{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YWMRH3RUAZWCAK5XFU6J4R7EVC","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":"1fa96fc5516d1baf856562f36b03f6dcc45a28b41f8da560362c0be168aed809","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-01T15:48:58Z","title_canon_sha256":"b53943b85e6515a99742bdfd0f99954e2364a99502ff4a4ad7f2e715e39b0464"},"schema_version":"1.0","source":{"id":"1509.00363","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00363","created_at":"2026-07-05T03:48:34Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00363v2","created_at":"2026-07-05T03:48:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00363","created_at":"2026-07-05T03:48:34Z"},{"alias_kind":"pith_short_12","alias_value":"YWMRH3RUAZWC","created_at":"2026-07-05T03:48:34Z"},{"alias_kind":"pith_short_16","alias_value":"YWMRH3RUAZWCAK5X","created_at":"2026-07-05T03:48:34Z"},{"alias_kind":"pith_short_8","alias_value":"YWMRH3RU","created_at":"2026-07-05T03:48:34Z"}],"graph_snapshots":[{"event_id":"sha256:e6b731d160758e43666eb998b4a3fad52b02803daf34f57f8214a2a8f93a4249","target":"graph","created_at":"2026-07-05T03:48:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1509.00363/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The coefficients of the higher-derivative terms in the low energy expansion of genus-one graviton Type II superstring scattering amplitudes are determined by integrating sums of non-holomorphic modular functions over the complex structure modulus of a torus. In the case of the four-graviton amplitude, each of these modular functions is a multiple sum associated with a Feynman diagram for a free massless scalar field on the torus. The lines in each diagram join pairs of vertex insertion points and the number of lines defines its weight $w$, which corresponds to its order in the low energy expan","authors_text":"Eric D'Hoker, Michael B. Green, Pierre Vanhove","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-01T15:48:58Z","title":"Proof of a modular relation between 1-, 2- and 3-loop Feynman diagrams on a torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00363","kind":"arxiv","version":2},"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:b943357106ccf2428345bc885b54b55ef41e2ef133152224c1a82164bdf63480","target":"record","created_at":"2026-07-05T03:48:34Z","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":"1fa96fc5516d1baf856562f36b03f6dcc45a28b41f8da560362c0be168aed809","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-09-01T15:48:58Z","title_canon_sha256":"b53943b85e6515a99742bdfd0f99954e2364a99502ff4a4ad7f2e715e39b0464"},"schema_version":"1.0","source":{"id":"1509.00363","kind":"arxiv","version":2}},"canonical_sha256":"c59913ee34066c202bb72d3c9e47e4a88742914a00b1c915ac21af3bfb9a9b2f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c59913ee34066c202bb72d3c9e47e4a88742914a00b1c915ac21af3bfb9a9b2f","first_computed_at":"2026-07-05T03:48:34.163748Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:48:34.163748Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B8wQU6qCTQQaRgRjApvKKJXwJYa6AcBZQoAdBiNoTlGjmRdxpt03qmFeO1k8AWfrXMwLmE8hSX3Tcr5DKuO7CQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:48:34.164236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00363","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b943357106ccf2428345bc885b54b55ef41e2ef133152224c1a82164bdf63480","sha256:e6b731d160758e43666eb998b4a3fad52b02803daf34f57f8214a2a8f93a4249"],"state_sha256":"60ba4bd9cfb83c1af73f6c15c8d9c539d72fc1f8345f6e8eead9fb062f9e287a"}