{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:COLYGCO4S6TPT4OJ3RLUIH6N7T","short_pith_number":"pith:COLYGCO4","canonical_record":{"source":{"id":"1810.07478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-17T11:22:11Z","cross_cats_sorted":[],"title_canon_sha256":"41db24584488316fdd380929cad3e4ec584069c6b47ac09d3e62ecbbf543ebbe","abstract_canon_sha256":"39f2796d6af447ebaa8c5b0bf09ae0d491354ce37857a00ce7060e53804a50c9"},"schema_version":"1.0"},"canonical_sha256":"13978309dc97a6f9f1c9dc57441fcdfce1d29626091feb711c3a888bd3e9f284","source":{"kind":"arxiv","id":"1810.07478","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07478","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07478v1","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07478","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"COLYGCO4S6TP","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"COLYGCO4S6TPT4OJ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"COLYGCO4","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:COLYGCO4S6TPT4OJ3RLUIH6N7T","target":"record","payload":{"canonical_record":{"source":{"id":"1810.07478","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-17T11:22:11Z","cross_cats_sorted":[],"title_canon_sha256":"41db24584488316fdd380929cad3e4ec584069c6b47ac09d3e62ecbbf543ebbe","abstract_canon_sha256":"39f2796d6af447ebaa8c5b0bf09ae0d491354ce37857a00ce7060e53804a50c9"},"schema_version":"1.0"},"canonical_sha256":"13978309dc97a6f9f1c9dc57441fcdfce1d29626091feb711c3a888bd3e9f284","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:56.275795Z","signature_b64":"gVmcLtw4Ywqbhj+Ocehs24dJwWSzuDma0VYnBmNIj8dVAoDmVz2M4vJ0AQIg+gCUJ7pWcMhgpQE1wyaguae8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"13978309dc97a6f9f1c9dc57441fcdfce1d29626091feb711c3a888bd3e9f284","last_reissued_at":"2026-05-18T00:02:56.275188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:56.275188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.07478","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GACADDbLywB06d88D17nKsySukW6h0alSNt/ezMzSGZgGBD4ya769jsKATPLmvGameQz78SDoh7EdDs8LbPQBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:32:37.667659Z"},"content_sha256":"3628819f526e8ce6e09e79be98ac28a7f28ef94b8526d3db6bf340200c787109","schema_version":"1.0","event_id":"sha256:3628819f526e8ce6e09e79be98ac28a7f28ef94b8526d3db6bf340200c787109"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:COLYGCO4S6TPT4OJ3RLUIH6N7T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Eta quotients and Rademacher sums","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"David Broadhurst, Kevin Acres","submitted_at":"2018-10-17T11:22:11Z","abstract_excerpt":"Eta quotients on $\\Gamma_0(6)$ yield evaluations of sunrise integrals at 2, 3, 4 and 6 loops. At 2 and 3 loops, they provide modular parametrizations of inhomogeneous differential equations whose solutions are readily obtained by expanding in the nome $q$. Atkin-Lehner transformations that permute cusps ensure fast convergence for all external momenta. At 4 and 6 loops, on-shell integrals are periods of modular forms of weights 4 and 6 given by Eichler integrals of eta quotients. Weakly holomorphic eta quotients determine quasi-periods. A Rademacher sum formula is given for Fourier coefficient"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07478","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:02:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LaMaNa+uZrPxjo7+Am1voBSQdJqkvohUSA64JTzoIXuoj/fi3uEfYqzdjZhCqsh+hoPgDXHQb4bi+duHWt0BAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T19:32:37.668001Z"},"content_sha256":"e2371da649f20602bd01c292292ea1fc2dc125e21446db92066597fd27b6fc70","schema_version":"1.0","event_id":"sha256:e2371da649f20602bd01c292292ea1fc2dc125e21446db92066597fd27b6fc70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/COLYGCO4S6TPT4OJ3RLUIH6N7T/bundle.json","state_url":"https://pith.science/pith/COLYGCO4S6TPT4OJ3RLUIH6N7T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/COLYGCO4S6TPT4OJ3RLUIH6N7T/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-20T19:32:37Z","links":{"resolver":"https://pith.science/pith/COLYGCO4S6TPT4OJ3RLUIH6N7T","bundle":"https://pith.science/pith/COLYGCO4S6TPT4OJ3RLUIH6N7T/bundle.json","state":"https://pith.science/pith/COLYGCO4S6TPT4OJ3RLUIH6N7T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/COLYGCO4S6TPT4OJ3RLUIH6N7T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:COLYGCO4S6TPT4OJ3RLUIH6N7T","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"39f2796d6af447ebaa8c5b0bf09ae0d491354ce37857a00ce7060e53804a50c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-17T11:22:11Z","title_canon_sha256":"41db24584488316fdd380929cad3e4ec584069c6b47ac09d3e62ecbbf543ebbe"},"schema_version":"1.0","source":{"id":"1810.07478","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07478","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07478v1","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07478","created_at":"2026-05-18T00:02:56Z"},{"alias_kind":"pith_short_12","alias_value":"COLYGCO4S6TP","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"COLYGCO4S6TPT4OJ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"COLYGCO4","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:e2371da649f20602bd01c292292ea1fc2dc125e21446db92066597fd27b6fc70","target":"graph","created_at":"2026-05-18T00:02:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Eta quotients on $\\Gamma_0(6)$ yield evaluations of sunrise integrals at 2, 3, 4 and 6 loops. At 2 and 3 loops, they provide modular parametrizations of inhomogeneous differential equations whose solutions are readily obtained by expanding in the nome $q$. Atkin-Lehner transformations that permute cusps ensure fast convergence for all external momenta. At 4 and 6 loops, on-shell integrals are periods of modular forms of weights 4 and 6 given by Eichler integrals of eta quotients. Weakly holomorphic eta quotients determine quasi-periods. A Rademacher sum formula is given for Fourier coefficient","authors_text":"David Broadhurst, Kevin Acres","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-17T11:22:11Z","title":"Eta quotients and Rademacher sums"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07478","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3628819f526e8ce6e09e79be98ac28a7f28ef94b8526d3db6bf340200c787109","target":"record","created_at":"2026-05-18T00:02:56Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"39f2796d6af447ebaa8c5b0bf09ae0d491354ce37857a00ce7060e53804a50c9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2018-10-17T11:22:11Z","title_canon_sha256":"41db24584488316fdd380929cad3e4ec584069c6b47ac09d3e62ecbbf543ebbe"},"schema_version":"1.0","source":{"id":"1810.07478","kind":"arxiv","version":1}},"canonical_sha256":"13978309dc97a6f9f1c9dc57441fcdfce1d29626091feb711c3a888bd3e9f284","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"13978309dc97a6f9f1c9dc57441fcdfce1d29626091feb711c3a888bd3e9f284","first_computed_at":"2026-05-18T00:02:56.275188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:02:56.275188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gVmcLtw4Ywqbhj+Ocehs24dJwWSzuDma0VYnBmNIj8dVAoDmVz2M4vJ0AQIg+gCUJ7pWcMhgpQE1wyaguae8Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:02:56.275795Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.07478","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3628819f526e8ce6e09e79be98ac28a7f28ef94b8526d3db6bf340200c787109","sha256:e2371da649f20602bd01c292292ea1fc2dc125e21446db92066597fd27b6fc70"],"state_sha256":"75222bcb1e839c4f6def27e126577dea0a1b3f4301fb57ebeb1a8af623606bee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sdQeLcwQ44M+TUHwdZ7hNc/0JEEnjnWNarjw+VP4FOHYjQBDjBbWHJgP8rXvNbn5HgYkUDucT/P1dFyO8L8YBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T19:32:37.669872Z","bundle_sha256":"e64cf5706b5b56225959db1fe4fb202498d6eae9ed16f39e23ea25b05a8292cd"}}