{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Q5SXLR2I2TYGSWP7IDQDLNMDQ5","short_pith_number":"pith:Q5SXLR2I","canonical_record":{"source":{"id":"1103.2762","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-14T19:54:42Z","cross_cats_sorted":[],"title_canon_sha256":"18586c36729744f1e57e387a8c2c418a07c1857df0cdd0e312b2e1caaf31e365","abstract_canon_sha256":"5e0ba96252518329a63a08df6bddacc05b05e55a3739dd4cbe202ac0a10d2e7c"},"schema_version":"1.0"},"canonical_sha256":"876575c748d4f06959ff40e035b583875aab2ae433d777396a9cb6c98fd2bea8","source":{"kind":"arxiv","id":"1103.2762","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2762","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2762v3","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2762","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"pith_short_12","alias_value":"Q5SXLR2I2TYG","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q5SXLR2I2TYGSWP7","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q5SXLR2I","created_at":"2026-05-18T12:26:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Q5SXLR2I2TYGSWP7IDQDLNMDQ5","target":"record","payload":{"canonical_record":{"source":{"id":"1103.2762","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-14T19:54:42Z","cross_cats_sorted":[],"title_canon_sha256":"18586c36729744f1e57e387a8c2c418a07c1857df0cdd0e312b2e1caaf31e365","abstract_canon_sha256":"5e0ba96252518329a63a08df6bddacc05b05e55a3739dd4cbe202ac0a10d2e7c"},"schema_version":"1.0"},"canonical_sha256":"876575c748d4f06959ff40e035b583875aab2ae433d777396a9cb6c98fd2bea8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:22:19.247747Z","signature_b64":"7QE5h6ndkBOX4daFlajfDjF8iYZoXNU5cils22BjKP+1bgK00QDe/AK1bxDMJBBut2yt62LQkEQPJp4DeYyYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"876575c748d4f06959ff40e035b583875aab2ae433d777396a9cb6c98fd2bea8","last_reissued_at":"2026-05-18T02:22:19.247043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:22:19.247043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.2762","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:22:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"frpTWZFuBMvu6QPHtRXFiaKBwhR84uIaiWvFolOQdBwo51Ar2znDO3wK7a5vaRaNdE+kG0mkscVPS5m3thPDAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:53:49.527840Z"},"content_sha256":"a69be4d83482e14c62664c11aaf032514b0fd42f985de813a12874f2abc9f02e","schema_version":"1.0","event_id":"sha256:a69be4d83482e14c62664c11aaf032514b0fd42f985de813a12874f2abc9f02e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Q5SXLR2I2TYGSWP7IDQDLNMDQ5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Grey subsets of Polish spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Ita\\\"i Ben Yaacov (ICJ), Julien Melleray (ICJ)","submitted_at":"2011-03-14T19:54:42Z","abstract_excerpt":"We develop the basics of an analogue of descriptive set theory for functions on a Polish space $X$. We use this to define a version of the small index property in the context of Polish topometric groups, and show that Polish topometric groups with ample generics have this property. We also extend classical theorems of Effros and Hausdorff to the topometric context."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2762","kind":"arxiv","version":3},"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":"2026-05-18T02:22:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kEZj65xgzCU6GbmXOn3XoOah2pOJHX7Wkpm9cCoJ7yJJHFuN9XOAPIDtXK6mMG/b8Kb8De/XRd8HhQoi074rCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:53:49.528183Z"},"content_sha256":"358575d426eeb1a4cf3da44dd21e7f7d9071f9da4bfbe1bc191af4fe97b7ab0b","schema_version":"1.0","event_id":"sha256:358575d426eeb1a4cf3da44dd21e7f7d9071f9da4bfbe1bc191af4fe97b7ab0b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q5SXLR2I2TYGSWP7IDQDLNMDQ5/bundle.json","state_url":"https://pith.science/pith/Q5SXLR2I2TYGSWP7IDQDLNMDQ5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q5SXLR2I2TYGSWP7IDQDLNMDQ5/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":"2026-06-24T04:53:49Z","links":{"resolver":"https://pith.science/pith/Q5SXLR2I2TYGSWP7IDQDLNMDQ5","bundle":"https://pith.science/pith/Q5SXLR2I2TYGSWP7IDQDLNMDQ5/bundle.json","state":"https://pith.science/pith/Q5SXLR2I2TYGSWP7IDQDLNMDQ5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q5SXLR2I2TYGSWP7IDQDLNMDQ5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Q5SXLR2I2TYGSWP7IDQDLNMDQ5","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":"5e0ba96252518329a63a08df6bddacc05b05e55a3739dd4cbe202ac0a10d2e7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-14T19:54:42Z","title_canon_sha256":"18586c36729744f1e57e387a8c2c418a07c1857df0cdd0e312b2e1caaf31e365"},"schema_version":"1.0","source":{"id":"1103.2762","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.2762","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"arxiv_version","alias_value":"1103.2762v3","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.2762","created_at":"2026-05-18T02:22:19Z"},{"alias_kind":"pith_short_12","alias_value":"Q5SXLR2I2TYG","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Q5SXLR2I2TYGSWP7","created_at":"2026-05-18T12:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Q5SXLR2I","created_at":"2026-05-18T12:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:358575d426eeb1a4cf3da44dd21e7f7d9071f9da4bfbe1bc191af4fe97b7ab0b","target":"graph","created_at":"2026-05-18T02:22:19Z","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 develop the basics of an analogue of descriptive set theory for functions on a Polish space $X$. We use this to define a version of the small index property in the context of Polish topometric groups, and show that Polish topometric groups with ample generics have this property. We also extend classical theorems of Effros and Hausdorff to the topometric context.","authors_text":"Ita\\\"i Ben Yaacov (ICJ), Julien Melleray (ICJ)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-14T19:54:42Z","title":"Grey subsets of Polish spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.2762","kind":"arxiv","version":3},"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:a69be4d83482e14c62664c11aaf032514b0fd42f985de813a12874f2abc9f02e","target":"record","created_at":"2026-05-18T02:22:19Z","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":"5e0ba96252518329a63a08df6bddacc05b05e55a3739dd4cbe202ac0a10d2e7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-03-14T19:54:42Z","title_canon_sha256":"18586c36729744f1e57e387a8c2c418a07c1857df0cdd0e312b2e1caaf31e365"},"schema_version":"1.0","source":{"id":"1103.2762","kind":"arxiv","version":3}},"canonical_sha256":"876575c748d4f06959ff40e035b583875aab2ae433d777396a9cb6c98fd2bea8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"876575c748d4f06959ff40e035b583875aab2ae433d777396a9cb6c98fd2bea8","first_computed_at":"2026-05-18T02:22:19.247043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:19.247043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7QE5h6ndkBOX4daFlajfDjF8iYZoXNU5cils22BjKP+1bgK00QDe/AK1bxDMJBBut2yt62LQkEQPJp4DeYyYCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:19.247747Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.2762","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a69be4d83482e14c62664c11aaf032514b0fd42f985de813a12874f2abc9f02e","sha256:358575d426eeb1a4cf3da44dd21e7f7d9071f9da4bfbe1bc191af4fe97b7ab0b"],"state_sha256":"2a8f090af7a7fbd5837cc5e15e255f85c34e2c69dc489301dace2d10c3251865"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wtjpo3RUVgfmZChW72cqZtpsxj5ngK2Gtgdne6m+X37EoOUycNPASn2UIPCFJtAiI1gcq89BZluynGkyLX89CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:53:49.530086Z","bundle_sha256":"4ef1b832f30add73bd8b3d1e5ab091db12763553554b8d4995cf4901c26c55d9"}}