{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3VBZTP3AKHK26QJHIMFA7DEPJJ","short_pith_number":"pith:3VBZTP3A","canonical_record":{"source":{"id":"1411.6062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-22T02:11:59Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"88b967a87dadb7e0b86e3c84c5cfac57f5b6424ab91cfa6748a75f74cfb83c06","abstract_canon_sha256":"ce36dd6d4b2d01aae8314c8ea592b7c43ea3366249e0d85c7ebf572eb2cc567f"},"schema_version":"1.0"},"canonical_sha256":"dd4399bf6051d5af4127430a0f8c8f4a5e91cea97fa860a1d10e3fe8b462da07","source":{"kind":"arxiv","id":"1411.6062","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6062","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6062v2","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6062","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"3VBZTP3AKHK2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3VBZTP3AKHK26QJH","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3VBZTP3A","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3VBZTP3AKHK26QJHIMFA7DEPJJ","target":"record","payload":{"canonical_record":{"source":{"id":"1411.6062","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-22T02:11:59Z","cross_cats_sorted":["hep-th"],"title_canon_sha256":"88b967a87dadb7e0b86e3c84c5cfac57f5b6424ab91cfa6748a75f74cfb83c06","abstract_canon_sha256":"ce36dd6d4b2d01aae8314c8ea592b7c43ea3366249e0d85c7ebf572eb2cc567f"},"schema_version":"1.0"},"canonical_sha256":"dd4399bf6051d5af4127430a0f8c8f4a5e91cea97fa860a1d10e3fe8b462da07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:51.651469Z","signature_b64":"6aO3GFLg/Ga96ObV4iGNoDWmTI5IOQLEMlSVA1tYJn+fi7WHKLv1DhtSkQGci3QFGW5lD4OW9fBMk6X7AecqBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd4399bf6051d5af4127430a0f8c8f4a5e91cea97fa860a1d10e3fe8b462da07","last_reissued_at":"2026-05-18T02:17:51.650922Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:51.650922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.6062","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:17:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eOFVf9AlfLIwlYFVW/qDQk3MPKvG7JhkihRgJCLKJTl/C4jsHD6L7kuXFe98D439LRrQnpRaoUM88OFRRh6RDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T08:07:56.646034Z"},"content_sha256":"cd71702aa6314a64b81b0fb01c3359ebd18faa31c519c7c21d36336f83863f0f","schema_version":"1.0","event_id":"sha256:cd71702aa6314a64b81b0fb01c3359ebd18faa31c519c7c21d36336f83863f0f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3VBZTP3AKHK26QJHIMFA7DEPJJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evaluation of state integrals at rational points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th"],"primary_cat":"math.GT","authors_text":"Rinat Kashaev, Stavros Garoufalidis","submitted_at":"2014-11-22T02:11:59Z","abstract_excerpt":"Multi-dimensional state-integrals of products of Faddeev's quantum dilogarithms arise frequently in Quantum Topology, quantum Teichm\\\"uller theory and complex Chern--Simons theory. Using the quasi-periodicity property of the quantum dilogarithm, we evaluate 1-dimensional state-integrals at rational points and express the answer in terms of the Rogers dilogarithm, the cyclic (quantum) dilogarithm and finite state-sums at roots of unity. We illustrate our results with the evaluation of the state-integrals of the $4_1$, $5_2$ and $(-2,3,7)$ pretzel knots at rational points."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6062","kind":"arxiv","version":2},"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":"2026-05-18T02:17:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G8/eq28LluwBxcxM1f7tzmUV6GWzlndVXYq+XGzEuM/t90L8CAidWFGcBBhiBMlK7vQEJtvGsMjcjKSFZCxZCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-21T08:07:56.646395Z"},"content_sha256":"c4d47319a0486cf0fa1858a74a18fa48461ee74a1622e36788033b8556ec6eb3","schema_version":"1.0","event_id":"sha256:c4d47319a0486cf0fa1858a74a18fa48461ee74a1622e36788033b8556ec6eb3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3VBZTP3AKHK26QJHIMFA7DEPJJ/bundle.json","state_url":"https://pith.science/pith/3VBZTP3AKHK26QJHIMFA7DEPJJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3VBZTP3AKHK26QJHIMFA7DEPJJ/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":"2026-05-21T08:07:56Z","links":{"resolver":"https://pith.science/pith/3VBZTP3AKHK26QJHIMFA7DEPJJ","bundle":"https://pith.science/pith/3VBZTP3AKHK26QJHIMFA7DEPJJ/bundle.json","state":"https://pith.science/pith/3VBZTP3AKHK26QJHIMFA7DEPJJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3VBZTP3AKHK26QJHIMFA7DEPJJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3VBZTP3AKHK26QJHIMFA7DEPJJ","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":"ce36dd6d4b2d01aae8314c8ea592b7c43ea3366249e0d85c7ebf572eb2cc567f","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-22T02:11:59Z","title_canon_sha256":"88b967a87dadb7e0b86e3c84c5cfac57f5b6424ab91cfa6748a75f74cfb83c06"},"schema_version":"1.0","source":{"id":"1411.6062","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6062","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6062v2","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6062","created_at":"2026-05-18T02:17:51Z"},{"alias_kind":"pith_short_12","alias_value":"3VBZTP3AKHK2","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3VBZTP3AKHK26QJH","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3VBZTP3A","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:c4d47319a0486cf0fa1858a74a18fa48461ee74a1622e36788033b8556ec6eb3","target":"graph","created_at":"2026-05-18T02:17:51Z","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":"Multi-dimensional state-integrals of products of Faddeev's quantum dilogarithms arise frequently in Quantum Topology, quantum Teichm\\\"uller theory and complex Chern--Simons theory. Using the quasi-periodicity property of the quantum dilogarithm, we evaluate 1-dimensional state-integrals at rational points and express the answer in terms of the Rogers dilogarithm, the cyclic (quantum) dilogarithm and finite state-sums at roots of unity. We illustrate our results with the evaluation of the state-integrals of the $4_1$, $5_2$ and $(-2,3,7)$ pretzel knots at rational points.","authors_text":"Rinat Kashaev, Stavros Garoufalidis","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-22T02:11:59Z","title":"Evaluation of state integrals at rational points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6062","kind":"arxiv","version":2},"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:cd71702aa6314a64b81b0fb01c3359ebd18faa31c519c7c21d36336f83863f0f","target":"record","created_at":"2026-05-18T02:17:51Z","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":"ce36dd6d4b2d01aae8314c8ea592b7c43ea3366249e0d85c7ebf572eb2cc567f","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-11-22T02:11:59Z","title_canon_sha256":"88b967a87dadb7e0b86e3c84c5cfac57f5b6424ab91cfa6748a75f74cfb83c06"},"schema_version":"1.0","source":{"id":"1411.6062","kind":"arxiv","version":2}},"canonical_sha256":"dd4399bf6051d5af4127430a0f8c8f4a5e91cea97fa860a1d10e3fe8b462da07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd4399bf6051d5af4127430a0f8c8f4a5e91cea97fa860a1d10e3fe8b462da07","first_computed_at":"2026-05-18T02:17:51.650922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:51.650922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6aO3GFLg/Ga96ObV4iGNoDWmTI5IOQLEMlSVA1tYJn+fi7WHKLv1DhtSkQGci3QFGW5lD4OW9fBMk6X7AecqBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:51.651469Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6062","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd71702aa6314a64b81b0fb01c3359ebd18faa31c519c7c21d36336f83863f0f","sha256:c4d47319a0486cf0fa1858a74a18fa48461ee74a1622e36788033b8556ec6eb3"],"state_sha256":"03986b73161a196678796d0517375f81c141dd43d95114be5c71b97e1a1ffa45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qMd0SYxnhbdnI47oarKx2c5ZP66NZvxpwpJUoAbFNs317dySsgsICn+NdVkTJbQmuCyoF9do50PBTjXdElcfCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-21T08:07:56.648845Z","bundle_sha256":"440fee8fda87d692d0e3f1498d4cae1ac6608dc0af7cc2e0189175777d9cba91"}}