{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:XIL6WW2HTT2XSQGSBKP2UKBEHU","short_pith_number":"pith:XIL6WW2H","canonical_record":{"source":{"id":"0911.5414","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-11-28T18:57:04Z","cross_cats_sorted":["math.GR","math.LO"],"title_canon_sha256":"0e344aec7f54a5c89e3bb24ee60c95d18b6f8796b93387536b407e0fe8337838","abstract_canon_sha256":"f9695d268ce195a010f9b0a1878a2fe5299b291cc9c3eded231f199eaaa601ff"},"schema_version":"1.0"},"canonical_sha256":"ba17eb5b479cf57940d20a9faa28243d1565598a2c84eb97f28e0ff781d6d8c4","source":{"kind":"arxiv","id":"0911.5414","version":8},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.5414","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"0911.5414v8","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.5414","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"XIL6WW2HTT2X","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XIL6WW2HTT2XSQGS","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XIL6WW2H","created_at":"2026-05-18T12:26:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:XIL6WW2HTT2XSQGSBKP2UKBEHU","target":"record","payload":{"canonical_record":{"source":{"id":"0911.5414","kind":"arxiv","version":8},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-11-28T18:57:04Z","cross_cats_sorted":["math.GR","math.LO"],"title_canon_sha256":"0e344aec7f54a5c89e3bb24ee60c95d18b6f8796b93387536b407e0fe8337838","abstract_canon_sha256":"f9695d268ce195a010f9b0a1878a2fe5299b291cc9c3eded231f199eaaa601ff"},"schema_version":"1.0"},"canonical_sha256":"ba17eb5b479cf57940d20a9faa28243d1565598a2c84eb97f28e0ff781d6d8c4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:27.734537Z","signature_b64":"R3NPWLZ/jkBW7M2HP5mWqIgg0salNLtpLvw8r8zSo7bomm3NwyDejzHMQ4QAoj2RM0dLny7e9EYSJ2b2MFpADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ba17eb5b479cf57940d20a9faa28243d1565598a2c84eb97f28e0ff781d6d8c4","last_reissued_at":"2026-05-18T01:08:27.733954Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:27.733954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.5414","source_version":8,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NI6GdYqdACBOPBKU5UnEqTuAQXeAh0zQhjyZeSkNPrqp2q92eCLAsj/cW6tMhDcizlGEUIKApr49iosRXOTcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:09:19.093912Z"},"content_sha256":"4a003e88010178aea89f55ebea9187e1df3747cbee85201c34d1c01c27bffc75","schema_version":"1.0","event_id":"sha256:4a003e88010178aea89f55ebea9187e1df3747cbee85201c34d1c01c27bffc75"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:XIL6WW2HTT2XSQGSBKP2UKBEHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the utility of Robinson-Amitsur ultrafilters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.LO"],"primary_cat":"math.RA","authors_text":"Pasha Zusmanovich","submitted_at":"2009-11-28T18:57:04Z","abstract_excerpt":"An embedding theorem for algebraic systems is presented, basing on a certain old ultrafilter construction. As an application, we outline alternative proofs of some results from the theory of PI algebras, and establish some properties of Tarski's monsters."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.5414","kind":"arxiv","version":8},"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":"2026-05-18T01:08:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FgGNxDu5ar0OlAcGy9LDpqs3vXi80th/QItv9ulrMFNo2+ck+Ok0iK5qjcvIVvLRKjTEZGbls7Aptz9nDEoHAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T09:09:19.094258Z"},"content_sha256":"93ec541eaab75398de9effaa5723c829bd29ac65ef5e6f399516181566a0a4e3","schema_version":"1.0","event_id":"sha256:93ec541eaab75398de9effaa5723c829bd29ac65ef5e6f399516181566a0a4e3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XIL6WW2HTT2XSQGSBKP2UKBEHU/bundle.json","state_url":"https://pith.science/pith/XIL6WW2HTT2XSQGSBKP2UKBEHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XIL6WW2HTT2XSQGSBKP2UKBEHU/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":"2026-06-26T09:09:19Z","links":{"resolver":"https://pith.science/pith/XIL6WW2HTT2XSQGSBKP2UKBEHU","bundle":"https://pith.science/pith/XIL6WW2HTT2XSQGSBKP2UKBEHU/bundle.json","state":"https://pith.science/pith/XIL6WW2HTT2XSQGSBKP2UKBEHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XIL6WW2HTT2XSQGSBKP2UKBEHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:XIL6WW2HTT2XSQGSBKP2UKBEHU","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":"f9695d268ce195a010f9b0a1878a2fe5299b291cc9c3eded231f199eaaa601ff","cross_cats_sorted":["math.GR","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-11-28T18:57:04Z","title_canon_sha256":"0e344aec7f54a5c89e3bb24ee60c95d18b6f8796b93387536b407e0fe8337838"},"schema_version":"1.0","source":{"id":"0911.5414","kind":"arxiv","version":8}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.5414","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"arxiv_version","alias_value":"0911.5414v8","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.5414","created_at":"2026-05-18T01:08:27Z"},{"alias_kind":"pith_short_12","alias_value":"XIL6WW2HTT2X","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_16","alias_value":"XIL6WW2HTT2XSQGS","created_at":"2026-05-18T12:26:02Z"},{"alias_kind":"pith_short_8","alias_value":"XIL6WW2H","created_at":"2026-05-18T12:26:02Z"}],"graph_snapshots":[{"event_id":"sha256:93ec541eaab75398de9effaa5723c829bd29ac65ef5e6f399516181566a0a4e3","target":"graph","created_at":"2026-05-18T01:08:27Z","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":"An embedding theorem for algebraic systems is presented, basing on a certain old ultrafilter construction. As an application, we outline alternative proofs of some results from the theory of PI algebras, and establish some properties of Tarski's monsters.","authors_text":"Pasha Zusmanovich","cross_cats":["math.GR","math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-11-28T18:57:04Z","title":"On the utility of Robinson-Amitsur ultrafilters"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.5414","kind":"arxiv","version":8},"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":"sha256:4a003e88010178aea89f55ebea9187e1df3747cbee85201c34d1c01c27bffc75","target":"record","created_at":"2026-05-18T01:08:27Z","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":"f9695d268ce195a010f9b0a1878a2fe5299b291cc9c3eded231f199eaaa601ff","cross_cats_sorted":["math.GR","math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2009-11-28T18:57:04Z","title_canon_sha256":"0e344aec7f54a5c89e3bb24ee60c95d18b6f8796b93387536b407e0fe8337838"},"schema_version":"1.0","source":{"id":"0911.5414","kind":"arxiv","version":8}},"canonical_sha256":"ba17eb5b479cf57940d20a9faa28243d1565598a2c84eb97f28e0ff781d6d8c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba17eb5b479cf57940d20a9faa28243d1565598a2c84eb97f28e0ff781d6d8c4","first_computed_at":"2026-05-18T01:08:27.733954Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:08:27.733954Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"R3NPWLZ/jkBW7M2HP5mWqIgg0salNLtpLvw8r8zSo7bomm3NwyDejzHMQ4QAoj2RM0dLny7e9EYSJ2b2MFpADA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:08:27.734537Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.5414","source_kind":"arxiv","source_version":8}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4a003e88010178aea89f55ebea9187e1df3747cbee85201c34d1c01c27bffc75","sha256:93ec541eaab75398de9effaa5723c829bd29ac65ef5e6f399516181566a0a4e3"],"state_sha256":"535f3287718f0651bb3876ad641298ea8e3fa4e75abdda743355bfd0a47f75cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q70NSz1FRjNPvFhlHXqz4Rm+pM7+PL1Lswhto7Hczp3c5mGvHzWMdttS8Qu5NhT/d9wyxPiqGLOseyGHG77BBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T09:09:19.096203Z","bundle_sha256":"a943ae5c1cd91df6a7f0979d5b66be7a7b953c4cfea761b702cfbcc195125244"}}