{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:R7FNDWQMRSEBX44ELUAJO3YDEO","short_pith_number":"pith:R7FNDWQM","schema_version":"1.0","canonical_sha256":"8fcad1da0c8c881bf3845d00976f032396c19dd811e07b2b56c38c79d4666ab8","source":{"kind":"arxiv","id":"1211.5536","version":1},"attestation_state":"computed","paper":{"title":"Self-similar continued root approximants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"S. Gluzman, V. I. Yukalov","submitted_at":"2012-11-23T16:04:56Z","abstract_excerpt":"A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Pad\\'{e} approximants. A theorem"},"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":"1211.5536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2012-11-23T16:04:56Z","cross_cats_sorted":["cond-mat.stat-mech","math.MP"],"title_canon_sha256":"8b3a779ba48254b1991ccda683027221f3a6591dd20f8b1bdbb583deb17687d0","abstract_canon_sha256":"a189f83f99ea9c1cac7c7e05bf332c4027577cbe96435ea7986b25a50e614312"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:53:01.116929Z","signature_b64":"vIqL/FmmZpgB2z2VaijVo4UPOFmgeJr/3fDvJ0IKzgpfHfTAQKEISp8ZKz+9iiwsWdaRj4Cht/wrK9xQA8V/Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fcad1da0c8c881bf3845d00976f032396c19dd811e07b2b56c38c79d4666ab8","last_reissued_at":"2026-05-18T01:53:01.116309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:53:01.116309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Self-similar continued root approximants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.MP"],"primary_cat":"math-ph","authors_text":"S. Gluzman, V. I. Yukalov","submitted_at":"2012-11-23T16:04:56Z","abstract_excerpt":"A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Pad\\'{e} approximants. A theorem"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.5536","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1211.5536","created_at":"2026-05-18T01:53:01.116421+00:00"},{"alias_kind":"arxiv_version","alias_value":"1211.5536v1","created_at":"2026-05-18T01:53:01.116421+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.5536","created_at":"2026-05-18T01:53:01.116421+00:00"},{"alias_kind":"pith_short_12","alias_value":"R7FNDWQMRSEB","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_16","alias_value":"R7FNDWQMRSEBX44E","created_at":"2026-05-18T12:27:20.899486+00:00"},{"alias_kind":"pith_short_8","alias_value":"R7FNDWQM","created_at":"2026-05-18T12:27:20.899486+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/R7FNDWQMRSEBX44ELUAJO3YDEO","json":"https://pith.science/pith/R7FNDWQMRSEBX44ELUAJO3YDEO.json","graph_json":"https://pith.science/api/pith-number/R7FNDWQMRSEBX44ELUAJO3YDEO/graph.json","events_json":"https://pith.science/api/pith-number/R7FNDWQMRSEBX44ELUAJO3YDEO/events.json","paper":"https://pith.science/paper/R7FNDWQM"},"agent_actions":{"view_html":"https://pith.science/pith/R7FNDWQMRSEBX44ELUAJO3YDEO","download_json":"https://pith.science/pith/R7FNDWQMRSEBX44ELUAJO3YDEO.json","view_paper":"https://pith.science/paper/R7FNDWQM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1211.5536&json=true","fetch_graph":"https://pith.science/api/pith-number/R7FNDWQMRSEBX44ELUAJO3YDEO/graph.json","fetch_events":"https://pith.science/api/pith-number/R7FNDWQMRSEBX44ELUAJO3YDEO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R7FNDWQMRSEBX44ELUAJO3YDEO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R7FNDWQMRSEBX44ELUAJO3YDEO/action/storage_attestation","attest_author":"https://pith.science/pith/R7FNDWQMRSEBX44ELUAJO3YDEO/action/author_attestation","sign_citation":"https://pith.science/pith/R7FNDWQMRSEBX44ELUAJO3YDEO/action/citation_signature","submit_replication":"https://pith.science/pith/R7FNDWQMRSEBX44ELUAJO3YDEO/action/replication_record"}},"created_at":"2026-05-18T01:53:01.116421+00:00","updated_at":"2026-05-18T01:53:01.116421+00:00"}