{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:5ATMJELVHONOE5CQO7GGMFV65T","short_pith_number":"pith:5ATMJELV","canonical_record":{"source":{"id":"1601.07099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-26T17:12:54Z","cross_cats_sorted":[],"title_canon_sha256":"c6c5c9fd445cc7fec485403f04f966198ae269919f735de45fce346a7e890fc5","abstract_canon_sha256":"8fc20ddb9526f5a284c43ff8f4916bdf5c6180425751d0a0219b00ce84c1ee5d"},"schema_version":"1.0"},"canonical_sha256":"e826c491753b9ae2745077cc6616beecfa3240c9f11d4b1f82b8e36af250bb41","source":{"kind":"arxiv","id":"1601.07099","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07099","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07099v2","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07099","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"5ATMJELVHONO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"5ATMJELVHONOE5CQ","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"5ATMJELV","created_at":"2026-05-18T12:29:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:5ATMJELVHONOE5CQO7GGMFV65T","target":"record","payload":{"canonical_record":{"source":{"id":"1601.07099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-26T17:12:54Z","cross_cats_sorted":[],"title_canon_sha256":"c6c5c9fd445cc7fec485403f04f966198ae269919f735de45fce346a7e890fc5","abstract_canon_sha256":"8fc20ddb9526f5a284c43ff8f4916bdf5c6180425751d0a0219b00ce84c1ee5d"},"schema_version":"1.0"},"canonical_sha256":"e826c491753b9ae2745077cc6616beecfa3240c9f11d4b1f82b8e36af250bb41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:50.028352Z","signature_b64":"A5EHWU1O66WaYzlEpXTQFPJ94tKt80N5XHYkVCYK6Il4T4NCsdPPDX3Dn6xMXv9G0OV+ExNXGGb0jcwO1dtlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e826c491753b9ae2745077cc6616beecfa3240c9f11d4b1f82b8e36af250bb41","last_reissued_at":"2026-05-18T01:20:50.027836Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:50.027836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.07099","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":"2026-05-18T01:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"djP1ik21J7oC3qtMW7JSZjFH3jS/fh9aVwBpTSdhqGdxthdko1D+LylXsu+GFIV1tw2etXaIbxaBHIzeNd8/Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:26:16.741850Z"},"content_sha256":"bfb63680f43de29dd0454e9133e402483bb3f1f72d893a75e453a64f8af61138","schema_version":"1.0","event_id":"sha256:bfb63680f43de29dd0454e9133e402483bb3f1f72d893a75e453a64f8af61138"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:5ATMJELVHONOE5CQO7GGMFV65T","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Decidability and classification of the theory of integers with primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Itay Kaplan, Saharon Shelah","submitted_at":"2016-01-26T17:12:54Z","abstract_excerpt":"We show that under Dickson's conjecture about the distribution of primes in the natural numbers, the theory Th(Z,+,1,0,Pr) where Pr is a predicate for the prime numbers and their negations is decidable, unstable and supersimple. This is in contrast with Th(Z,+,0,Pr,<) which is known to be undecidable by the works of Jockusch, Bateman and Woods."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07099","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":"2026-05-18T01:20:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BefbKtsZ/VSsNcXgerqRhwKyBSexiwP84//U38A89mCOwh2KJyu4xToguYQmt1yrmhHYc2clz5q7ygWg5lvqBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T01:26:16.742187Z"},"content_sha256":"a476b5232d9739b13732bd61eaf50ef242218fe94e8d86b96b78d49edae48642","schema_version":"1.0","event_id":"sha256:a476b5232d9739b13732bd61eaf50ef242218fe94e8d86b96b78d49edae48642"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5ATMJELVHONOE5CQO7GGMFV65T/bundle.json","state_url":"https://pith.science/pith/5ATMJELVHONOE5CQO7GGMFV65T/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5ATMJELVHONOE5CQO7GGMFV65T/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":"2026-06-02T01:26:16Z","links":{"resolver":"https://pith.science/pith/5ATMJELVHONOE5CQO7GGMFV65T","bundle":"https://pith.science/pith/5ATMJELVHONOE5CQO7GGMFV65T/bundle.json","state":"https://pith.science/pith/5ATMJELVHONOE5CQO7GGMFV65T/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5ATMJELVHONOE5CQO7GGMFV65T/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:5ATMJELVHONOE5CQO7GGMFV65T","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":"8fc20ddb9526f5a284c43ff8f4916bdf5c6180425751d0a0219b00ce84c1ee5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-26T17:12:54Z","title_canon_sha256":"c6c5c9fd445cc7fec485403f04f966198ae269919f735de45fce346a7e890fc5"},"schema_version":"1.0","source":{"id":"1601.07099","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.07099","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"arxiv_version","alias_value":"1601.07099v2","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.07099","created_at":"2026-05-18T01:20:50Z"},{"alias_kind":"pith_short_12","alias_value":"5ATMJELVHONO","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_16","alias_value":"5ATMJELVHONOE5CQ","created_at":"2026-05-18T12:29:58Z"},{"alias_kind":"pith_short_8","alias_value":"5ATMJELV","created_at":"2026-05-18T12:29:58Z"}],"graph_snapshots":[{"event_id":"sha256:a476b5232d9739b13732bd61eaf50ef242218fe94e8d86b96b78d49edae48642","target":"graph","created_at":"2026-05-18T01:20:50Z","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":"We show that under Dickson's conjecture about the distribution of primes in the natural numbers, the theory Th(Z,+,1,0,Pr) where Pr is a predicate for the prime numbers and their negations is decidable, unstable and supersimple. This is in contrast with Th(Z,+,0,Pr,<) which is known to be undecidable by the works of Jockusch, Bateman and Woods.","authors_text":"Itay Kaplan, Saharon Shelah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-26T17:12:54Z","title":"Decidability and classification of the theory of integers with primes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07099","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:bfb63680f43de29dd0454e9133e402483bb3f1f72d893a75e453a64f8af61138","target":"record","created_at":"2026-05-18T01:20:50Z","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":"8fc20ddb9526f5a284c43ff8f4916bdf5c6180425751d0a0219b00ce84c1ee5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-01-26T17:12:54Z","title_canon_sha256":"c6c5c9fd445cc7fec485403f04f966198ae269919f735de45fce346a7e890fc5"},"schema_version":"1.0","source":{"id":"1601.07099","kind":"arxiv","version":2}},"canonical_sha256":"e826c491753b9ae2745077cc6616beecfa3240c9f11d4b1f82b8e36af250bb41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e826c491753b9ae2745077cc6616beecfa3240c9f11d4b1f82b8e36af250bb41","first_computed_at":"2026-05-18T01:20:50.027836Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:50.027836Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"A5EHWU1O66WaYzlEpXTQFPJ94tKt80N5XHYkVCYK6Il4T4NCsdPPDX3Dn6xMXv9G0OV+ExNXGGb0jcwO1dtlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:50.028352Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.07099","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfb63680f43de29dd0454e9133e402483bb3f1f72d893a75e453a64f8af61138","sha256:a476b5232d9739b13732bd61eaf50ef242218fe94e8d86b96b78d49edae48642"],"state_sha256":"71c53c7f00f71dbf118d462f7486bf78c2119408d11ba1beb30f8b3be5f8ce00"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XBB+a1tT1nNdMcIIFgBKULC0jVmrpcgMG/7ulYkoxTIDz7iOH7ZL90tnNvRMbi0c/ei6s71GGASDcgqJSEM5CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T01:26:16.744743Z","bundle_sha256":"ac7ea99d6a314f9634ec87cc011a3a476b34ad44a701c10447cbbcf87f28e8e4"}}