{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:6ZLDMXROB5EUZZWLKG2XN3B7JA","short_pith_number":"pith:6ZLDMXRO","canonical_record":{"source":{"id":"1812.07970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-12-19T14:24:33Z","cross_cats_sorted":[],"title_canon_sha256":"5c6da54d5bbdfb2ac6b0972d2868d0bcd7850bb5397084594fc31f3144b07706","abstract_canon_sha256":"bf1dcff9d649462ce56e9db03fd0720baed7b085dffe61865c8c276a413abbb6"},"schema_version":"1.0"},"canonical_sha256":"f656365e2e0f494ce6cb51b576ec3f48027247d2d8f6623646b9bedcaed5b5d8","source":{"kind":"arxiv","id":"1812.07970","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07970","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07970v1","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07970","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"pith_short_12","alias_value":"6ZLDMXROB5EU","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6ZLDMXROB5EUZZWL","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6ZLDMXRO","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:6ZLDMXROB5EUZZWLKG2XN3B7JA","target":"record","payload":{"canonical_record":{"source":{"id":"1812.07970","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-12-19T14:24:33Z","cross_cats_sorted":[],"title_canon_sha256":"5c6da54d5bbdfb2ac6b0972d2868d0bcd7850bb5397084594fc31f3144b07706","abstract_canon_sha256":"bf1dcff9d649462ce56e9db03fd0720baed7b085dffe61865c8c276a413abbb6"},"schema_version":"1.0"},"canonical_sha256":"f656365e2e0f494ce6cb51b576ec3f48027247d2d8f6623646b9bedcaed5b5d8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:55.360257Z","signature_b64":"PZLZl4q4R1LNS/9JDx54yIesLoz6CnXc1ZQYnkoVIv65CmTzSCgHsH7LOaVBRFOmcQXgjsmQF3CNGRs+IclYAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f656365e2e0f494ce6cb51b576ec3f48027247d2d8f6623646b9bedcaed5b5d8","last_reissued_at":"2026-05-17T23:57:55.359597Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:55.359597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1812.07970","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":"2026-05-17T23:57:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"n7bGbwVXr20dLHKhvQ9ru8QLwMfoXDglwF/4rLW2KIEhBMatOXZ3oUzQda6dL7J9Ng0W96VvqrZJ00E3fZk6Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:37:49.777307Z"},"content_sha256":"336b2fa61b8bfac8f842987487888758f4f6e669c6c6ae87c019dc512d7f26e4","schema_version":"1.0","event_id":"sha256:336b2fa61b8bfac8f842987487888758f4f6e669c6c6ae87c019dc512d7f26e4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:6ZLDMXROB5EUZZWLKG2XN3B7JA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small sets in Mann pairs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Pantelis E. Eleftheriou","submitted_at":"2018-12-19T14:24:33Z","abstract_excerpt":"Let $\\widetilde{\\mathcal M}=\\langle \\mathcal M, G\\rangle$ be an expansion of a real closed field $\\mathcal M$ by a dense subgroup $G$ of $\\langle M^{>0}, \\cdot\\rangle$ with the Mann property. We prove that the induced structure on $G$ by $\\mathcal M$ eliminates imaginaries. As a consequence, every small set $X$ definable in $\\mathcal M$ can be definably embedded into some $G^l$, uniformly in parameters. These results are proved in a more general setting, where $\\widetilde{\\mathcal M}=\\langle \\mathcal M, P\\rangle$ is an expansion of an o-minimal structure $\\mathcal M$ by a dense set $P\\subseteq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07970","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":"2026-05-17T23:57:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B6tXRrOenkmoSfZyVArS+0tjJT5oq7vokvjV8YOINKNGvYO++sMduF39GjSO+oziy6WW5hz00XNmxALxvy28Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T11:37:49.777993Z"},"content_sha256":"a272bda0f0aeda28e40c69601d3018b05e6b8a77806968fffc182c02ca874d2a","schema_version":"1.0","event_id":"sha256:a272bda0f0aeda28e40c69601d3018b05e6b8a77806968fffc182c02ca874d2a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6ZLDMXROB5EUZZWLKG2XN3B7JA/bundle.json","state_url":"https://pith.science/pith/6ZLDMXROB5EUZZWLKG2XN3B7JA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6ZLDMXROB5EUZZWLKG2XN3B7JA/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":"2026-05-26T11:37:49Z","links":{"resolver":"https://pith.science/pith/6ZLDMXROB5EUZZWLKG2XN3B7JA","bundle":"https://pith.science/pith/6ZLDMXROB5EUZZWLKG2XN3B7JA/bundle.json","state":"https://pith.science/pith/6ZLDMXROB5EUZZWLKG2XN3B7JA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6ZLDMXROB5EUZZWLKG2XN3B7JA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:6ZLDMXROB5EUZZWLKG2XN3B7JA","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":"bf1dcff9d649462ce56e9db03fd0720baed7b085dffe61865c8c276a413abbb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-12-19T14:24:33Z","title_canon_sha256":"5c6da54d5bbdfb2ac6b0972d2868d0bcd7850bb5397084594fc31f3144b07706"},"schema_version":"1.0","source":{"id":"1812.07970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1812.07970","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"arxiv_version","alias_value":"1812.07970v1","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.07970","created_at":"2026-05-17T23:57:55Z"},{"alias_kind":"pith_short_12","alias_value":"6ZLDMXROB5EU","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"6ZLDMXROB5EUZZWL","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"6ZLDMXRO","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:a272bda0f0aeda28e40c69601d3018b05e6b8a77806968fffc182c02ca874d2a","target":"graph","created_at":"2026-05-17T23:57:55Z","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 $\\widetilde{\\mathcal M}=\\langle \\mathcal M, G\\rangle$ be an expansion of a real closed field $\\mathcal M$ by a dense subgroup $G$ of $\\langle M^{>0}, \\cdot\\rangle$ with the Mann property. We prove that the induced structure on $G$ by $\\mathcal M$ eliminates imaginaries. As a consequence, every small set $X$ definable in $\\mathcal M$ can be definably embedded into some $G^l$, uniformly in parameters. These results are proved in a more general setting, where $\\widetilde{\\mathcal M}=\\langle \\mathcal M, P\\rangle$ is an expansion of an o-minimal structure $\\mathcal M$ by a dense set $P\\subseteq","authors_text":"Pantelis E. Eleftheriou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-12-19T14:24:33Z","title":"Small sets in Mann pairs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.07970","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":"sha256:336b2fa61b8bfac8f842987487888758f4f6e669c6c6ae87c019dc512d7f26e4","target":"record","created_at":"2026-05-17T23:57:55Z","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":"bf1dcff9d649462ce56e9db03fd0720baed7b085dffe61865c8c276a413abbb6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-12-19T14:24:33Z","title_canon_sha256":"5c6da54d5bbdfb2ac6b0972d2868d0bcd7850bb5397084594fc31f3144b07706"},"schema_version":"1.0","source":{"id":"1812.07970","kind":"arxiv","version":1}},"canonical_sha256":"f656365e2e0f494ce6cb51b576ec3f48027247d2d8f6623646b9bedcaed5b5d8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f656365e2e0f494ce6cb51b576ec3f48027247d2d8f6623646b9bedcaed5b5d8","first_computed_at":"2026-05-17T23:57:55.359597Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:55.359597Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PZLZl4q4R1LNS/9JDx54yIesLoz6CnXc1ZQYnkoVIv65CmTzSCgHsH7LOaVBRFOmcQXgjsmQF3CNGRs+IclYAQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:55.360257Z","signed_message":"canonical_sha256_bytes"},"source_id":"1812.07970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:336b2fa61b8bfac8f842987487888758f4f6e669c6c6ae87c019dc512d7f26e4","sha256:a272bda0f0aeda28e40c69601d3018b05e6b8a77806968fffc182c02ca874d2a"],"state_sha256":"20bb2ed83172610455bb27d7f0ba13a5d020ca232a2f5a23680e5681445587d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zWzwFG4UlvxTpzisv6bCeZkUJKuTnzcJQSHXxai6vf/xd8hSHK8owKr59KtCNsgwqAfkwBlXFiVLgF4kmdmsAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T11:37:49.781399Z","bundle_sha256":"eb0af836afe249de703bac51ca3e1726bb7c1353313b590aded4783aba1fa1de"}}