{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:YMQK25GU44QDMUEUCTIRFNM4BD","short_pith_number":"pith:YMQK25GU","canonical_record":{"source":{"id":"1310.4533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-16T22:08:00Z","cross_cats_sorted":[],"title_canon_sha256":"27b91b4197b4f36221481bc0c3178e827362cb99d5ba8a512bf49283982ad1ab","abstract_canon_sha256":"16107caa8802389126e87020daf635cc660796b7d15333e51005e6239f6d3f01"},"schema_version":"1.0"},"canonical_sha256":"c320ad74d4e72036509414d112b59c08ec56c95acdf14cf5d2c6cd3fb2430d21","source":{"kind":"arxiv","id":"1310.4533","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4533","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4533v1","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4533","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"pith_short_12","alias_value":"YMQK25GU44QD","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YMQK25GU44QDMUEU","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YMQK25GU","created_at":"2026-05-18T12:28:06Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:YMQK25GU44QDMUEUCTIRFNM4BD","target":"record","payload":{"canonical_record":{"source":{"id":"1310.4533","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-16T22:08:00Z","cross_cats_sorted":[],"title_canon_sha256":"27b91b4197b4f36221481bc0c3178e827362cb99d5ba8a512bf49283982ad1ab","abstract_canon_sha256":"16107caa8802389126e87020daf635cc660796b7d15333e51005e6239f6d3f01"},"schema_version":"1.0"},"canonical_sha256":"c320ad74d4e72036509414d112b59c08ec56c95acdf14cf5d2c6cd3fb2430d21","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:13.848017Z","signature_b64":"WcKuGws0sl0ZrzNkczeFP5YGSJCk6JMR9eRC517qf16vBxg//nqCWMVKCIjF4C4bzoXPwfGfejiXjLhJPTGoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c320ad74d4e72036509414d112b59c08ec56c95acdf14cf5d2c6cd3fb2430d21","last_reissued_at":"2026-05-18T03:10:13.847469Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:13.847469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.4533","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":"2026-05-18T03:10:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YzMneAIL9CHZU5D3azJEQf4Pp2JDXLeYZgiGzYzVGmSdX2dU8eU2BMHAXGcvhtofpLytDYpY/w4MhnAVIHhOBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:54:03.659880Z"},"content_sha256":"1f9888538f90db2f1201d79b6215f78b8302d5a5c5305bdb68ead7df66e25b16","schema_version":"1.0","event_id":"sha256:1f9888538f90db2f1201d79b6215f78b8302d5a5c5305bdb68ead7df66e25b16"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:YMQK25GU44QDMUEUCTIRFNM4BD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ultrafilter extensions of linear orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Denis I. Saveliev","submitted_at":"2013-10-16T22:08:00Z","abstract_excerpt":"It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a technique allowing to obtain significant results in algebra and dynamics. Here we consider another particular case where the models are linearly ordered sets. We explicitly calculate the extensions of a given linear order and the corresponding operations of minimum and maximum on a set. We show that the extended relation is not more an order however is clos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4533","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":"2026-05-18T03:10:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJOg4cB96jHat+aNosA3fl/ULCjzO1JPcf91ITf4hrZoD0e7EGhvfhhX2pyEnIgFuTZDgJ4Jvnwf9pTvsfA/Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:54:03.660680Z"},"content_sha256":"2d86538da384361ad72b3a3e28bfdccc7da6708b618c6b46e62d7e7bc5e9f77d","schema_version":"1.0","event_id":"sha256:2d86538da384361ad72b3a3e28bfdccc7da6708b618c6b46e62d7e7bc5e9f77d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YMQK25GU44QDMUEUCTIRFNM4BD/bundle.json","state_url":"https://pith.science/pith/YMQK25GU44QDMUEUCTIRFNM4BD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YMQK25GU44QDMUEUCTIRFNM4BD/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":"2026-05-31T23:54:03Z","links":{"resolver":"https://pith.science/pith/YMQK25GU44QDMUEUCTIRFNM4BD","bundle":"https://pith.science/pith/YMQK25GU44QDMUEUCTIRFNM4BD/bundle.json","state":"https://pith.science/pith/YMQK25GU44QDMUEUCTIRFNM4BD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YMQK25GU44QDMUEUCTIRFNM4BD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:YMQK25GU44QDMUEUCTIRFNM4BD","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":"16107caa8802389126e87020daf635cc660796b7d15333e51005e6239f6d3f01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-16T22:08:00Z","title_canon_sha256":"27b91b4197b4f36221481bc0c3178e827362cb99d5ba8a512bf49283982ad1ab"},"schema_version":"1.0","source":{"id":"1310.4533","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.4533","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"arxiv_version","alias_value":"1310.4533v1","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.4533","created_at":"2026-05-18T03:10:13Z"},{"alias_kind":"pith_short_12","alias_value":"YMQK25GU44QD","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_16","alias_value":"YMQK25GU44QDMUEU","created_at":"2026-05-18T12:28:06Z"},{"alias_kind":"pith_short_8","alias_value":"YMQK25GU","created_at":"2026-05-18T12:28:06Z"}],"graph_snapshots":[{"event_id":"sha256:2d86538da384361ad72b3a3e28bfdccc7da6708b618c6b46e62d7e7bc5e9f77d","target":"graph","created_at":"2026-05-18T03:10:13Z","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":"It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a technique allowing to obtain significant results in algebra and dynamics. Here we consider another particular case where the models are linearly ordered sets. We explicitly calculate the extensions of a given linear order and the corresponding operations of minimum and maximum on a set. We show that the extended relation is not more an order however is clos","authors_text":"Denis I. Saveliev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-16T22:08:00Z","title":"Ultrafilter extensions of linear orders"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.4533","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":"sha256:1f9888538f90db2f1201d79b6215f78b8302d5a5c5305bdb68ead7df66e25b16","target":"record","created_at":"2026-05-18T03:10:13Z","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":"16107caa8802389126e87020daf635cc660796b7d15333e51005e6239f6d3f01","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-16T22:08:00Z","title_canon_sha256":"27b91b4197b4f36221481bc0c3178e827362cb99d5ba8a512bf49283982ad1ab"},"schema_version":"1.0","source":{"id":"1310.4533","kind":"arxiv","version":1}},"canonical_sha256":"c320ad74d4e72036509414d112b59c08ec56c95acdf14cf5d2c6cd3fb2430d21","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c320ad74d4e72036509414d112b59c08ec56c95acdf14cf5d2c6cd3fb2430d21","first_computed_at":"2026-05-18T03:10:13.847469Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:13.847469Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WcKuGws0sl0ZrzNkczeFP5YGSJCk6JMR9eRC517qf16vBxg//nqCWMVKCIjF4C4bzoXPwfGfejiXjLhJPTGoCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:13.848017Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.4533","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f9888538f90db2f1201d79b6215f78b8302d5a5c5305bdb68ead7df66e25b16","sha256:2d86538da384361ad72b3a3e28bfdccc7da6708b618c6b46e62d7e7bc5e9f77d"],"state_sha256":"ed21b6722737c0c3d509180122aa59cc1b729805dacb150d1a0efdb13c15c450"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rmanN5oSMn/BiU6W3aqckwDQq8V5GFoOwNaoWu3sDDQFPmNNUhkuOmttyazVj5ipga8mYHqM063Gqbp0H2dGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:54:03.664923Z","bundle_sha256":"dbe4f1337214a871e527b6b778c24a8eba746be2c0e6b87c55977a091e102f90"}}