{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Y2OS3PGTR3Z745ELSSAUQQG2ED","short_pith_number":"pith:Y2OS3PGT","canonical_record":{"source":{"id":"1103.4298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-22T16:28:04Z","cross_cats_sorted":["cs.SC","math-ph","math.MP"],"title_canon_sha256":"4ca23e262f034748a9fb73aa231ff3953ccddc3bd3c699552fd1d270412d106a","abstract_canon_sha256":"57413908ba4140c7b02293ccde0b336c6c235a7fd7a3b1771c04eb08bec4edc2"},"schema_version":"1.0"},"canonical_sha256":"c69d2dbcd38ef3fe748b94814840da20fab5c921b001cb925352db03c51fcb15","source":{"kind":"arxiv","id":"1103.4298","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4298","created_at":"2026-05-18T04:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4298v1","created_at":"2026-05-18T04:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4298","created_at":"2026-05-18T04:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"Y2OS3PGTR3Z7","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y2OS3PGTR3Z745EL","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y2OS3PGT","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Y2OS3PGTR3Z745ELSSAUQQG2ED","target":"record","payload":{"canonical_record":{"source":{"id":"1103.4298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-22T16:28:04Z","cross_cats_sorted":["cs.SC","math-ph","math.MP"],"title_canon_sha256":"4ca23e262f034748a9fb73aa231ff3953ccddc3bd3c699552fd1d270412d106a","abstract_canon_sha256":"57413908ba4140c7b02293ccde0b336c6c235a7fd7a3b1771c04eb08bec4edc2"},"schema_version":"1.0"},"canonical_sha256":"c69d2dbcd38ef3fe748b94814840da20fab5c921b001cb925352db03c51fcb15","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:12.612720Z","signature_b64":"3HkYq2rcb29RLMXVSmukKF8aZh6FMi5or1SF8m/fMfWaZDU2FmsrFq0/qdhr1xMmALiYwckF1sr8k04sQsB4Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c69d2dbcd38ef3fe748b94814840da20fab5c921b001cb925352db03c51fcb15","last_reissued_at":"2026-05-18T04:26:12.612097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:12.612097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.4298","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":"2026-05-18T04:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RjjWBbBimdlcPpJyC9dUP1ixbAJCzc+iyiI2J+CZ/PrhagmDEiVHN0dD/tzWBNIh2iBr2x2bqVm0cTSgu5B8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:53:56.499445Z"},"content_sha256":"cfdcb6978bad49cfbd076fdde4bec12633d40e19dcebb61672be6a42d2d09215","schema_version":"1.0","event_id":"sha256:cfdcb6978bad49cfbd076fdde4bec12633d40e19dcebb61672be6a42d2d09215"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Y2OS3PGTR3Z745ELSSAUQQG2ED","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Special Values of Generalized Log-sine Integrals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC","math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Armin Straub, Jonathan M. Borwein","submitted_at":"2011-03-22T16:28:04Z","abstract_excerpt":"We study generalized log-sine integrals at special values. At $\\pi$ and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at $\\pm1$. For general arguments we present algorithmic evaluations involving Nielsen polylogarithms at related arguments. In particular, we consider log-sine integrals at $\\pi/3$ which evaluate in terms of polylogarithms at the sixth root of unity. An implementation of our results for the computer algebra systems Mathematica and SAGE is provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4298","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":"2026-05-18T04:26:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n4Rt1gNYKL+VKF9O79Es1p422HQskLQ7oTej/5P3qY1CHybJPGvurV9cODcMUJJbKKcgsEo8QjtXOtMFgRkSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T16:53:56.500078Z"},"content_sha256":"9878df7f10525bb698e20efee8c5e33166cc72d008128ac6d0714aa5943d832b","schema_version":"1.0","event_id":"sha256:9878df7f10525bb698e20efee8c5e33166cc72d008128ac6d0714aa5943d832b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2OS3PGTR3Z745ELSSAUQQG2ED/bundle.json","state_url":"https://pith.science/pith/Y2OS3PGTR3Z745ELSSAUQQG2ED/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2OS3PGTR3Z745ELSSAUQQG2ED/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":"2026-05-27T16:53:56Z","links":{"resolver":"https://pith.science/pith/Y2OS3PGTR3Z745ELSSAUQQG2ED","bundle":"https://pith.science/pith/Y2OS3PGTR3Z745ELSSAUQQG2ED/bundle.json","state":"https://pith.science/pith/Y2OS3PGTR3Z745ELSSAUQQG2ED/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2OS3PGTR3Z745ELSSAUQQG2ED/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Y2OS3PGTR3Z745ELSSAUQQG2ED","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":"57413908ba4140c7b02293ccde0b336c6c235a7fd7a3b1771c04eb08bec4edc2","cross_cats_sorted":["cs.SC","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-22T16:28:04Z","title_canon_sha256":"4ca23e262f034748a9fb73aa231ff3953ccddc3bd3c699552fd1d270412d106a"},"schema_version":"1.0","source":{"id":"1103.4298","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4298","created_at":"2026-05-18T04:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4298v1","created_at":"2026-05-18T04:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4298","created_at":"2026-05-18T04:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"Y2OS3PGTR3Z7","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Y2OS3PGTR3Z745EL","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Y2OS3PGT","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:9878df7f10525bb698e20efee8c5e33166cc72d008128ac6d0714aa5943d832b","target":"graph","created_at":"2026-05-18T04:26:12Z","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 generalized log-sine integrals at special values. At $\\pi$ and multiples thereof explicit evaluations are obtained in terms of Nielsen polylogarithms at $\\pm1$. For general arguments we present algorithmic evaluations involving Nielsen polylogarithms at related arguments. In particular, we consider log-sine integrals at $\\pi/3$ which evaluate in terms of polylogarithms at the sixth root of unity. An implementation of our results for the computer algebra systems Mathematica and SAGE is provided.","authors_text":"Armin Straub, Jonathan M. Borwein","cross_cats":["cs.SC","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-22T16:28:04Z","title":"Special Values of Generalized Log-sine Integrals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4298","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:cfdcb6978bad49cfbd076fdde4bec12633d40e19dcebb61672be6a42d2d09215","target":"record","created_at":"2026-05-18T04:26:12Z","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":"57413908ba4140c7b02293ccde0b336c6c235a7fd7a3b1771c04eb08bec4edc2","cross_cats_sorted":["cs.SC","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-22T16:28:04Z","title_canon_sha256":"4ca23e262f034748a9fb73aa231ff3953ccddc3bd3c699552fd1d270412d106a"},"schema_version":"1.0","source":{"id":"1103.4298","kind":"arxiv","version":1}},"canonical_sha256":"c69d2dbcd38ef3fe748b94814840da20fab5c921b001cb925352db03c51fcb15","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c69d2dbcd38ef3fe748b94814840da20fab5c921b001cb925352db03c51fcb15","first_computed_at":"2026-05-18T04:26:12.612097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:12.612097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3HkYq2rcb29RLMXVSmukKF8aZh6FMi5or1SF8m/fMfWaZDU2FmsrFq0/qdhr1xMmALiYwckF1sr8k04sQsB4Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:12.612720Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4298","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cfdcb6978bad49cfbd076fdde4bec12633d40e19dcebb61672be6a42d2d09215","sha256:9878df7f10525bb698e20efee8c5e33166cc72d008128ac6d0714aa5943d832b"],"state_sha256":"36fc64655fd4244d476785f0e420411ae478e1e69c0a92be5cab61d848d00f38"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mGtu2VHogxc0Dtz8CG3QSGKvBrgAWgJDJs5TIL2ZkYxsS7cg2Z8vAQ3gTl3mTZ6rWakTa/WkwPl0OZZ9PuTqDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T16:53:56.503498Z","bundle_sha256":"01e404b599d16308e2bc8120c37122e8f1646a13d53142e80c218c2641213d93"}}