{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:MT2BBU26VFYFNH57VOORAUQER5","short_pith_number":"pith:MT2BBU26","canonical_record":{"source":{"id":"2607.19337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-21T17:55:49Z","cross_cats_sorted":[],"title_canon_sha256":"cfb26c6fd20451b89993687f47c441826fc064e71c898102464e53dd4091a1c4","abstract_canon_sha256":"d396a1b67aa0816f1f0c10ee237110d3f20e1352de3f886d829e29e2aa824118"},"schema_version":"1.0"},"canonical_sha256":"64f410d35ea970569fbfab9d1052048f729e065b1e4299c8029398220271227f","source":{"kind":"arxiv","id":"2607.19337","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19337","created_at":"2026-07-22T01:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19337v1","created_at":"2026-07-22T01:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19337","created_at":"2026-07-22T01:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"MT2BBU26VFYF","created_at":"2026-07-22T01:24:37Z"},{"alias_kind":"pith_short_16","alias_value":"MT2BBU26VFYFNH57","created_at":"2026-07-22T01:24:37Z"},{"alias_kind":"pith_short_8","alias_value":"MT2BBU26","created_at":"2026-07-22T01:24:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:MT2BBU26VFYFNH57VOORAUQER5","target":"record","payload":{"canonical_record":{"source":{"id":"2607.19337","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-21T17:55:49Z","cross_cats_sorted":[],"title_canon_sha256":"cfb26c6fd20451b89993687f47c441826fc064e71c898102464e53dd4091a1c4","abstract_canon_sha256":"d396a1b67aa0816f1f0c10ee237110d3f20e1352de3f886d829e29e2aa824118"},"schema_version":"1.0"},"canonical_sha256":"64f410d35ea970569fbfab9d1052048f729e065b1e4299c8029398220271227f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-22T01:24:37.769325Z","signature_b64":"GyrdpVJMsbBIWfrlxkaaWIqQoIkXd+G+RHU9tZzNV3QtrW0osb8Kok9nM3ET09FQvVIJJrgsRzXoqfrlMv5bCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64f410d35ea970569fbfab9d1052048f729e065b1e4299c8029398220271227f","last_reissued_at":"2026-07-22T01:24:37.768516Z","signature_status":"signed_v1","first_computed_at":"2026-07-22T01:24:37.768516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.19337","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":"2026-07-22T01:24:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZdgCW2lO4u/KUnTFSaWvDpQMI9q4BrYmaafEVHPu4mfTkLnrImdy5iQez53lLpaQpvTcxOSL2cEFFxKfOtT8CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T17:49:18.269735Z"},"content_sha256":"98f0bc61d2cb5b91ac014106d649df5dc2b1433ea46cda41d57ed204ec24894b","schema_version":"1.0","event_id":"sha256:98f0bc61d2cb5b91ac014106d649df5dc2b1433ea46cda41d57ed204ec24894b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:MT2BBU26VFYFNH57VOORAUQER5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the $\\mathcal{A}$-transcendence of a Champernowne-type constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Shin-ichiro Seki","submitted_at":"2026-07-21T17:55:49Z","abstract_excerpt":"Let $p_n$ denote the $n$-th prime. We prove that for every nonzero polynomial $f(x)\\in\\mathbb{Z}[x]$, there exist infinitely many positive integers $n$ such that $p_n\\nmid f(n)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19337","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.19337/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-22T01:24:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e8mBZCznI/eRWbI7J4uDkKBL+NyqZYkNKCitT0tZevyd6sswex5KPgN1m5prDftWEHYusj0tWYFZzrRtpWVgBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T17:49:18.270642Z"},"content_sha256":"1742ba66f777a3425cf3c994a72b24f3ded92103b9e5a08dddc3c36eec99fc87","schema_version":"1.0","event_id":"sha256:1742ba66f777a3425cf3c994a72b24f3ded92103b9e5a08dddc3c36eec99fc87"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MT2BBU26VFYFNH57VOORAUQER5/bundle.json","state_url":"https://pith.science/pith/MT2BBU26VFYFNH57VOORAUQER5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MT2BBU26VFYFNH57VOORAUQER5/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":"2026-08-11T17:49:18Z","links":{"resolver":"https://pith.science/pith/MT2BBU26VFYFNH57VOORAUQER5","bundle":"https://pith.science/pith/MT2BBU26VFYFNH57VOORAUQER5/bundle.json","state":"https://pith.science/pith/MT2BBU26VFYFNH57VOORAUQER5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MT2BBU26VFYFNH57VOORAUQER5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:MT2BBU26VFYFNH57VOORAUQER5","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":"d396a1b67aa0816f1f0c10ee237110d3f20e1352de3f886d829e29e2aa824118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-21T17:55:49Z","title_canon_sha256":"cfb26c6fd20451b89993687f47c441826fc064e71c898102464e53dd4091a1c4"},"schema_version":"1.0","source":{"id":"2607.19337","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.19337","created_at":"2026-07-22T01:24:37Z"},{"alias_kind":"arxiv_version","alias_value":"2607.19337v1","created_at":"2026-07-22T01:24:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.19337","created_at":"2026-07-22T01:24:37Z"},{"alias_kind":"pith_short_12","alias_value":"MT2BBU26VFYF","created_at":"2026-07-22T01:24:37Z"},{"alias_kind":"pith_short_16","alias_value":"MT2BBU26VFYFNH57","created_at":"2026-07-22T01:24:37Z"},{"alias_kind":"pith_short_8","alias_value":"MT2BBU26","created_at":"2026-07-22T01:24:37Z"}],"graph_snapshots":[{"event_id":"sha256:1742ba66f777a3425cf3c994a72b24f3ded92103b9e5a08dddc3c36eec99fc87","target":"graph","created_at":"2026-07-22T01:24:37Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.19337/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $p_n$ denote the $n$-th prime. We prove that for every nonzero polynomial $f(x)\\in\\mathbb{Z}[x]$, there exist infinitely many positive integers $n$ such that $p_n\\nmid f(n)$.","authors_text":"Shin-ichiro Seki","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-21T17:55:49Z","title":"On the $\\mathcal{A}$-transcendence of a Champernowne-type constant"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.19337","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":"sha256:98f0bc61d2cb5b91ac014106d649df5dc2b1433ea46cda41d57ed204ec24894b","target":"record","created_at":"2026-07-22T01:24:37Z","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":"d396a1b67aa0816f1f0c10ee237110d3f20e1352de3f886d829e29e2aa824118","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-07-21T17:55:49Z","title_canon_sha256":"cfb26c6fd20451b89993687f47c441826fc064e71c898102464e53dd4091a1c4"},"schema_version":"1.0","source":{"id":"2607.19337","kind":"arxiv","version":1}},"canonical_sha256":"64f410d35ea970569fbfab9d1052048f729e065b1e4299c8029398220271227f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64f410d35ea970569fbfab9d1052048f729e065b1e4299c8029398220271227f","first_computed_at":"2026-07-22T01:24:37.768516Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-22T01:24:37.768516Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GyrdpVJMsbBIWfrlxkaaWIqQoIkXd+G+RHU9tZzNV3QtrW0osb8Kok9nM3ET09FQvVIJJrgsRzXoqfrlMv5bCQ==","signature_status":"signed_v1","signed_at":"2026-07-22T01:24:37.769325Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.19337","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:98f0bc61d2cb5b91ac014106d649df5dc2b1433ea46cda41d57ed204ec24894b","sha256:1742ba66f777a3425cf3c994a72b24f3ded92103b9e5a08dddc3c36eec99fc87"],"state_sha256":"5a2f91ef1521b064128303758ee17bbb3aedb8ead3bd87e2beabdafbf99a3355"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FnF5JCOEcWxdU0OrAWfo8V+oE9teShHDTnL3Sc1PJ7LsEwh6y8jUoZMfbCzlr3yr3TWAdFbmQoGZbYyXW53YCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T17:49:18.277730Z","bundle_sha256":"b7161e947764f5770860a99d4759f42d61890b86f41772771bf0f0e0a4f71844"}}