{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:MUKMJQWCDLPDXG6JZJZL5IAKOQ","short_pith_number":"pith:MUKMJQWC","canonical_record":{"source":{"id":"math/0510120","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GN","submitted_at":"2005-10-06T13:18:04Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a8b3a0fb43983617cd3c0412587d830c33fee72ce86de3b95235f0ef9d4bf0de","abstract_canon_sha256":"f1f451cb27f147efe2f947ecda26bf5b4abc091fe1982b9ac7875f7d8b640b2c"},"schema_version":"1.0"},"canonical_sha256":"6514c4c2c21ade3b9bc9ca72bea00a742282a2b9bb05c3e69dd8d962f135ae41","source":{"kind":"arxiv","id":"math/0510120","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510120","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510120v1","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510120","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"MUKMJQWCDLPD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"MUKMJQWCDLPDXG6J","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"MUKMJQWC","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:MUKMJQWCDLPDXG6JZJZL5IAKOQ","target":"record","payload":{"canonical_record":{"source":{"id":"math/0510120","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.GN","submitted_at":"2005-10-06T13:18:04Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"a8b3a0fb43983617cd3c0412587d830c33fee72ce86de3b95235f0ef9d4bf0de","abstract_canon_sha256":"f1f451cb27f147efe2f947ecda26bf5b4abc091fe1982b9ac7875f7d8b640b2c"},"schema_version":"1.0"},"canonical_sha256":"6514c4c2c21ade3b9bc9ca72bea00a742282a2b9bb05c3e69dd8d962f135ae41","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:22.982014Z","signature_b64":"mCodfP0lP4bniruAF4OB/qaUDC5CnGeW4bM2GwWYnHWUL61KDvKn9zKhoK61xa1VX+1gBEQ7VWqPBRWob4v2Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6514c4c2c21ade3b9bc9ca72bea00a742282a2b9bb05c3e69dd8d962f135ae41","last_reissued_at":"2026-05-18T01:05:22.981549Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:22.981549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0510120","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":"2026-05-18T01:05:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"urcFN9hx5/plww/O8iLb6T5cr7SK7b9CM3jOLSkJpWzVEKn9uI9EMReYRYMVyr286K1TkMG7XzKBwMmzifUTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:30:58.461516Z"},"content_sha256":"693beed6fb2242d9eec0ef2516cd30db9cb9b4ae590a3382ccdcf633ff338164","schema_version":"1.0","event_id":"sha256:693beed6fb2242d9eec0ef2516cd30db9cb9b4ae590a3382ccdcf633ff338164"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:MUKMJQWCDLPDXG6JZJZL5IAKOQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reconstruction theorem for homeomorphism groups without small sets and non-shrinking functions of a normed space","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.GN","authors_text":"Matatyahu Rubin, Vladimir P. Fonf","submitted_at":"2005-10-06T13:18:04Z","abstract_excerpt":"We prove a reconstruction theorem for homeomorphism groups of open sets in metrizable locally convex topological vector spaces. We show that certain small subgroups of the full homeomorphism group obey the conditions of the above theorem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510120","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":"2026-05-18T01:05:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"i/SCRbUYQo/6BqJOoS/fzxO3++LvObj9IkSU63phdvNfUUud6TwrZYuBZExiVhAd12y4RWiGVCsP7+KrEIRmAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T06:30:58.461857Z"},"content_sha256":"3e39f263393fa0117c4aed422cf4d37f89b73412f5c81fbf0315196bccc801d0","schema_version":"1.0","event_id":"sha256:3e39f263393fa0117c4aed422cf4d37f89b73412f5c81fbf0315196bccc801d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MUKMJQWCDLPDXG6JZJZL5IAKOQ/bundle.json","state_url":"https://pith.science/pith/MUKMJQWCDLPDXG6JZJZL5IAKOQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MUKMJQWCDLPDXG6JZJZL5IAKOQ/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":"2026-06-05T06:30:58Z","links":{"resolver":"https://pith.science/pith/MUKMJQWCDLPDXG6JZJZL5IAKOQ","bundle":"https://pith.science/pith/MUKMJQWCDLPDXG6JZJZL5IAKOQ/bundle.json","state":"https://pith.science/pith/MUKMJQWCDLPDXG6JZJZL5IAKOQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MUKMJQWCDLPDXG6JZJZL5IAKOQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:MUKMJQWCDLPDXG6JZJZL5IAKOQ","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":"f1f451cb27f147efe2f947ecda26bf5b4abc091fe1982b9ac7875f7d8b640b2c","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"math.GN","submitted_at":"2005-10-06T13:18:04Z","title_canon_sha256":"a8b3a0fb43983617cd3c0412587d830c33fee72ce86de3b95235f0ef9d4bf0de"},"schema_version":"1.0","source":{"id":"math/0510120","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510120","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510120v1","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510120","created_at":"2026-05-18T01:05:22Z"},{"alias_kind":"pith_short_12","alias_value":"MUKMJQWCDLPD","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"MUKMJQWCDLPDXG6J","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"MUKMJQWC","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:3e39f263393fa0117c4aed422cf4d37f89b73412f5c81fbf0315196bccc801d0","target":"graph","created_at":"2026-05-18T01:05:22Z","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 prove a reconstruction theorem for homeomorphism groups of open sets in metrizable locally convex topological vector spaces. We show that certain small subgroups of the full homeomorphism group obey the conditions of the above theorem.","authors_text":"Matatyahu Rubin, Vladimir P. Fonf","cross_cats":["math.FA"],"headline":"","license":"","primary_cat":"math.GN","submitted_at":"2005-10-06T13:18:04Z","title":"Reconstruction theorem for homeomorphism groups without small sets and non-shrinking functions of a normed space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510120","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":"sha256:693beed6fb2242d9eec0ef2516cd30db9cb9b4ae590a3382ccdcf633ff338164","target":"record","created_at":"2026-05-18T01:05:22Z","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":"f1f451cb27f147efe2f947ecda26bf5b4abc091fe1982b9ac7875f7d8b640b2c","cross_cats_sorted":["math.FA"],"license":"","primary_cat":"math.GN","submitted_at":"2005-10-06T13:18:04Z","title_canon_sha256":"a8b3a0fb43983617cd3c0412587d830c33fee72ce86de3b95235f0ef9d4bf0de"},"schema_version":"1.0","source":{"id":"math/0510120","kind":"arxiv","version":1}},"canonical_sha256":"6514c4c2c21ade3b9bc9ca72bea00a742282a2b9bb05c3e69dd8d962f135ae41","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6514c4c2c21ade3b9bc9ca72bea00a742282a2b9bb05c3e69dd8d962f135ae41","first_computed_at":"2026-05-18T01:05:22.981549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:22.981549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mCodfP0lP4bniruAF4OB/qaUDC5CnGeW4bM2GwWYnHWUL61KDvKn9zKhoK61xa1VX+1gBEQ7VWqPBRWob4v2Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:22.982014Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0510120","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:693beed6fb2242d9eec0ef2516cd30db9cb9b4ae590a3382ccdcf633ff338164","sha256:3e39f263393fa0117c4aed422cf4d37f89b73412f5c81fbf0315196bccc801d0"],"state_sha256":"bb1f7a91a8501048af435b911b414c3ee92f2fdad7ddf2f7a38223e6c6b50be3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6kIQmIzxkUq0JbDuAtyHANPK4VHjmIytVeecME92PCWPjxU6wV5oU+1etlskOcd9JvRWKXTiXyIMGvja5Wk3Cw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T06:30:58.463792Z","bundle_sha256":"019894f395e325c82d8e33ffabdb14ad9600c64f156dd21afe4dfff7b6032266"}}