{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:ZNZTBAQPODMN3O7IIMVZM53SAG","short_pith_number":"pith:ZNZTBAQP","canonical_record":{"source":{"id":"1310.1827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-07T15:47:15Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"3cf4c4ba16aecb67941df5ecab1b4e66b325aecc964dd4b366fb46a7e0a1263b","abstract_canon_sha256":"8aae9f2ba1489001edc132e0e14560705ad6d63036e98ac938cb7afd082f9344"},"schema_version":"1.0"},"canonical_sha256":"cb7330820f70d8ddbbe8432b9677720197dfe7d2c3b051cc2213dafddaeee184","source":{"kind":"arxiv","id":"1310.1827","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1827","created_at":"2026-05-18T00:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1827v1","created_at":"2026-05-18T00:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1827","created_at":"2026-05-18T00:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZNZTBAQPODMN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZNZTBAQPODMN3O7I","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZNZTBAQP","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:ZNZTBAQPODMN3O7IIMVZM53SAG","target":"record","payload":{"canonical_record":{"source":{"id":"1310.1827","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-07T15:47:15Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"3cf4c4ba16aecb67941df5ecab1b4e66b325aecc964dd4b366fb46a7e0a1263b","abstract_canon_sha256":"8aae9f2ba1489001edc132e0e14560705ad6d63036e98ac938cb7afd082f9344"},"schema_version":"1.0"},"canonical_sha256":"cb7330820f70d8ddbbe8432b9677720197dfe7d2c3b051cc2213dafddaeee184","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:45.439673Z","signature_b64":"DrxJe8AV6UJHM53MdSLK7fFOC0jLHxfYJngEkfzzcSN4/dkhH4H+c4gy9tOneCsJP45pUFEXYQoPxBvmcrr0Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cb7330820f70d8ddbbe8432b9677720197dfe7d2c3b051cc2213dafddaeee184","last_reissued_at":"2026-05-18T00:32:45.439072Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:45.439072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.1827","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":"2026-05-18T00:32:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7FZt1cDvGQdihOGGFbujTeljOm6kRXeqCoqhS01XXmtb3dQ7zjGM42ns44f2YwxR9uHTqB2ussHCl2JLcIWyBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:51:14.832183Z"},"content_sha256":"ec83bba925241f2c44b99b8fc554e354859c0d168664a4b265c22267ff6733fa","schema_version":"1.0","event_id":"sha256:ec83bba925241f2c44b99b8fc554e354859c0d168664a4b265c22267ff6733fa"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:ZNZTBAQPODMN3O7IIMVZM53SAG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Selective and Ramsey ultrafilters on $G$-spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.CO","authors_text":"I.V. Protasov, O.V. Petrenko","submitted_at":"2013-10-07T15:47:15Z","abstract_excerpt":"Let $G$ be a group, $X$ be an infinite transitive $G$-space. A free ultrafilter $\\UU$ on $X$ is called $G$-selective if, for any $G$-invariant partition $\\PP$ of $X$, either one cell of $\\PP$ is a member of $\\UU$, or there is a member of $\\UU$ which meets each cell of $\\PP$ in at most one point. We show (Theorem 1) that in ZFC with no additional set-theoretical assumptions there exists a $G$-selective ultrafilter on $X$, describe all $G$-spaces $X$ (Theorem 2) such that each free ultrafilter on $X$ is $G$-selective, and prove (Theorem 3) that a free ultrafilter $\\UU$ on $\\omega$ is selective i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1827","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":"2026-05-18T00:32:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wnFzikwrFG1fgq9Exn9sKyMMpEKz9TGRTJkKzyMEwXsqhyovivG1IYCg5d6LF/GX2wtIepFjksWtSmmnix3JDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T00:51:14.832526Z"},"content_sha256":"64027807bd9eded479e8c089bb33ac3b2b66d93d748f30a77b511b2f7888f595","schema_version":"1.0","event_id":"sha256:64027807bd9eded479e8c089bb33ac3b2b66d93d748f30a77b511b2f7888f595"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZNZTBAQPODMN3O7IIMVZM53SAG/bundle.json","state_url":"https://pith.science/pith/ZNZTBAQPODMN3O7IIMVZM53SAG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZNZTBAQPODMN3O7IIMVZM53SAG/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":"2026-06-29T00:51:14Z","links":{"resolver":"https://pith.science/pith/ZNZTBAQPODMN3O7IIMVZM53SAG","bundle":"https://pith.science/pith/ZNZTBAQPODMN3O7IIMVZM53SAG/bundle.json","state":"https://pith.science/pith/ZNZTBAQPODMN3O7IIMVZM53SAG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZNZTBAQPODMN3O7IIMVZM53SAG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:ZNZTBAQPODMN3O7IIMVZM53SAG","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":"8aae9f2ba1489001edc132e0e14560705ad6d63036e98ac938cb7afd082f9344","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-07T15:47:15Z","title_canon_sha256":"3cf4c4ba16aecb67941df5ecab1b4e66b325aecc964dd4b366fb46a7e0a1263b"},"schema_version":"1.0","source":{"id":"1310.1827","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1827","created_at":"2026-05-18T00:32:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1827v1","created_at":"2026-05-18T00:32:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1827","created_at":"2026-05-18T00:32:45Z"},{"alias_kind":"pith_short_12","alias_value":"ZNZTBAQPODMN","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"ZNZTBAQPODMN3O7I","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"ZNZTBAQP","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:64027807bd9eded479e8c089bb33ac3b2b66d93d748f30a77b511b2f7888f595","target":"graph","created_at":"2026-05-18T00:32:45Z","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":"Let $G$ be a group, $X$ be an infinite transitive $G$-space. A free ultrafilter $\\UU$ on $X$ is called $G$-selective if, for any $G$-invariant partition $\\PP$ of $X$, either one cell of $\\PP$ is a member of $\\UU$, or there is a member of $\\UU$ which meets each cell of $\\PP$ in at most one point. We show (Theorem 1) that in ZFC with no additional set-theoretical assumptions there exists a $G$-selective ultrafilter on $X$, describe all $G$-spaces $X$ (Theorem 2) such that each free ultrafilter on $X$ is $G$-selective, and prove (Theorem 3) that a free ultrafilter $\\UU$ on $\\omega$ is selective i","authors_text":"I.V. Protasov, O.V. Petrenko","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-07T15:47:15Z","title":"Selective and Ramsey ultrafilters on $G$-spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1827","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:ec83bba925241f2c44b99b8fc554e354859c0d168664a4b265c22267ff6733fa","target":"record","created_at":"2026-05-18T00:32:45Z","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":"8aae9f2ba1489001edc132e0e14560705ad6d63036e98ac938cb7afd082f9344","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-07T15:47:15Z","title_canon_sha256":"3cf4c4ba16aecb67941df5ecab1b4e66b325aecc964dd4b366fb46a7e0a1263b"},"schema_version":"1.0","source":{"id":"1310.1827","kind":"arxiv","version":1}},"canonical_sha256":"cb7330820f70d8ddbbe8432b9677720197dfe7d2c3b051cc2213dafddaeee184","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cb7330820f70d8ddbbe8432b9677720197dfe7d2c3b051cc2213dafddaeee184","first_computed_at":"2026-05-18T00:32:45.439072Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:45.439072Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DrxJe8AV6UJHM53MdSLK7fFOC0jLHxfYJngEkfzzcSN4/dkhH4H+c4gy9tOneCsJP45pUFEXYQoPxBvmcrr0Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:45.439673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1827","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ec83bba925241f2c44b99b8fc554e354859c0d168664a4b265c22267ff6733fa","sha256:64027807bd9eded479e8c089bb33ac3b2b66d93d748f30a77b511b2f7888f595"],"state_sha256":"d57e5edea6ffe63de096744ce830a02416461148f43994077a0f361450026b8b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KV5v7hvFzJP9/oFf/ksyXDFrOfPpgtajQZLGrcLYShGd8QfC8hZZsaaZtpDeCOk4xtd2twb56qjLQR9g0Y6nAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T00:51:14.834452Z","bundle_sha256":"cf72859af84d226c8cfed3bea9b1e67bd0966cf46ac66de3f2febb400f617eb7"}}