{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:PQJEXPI56HA3CWXKKHMDNPOAOB","short_pith_number":"pith:PQJEXPI5","schema_version":"1.0","canonical_sha256":"7c124bbd1df1c1b15aea51d836bdc0705fabd1488db7f4d140b79d823df3c52b","source":{"kind":"arxiv","id":"1908.08667","version":1},"attestation_state":"computed","paper":{"title":"Analytic expressions for Debye functions and the heat capacity of a solid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alfredo Vega, Igor Kondrashuk, Ivan Gonzalez, Victor H. Moll","submitted_at":"2019-08-23T05:12:30Z","abstract_excerpt":"Analytic expressions for the $N$-dimensional Debye function are obtained by the method of brackets. The new expressions are suitable for the analysis of the asymptotic behavior of this function, both in the high and low temperature limits."},"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":"1908.08667","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-23T05:12:30Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"1faec7fad4afe1f670362bc20e2f0c5c59c1435afe48770bdb0b1320fa7a9b0d","abstract_canon_sha256":"41bdaf7bed06a341c4afee5962f9678b181b92204cb96fbffe980bc433dc0d18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:32:46.425171Z","signature_b64":"bmwcQZDIsvFYAi1Pn1T86EA15e8/SYizcLzzGoLrUnclnR4UQOJByiECb7/8NlzgxPXzMKiHwDIPN9mNwk/JBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c124bbd1df1c1b15aea51d836bdc0705fabd1488db7f4d140b79d823df3c52b","last_reissued_at":"2026-07-05T04:32:46.424667Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:32:46.424667Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Analytic expressions for Debye functions and the heat capacity of a solid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Alfredo Vega, Igor Kondrashuk, Ivan Gonzalez, Victor H. Moll","submitted_at":"2019-08-23T05:12:30Z","abstract_excerpt":"Analytic expressions for the $N$-dimensional Debye function are obtained by the method of brackets. The new expressions are suitable for the analysis of the asymptotic behavior of this function, both in the high and low temperature limits."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08667","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.08667/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1908.08667","created_at":"2026-07-05T04:32:46.424725+00:00"},{"alias_kind":"arxiv_version","alias_value":"1908.08667v1","created_at":"2026-07-05T04:32:46.424725+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.08667","created_at":"2026-07-05T04:32:46.424725+00:00"},{"alias_kind":"pith_short_12","alias_value":"PQJEXPI56HA3","created_at":"2026-07-05T04:32:46.424725+00:00"},{"alias_kind":"pith_short_16","alias_value":"PQJEXPI56HA3CWXK","created_at":"2026-07-05T04:32:46.424725+00:00"},{"alias_kind":"pith_short_8","alias_value":"PQJEXPI5","created_at":"2026-07-05T04:32:46.424725+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2604.07787","citing_title":"Inverse Laplace and Mellin integral transforms modified for use in quantum communications","ref_index":19,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PQJEXPI56HA3CWXKKHMDNPOAOB","json":"https://pith.science/pith/PQJEXPI56HA3CWXKKHMDNPOAOB.json","graph_json":"https://pith.science/api/pith-number/PQJEXPI56HA3CWXKKHMDNPOAOB/graph.json","events_json":"https://pith.science/api/pith-number/PQJEXPI56HA3CWXKKHMDNPOAOB/events.json","paper":"https://pith.science/paper/PQJEXPI5"},"agent_actions":{"view_html":"https://pith.science/pith/PQJEXPI56HA3CWXKKHMDNPOAOB","download_json":"https://pith.science/pith/PQJEXPI56HA3CWXKKHMDNPOAOB.json","view_paper":"https://pith.science/paper/PQJEXPI5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1908.08667&json=true","fetch_graph":"https://pith.science/api/pith-number/PQJEXPI56HA3CWXKKHMDNPOAOB/graph.json","fetch_events":"https://pith.science/api/pith-number/PQJEXPI56HA3CWXKKHMDNPOAOB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PQJEXPI56HA3CWXKKHMDNPOAOB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PQJEXPI56HA3CWXKKHMDNPOAOB/action/storage_attestation","attest_author":"https://pith.science/pith/PQJEXPI56HA3CWXKKHMDNPOAOB/action/author_attestation","sign_citation":"https://pith.science/pith/PQJEXPI56HA3CWXKKHMDNPOAOB/action/citation_signature","submit_replication":"https://pith.science/pith/PQJEXPI56HA3CWXKKHMDNPOAOB/action/replication_record"}},"created_at":"2026-07-05T04:32:46.424725+00:00","updated_at":"2026-07-05T04:32:46.424725+00:00"}