{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:D365ZDTEFF7CFUQ3R6H2HZSAWO","short_pith_number":"pith:D365ZDTE","canonical_record":{"source":{"id":"1606.07489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-06-23T21:45:40Z","cross_cats_sorted":[],"title_canon_sha256":"465d3b4bbcc42cf6bee1f433fe38743144f94998d6fad4479296f26757e39712","abstract_canon_sha256":"5ecab2fae2ca8d5a049beb325d7969c15a27a5ecf3201ae3a3309a2b2e3d9ca3"},"schema_version":"1.0"},"canonical_sha256":"1efddc8e64297e22d21b8f8fa3e640b3b06e1ff1c302349f365e3ee0c4770833","source":{"kind":"arxiv","id":"1606.07489","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07489","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07489v1","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07489","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"D365ZDTEFF7C","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D365ZDTEFF7CFUQ3","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D365ZDTE","created_at":"2026-05-18T12:30:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:D365ZDTEFF7CFUQ3R6H2HZSAWO","target":"record","payload":{"canonical_record":{"source":{"id":"1606.07489","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-06-23T21:45:40Z","cross_cats_sorted":[],"title_canon_sha256":"465d3b4bbcc42cf6bee1f433fe38743144f94998d6fad4479296f26757e39712","abstract_canon_sha256":"5ecab2fae2ca8d5a049beb325d7969c15a27a5ecf3201ae3a3309a2b2e3d9ca3"},"schema_version":"1.0"},"canonical_sha256":"1efddc8e64297e22d21b8f8fa3e640b3b06e1ff1c302349f365e3ee0c4770833","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:34.175445Z","signature_b64":"gCrMXw2jUm7FBl4mhVqq+5dnW71lBju8BfHTp6nXj1Ej3ahUsfFW/KKzBSd1W42nKiOHuFKZXTw1MApoUboDCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1efddc8e64297e22d21b8f8fa3e640b3b06e1ff1c302349f365e3ee0c4770833","last_reissued_at":"2026-05-17T23:53:34.174760Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:34.174760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1606.07489","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":"2026-05-17T23:53:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H4EdladTAIGrSAp/6C+lnOYG7q088mrlJ1T6fKUe4u9Vnh9vHJzy9GFbAWe7NdCYTubm7nxXYM6Lot4Apip7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:07:29.993691Z"},"content_sha256":"6bd1b19520c136eaed5ab5b2ab9b8e45e94928169642882687259738d8ddffd4","schema_version":"1.0","event_id":"sha256:6bd1b19520c136eaed5ab5b2ab9b8e45e94928169642882687259738d8ddffd4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:D365ZDTEFF7CFUQ3R6H2HZSAWO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Borel Functors and Infinitary Interpretations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Antonio Montalb\\'an, Matthew Harrison-Trainor, Russell Miller","submitted_at":"2016-06-23T21:45:40Z","abstract_excerpt":"We introduce the notion of infinitary interpretation of structures. In general, an interpretation between structures induces a continuous homomorphism between their automorphism groups, and furthermore, it induces a functor between the categories of copies of each structure. We show that for the case of infinitary interpretation the reversals are also true: Every Baire-measurable homomorphism between the automorphism groups of two countable structures is induced by an infinitary interpretation, and every Baire-measurable functor between the set of copies of two countable structures is induced "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07489","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":"2026-05-17T23:53:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZ8Qde74l5wYqOsf/JRZtL8WzZ3pyqAMuXJ8gnE1fJpNPeqQOVmWwddF7Q893452kF7V8N3Wybvr/8+P1xApCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T08:07:29.994353Z"},"content_sha256":"7e46c5bab26822c5ef809d4cb7234813ef593cafb264b877c8f06a40189b6563","schema_version":"1.0","event_id":"sha256:7e46c5bab26822c5ef809d4cb7234813ef593cafb264b877c8f06a40189b6563"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/D365ZDTEFF7CFUQ3R6H2HZSAWO/bundle.json","state_url":"https://pith.science/pith/D365ZDTEFF7CFUQ3R6H2HZSAWO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/D365ZDTEFF7CFUQ3R6H2HZSAWO/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":"2026-05-25T08:07:29Z","links":{"resolver":"https://pith.science/pith/D365ZDTEFF7CFUQ3R6H2HZSAWO","bundle":"https://pith.science/pith/D365ZDTEFF7CFUQ3R6H2HZSAWO/bundle.json","state":"https://pith.science/pith/D365ZDTEFF7CFUQ3R6H2HZSAWO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/D365ZDTEFF7CFUQ3R6H2HZSAWO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:D365ZDTEFF7CFUQ3R6H2HZSAWO","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":"5ecab2fae2ca8d5a049beb325d7969c15a27a5ecf3201ae3a3309a2b2e3d9ca3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-06-23T21:45:40Z","title_canon_sha256":"465d3b4bbcc42cf6bee1f433fe38743144f94998d6fad4479296f26757e39712"},"schema_version":"1.0","source":{"id":"1606.07489","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.07489","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"arxiv_version","alias_value":"1606.07489v1","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.07489","created_at":"2026-05-17T23:53:34Z"},{"alias_kind":"pith_short_12","alias_value":"D365ZDTEFF7C","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_16","alias_value":"D365ZDTEFF7CFUQ3","created_at":"2026-05-18T12:30:09Z"},{"alias_kind":"pith_short_8","alias_value":"D365ZDTE","created_at":"2026-05-18T12:30:09Z"}],"graph_snapshots":[{"event_id":"sha256:7e46c5bab26822c5ef809d4cb7234813ef593cafb264b877c8f06a40189b6563","target":"graph","created_at":"2026-05-17T23:53:34Z","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 introduce the notion of infinitary interpretation of structures. In general, an interpretation between structures induces a continuous homomorphism between their automorphism groups, and furthermore, it induces a functor between the categories of copies of each structure. We show that for the case of infinitary interpretation the reversals are also true: Every Baire-measurable homomorphism between the automorphism groups of two countable structures is induced by an infinitary interpretation, and every Baire-measurable functor between the set of copies of two countable structures is induced ","authors_text":"Antonio Montalb\\'an, Matthew Harrison-Trainor, Russell Miller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-06-23T21:45:40Z","title":"Borel Functors and Infinitary Interpretations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.07489","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":"sha256:6bd1b19520c136eaed5ab5b2ab9b8e45e94928169642882687259738d8ddffd4","target":"record","created_at":"2026-05-17T23:53:34Z","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":"5ecab2fae2ca8d5a049beb325d7969c15a27a5ecf3201ae3a3309a2b2e3d9ca3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-06-23T21:45:40Z","title_canon_sha256":"465d3b4bbcc42cf6bee1f433fe38743144f94998d6fad4479296f26757e39712"},"schema_version":"1.0","source":{"id":"1606.07489","kind":"arxiv","version":1}},"canonical_sha256":"1efddc8e64297e22d21b8f8fa3e640b3b06e1ff1c302349f365e3ee0c4770833","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1efddc8e64297e22d21b8f8fa3e640b3b06e1ff1c302349f365e3ee0c4770833","first_computed_at":"2026-05-17T23:53:34.174760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:34.174760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gCrMXw2jUm7FBl4mhVqq+5dnW71lBju8BfHTp6nXj1Ej3ahUsfFW/KKzBSd1W42nKiOHuFKZXTw1MApoUboDCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:34.175445Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.07489","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6bd1b19520c136eaed5ab5b2ab9b8e45e94928169642882687259738d8ddffd4","sha256:7e46c5bab26822c5ef809d4cb7234813ef593cafb264b877c8f06a40189b6563"],"state_sha256":"50dcdc9fd1ec50627d467f251830284a82c26f9e61d70e3b9e6cb363f7501375"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"USE9Op0Ml0biehtcKERSaJ/N+1k6Ze/ByrJV0XgzlocuyJ0Nsru+EkeojYE3sVGNomkNcqCNzKOE1nNo1527Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T08:07:29.997847Z","bundle_sha256":"4216c78b19c8730c493782d971e25c157c7ad70ec89b5fb7cf0436bd4f6b03d2"}}