{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:OSI42Z6D43EO4WSGNESQAJTUYO","short_pith_number":"pith:OSI42Z6D","schema_version":"1.0","canonical_sha256":"7491cd67c3e6c8ee5a466925002674c38624870dc3307717c416cb8d140a4fec","source":{"kind":"arxiv","id":"1009.4080","version":2},"attestation_state":"computed","paper":{"title":"Perturbed invariant under a cyclic permutation with trace of neutrino mass matrix remain constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Asan Damanik","submitted_at":"2010-09-21T13:03:32Z","abstract_excerpt":"We construct a neutrino mass matrix $M_{\\nu}$ via a seesaw mechanism whith perturbed invariant under a cyclic permutation by introducing one parameter $\\delta$ into the diagonal elements of $M_{\\nu}$ with assumption that trace of the perturbed $M_{\\nu}$ is equal to trace of the unperturbed $M_{\\nu}$. We found that the perturbed neutrino mass matrices $M_{\\nu}$ can predicts the mass-squared difference $\\Delta m_{ij}^{2}\\neq 0$ with the possible hierarchy of neutrino mass is normal or inverted hierarchy. By using the advantages of the mass-squared differences and mixing parameters data from neut"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1009.4080","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-ph","submitted_at":"2010-09-21T13:03:32Z","cross_cats_sorted":[],"title_canon_sha256":"a67fd08a48b9d7aafe18554c2c1491e26ad3842fe9f625ab0e5a0ac2452ea571","abstract_canon_sha256":"e909799358aa31de43cf0ab6d888703f16c1e1e719ca5594ebcfe55365a3e731"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:22:31.895528Z","signature_b64":"/9cRdPXXKLF/PdV9A5eGT7W9za52vlHExQFkN1sn+cdBbVouQK9eDPiZfL1YijVM9YJfz3Y70bmfEs4DxOdPDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7491cd67c3e6c8ee5a466925002674c38624870dc3307717c416cb8d140a4fec","last_reissued_at":"2026-05-18T04:22:31.895142Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:22:31.895142Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Perturbed invariant under a cyclic permutation with trace of neutrino mass matrix remain constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-ph","authors_text":"Asan Damanik","submitted_at":"2010-09-21T13:03:32Z","abstract_excerpt":"We construct a neutrino mass matrix $M_{\\nu}$ via a seesaw mechanism whith perturbed invariant under a cyclic permutation by introducing one parameter $\\delta$ into the diagonal elements of $M_{\\nu}$ with assumption that trace of the perturbed $M_{\\nu}$ is equal to trace of the unperturbed $M_{\\nu}$. We found that the perturbed neutrino mass matrices $M_{\\nu}$ can predicts the mass-squared difference $\\Delta m_{ij}^{2}\\neq 0$ with the possible hierarchy of neutrino mass is normal or inverted hierarchy. By using the advantages of the mass-squared differences and mixing parameters data from neut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4080","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1009.4080","created_at":"2026-05-18T04:22:31.895197+00:00"},{"alias_kind":"arxiv_version","alias_value":"1009.4080v2","created_at":"2026-05-18T04:22:31.895197+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.4080","created_at":"2026-05-18T04:22:31.895197+00:00"},{"alias_kind":"pith_short_12","alias_value":"OSI42Z6D43EO","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_16","alias_value":"OSI42Z6D43EO4WSG","created_at":"2026-05-18T12:26:12.377268+00:00"},{"alias_kind":"pith_short_8","alias_value":"OSI42Z6D","created_at":"2026-05-18T12:26:12.377268+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/OSI42Z6D43EO4WSGNESQAJTUYO","json":"https://pith.science/pith/OSI42Z6D43EO4WSGNESQAJTUYO.json","graph_json":"https://pith.science/api/pith-number/OSI42Z6D43EO4WSGNESQAJTUYO/graph.json","events_json":"https://pith.science/api/pith-number/OSI42Z6D43EO4WSGNESQAJTUYO/events.json","paper":"https://pith.science/paper/OSI42Z6D"},"agent_actions":{"view_html":"https://pith.science/pith/OSI42Z6D43EO4WSGNESQAJTUYO","download_json":"https://pith.science/pith/OSI42Z6D43EO4WSGNESQAJTUYO.json","view_paper":"https://pith.science/paper/OSI42Z6D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1009.4080&json=true","fetch_graph":"https://pith.science/api/pith-number/OSI42Z6D43EO4WSGNESQAJTUYO/graph.json","fetch_events":"https://pith.science/api/pith-number/OSI42Z6D43EO4WSGNESQAJTUYO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OSI42Z6D43EO4WSGNESQAJTUYO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OSI42Z6D43EO4WSGNESQAJTUYO/action/storage_attestation","attest_author":"https://pith.science/pith/OSI42Z6D43EO4WSGNESQAJTUYO/action/author_attestation","sign_citation":"https://pith.science/pith/OSI42Z6D43EO4WSGNESQAJTUYO/action/citation_signature","submit_replication":"https://pith.science/pith/OSI42Z6D43EO4WSGNESQAJTUYO/action/replication_record"}},"created_at":"2026-05-18T04:22:31.895197+00:00","updated_at":"2026-05-18T04:22:31.895197+00:00"}