{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ULAWHKN5OD457IU3CNMWHJG3EW","short_pith_number":"pith:ULAWHKN5","canonical_record":{"source":{"id":"1609.07926","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-26T11:32:08Z","cross_cats_sorted":[],"title_canon_sha256":"72173eb1687f892f82f0f6451e9f7e210c4a75761af3a44338ae9b9866a2e099","abstract_canon_sha256":"2fcc0b75f643418336c254b90f88538a304c9a4acf4971ef1306266102374675"},"schema_version":"1.0"},"canonical_sha256":"a2c163a9bd70f9dfa29b135963a4db25a0de01a9cff540927cde6101fd573f0a","source":{"kind":"arxiv","id":"1609.07926","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07926","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07926v1","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07926","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"ULAWHKN5OD45","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"ULAWHKN5OD457IU3","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"ULAWHKN5","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ULAWHKN5OD457IU3CNMWHJG3EW","target":"record","payload":{"canonical_record":{"source":{"id":"1609.07926","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-26T11:32:08Z","cross_cats_sorted":[],"title_canon_sha256":"72173eb1687f892f82f0f6451e9f7e210c4a75761af3a44338ae9b9866a2e099","abstract_canon_sha256":"2fcc0b75f643418336c254b90f88538a304c9a4acf4971ef1306266102374675"},"schema_version":"1.0"},"canonical_sha256":"a2c163a9bd70f9dfa29b135963a4db25a0de01a9cff540927cde6101fd573f0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:54.984055Z","signature_b64":"u4cJgugyfCRXE5asL/nUmSK3xghA7LeAECJegI5fQL/8FkxS4hxOr9T9+QkfGtw4/uyvH5TK308RHd4a780ICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2c163a9bd70f9dfa29b135963a4db25a0de01a9cff540927cde6101fd573f0a","last_reissued_at":"2026-05-18T01:03:54.983527Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:54.983527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.07926","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":"2026-05-18T01:03:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZqrZGb8r3Rr6pFNZKIajOYqPfUAmQtP+1t76EbvejW9bKarodY0AgN45pwNccfXKsrBMvMPIwgf2JHQBwt3FBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:12:21.680022Z"},"content_sha256":"191a9e0c88851f9bffa58affa5bf7919d0d27850222bc0a5d4e03925afad1268","schema_version":"1.0","event_id":"sha256:191a9e0c88851f9bffa58affa5bf7919d0d27850222bc0a5d4e03925afad1268"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ULAWHKN5OD457IU3CNMWHJG3EW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the digital representation of integers with bounded prime factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Yann Bugeaud","submitted_at":"2016-09-26T11:32:08Z","abstract_excerpt":"Let $b \\ge 2$ be an integer. Not much is known on the representation in base $b$ of prime numbers or of numbers whose prime factors belong to a given, finite set. Among other results, we establish that any sufficiently large integer which is not a multiple of $b$ and has only small (in a suitable sense) prime factors has at least four nonzero digits in its representation in base $b$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07926","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":"2026-05-18T01:03:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RFjvS7rPHMPsLtJPg+NCYKbuBKl0Ll6Ys1OfS+j3qkSBzxL/OtLDpOYt7x0Z+jbu/r9qriN6nWWh9n1ULlO7CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:12:21.680398Z"},"content_sha256":"4f46073a6f6b0041052458857669213d6e567a7509827ed5e3d7469ba3642c3c","schema_version":"1.0","event_id":"sha256:4f46073a6f6b0041052458857669213d6e567a7509827ed5e3d7469ba3642c3c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULAWHKN5OD457IU3CNMWHJG3EW/bundle.json","state_url":"https://pith.science/pith/ULAWHKN5OD457IU3CNMWHJG3EW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULAWHKN5OD457IU3CNMWHJG3EW/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":"2026-05-26T20:12:21Z","links":{"resolver":"https://pith.science/pith/ULAWHKN5OD457IU3CNMWHJG3EW","bundle":"https://pith.science/pith/ULAWHKN5OD457IU3CNMWHJG3EW/bundle.json","state":"https://pith.science/pith/ULAWHKN5OD457IU3CNMWHJG3EW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULAWHKN5OD457IU3CNMWHJG3EW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ULAWHKN5OD457IU3CNMWHJG3EW","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":"2fcc0b75f643418336c254b90f88538a304c9a4acf4971ef1306266102374675","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-26T11:32:08Z","title_canon_sha256":"72173eb1687f892f82f0f6451e9f7e210c4a75761af3a44338ae9b9866a2e099"},"schema_version":"1.0","source":{"id":"1609.07926","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.07926","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"arxiv_version","alias_value":"1609.07926v1","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.07926","created_at":"2026-05-18T01:03:54Z"},{"alias_kind":"pith_short_12","alias_value":"ULAWHKN5OD45","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"ULAWHKN5OD457IU3","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"ULAWHKN5","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:4f46073a6f6b0041052458857669213d6e567a7509827ed5e3d7469ba3642c3c","target":"graph","created_at":"2026-05-18T01:03:54Z","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":"Let $b \\ge 2$ be an integer. Not much is known on the representation in base $b$ of prime numbers or of numbers whose prime factors belong to a given, finite set. Among other results, we establish that any sufficiently large integer which is not a multiple of $b$ and has only small (in a suitable sense) prime factors has at least four nonzero digits in its representation in base $b$.","authors_text":"Yann Bugeaud","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-26T11:32:08Z","title":"On the digital representation of integers with bounded prime factors"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.07926","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":"sha256:191a9e0c88851f9bffa58affa5bf7919d0d27850222bc0a5d4e03925afad1268","target":"record","created_at":"2026-05-18T01:03:54Z","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":"2fcc0b75f643418336c254b90f88538a304c9a4acf4971ef1306266102374675","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-09-26T11:32:08Z","title_canon_sha256":"72173eb1687f892f82f0f6451e9f7e210c4a75761af3a44338ae9b9866a2e099"},"schema_version":"1.0","source":{"id":"1609.07926","kind":"arxiv","version":1}},"canonical_sha256":"a2c163a9bd70f9dfa29b135963a4db25a0de01a9cff540927cde6101fd573f0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2c163a9bd70f9dfa29b135963a4db25a0de01a9cff540927cde6101fd573f0a","first_computed_at":"2026-05-18T01:03:54.983527Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:54.983527Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u4cJgugyfCRXE5asL/nUmSK3xghA7LeAECJegI5fQL/8FkxS4hxOr9T9+QkfGtw4/uyvH5TK308RHd4a780ICw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:54.984055Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.07926","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:191a9e0c88851f9bffa58affa5bf7919d0d27850222bc0a5d4e03925afad1268","sha256:4f46073a6f6b0041052458857669213d6e567a7509827ed5e3d7469ba3642c3c"],"state_sha256":"486813bfc9b0d843455e8ecfb21327e53bb971c5bc4359c3c3292612e86ed122"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CRzIx4D3ym63UuUkx3bmnug8DqSBzINy1rW70uN5cFDZVu4CD6BitqwEc9C8bn4dUCbfo41fhL/bUhBxhRYfDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:12:21.683083Z","bundle_sha256":"3e0e02c7ba2687a1da808ebf9c97fd461e37c05f461f99177e1b640f9938f901"}}