{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:HRVAQN3XPJSA5PHEVGGADRBSNU","short_pith_number":"pith:HRVAQN3X","canonical_record":{"source":{"id":"2311.07287","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-11-13T12:28:04Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"e28bc0c0f7971d6d5b25dfcb012be2637b11d5969c37c22c75fb8a1dd4c58cfe","abstract_canon_sha256":"4ee7ab786d9467a9fd2597571f001b1f121cf0bee0a1bd141bf3c0899fd98719"},"schema_version":"1.0"},"canonical_sha256":"3c6a0837777a640ebce4a98c01c4326d39305f7afe4ba920732d8303f8853f1a","source":{"kind":"arxiv","id":"2311.07287","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.07287","created_at":"2026-07-05T08:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"2311.07287v3","created_at":"2026-07-05T08:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.07287","created_at":"2026-07-05T08:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"HRVAQN3XPJSA","created_at":"2026-07-05T08:40:10Z"},{"alias_kind":"pith_short_16","alias_value":"HRVAQN3XPJSA5PHE","created_at":"2026-07-05T08:40:10Z"},{"alias_kind":"pith_short_8","alias_value":"HRVAQN3X","created_at":"2026-07-05T08:40:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:HRVAQN3XPJSA5PHEVGGADRBSNU","target":"record","payload":{"canonical_record":{"source":{"id":"2311.07287","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-11-13T12:28:04Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"e28bc0c0f7971d6d5b25dfcb012be2637b11d5969c37c22c75fb8a1dd4c58cfe","abstract_canon_sha256":"4ee7ab786d9467a9fd2597571f001b1f121cf0bee0a1bd141bf3c0899fd98719"},"schema_version":"1.0"},"canonical_sha256":"3c6a0837777a640ebce4a98c01c4326d39305f7afe4ba920732d8303f8853f1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:40:10.356496Z","signature_b64":"Pb/oRmAQn+bpdKrVUn+M57bnEePgIutySXMwf0yQAF4BSSjzonw3PeogELgGdujmJPQPUZj/JQpqTKalZD9fCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c6a0837777a640ebce4a98c01c4326d39305f7afe4ba920732d8303f8853f1a","last_reissued_at":"2026-07-05T08:40:10.355997Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:40:10.355997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2311.07287","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:40:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l/p5Q0EBT3lIMDgby1XlACA5eHdPMpm1wLGVz15v3t8ITbh8bGLsGlBvFX86JCsX+04GLAphv1teyDSeBZ/zAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:19:49.903983Z"},"content_sha256":"88c4ef0f6f6fbbd7f6fd905b514066af1b560dcf2435f693c9cb4e99010187e6","schema_version":"1.0","event_id":"sha256:88c4ef0f6f6fbbd7f6fd905b514066af1b560dcf2435f693c9cb4e99010187e6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:HRVAQN3XPJSA5PHEVGGADRBSNU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Integral of depth zero to three basis of Modular Graph Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"hep-th","authors_text":"Mehregan Doroudiani","submitted_at":"2023-11-13T12:28:04Z","abstract_excerpt":"Modular Graph Functions (MGFs) are SL(2,$\\mathbb{Z}$)-invariant functions that emerge in the study of the low-energy expansion of the one-loop closed string amplitude. To find the string scattering amplitude, we must integrate MGFs over the moduli space of the torus. In this paper, we use the iterated integral representation of MGFs to establish a depth-dependent basis for them, where \"depth\" refers to the number of iterations in the integral. This basis has a suitable Laplace equation. We integrate this basis from depth zero to depth three over the fundamental domain of SL(2,$\\mathbb{Z}$) wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.07287","kind":"arxiv","version":3},"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/2311.07287/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:40:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D/t2xKJFvVHM8yG92TcpQT7o7Yt7z2HLiqamZybhlOttEH4fDsxQgnmOICw574xDtq9vD+9740cZku7v5U8pCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:19:49.904885Z"},"content_sha256":"b2483ca2282e480fda621f6ed03c560bfddecb4afb2d1a22533c4bbd196c7526","schema_version":"1.0","event_id":"sha256:b2483ca2282e480fda621f6ed03c560bfddecb4afb2d1a22533c4bbd196c7526"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HRVAQN3XPJSA5PHEVGGADRBSNU/bundle.json","state_url":"https://pith.science/pith/HRVAQN3XPJSA5PHEVGGADRBSNU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HRVAQN3XPJSA5PHEVGGADRBSNU/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":"2026-08-14T17:19:49Z","links":{"resolver":"https://pith.science/pith/HRVAQN3XPJSA5PHEVGGADRBSNU","bundle":"https://pith.science/pith/HRVAQN3XPJSA5PHEVGGADRBSNU/bundle.json","state":"https://pith.science/pith/HRVAQN3XPJSA5PHEVGGADRBSNU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HRVAQN3XPJSA5PHEVGGADRBSNU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:HRVAQN3XPJSA5PHEVGGADRBSNU","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":"4ee7ab786d9467a9fd2597571f001b1f121cf0bee0a1bd141bf3c0899fd98719","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-11-13T12:28:04Z","title_canon_sha256":"e28bc0c0f7971d6d5b25dfcb012be2637b11d5969c37c22c75fb8a1dd4c58cfe"},"schema_version":"1.0","source":{"id":"2311.07287","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2311.07287","created_at":"2026-07-05T08:40:10Z"},{"alias_kind":"arxiv_version","alias_value":"2311.07287v3","created_at":"2026-07-05T08:40:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2311.07287","created_at":"2026-07-05T08:40:10Z"},{"alias_kind":"pith_short_12","alias_value":"HRVAQN3XPJSA","created_at":"2026-07-05T08:40:10Z"},{"alias_kind":"pith_short_16","alias_value":"HRVAQN3XPJSA5PHE","created_at":"2026-07-05T08:40:10Z"},{"alias_kind":"pith_short_8","alias_value":"HRVAQN3X","created_at":"2026-07-05T08:40:10Z"}],"graph_snapshots":[{"event_id":"sha256:b2483ca2282e480fda621f6ed03c560bfddecb4afb2d1a22533c4bbd196c7526","target":"graph","created_at":"2026-07-05T08:40:10Z","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/2311.07287/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Modular Graph Functions (MGFs) are SL(2,$\\mathbb{Z}$)-invariant functions that emerge in the study of the low-energy expansion of the one-loop closed string amplitude. To find the string scattering amplitude, we must integrate MGFs over the moduli space of the torus. In this paper, we use the iterated integral representation of MGFs to establish a depth-dependent basis for them, where \"depth\" refers to the number of iterations in the integral. This basis has a suitable Laplace equation. We integrate this basis from depth zero to depth three over the fundamental domain of SL(2,$\\mathbb{Z}$) wit","authors_text":"Mehregan Doroudiani","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-11-13T12:28:04Z","title":"Integral of depth zero to three basis of Modular Graph Functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.07287","kind":"arxiv","version":3},"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":"sha256:88c4ef0f6f6fbbd7f6fd905b514066af1b560dcf2435f693c9cb4e99010187e6","target":"record","created_at":"2026-07-05T08:40:10Z","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":"4ee7ab786d9467a9fd2597571f001b1f121cf0bee0a1bd141bf3c0899fd98719","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2023-11-13T12:28:04Z","title_canon_sha256":"e28bc0c0f7971d6d5b25dfcb012be2637b11d5969c37c22c75fb8a1dd4c58cfe"},"schema_version":"1.0","source":{"id":"2311.07287","kind":"arxiv","version":3}},"canonical_sha256":"3c6a0837777a640ebce4a98c01c4326d39305f7afe4ba920732d8303f8853f1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c6a0837777a640ebce4a98c01c4326d39305f7afe4ba920732d8303f8853f1a","first_computed_at":"2026-07-05T08:40:10.355997Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:40:10.355997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Pb/oRmAQn+bpdKrVUn+M57bnEePgIutySXMwf0yQAF4BSSjzonw3PeogELgGdujmJPQPUZj/JQpqTKalZD9fCA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:40:10.356496Z","signed_message":"canonical_sha256_bytes"},"source_id":"2311.07287","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88c4ef0f6f6fbbd7f6fd905b514066af1b560dcf2435f693c9cb4e99010187e6","sha256:b2483ca2282e480fda621f6ed03c560bfddecb4afb2d1a22533c4bbd196c7526"],"state_sha256":"e8584be4d90c2e5f41fd83bf6a967a8844070891f8712df3a369ef2c13774bee"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9nm/HCFVZxpTYMzyApydi6eXpCQBfNovp5arliiCbBPJwviS8IZ5lsIRzx/5mbA0gLE3XabSNmTiRnOgngx/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T17:19:49.910874Z","bundle_sha256":"35326203b7877048d37cfe97708bc8658afb126ba62ea3a97f708034133b6982"}}