{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:XE3IZB5IQIV7NKAJYMYSQ45A57","short_pith_number":"pith:XE3IZB5I","schema_version":"1.0","canonical_sha256":"b9368c87a8822bf6a809c3312873a0effa70013453f97c3d1793f36b2e2536f1","source":{"kind":"arxiv","id":"2607.14020","version":1},"attestation_state":"computed","paper":{"title":"Resurgent Lambert series from Feynman and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"Daniele Dorigoni, David Broadhurst","submitted_at":"2026-07-15T16:52:52Z","abstract_excerpt":"Lambert series of the form $\\sum_{n>0}a(n)q^n/(1-q^n)$ are ubiquitous in mathematical physics. In particular, 2-loop sunrise and 3-loop banana Feynman diagrams yield Lambert series with $a(n)$ of the form $\\chi(n)/n^s$ where $\\chi(n)$ is a Dirichlet character. Resurgence concerns the singular limit as $|q|$ approaches 1. In the Feynman cases we can control this limit, obtaining rapidly convergent expressions, since the Lambert series are iterated integrals of holomorphic Eisenstein series twisted by a character. We generalize this result, to include modular resurgent structures found in topolo"},"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":"2607.14020","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2026-07-15T16:52:52Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"da55be1d1e92872b815753fc68bc98f82836ce62d26349f519bb74536778b5a2","abstract_canon_sha256":"99ccd179df4faf2ff045733bd7611f41f5d8a95771cc4ed103371920304b5023"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-16T01:23:19.895291Z","signature_b64":"lCWE+XxWvz7SP2SIZuRKtCpCoGqLEJ+LyhVkrZDYjKQmpb/SvQ8K8+aKeErwyJ1nDe9CG+tSkHkE1RMwP5CLAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b9368c87a8822bf6a809c3312873a0effa70013453f97c3d1793f36b2e2536f1","last_reissued_at":"2026-07-16T01:23:19.894417Z","signature_status":"signed_v1","first_computed_at":"2026-07-16T01:23:19.894417Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Resurgent Lambert series from Feynman and beyond","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"Daniele Dorigoni, David Broadhurst","submitted_at":"2026-07-15T16:52:52Z","abstract_excerpt":"Lambert series of the form $\\sum_{n>0}a(n)q^n/(1-q^n)$ are ubiquitous in mathematical physics. In particular, 2-loop sunrise and 3-loop banana Feynman diagrams yield Lambert series with $a(n)$ of the form $\\chi(n)/n^s$ where $\\chi(n)$ is a Dirichlet character. Resurgence concerns the singular limit as $|q|$ approaches 1. In the Feynman cases we can control this limit, obtaining rapidly convergent expressions, since the Lambert series are iterated integrals of holomorphic Eisenstein series twisted by a character. We generalize this result, to include modular resurgent structures found in topolo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14020","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/2607.14020/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":"2607.14020","created_at":"2026-07-16T01:23:19.894868+00:00"},{"alias_kind":"arxiv_version","alias_value":"2607.14020v1","created_at":"2026-07-16T01:23:19.894868+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.14020","created_at":"2026-07-16T01:23:19.894868+00:00"},{"alias_kind":"pith_short_12","alias_value":"XE3IZB5IQIV7","created_at":"2026-07-16T01:23:19.894868+00:00"},{"alias_kind":"pith_short_16","alias_value":"XE3IZB5IQIV7NKAJ","created_at":"2026-07-16T01:23:19.894868+00:00"},{"alias_kind":"pith_short_8","alias_value":"XE3IZB5I","created_at":"2026-07-16T01:23:19.894868+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/XE3IZB5IQIV7NKAJYMYSQ45A57","json":"https://pith.science/pith/XE3IZB5IQIV7NKAJYMYSQ45A57.json","graph_json":"https://pith.science/api/pith-number/XE3IZB5IQIV7NKAJYMYSQ45A57/graph.json","events_json":"https://pith.science/api/pith-number/XE3IZB5IQIV7NKAJYMYSQ45A57/events.json","paper":"https://pith.science/paper/XE3IZB5I"},"agent_actions":{"view_html":"https://pith.science/pith/XE3IZB5IQIV7NKAJYMYSQ45A57","download_json":"https://pith.science/pith/XE3IZB5IQIV7NKAJYMYSQ45A57.json","view_paper":"https://pith.science/paper/XE3IZB5I","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2607.14020&json=true","fetch_graph":"https://pith.science/api/pith-number/XE3IZB5IQIV7NKAJYMYSQ45A57/graph.json","fetch_events":"https://pith.science/api/pith-number/XE3IZB5IQIV7NKAJYMYSQ45A57/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XE3IZB5IQIV7NKAJYMYSQ45A57/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XE3IZB5IQIV7NKAJYMYSQ45A57/action/storage_attestation","attest_author":"https://pith.science/pith/XE3IZB5IQIV7NKAJYMYSQ45A57/action/author_attestation","sign_citation":"https://pith.science/pith/XE3IZB5IQIV7NKAJYMYSQ45A57/action/citation_signature","submit_replication":"https://pith.science/pith/XE3IZB5IQIV7NKAJYMYSQ45A57/action/replication_record"}},"created_at":"2026-07-16T01:23:19.894868+00:00","updated_at":"2026-07-16T01:23:19.894868+00:00"}