{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:U3DBMHNBC22JMERYTTDS66Y54J","short_pith_number":"pith:U3DBMHNB","canonical_record":{"source":{"id":"1608.06185","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-19T01:57:14Z","cross_cats_sorted":[],"title_canon_sha256":"9188f506a38906a64c856a6d7f7edd9b63ff71710329ca69b315a07de1562ff7","abstract_canon_sha256":"6de68f338d18b56f1fa2a68f7f2d39ace6857a9de900b7910e34209effd2a5dd"},"schema_version":"1.0"},"canonical_sha256":"a6c6161da116b49612389cc72f7b1de27c2c814d3d672e9680d8c0aaa30cff6e","source":{"kind":"arxiv","id":"1608.06185","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06185","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06185v2","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06185","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"U3DBMHNBC22J","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U3DBMHNBC22JMERY","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U3DBMHNB","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:U3DBMHNBC22JMERYTTDS66Y54J","target":"record","payload":{"canonical_record":{"source":{"id":"1608.06185","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-19T01:57:14Z","cross_cats_sorted":[],"title_canon_sha256":"9188f506a38906a64c856a6d7f7edd9b63ff71710329ca69b315a07de1562ff7","abstract_canon_sha256":"6de68f338d18b56f1fa2a68f7f2d39ace6857a9de900b7910e34209effd2a5dd"},"schema_version":"1.0"},"canonical_sha256":"a6c6161da116b49612389cc72f7b1de27c2c814d3d672e9680d8c0aaa30cff6e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:27.150117Z","signature_b64":"r4zHiTjh53NipZWprP2KK06LvrBd9HaeLXAJgMAVI+Zn15gRyrLlCjmkolkhZmKaat4GnBtdx8ZbZGHhxb1mBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a6c6161da116b49612389cc72f7b1de27c2c814d3d672e9680d8c0aaa30cff6e","last_reissued_at":"2026-05-18T01:04:27.149434Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:27.149434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1608.06185","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":"2026-05-18T01:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"26+En2M0GNZYIvt0d4IheDgxw4uaFB9yAQpWOhWMSwubTME1H0X98K3WUWjTDlrhUQQ308LlignKwxRk+GhMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T06:03:53.588751Z"},"content_sha256":"8541b4a3f374e8bb56f083ff1db21ecba1642c3e152a59c68e77ebfcd94d94fc","schema_version":"1.0","event_id":"sha256:8541b4a3f374e8bb56f083ff1db21ecba1642c3e152a59c68e77ebfcd94d94fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:U3DBMHNBC22JMERYTTDS66Y54J","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An alternative representation of the Vi\\`ete's formula for pi by Chebyshev polynomials of the first kind","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"B. M. Quine, S. M. Abrarov","submitted_at":"2016-08-19T01:57:14Z","abstract_excerpt":"There are several reformulations of the Vi\\`ete's formula for pi that have been reported in the modern literature. In this paper we show another analog to the Vi\\`ete's formula for pi by Chebyshev polynomials of the first kind."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06185","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":"2026-05-18T01:04:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DyxS7Ykukcs9Auw2X3p8xbLndkW2KvpNlnGTHCSMwpKrT2tWQpO91gqw51CyNb9hjOXnQNwFcPVKt8mdn2lrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T06:03:53.589093Z"},"content_sha256":"cc7ec9e287c8a69134ed83397a39d168f3aa5035d677dbf7c75d065f1a1f54c5","schema_version":"1.0","event_id":"sha256:cc7ec9e287c8a69134ed83397a39d168f3aa5035d677dbf7c75d065f1a1f54c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U3DBMHNBC22JMERYTTDS66Y54J/bundle.json","state_url":"https://pith.science/pith/U3DBMHNBC22JMERYTTDS66Y54J/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U3DBMHNBC22JMERYTTDS66Y54J/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":"2026-07-02T06:03:53Z","links":{"resolver":"https://pith.science/pith/U3DBMHNBC22JMERYTTDS66Y54J","bundle":"https://pith.science/pith/U3DBMHNBC22JMERYTTDS66Y54J/bundle.json","state":"https://pith.science/pith/U3DBMHNBC22JMERYTTDS66Y54J/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U3DBMHNBC22JMERYTTDS66Y54J/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:U3DBMHNBC22JMERYTTDS66Y54J","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":"6de68f338d18b56f1fa2a68f7f2d39ace6857a9de900b7910e34209effd2a5dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-19T01:57:14Z","title_canon_sha256":"9188f506a38906a64c856a6d7f7edd9b63ff71710329ca69b315a07de1562ff7"},"schema_version":"1.0","source":{"id":"1608.06185","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06185","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06185v2","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06185","created_at":"2026-05-18T01:04:27Z"},{"alias_kind":"pith_short_12","alias_value":"U3DBMHNBC22J","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"U3DBMHNBC22JMERY","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"U3DBMHNB","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:cc7ec9e287c8a69134ed83397a39d168f3aa5035d677dbf7c75d065f1a1f54c5","target":"graph","created_at":"2026-05-18T01:04:27Z","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":"There are several reformulations of the Vi\\`ete's formula for pi that have been reported in the modern literature. In this paper we show another analog to the Vi\\`ete's formula for pi by Chebyshev polynomials of the first kind.","authors_text":"B. M. Quine, S. M. Abrarov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-19T01:57:14Z","title":"An alternative representation of the Vi\\`ete's formula for pi by Chebyshev polynomials of the first kind"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06185","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":"sha256:8541b4a3f374e8bb56f083ff1db21ecba1642c3e152a59c68e77ebfcd94d94fc","target":"record","created_at":"2026-05-18T01:04:27Z","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":"6de68f338d18b56f1fa2a68f7f2d39ace6857a9de900b7910e34209effd2a5dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-08-19T01:57:14Z","title_canon_sha256":"9188f506a38906a64c856a6d7f7edd9b63ff71710329ca69b315a07de1562ff7"},"schema_version":"1.0","source":{"id":"1608.06185","kind":"arxiv","version":2}},"canonical_sha256":"a6c6161da116b49612389cc72f7b1de27c2c814d3d672e9680d8c0aaa30cff6e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a6c6161da116b49612389cc72f7b1de27c2c814d3d672e9680d8c0aaa30cff6e","first_computed_at":"2026-05-18T01:04:27.149434Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:27.149434Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"r4zHiTjh53NipZWprP2KK06LvrBd9HaeLXAJgMAVI+Zn15gRyrLlCjmkolkhZmKaat4GnBtdx8ZbZGHhxb1mBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:27.150117Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06185","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8541b4a3f374e8bb56f083ff1db21ecba1642c3e152a59c68e77ebfcd94d94fc","sha256:cc7ec9e287c8a69134ed83397a39d168f3aa5035d677dbf7c75d065f1a1f54c5"],"state_sha256":"1335d521381d5b7d2012f4dfe61fca5e3396e982987c08d35d83d75ee0ee3a01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OBozUnyIqSca1NfzqsnRhIV7PEC4LvhDkqEE6UVcWCm8w5W9e1cQfOemAeX45tjBIvr/Ni6OhLgnhRHPQKACDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T06:03:53.591148Z","bundle_sha256":"f7c316c119f8a06fb1cec44a74b25999f797dd3a19380229e4b9f38324167c44"}}