{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:2JHKON76O2STGYEKQNN5TU4OPL","short_pith_number":"pith:2JHKON76","canonical_record":{"source":{"id":"1812.09001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-12-21T08:56:15Z","cross_cats_sorted":[],"title_canon_sha256":"056c732f9e48ae7d67debf9ce31bf224e74c6638b1d86dcd7657678b2c5412f1","abstract_canon_sha256":"7d1087a36dd51633295cc9758de11acc7fa2eade77a4f29f0f13e0c0c184a988"},"schema_version":"1.0"},"canonical_sha256":"d24ea737fe76a533608a835bd9d38e7ae3bdd19d0b9d859ac5b876cb2f3e1d1d","source":{"kind":"arxiv","id":"1812.09001","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09001","created_at":"2026-05-17T23:50:08Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09001v1","created_at":"2026-05-17T23:50:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09001","created_at":"2026-05-17T23:50:08Z"},{"alias_kind":"pith_short_12","alias_value":"2JHKON76O2ST","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2JHKON76O2STGYEK","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2JHKON76","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:2JHKON76O2STGYEKQNN5TU4OPL","target":"record","payload":{"canonical_record":{"source":{"id":"1812.09001","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-12-21T08:56:15Z","cross_cats_sorted":[],"title_canon_sha256":"056c732f9e48ae7d67debf9ce31bf224e74c6638b1d86dcd7657678b2c5412f1","abstract_canon_sha256":"7d1087a36dd51633295cc9758de11acc7fa2eade77a4f29f0f13e0c0c184a988"},"schema_version":"1.0"},"canonical_sha256":"d24ea737fe76a533608a835bd9d38e7ae3bdd19d0b9d859ac5b876cb2f3e1d1d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:08.947128Z","signature_b64":"mdwi76TQrtnyvT1KukhvdoWz74znlf9Tc1vVW6lcF7cgQM7F1ORNLW8mpkhqJoC+VeSIKPQMJeSX/hJb7GvODg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d24ea737fe76a533608a835bd9d38e7ae3bdd19d0b9d859ac5b876cb2f3e1d1d","last_reissued_at":"2026-05-17T23:50:08.946714Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:08.946714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.09001","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":"2026-05-17T23:50:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HBqGU2t2MbKI6QIVWB51uju/1pbEmiWEI2ycPiftCc1tLZ5xV0TxgSbqScN3CMvKUDuMVD+wccqOJHeW2ZJ4Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T17:17:03.620400Z"},"content_sha256":"612ba2e9ddc3bafc78bfd2c3d22cba4db5309008790be629eff7dcf445c8c60e","schema_version":"1.0","event_id":"sha256:612ba2e9ddc3bafc78bfd2c3d22cba4db5309008790be629eff7dcf445c8c60e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:2JHKON76O2STGYEKQNN5TU4OPL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Form factor recursion relations at loop level","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Andreas Brandhuber, Gabriele Travaglini, Lorenzo Bianchi, Rodolfo Panerai","submitted_at":"2018-12-21T08:56:15Z","abstract_excerpt":"We introduce a prescription to define form factor integrands at loop level in planar $\\mathcal{N}=4$ supersymmetric Yang-Mills theory. This relies on a periodic kinematic configuration that has been instrumental to describe form factors at strong coupling in terms of periodic Wilson loops. With this prescription, we are able to formulate loop-level recursion relations for planar form factor integrands, using a two-line (BCFW) and an all-line shift. We also point out important differences with the known recursion relations of integrands of planar loop amplitudes. We present a number of concrete"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09001","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":"2026-05-17T23:50:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CcP/xZzQqVHTDPj809CWXmdSXh868kUHubPoTUZx46a6XqpyFkmOnaZMp0h8VKZvEOQihZMiyxSzD9uUAGidAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-18T17:17:03.621003Z"},"content_sha256":"9099554a0f1f088165b8904eaac6ac97bc96b2dc6db65f0b397512cbfe489fe6","schema_version":"1.0","event_id":"sha256:9099554a0f1f088165b8904eaac6ac97bc96b2dc6db65f0b397512cbfe489fe6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2JHKON76O2STGYEKQNN5TU4OPL/bundle.json","state_url":"https://pith.science/pith/2JHKON76O2STGYEKQNN5TU4OPL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2JHKON76O2STGYEKQNN5TU4OPL/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":"2026-05-18T17:17:03Z","links":{"resolver":"https://pith.science/pith/2JHKON76O2STGYEKQNN5TU4OPL","bundle":"https://pith.science/pith/2JHKON76O2STGYEKQNN5TU4OPL/bundle.json","state":"https://pith.science/pith/2JHKON76O2STGYEKQNN5TU4OPL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2JHKON76O2STGYEKQNN5TU4OPL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:2JHKON76O2STGYEKQNN5TU4OPL","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":"7d1087a36dd51633295cc9758de11acc7fa2eade77a4f29f0f13e0c0c184a988","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-12-21T08:56:15Z","title_canon_sha256":"056c732f9e48ae7d67debf9ce31bf224e74c6638b1d86dcd7657678b2c5412f1"},"schema_version":"1.0","source":{"id":"1812.09001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.09001","created_at":"2026-05-17T23:50:08Z"},{"alias_kind":"arxiv_version","alias_value":"1812.09001v1","created_at":"2026-05-17T23:50:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.09001","created_at":"2026-05-17T23:50:08Z"},{"alias_kind":"pith_short_12","alias_value":"2JHKON76O2ST","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"2JHKON76O2STGYEK","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"2JHKON76","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:9099554a0f1f088165b8904eaac6ac97bc96b2dc6db65f0b397512cbfe489fe6","target":"graph","created_at":"2026-05-17T23:50:08Z","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 introduce a prescription to define form factor integrands at loop level in planar $\\mathcal{N}=4$ supersymmetric Yang-Mills theory. This relies on a periodic kinematic configuration that has been instrumental to describe form factors at strong coupling in terms of periodic Wilson loops. With this prescription, we are able to formulate loop-level recursion relations for planar form factor integrands, using a two-line (BCFW) and an all-line shift. We also point out important differences with the known recursion relations of integrands of planar loop amplitudes. We present a number of concrete","authors_text":"Andreas Brandhuber, Gabriele Travaglini, Lorenzo Bianchi, Rodolfo Panerai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-12-21T08:56:15Z","title":"Form factor recursion relations at loop level"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09001","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":"sha256:612ba2e9ddc3bafc78bfd2c3d22cba4db5309008790be629eff7dcf445c8c60e","target":"record","created_at":"2026-05-17T23:50:08Z","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":"7d1087a36dd51633295cc9758de11acc7fa2eade77a4f29f0f13e0c0c184a988","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2018-12-21T08:56:15Z","title_canon_sha256":"056c732f9e48ae7d67debf9ce31bf224e74c6638b1d86dcd7657678b2c5412f1"},"schema_version":"1.0","source":{"id":"1812.09001","kind":"arxiv","version":1}},"canonical_sha256":"d24ea737fe76a533608a835bd9d38e7ae3bdd19d0b9d859ac5b876cb2f3e1d1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d24ea737fe76a533608a835bd9d38e7ae3bdd19d0b9d859ac5b876cb2f3e1d1d","first_computed_at":"2026-05-17T23:50:08.946714Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:08.946714Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mdwi76TQrtnyvT1KukhvdoWz74znlf9Tc1vVW6lcF7cgQM7F1ORNLW8mpkhqJoC+VeSIKPQMJeSX/hJb7GvODg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:08.947128Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.09001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:612ba2e9ddc3bafc78bfd2c3d22cba4db5309008790be629eff7dcf445c8c60e","sha256:9099554a0f1f088165b8904eaac6ac97bc96b2dc6db65f0b397512cbfe489fe6"],"state_sha256":"34b71b4dbd34ba7f6cc4274983ddba76b06079b0d76a8badd99f63a3ed595100"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5of5Gypk05Kn3dqvw7RJFtsauebmXFcmPopComVMXwUsxMFo5uhEGSnundRhHIoKOSzUXnslhZjEmzmO5tq9DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-18T17:17:03.622681Z","bundle_sha256":"946a2192db8eb86690bcd5216ee656f84baf2f7ae56195507cc56314bcdef9eb"}}