{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:M6KZZH7GG73SSYSXRUAPJYB5SV","short_pith_number":"pith:M6KZZH7G","schema_version":"1.0","canonical_sha256":"67959c9fe637f72962578d00f4e03d954094b80492e45085a7367f875de6e8cd","source":{"kind":"arxiv","id":"1112.4015","version":2},"attestation_state":"computed","paper":{"title":"Feynman Graph Integrals and Almost Modular Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO"],"primary_cat":"math.NT","authors_text":"Si Li","submitted_at":"2011-12-17T03:22:53Z","abstract_excerpt":"We introduce a type of graph integrals on elliptic curves from the heat kernel. We show that such graph integrals have modular properties under the modular group $SL(2, \\Z)$, and prove the polynomial nature of the anti-holomorphic dependence."},"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":"1112.4015","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2011-12-17T03:22:53Z","cross_cats_sorted":["hep-th","math.CO"],"title_canon_sha256":"6d3120a14132e1dbd15c99d2f2b31f4a29c6dee64ea9afac9239e3a507b9d043","abstract_canon_sha256":"e329e4ec55e5591534ea9c4b042861861bc5bc1410b768a629d63530ca9356cc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:58.766070Z","signature_b64":"mhf4OIStZXh1e40nnjX9ByqmsDHpJb+nFh/0nLLax3+9KY0d+UROBq+kBLGGOUVGK1wEkzVARmVnBg/+dW21Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67959c9fe637f72962578d00f4e03d954094b80492e45085a7367f875de6e8cd","last_reissued_at":"2026-05-18T04:05:58.765622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:58.765622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Feynman Graph Integrals and Almost Modular Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.CO"],"primary_cat":"math.NT","authors_text":"Si Li","submitted_at":"2011-12-17T03:22:53Z","abstract_excerpt":"We introduce a type of graph integrals on elliptic curves from the heat kernel. We show that such graph integrals have modular properties under the modular group $SL(2, \\Z)$, and prove the polynomial nature of the anti-holomorphic dependence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4015","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":"1112.4015","created_at":"2026-05-18T04:05:58.765694+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.4015v2","created_at":"2026-05-18T04:05:58.765694+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.4015","created_at":"2026-05-18T04:05:58.765694+00:00"},{"alias_kind":"pith_short_12","alias_value":"M6KZZH7GG73S","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"M6KZZH7GG73SSYSX","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"M6KZZH7G","created_at":"2026-05-18T12:26:34.985390+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/M6KZZH7GG73SSYSXRUAPJYB5SV","json":"https://pith.science/pith/M6KZZH7GG73SSYSXRUAPJYB5SV.json","graph_json":"https://pith.science/api/pith-number/M6KZZH7GG73SSYSXRUAPJYB5SV/graph.json","events_json":"https://pith.science/api/pith-number/M6KZZH7GG73SSYSXRUAPJYB5SV/events.json","paper":"https://pith.science/paper/M6KZZH7G"},"agent_actions":{"view_html":"https://pith.science/pith/M6KZZH7GG73SSYSXRUAPJYB5SV","download_json":"https://pith.science/pith/M6KZZH7GG73SSYSXRUAPJYB5SV.json","view_paper":"https://pith.science/paper/M6KZZH7G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.4015&json=true","fetch_graph":"https://pith.science/api/pith-number/M6KZZH7GG73SSYSXRUAPJYB5SV/graph.json","fetch_events":"https://pith.science/api/pith-number/M6KZZH7GG73SSYSXRUAPJYB5SV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/M6KZZH7GG73SSYSXRUAPJYB5SV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/M6KZZH7GG73SSYSXRUAPJYB5SV/action/storage_attestation","attest_author":"https://pith.science/pith/M6KZZH7GG73SSYSXRUAPJYB5SV/action/author_attestation","sign_citation":"https://pith.science/pith/M6KZZH7GG73SSYSXRUAPJYB5SV/action/citation_signature","submit_replication":"https://pith.science/pith/M6KZZH7GG73SSYSXRUAPJYB5SV/action/replication_record"}},"created_at":"2026-05-18T04:05:58.765694+00:00","updated_at":"2026-05-18T04:05:58.765694+00:00"}