith.science/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZUJ5V2DFOD3QJUZE5CLVU7UDEV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:ZUJ5V2DFOD3QJUZE5CLVU7UDEV","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":"d03e5d4fac45e3776170cb2cabaa8b97222d36257f08bd8e7552077267747fab","cross_cats_sorted":[],"license":"","primary_cat":"nucl-th","submitted_at":"2006-12-02T07:05:58Z","title_canon_sha256":"cc6c0bced11067b85ab1ccea293c60165900b11e5862080ee5ef8735a120d590"},"schema_version":"1.0","source":{"id":"nucl-th/0612003","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"nucl-th/0612003","created_at":"2026-05-18T01:38:12Z"},{"alias_kind":"arxiv_version","alias_value":"nucl-th/0612003v2","created_at":"2026-05-18T01:38:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.nucl-th/0612003","created_at":"2026-05-18T01:38:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZUJ5V2DFOD3Q","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"ZUJ5V2DFOD3QJUZE","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"ZUJ5V2DF","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:bac4e04599417342ff03415ebfc39e05365d5869d382d063b07eb723a585be37","target":"graph","created_at":"2026-05-18T01:38:12Z","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 report empirical findings that a simple formula in terms of the mass number $A$, the valence proton number $N_p$, and the valence neutron number $N_n$ can describe the essential trends of excitation energies $E_x$ of the first $2^+$ and $3^-$ states in even-even nuclei throughout the periodic table. The formula reads as $E_x = \\alpha A^{-\\beta} + \\exp (- \\lambda N_p) + \\exp (- \\lambda N_n)$. The parameter $\\beta$ in the first term is determined by the mass number $A$ dependence of the bottom contour line of the excitation energy systematics. The other two parameters $\\alpha$ and $\\lambda$ a","authors_text":"Dongwoo Cha, Eunja Ha","cross_cats":[],"headline":"","license":"","primary_cat":"nucl-th","submitted_at":"2006-12-02T07:05:58Z","title":"Empirical formula for the excitation energies of the first $2^+$ and $3^-$ states in even-even nuclei"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"nucl-th/0612003","kind":"arxiv","version":2},"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":"sha256:391043d7b9eee6c4a1a4a659d7bc2343ca5e1f278b06ad6d64a5e677388bded3","target":"record","created_at":"2026-05-18T01:38:12Z","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":"d03e5d4fac45e3776170cb2cabaa8b97222d36257f08bd8e7552077267747fab","cross_cats_sorted":[],"license":"","primary_cat":"nucl-th","submitted_at":"2006-12-02T07:05:58Z","title_canon_sha256":"cc6c0bced11067b85ab1ccea293c60165900b11e5862080ee5ef8735a120d590"},"schema_version":"1.0","source":{"id":"nucl-th/0612003","kind":"arxiv","version":2}},"canonical_sha256":"cd13dae86570f704d324e8975a7e832554c46aec441abbb4225efba12ac110ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cd13dae86570f704d324e8975a7e832554c46aec441abbb4225efba12ac110ff","first_computed_at":"2026-05-18T01:38:12.952347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:38:12.952347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4vU7tUmK18rzK9BwAawRUpOE6L48CXWEb1Wneu3IeJ0p2Xk4ZKebCRAWtuj7Kp2VuRRheJfoDYA4qjrGniQUCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:38:12.952998Z","signed_message":"canonical_sha256_bytes"},"source_id":"nucl-th/0612003","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:391043d7b9eee6c4a1a4a659d7bc2343ca5e1f278b06ad6d64a5e677388bded3","sha256:bac4e04599417342ff03415ebfc39e05365d5869d382d063b07eb723a585be37"],"state_sha256":"4568bffaf695c330104da64bd92f0919d20374e80ea03e4681e6101a36414d64"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/HtPnSFcmwCdIkyLx3pVD548qnJSNVIE2/y3T3ALSDdhgK2kD8c95J/Ty556kIGfFZTeNmAVTDBE+a1pdi9MCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T19:27:46.513349Z","bundle_sha256":"2f1177b8c1fd47495133a5a2125d4ff1f3d75eca1d5911a6c1aa836f77cffbb7"}}