{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:4SM7U5L7W7DF46J2X7CMGH7POG","short_pith_number":"pith:4SM7U5L7","schema_version":"1.0","canonical_sha256":"e499fa757fb7c65e793abfc4c31fef71bf853314a48d2790a27e4c5bf1523330","source":{"kind":"arxiv","id":"1503.06010","version":2},"attestation_state":"computed","paper":{"title":"A New Blackbody Radiation Law Based on Fractional Calculus and its Application to NASA COBE Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Minoru Biyajima, Naomichi Suzuki, Takuya Mizoguchi","submitted_at":"2015-03-20T07:28:24Z","abstract_excerpt":"By applying fractional calculus to the equation proposed by M. Planck in 1900, we obtain a new blackbody radiation law described by a Mittag-Leffler (ML) function. We have analyzed NASA COBE data by means of a non-extensive formula with a parameter $(q-1)$, a formula proposed by Ertik et al. with a fractional parameter $(\\alpha-1)$, and our new formula including a parameter $(p-1)$, as well as the Bose-Einstein distribution with a dimensionless chemical potential $\\mu$. It can be said that one role of the fractional parameter $(p-1)$ is almost the same as that of chemical potential $(\\mu)$ as "},"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":"1503.06010","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-03-20T07:28:24Z","cross_cats_sorted":["astro-ph.CO","hep-ph"],"title_canon_sha256":"bcf5ad1ddfa55ad51ab20c4a1ca8c905233bb3751df07f81286b07af79de25cc","abstract_canon_sha256":"b62deaaf507a5b8a265b203dbc563f18aaf5041161b887c47287e53197cc3ff5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:40.123614Z","signature_b64":"MmCnvVCS+pAqiTT5mtbEwIUziR4FYgC4vHpdYj+USKx9fnVVPC+KXiLK4kTtWjKzPni4FdQqCA3eEbtO6a9wAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e499fa757fb7c65e793abfc4c31fef71bf853314a48d2790a27e4c5bf1523330","last_reissued_at":"2026-05-18T01:31:40.123067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:40.123067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A New Blackbody Radiation Law Based on Fractional Calculus and its Application to NASA COBE Data","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-ph"],"primary_cat":"cond-mat.stat-mech","authors_text":"Minoru Biyajima, Naomichi Suzuki, Takuya Mizoguchi","submitted_at":"2015-03-20T07:28:24Z","abstract_excerpt":"By applying fractional calculus to the equation proposed by M. Planck in 1900, we obtain a new blackbody radiation law described by a Mittag-Leffler (ML) function. We have analyzed NASA COBE data by means of a non-extensive formula with a parameter $(q-1)$, a formula proposed by Ertik et al. with a fractional parameter $(\\alpha-1)$, and our new formula including a parameter $(p-1)$, as well as the Bose-Einstein distribution with a dimensionless chemical potential $\\mu$. It can be said that one role of the fractional parameter $(p-1)$ is almost the same as that of chemical potential $(\\mu)$ as "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.06010","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":"1503.06010","created_at":"2026-05-18T01:31:40.123144+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.06010v2","created_at":"2026-05-18T01:31:40.123144+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.06010","created_at":"2026-05-18T01:31:40.123144+00:00"},{"alias_kind":"pith_short_12","alias_value":"4SM7U5L7W7DF","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4SM7U5L7W7DF46J2","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4SM7U5L7","created_at":"2026-05-18T12:29:05.191682+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/4SM7U5L7W7DF46J2X7CMGH7POG","json":"https://pith.science/pith/4SM7U5L7W7DF46J2X7CMGH7POG.json","graph_json":"https://pith.science/api/pith-number/4SM7U5L7W7DF46J2X7CMGH7POG/graph.json","events_json":"https://pith.science/api/pith-number/4SM7U5L7W7DF46J2X7CMGH7POG/events.json","paper":"https://pith.science/paper/4SM7U5L7"},"agent_actions":{"view_html":"https://pith.science/pith/4SM7U5L7W7DF46J2X7CMGH7POG","download_json":"https://pith.science/pith/4SM7U5L7W7DF46J2X7CMGH7POG.json","view_paper":"https://pith.science/paper/4SM7U5L7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.06010&json=true","fetch_graph":"https://pith.science/api/pith-number/4SM7U5L7W7DF46J2X7CMGH7POG/graph.json","fetch_events":"https://pith.science/api/pith-number/4SM7U5L7W7DF46J2X7CMGH7POG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4SM7U5L7W7DF46J2X7CMGH7POG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4SM7U5L7W7DF46J2X7CMGH7POG/action/storage_attestation","attest_author":"https://pith.science/pith/4SM7U5L7W7DF46J2X7CMGH7POG/action/author_attestation","sign_citation":"https://pith.science/pith/4SM7U5L7W7DF46J2X7CMGH7POG/action/citation_signature","submit_replication":"https://pith.science/pith/4SM7U5L7W7DF46J2X7CMGH7POG/action/replication_record"}},"created_at":"2026-05-18T01:31:40.123144+00:00","updated_at":"2026-05-18T01:31:40.123144+00:00"}