{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:VEUUEI3HW4ZV2IPJAC2TLDRAUI","short_pith_number":"pith:VEUUEI3H","canonical_record":{"source":{"id":"1709.01706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-09-06T08:05:30Z","cross_cats_sorted":[],"title_canon_sha256":"f281bf56d972e830aa4eb0bd75c6476ead79b179931d2b37093082e787896088","abstract_canon_sha256":"54c966737d4e7082245514028a99d33b145ccf266e6c6ab4fb4aed29730ffd53"},"schema_version":"1.0"},"canonical_sha256":"a929422367b7335d21e900b5358e20a23e28a6ac8dfea093c975e0b1d096b85c","source":{"kind":"arxiv","id":"1709.01706","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01706","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01706v1","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01706","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"VEUUEI3HW4ZV","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VEUUEI3HW4ZV2IPJ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VEUUEI3H","created_at":"2026-05-18T12:31:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:VEUUEI3HW4ZV2IPJAC2TLDRAUI","target":"record","payload":{"canonical_record":{"source":{"id":"1709.01706","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-09-06T08:05:30Z","cross_cats_sorted":[],"title_canon_sha256":"f281bf56d972e830aa4eb0bd75c6476ead79b179931d2b37093082e787896088","abstract_canon_sha256":"54c966737d4e7082245514028a99d33b145ccf266e6c6ab4fb4aed29730ffd53"},"schema_version":"1.0"},"canonical_sha256":"a929422367b7335d21e900b5358e20a23e28a6ac8dfea093c975e0b1d096b85c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:23.801924Z","signature_b64":"eXGCoG120YHAlLgQH8LqcMN/fsRv5Z73lDXmjjxKnZeIVjkQO188togXEHiNxO6DBCNtnPjYYAitmliZQdq9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a929422367b7335d21e900b5358e20a23e28a6ac8dfea093c975e0b1d096b85c","last_reissued_at":"2026-05-18T00:07:23.801458Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:23.801458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1709.01706","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":"2026-05-18T00:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pYZjFBDyI8eSc7GWR17ti0Zyd5Xqv7LBuTnrNNvWnSMJJkFWCUiuPbPzwtDxtUnvGxvCJmn5YfFLf7BF8DnKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:13:23.759070Z"},"content_sha256":"f7ff2d734d69b71b04b8a1fa12cf5a84734fae177a4e05c77bd9779aa5fc7393","schema_version":"1.0","event_id":"sha256:f7ff2d734d69b71b04b8a1fa12cf5a84734fae177a4e05c77bd9779aa5fc7393"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:VEUUEI3HW4ZV2IPJAC2TLDRAUI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CT","authors_text":"Enric Cosme Ll\\'opez, Juan Climent Vidal","submitted_at":"2017-09-06T08:05:30Z","abstract_excerpt":"For a set of sorts $S$ and an $S$-sorted signature $\\Sigma$ we prove that a profinite $\\Sigma$-algebra, i.e., a projective limit of a projective system of finite $\\Sigma$-algebras, is a retract of an ultraproduct of finite $\\Sigma$-algebras if the family consisting of the finite $\\Sigma$-algebras underlying the projective system is with constant support. In addition, we provide a categorial rendering of the above result. Specifically, after obtaining a category where the objects are the pairs formed by a nonempty upward directed preordered set and by an ultrafilter containing the filter of the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01706","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":"2026-05-18T00:07:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mg3xHyc3Q8TCmyLKPwqZTis3u48c0/tFfjve4df8WMbmzkCJgR/XjYkBFzAmk5pgQ1e+40cK9PKl5JM6BptdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-03T13:13:23.759436Z"},"content_sha256":"523e72b4651d5a89c09c1149f900a8d97e4b3ac8888ef73f25f8834f746fa5da","schema_version":"1.0","event_id":"sha256:523e72b4651d5a89c09c1149f900a8d97e4b3ac8888ef73f25f8834f746fa5da"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VEUUEI3HW4ZV2IPJAC2TLDRAUI/bundle.json","state_url":"https://pith.science/pith/VEUUEI3HW4ZV2IPJAC2TLDRAUI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VEUUEI3HW4ZV2IPJAC2TLDRAUI/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":"2026-07-03T13:13:23Z","links":{"resolver":"https://pith.science/pith/VEUUEI3HW4ZV2IPJAC2TLDRAUI","bundle":"https://pith.science/pith/VEUUEI3HW4ZV2IPJAC2TLDRAUI/bundle.json","state":"https://pith.science/pith/VEUUEI3HW4ZV2IPJAC2TLDRAUI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VEUUEI3HW4ZV2IPJAC2TLDRAUI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VEUUEI3HW4ZV2IPJAC2TLDRAUI","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":"54c966737d4e7082245514028a99d33b145ccf266e6c6ab4fb4aed29730ffd53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-09-06T08:05:30Z","title_canon_sha256":"f281bf56d972e830aa4eb0bd75c6476ead79b179931d2b37093082e787896088"},"schema_version":"1.0","source":{"id":"1709.01706","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1709.01706","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"arxiv_version","alias_value":"1709.01706v1","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.01706","created_at":"2026-05-18T00:07:23Z"},{"alias_kind":"pith_short_12","alias_value":"VEUUEI3HW4ZV","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VEUUEI3HW4ZV2IPJ","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VEUUEI3H","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:523e72b4651d5a89c09c1149f900a8d97e4b3ac8888ef73f25f8834f746fa5da","target":"graph","created_at":"2026-05-18T00:07:23Z","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":"For a set of sorts $S$ and an $S$-sorted signature $\\Sigma$ we prove that a profinite $\\Sigma$-algebra, i.e., a projective limit of a projective system of finite $\\Sigma$-algebras, is a retract of an ultraproduct of finite $\\Sigma$-algebras if the family consisting of the finite $\\Sigma$-algebras underlying the projective system is with constant support. In addition, we provide a categorial rendering of the above result. Specifically, after obtaining a category where the objects are the pairs formed by a nonempty upward directed preordered set and by an ultrafilter containing the filter of the","authors_text":"Enric Cosme Ll\\'opez, Juan Climent Vidal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-09-06T08:05:30Z","title":"When are profinite many-sorted algebras retracts of ultraproducts of finite many-sorted algebras?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.01706","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:f7ff2d734d69b71b04b8a1fa12cf5a84734fae177a4e05c77bd9779aa5fc7393","target":"record","created_at":"2026-05-18T00:07:23Z","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":"54c966737d4e7082245514028a99d33b145ccf266e6c6ab4fb4aed29730ffd53","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CT","submitted_at":"2017-09-06T08:05:30Z","title_canon_sha256":"f281bf56d972e830aa4eb0bd75c6476ead79b179931d2b37093082e787896088"},"schema_version":"1.0","source":{"id":"1709.01706","kind":"arxiv","version":1}},"canonical_sha256":"a929422367b7335d21e900b5358e20a23e28a6ac8dfea093c975e0b1d096b85c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a929422367b7335d21e900b5358e20a23e28a6ac8dfea093c975e0b1d096b85c","first_computed_at":"2026-05-18T00:07:23.801458Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:07:23.801458Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eXGCoG120YHAlLgQH8LqcMN/fsRv5Z73lDXmjjxKnZeIVjkQO188togXEHiNxO6DBCNtnPjYYAitmliZQdq9AA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:07:23.801924Z","signed_message":"canonical_sha256_bytes"},"source_id":"1709.01706","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f7ff2d734d69b71b04b8a1fa12cf5a84734fae177a4e05c77bd9779aa5fc7393","sha256:523e72b4651d5a89c09c1149f900a8d97e4b3ac8888ef73f25f8834f746fa5da"],"state_sha256":"dba0222c0b1e7c3f7c43a9ac17c778f5410b4bf65ca325afa62e4092d6ff50fb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wCRAc60IWGEkiQXpB9+EYPlDrI+Gg6H/Or/CLwgbGhxX5eqz5Zci48n1vHSxKeKbS7Tpa68U7m9HOU3kESCNCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-03T13:13:23.761416Z","bundle_sha256":"1435752e884fbae350c11d9a1e1d92c50b1c687f774c402913a19a397512733f"}}