{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:GIOEQ44KUKEG2F7KSYHIX6EL4D","short_pith_number":"pith:GIOEQ44K","canonical_record":{"source":{"id":"1207.3824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-16T21:01:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c1d7b93afd6472600b5bda8f900047eb400f688162f89d4bdbc15a261ad2cf06","abstract_canon_sha256":"6a8239501feb6e2c723888babc3cd18c6e965aeaf46b6496b22332d643e8be71"},"schema_version":"1.0"},"canonical_sha256":"321c48738aa2886d17ea960e8bf88be0ffa91ed1f3971c8c302b3d05d3409996","source":{"kind":"arxiv","id":"1207.3824","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3824","created_at":"2026-05-18T01:56:17Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3824v1","created_at":"2026-05-18T01:56:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3824","created_at":"2026-05-18T01:56:17Z"},{"alias_kind":"pith_short_12","alias_value":"GIOEQ44KUKEG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GIOEQ44KUKEG2F7K","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GIOEQ44K","created_at":"2026-05-18T12:27:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:GIOEQ44KUKEG2F7KSYHIX6EL4D","target":"record","payload":{"canonical_record":{"source":{"id":"1207.3824","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-16T21:01:05Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"c1d7b93afd6472600b5bda8f900047eb400f688162f89d4bdbc15a261ad2cf06","abstract_canon_sha256":"6a8239501feb6e2c723888babc3cd18c6e965aeaf46b6496b22332d643e8be71"},"schema_version":"1.0"},"canonical_sha256":"321c48738aa2886d17ea960e8bf88be0ffa91ed1f3971c8c302b3d05d3409996","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:56:17.735324Z","signature_b64":"Yol9fPVHLdUiIOUFWIGERBUZBXHTCuFmmYRnStBW19ibwcBQxIx3yxkSUQ5Yv/e9DWcfVGT1ZsZZdVlHTpevAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"321c48738aa2886d17ea960e8bf88be0ffa91ed1f3971c8c302b3d05d3409996","last_reissued_at":"2026-05-18T01:56:17.734820Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:56:17.734820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.3824","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":"2026-05-18T01:56:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VtFrETL6Cu1vGSjFWQ1qacUjPRa3U7RIDpqgTmjiKTdH8Yqd7KHPw5AmXM9K8rS2yw4VzKNFhv6hCVXuqvpOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T08:44:23.971336Z"},"content_sha256":"f302cef7832a5befa618788416990b1918e23b5954bc7937623f3b1ac0cc2948","schema_version":"1.0","event_id":"sha256:f302cef7832a5befa618788416990b1918e23b5954bc7937623f3b1ac0cc2948"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:GIOEQ44KUKEG2F7KSYHIX6EL4D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Generalised ladders and single-valued polylogarithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"J. M. Drummond","submitted_at":"2012-07-16T21:01:05Z","abstract_excerpt":"We introduce and solve an infinite class of loop integrals which generalises the well-known ladder series. The integrals are described in terms of single-valued polylogarithmic functions which satisfy certain differential equations. The combination of the differential equations and single-valued behaviour allow us to explicitly construct the polylogarithms recursively. For this class of integrals the symbol may be read off from the integrand in a particularly simple way. We give an explicit formula for the simplest generalisation of the ladder series. We also relate the generalised ladder inte"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3824","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":"2026-05-18T01:56:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7quTBUUmh6G0Pp783sn3BSLL+rUIGvVtMnA4iZOiQs950//AMxVU7eLIFOjZHfmJXDBHma9rntRCaHoTVsUHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T08:44:23.971700Z"},"content_sha256":"ef1f59519c3df4023165462341e68ca8aa9e17ef36e9ef1fbd957968c00accac","schema_version":"1.0","event_id":"sha256:ef1f59519c3df4023165462341e68ca8aa9e17ef36e9ef1fbd957968c00accac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GIOEQ44KUKEG2F7KSYHIX6EL4D/bundle.json","state_url":"https://pith.science/pith/GIOEQ44KUKEG2F7KSYHIX6EL4D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GIOEQ44KUKEG2F7KSYHIX6EL4D/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":"2026-05-20T08:44:23Z","links":{"resolver":"https://pith.science/pith/GIOEQ44KUKEG2F7KSYHIX6EL4D","bundle":"https://pith.science/pith/GIOEQ44KUKEG2F7KSYHIX6EL4D/bundle.json","state":"https://pith.science/pith/GIOEQ44KUKEG2F7KSYHIX6EL4D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GIOEQ44KUKEG2F7KSYHIX6EL4D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:GIOEQ44KUKEG2F7KSYHIX6EL4D","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":"6a8239501feb6e2c723888babc3cd18c6e965aeaf46b6496b22332d643e8be71","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-16T21:01:05Z","title_canon_sha256":"c1d7b93afd6472600b5bda8f900047eb400f688162f89d4bdbc15a261ad2cf06"},"schema_version":"1.0","source":{"id":"1207.3824","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.3824","created_at":"2026-05-18T01:56:17Z"},{"alias_kind":"arxiv_version","alias_value":"1207.3824v1","created_at":"2026-05-18T01:56:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.3824","created_at":"2026-05-18T01:56:17Z"},{"alias_kind":"pith_short_12","alias_value":"GIOEQ44KUKEG","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_16","alias_value":"GIOEQ44KUKEG2F7K","created_at":"2026-05-18T12:27:06Z"},{"alias_kind":"pith_short_8","alias_value":"GIOEQ44K","created_at":"2026-05-18T12:27:06Z"}],"graph_snapshots":[{"event_id":"sha256:ef1f59519c3df4023165462341e68ca8aa9e17ef36e9ef1fbd957968c00accac","target":"graph","created_at":"2026-05-18T01:56:17Z","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 and solve an infinite class of loop integrals which generalises the well-known ladder series. The integrals are described in terms of single-valued polylogarithmic functions which satisfy certain differential equations. The combination of the differential equations and single-valued behaviour allow us to explicitly construct the polylogarithms recursively. For this class of integrals the symbol may be read off from the integrand in a particularly simple way. We give an explicit formula for the simplest generalisation of the ladder series. We also relate the generalised ladder inte","authors_text":"J. M. Drummond","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-16T21:01:05Z","title":"Generalised ladders and single-valued polylogarithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3824","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:f302cef7832a5befa618788416990b1918e23b5954bc7937623f3b1ac0cc2948","target":"record","created_at":"2026-05-18T01:56:17Z","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":"6a8239501feb6e2c723888babc3cd18c6e965aeaf46b6496b22332d643e8be71","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2012-07-16T21:01:05Z","title_canon_sha256":"c1d7b93afd6472600b5bda8f900047eb400f688162f89d4bdbc15a261ad2cf06"},"schema_version":"1.0","source":{"id":"1207.3824","kind":"arxiv","version":1}},"canonical_sha256":"321c48738aa2886d17ea960e8bf88be0ffa91ed1f3971c8c302b3d05d3409996","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"321c48738aa2886d17ea960e8bf88be0ffa91ed1f3971c8c302b3d05d3409996","first_computed_at":"2026-05-18T01:56:17.734820Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:56:17.734820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yol9fPVHLdUiIOUFWIGERBUZBXHTCuFmmYRnStBW19ibwcBQxIx3yxkSUQ5Yv/e9DWcfVGT1ZsZZdVlHTpevAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:56:17.735324Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.3824","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f302cef7832a5befa618788416990b1918e23b5954bc7937623f3b1ac0cc2948","sha256:ef1f59519c3df4023165462341e68ca8aa9e17ef36e9ef1fbd957968c00accac"],"state_sha256":"a35e176d470cdd2e56db48a473b421e86a3bebc2e088801f7d28b83542e10f7f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SPXgD0Vh9e+hlU74cACkruBvnPvGgZbVkWi+ClVDfm446hEU+XcfXoq+pE9R/D5VdIhdiYJX6pJh9fz8Q+3eDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T08:44:23.973822Z","bundle_sha256":"c9b271b1785b24f187f1b26ea75ae78df14a1f2fec91dd1cf36b9b3935ba4432"}}