{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:DNBBQ7BXMRJ3YE6UA66HA3WC5O","short_pith_number":"pith:DNBBQ7BX","canonical_record":{"source":{"id":"1510.07859","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-27T10:59:53Z","cross_cats_sorted":[],"title_canon_sha256":"84fefb85f0ef9366d97b8b045013fc260de2c1a336303a91706e9ba1582641c2","abstract_canon_sha256":"4a313f740a843020caae53d0f2b7e01b6b505ea18045c10284357d83a14ee452"},"schema_version":"1.0"},"canonical_sha256":"1b42187c376453bc13d407bc706ec2eb8536f8e25bcd5c12e0c9832a91d48ae7","source":{"kind":"arxiv","id":"1510.07859","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07859","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07859v3","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07859","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"pith_short_12","alias_value":"DNBBQ7BXMRJ3","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DNBBQ7BXMRJ3YE6U","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DNBBQ7BX","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:DNBBQ7BXMRJ3YE6UA66HA3WC5O","target":"record","payload":{"canonical_record":{"source":{"id":"1510.07859","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-27T10:59:53Z","cross_cats_sorted":[],"title_canon_sha256":"84fefb85f0ef9366d97b8b045013fc260de2c1a336303a91706e9ba1582641c2","abstract_canon_sha256":"4a313f740a843020caae53d0f2b7e01b6b505ea18045c10284357d83a14ee452"},"schema_version":"1.0"},"canonical_sha256":"1b42187c376453bc13d407bc706ec2eb8536f8e25bcd5c12e0c9832a91d48ae7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:32.675151Z","signature_b64":"BWpLSgEmxrJVuDSelaV1V06VKYSDs3rxGthVw7zYKMyT0YB0eccTGvOz2pf+6gK8E0poxhRPlPny+kU2e+YrBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b42187c376453bc13d407bc706ec2eb8536f8e25bcd5c12e0c9832a91d48ae7","last_reissued_at":"2026-05-18T00:28:32.674512Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:32.674512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.07859","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":"2026-05-18T00:28:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SzeI04Jwa1cZ78SlFCrXx1J/IiuIXQnsSCMjA1Re67jFy3gz4DL93l0qo3MchTUluUoFLQTkvK1bKG9N2bEPDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:37:32.193475Z"},"content_sha256":"bcc67088016bcf626d39fea37a422d69da0e2f499fb975dcaa427e31a1368c85","schema_version":"1.0","event_id":"sha256:bcc67088016bcf626d39fea37a422d69da0e2f499fb975dcaa427e31a1368c85"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:DNBBQ7BXMRJ3YE6UA66HA3WC5O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Loops in exceptional field theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Axel Kleinschmidt, Guillaume Bossard","submitted_at":"2015-10-27T10:59:53Z","abstract_excerpt":"We study certain four-graviton amplitudes in exceptional field theory in dimensions $D\\geq 4$ up to two loops. As the formulation is manifestly invariant under the U-duality group $E_{11-D}(\\mathbb{Z})$, our resulting expressions can be expressed in terms of automorphic forms. In the low energy expansion, we find terms in the M-theory effective action of type $R^4$, $\\nabla^4R^4$ and $\\nabla^6 R^4$ with automorphic coefficient functions in agreement with independent derivations from string theory. This provides in particular an explicit integral formula for the exact string theory $\\nabla^6 R^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07859","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":""},"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":"2026-05-18T00:28:32Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MS1CvRHHZf5+OZC9gqONVSOWJaMDCj78xY/sa2y0KJV8N1U+5i2YN+y0vm3+9esVk3GtGhpHCkU66YKmDyE7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T14:37:32.193820Z"},"content_sha256":"5f108263b31fbb64b46e4cf3c1bfeb6988886bd7b429ed93694dc29d33472c4b","schema_version":"1.0","event_id":"sha256:5f108263b31fbb64b46e4cf3c1bfeb6988886bd7b429ed93694dc29d33472c4b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DNBBQ7BXMRJ3YE6UA66HA3WC5O/bundle.json","state_url":"https://pith.science/pith/DNBBQ7BXMRJ3YE6UA66HA3WC5O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DNBBQ7BXMRJ3YE6UA66HA3WC5O/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":"2026-06-11T14:37:32Z","links":{"resolver":"https://pith.science/pith/DNBBQ7BXMRJ3YE6UA66HA3WC5O","bundle":"https://pith.science/pith/DNBBQ7BXMRJ3YE6UA66HA3WC5O/bundle.json","state":"https://pith.science/pith/DNBBQ7BXMRJ3YE6UA66HA3WC5O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DNBBQ7BXMRJ3YE6UA66HA3WC5O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DNBBQ7BXMRJ3YE6UA66HA3WC5O","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":"4a313f740a843020caae53d0f2b7e01b6b505ea18045c10284357d83a14ee452","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-27T10:59:53Z","title_canon_sha256":"84fefb85f0ef9366d97b8b045013fc260de2c1a336303a91706e9ba1582641c2"},"schema_version":"1.0","source":{"id":"1510.07859","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.07859","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"arxiv_version","alias_value":"1510.07859v3","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.07859","created_at":"2026-05-18T00:28:32Z"},{"alias_kind":"pith_short_12","alias_value":"DNBBQ7BXMRJ3","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DNBBQ7BXMRJ3YE6U","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DNBBQ7BX","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:5f108263b31fbb64b46e4cf3c1bfeb6988886bd7b429ed93694dc29d33472c4b","target":"graph","created_at":"2026-05-18T00:28:32Z","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":"We study certain four-graviton amplitudes in exceptional field theory in dimensions $D\\geq 4$ up to two loops. As the formulation is manifestly invariant under the U-duality group $E_{11-D}(\\mathbb{Z})$, our resulting expressions can be expressed in terms of automorphic forms. In the low energy expansion, we find terms in the M-theory effective action of type $R^4$, $\\nabla^4R^4$ and $\\nabla^6 R^4$ with automorphic coefficient functions in agreement with independent derivations from string theory. This provides in particular an explicit integral formula for the exact string theory $\\nabla^6 R^","authors_text":"Axel Kleinschmidt, Guillaume Bossard","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-27T10:59:53Z","title":"Loops in exceptional field theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07859","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:bcc67088016bcf626d39fea37a422d69da0e2f499fb975dcaa427e31a1368c85","target":"record","created_at":"2026-05-18T00:28:32Z","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":"4a313f740a843020caae53d0f2b7e01b6b505ea18045c10284357d83a14ee452","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2015-10-27T10:59:53Z","title_canon_sha256":"84fefb85f0ef9366d97b8b045013fc260de2c1a336303a91706e9ba1582641c2"},"schema_version":"1.0","source":{"id":"1510.07859","kind":"arxiv","version":3}},"canonical_sha256":"1b42187c376453bc13d407bc706ec2eb8536f8e25bcd5c12e0c9832a91d48ae7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b42187c376453bc13d407bc706ec2eb8536f8e25bcd5c12e0c9832a91d48ae7","first_computed_at":"2026-05-18T00:28:32.674512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:32.674512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BWpLSgEmxrJVuDSelaV1V06VKYSDs3rxGthVw7zYKMyT0YB0eccTGvOz2pf+6gK8E0poxhRPlPny+kU2e+YrBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:32.675151Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.07859","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcc67088016bcf626d39fea37a422d69da0e2f499fb975dcaa427e31a1368c85","sha256:5f108263b31fbb64b46e4cf3c1bfeb6988886bd7b429ed93694dc29d33472c4b"],"state_sha256":"29019e75d38a25192a112ad0ce3edffecd4f63de66386acf21717c10fdb57b6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xYpT01I34Lrs+NkX/muABoGKXLjesP8Ebfjp2HzO3VCns62L9Y+SDVylalUS4u+09KzSnxg71srIYMOBrkC2Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T14:37:32.195785Z","bundle_sha256":"d4addc07d1adee2d3c191f0a53a713a8931e706ce9ec16c3bf5a7cf2a205c3bb"}}