{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:B4OLQ5A3J2C4QOHEJO67ACCWRO","short_pith_number":"pith:B4OLQ5A3","canonical_record":{"source":{"id":"1409.2218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-08T06:49:33Z","cross_cats_sorted":[],"title_canon_sha256":"fd92d9d495d874355ec9e62e4acd6e0a0b5017b6d8d1d3db234bac7e37811df3","abstract_canon_sha256":"0550f71a679a8ff17cad92088d57d47437c82d0dfb675932654872d523a7a674"},"schema_version":"1.0"},"canonical_sha256":"0f1cb8741b4e85c838e44bbdf008568baab8fba3a759d55debd61847abb9f7bc","source":{"kind":"arxiv","id":"1409.2218","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2218","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2218v1","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2218","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"B4OLQ5A3J2C4","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B4OLQ5A3J2C4QOHE","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B4OLQ5A3","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:B4OLQ5A3J2C4QOHEJO67ACCWRO","target":"record","payload":{"canonical_record":{"source":{"id":"1409.2218","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-08T06:49:33Z","cross_cats_sorted":[],"title_canon_sha256":"fd92d9d495d874355ec9e62e4acd6e0a0b5017b6d8d1d3db234bac7e37811df3","abstract_canon_sha256":"0550f71a679a8ff17cad92088d57d47437c82d0dfb675932654872d523a7a674"},"schema_version":"1.0"},"canonical_sha256":"0f1cb8741b4e85c838e44bbdf008568baab8fba3a759d55debd61847abb9f7bc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:17.583011Z","signature_b64":"MruAqrdBM9wc42xoNG00sW4RbiMCYMuCe9QOdUm6n4XNehhXQC8zViPXSVVmbh3hqrl9zjLnYWE5KoOM5gYBBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f1cb8741b4e85c838e44bbdf008568baab8fba3a759d55debd61847abb9f7bc","last_reissued_at":"2026-05-18T02:43:17.582566Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:17.582566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.2218","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":"2026-05-18T02:43:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hDmftVT/+JKpjJBYua7Vw01f4EZWyVPSL5Io8W1Jc1M2E++Gu4CAniT3uGWC7B03ooJ1001ZG0PzUVIS6/zyBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:30:11.084584Z"},"content_sha256":"9057c8fe5380dba35eb5f9d4b132c6a807b0d0a2e5651574b0f127aec1d51c89","schema_version":"1.0","event_id":"sha256:9057c8fe5380dba35eb5f9d4b132c6a807b0d0a2e5651574b0f127aec1d51c89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:B4OLQ5A3J2C4QOHEJO67ACCWRO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On conjectures and problems of Ruzsa concerning difference graphs of S-units","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ante Custic, Dijana Kreso, Lajos Hajdu, Robert Tijdeman","submitted_at":"2014-09-08T06:49:33Z","abstract_excerpt":"Given a finite nonempty set of primes S, we build a graph $\\mathcal{G}$ with vertex set $\\mathbb{Q}$ by connecting x and y if the prime divisors of both the numerator and denominator of x-y are from S. In this paper we resolve two conjectures posed by Ruzsa concerning the possible sizes of induced nondegenerate cycles of $\\mathcal{G}$, and also a problem of Ruzsa concerning the existence of subgraphs of $\\mathcal{G}$ which are not induced subgraphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2218","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":"2026-05-18T02:43:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TyNCx3JkQnjGcvtS1H9StcHBfTdBGPVEZj6Eb2W6tUmQgnpg5lA7+JKnQCt06xhdJl3MsIEy9NTKlm13FDyvDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:30:11.084997Z"},"content_sha256":"b94c16e8bfde6aff642c30ec1aa0668c81793efe020a75d59f4707518eb40fff","schema_version":"1.0","event_id":"sha256:b94c16e8bfde6aff642c30ec1aa0668c81793efe020a75d59f4707518eb40fff"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/B4OLQ5A3J2C4QOHEJO67ACCWRO/bundle.json","state_url":"https://pith.science/pith/B4OLQ5A3J2C4QOHEJO67ACCWRO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/B4OLQ5A3J2C4QOHEJO67ACCWRO/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":"2026-05-31T21:30:11Z","links":{"resolver":"https://pith.science/pith/B4OLQ5A3J2C4QOHEJO67ACCWRO","bundle":"https://pith.science/pith/B4OLQ5A3J2C4QOHEJO67ACCWRO/bundle.json","state":"https://pith.science/pith/B4OLQ5A3J2C4QOHEJO67ACCWRO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/B4OLQ5A3J2C4QOHEJO67ACCWRO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:B4OLQ5A3J2C4QOHEJO67ACCWRO","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":"0550f71a679a8ff17cad92088d57d47437c82d0dfb675932654872d523a7a674","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-08T06:49:33Z","title_canon_sha256":"fd92d9d495d874355ec9e62e4acd6e0a0b5017b6d8d1d3db234bac7e37811df3"},"schema_version":"1.0","source":{"id":"1409.2218","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2218","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2218v1","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2218","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"B4OLQ5A3J2C4","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"B4OLQ5A3J2C4QOHE","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"B4OLQ5A3","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:b94c16e8bfde6aff642c30ec1aa0668c81793efe020a75d59f4707518eb40fff","target":"graph","created_at":"2026-05-18T02:43:17Z","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":"Given a finite nonempty set of primes S, we build a graph $\\mathcal{G}$ with vertex set $\\mathbb{Q}$ by connecting x and y if the prime divisors of both the numerator and denominator of x-y are from S. In this paper we resolve two conjectures posed by Ruzsa concerning the possible sizes of induced nondegenerate cycles of $\\mathcal{G}$, and also a problem of Ruzsa concerning the existence of subgraphs of $\\mathcal{G}$ which are not induced subgraphs.","authors_text":"Ante Custic, Dijana Kreso, Lajos Hajdu, Robert Tijdeman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-08T06:49:33Z","title":"On conjectures and problems of Ruzsa concerning difference graphs of S-units"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2218","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":"sha256:9057c8fe5380dba35eb5f9d4b132c6a807b0d0a2e5651574b0f127aec1d51c89","target":"record","created_at":"2026-05-18T02:43:17Z","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":"0550f71a679a8ff17cad92088d57d47437c82d0dfb675932654872d523a7a674","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-09-08T06:49:33Z","title_canon_sha256":"fd92d9d495d874355ec9e62e4acd6e0a0b5017b6d8d1d3db234bac7e37811df3"},"schema_version":"1.0","source":{"id":"1409.2218","kind":"arxiv","version":1}},"canonical_sha256":"0f1cb8741b4e85c838e44bbdf008568baab8fba3a759d55debd61847abb9f7bc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0f1cb8741b4e85c838e44bbdf008568baab8fba3a759d55debd61847abb9f7bc","first_computed_at":"2026-05-18T02:43:17.582566Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:17.582566Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MruAqrdBM9wc42xoNG00sW4RbiMCYMuCe9QOdUm6n4XNehhXQC8zViPXSVVmbh3hqrl9zjLnYWE5KoOM5gYBBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:17.583011Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2218","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9057c8fe5380dba35eb5f9d4b132c6a807b0d0a2e5651574b0f127aec1d51c89","sha256:b94c16e8bfde6aff642c30ec1aa0668c81793efe020a75d59f4707518eb40fff"],"state_sha256":"cf6e4ae17d3a99b2bee0bc945582530f0816c23ef5d9e7f73848e06c4b7ddddf"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NExXrbUwT9+TlxoPhArvChhvoBHk9krxbW5ed/uqAdX254UocbX2Gb8iIb4Ry8XDkOPsKFQTjNrKgZ6MLDxmBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:30:11.086967Z","bundle_sha256":"d59ccefd58e6d1f793efa152a6add4a36ab1ea49512683c4c009a91c59056283"}}