{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:JPB5QNN4M2IIRDNYOKKS3CSYYL","short_pith_number":"pith:JPB5QNN4","canonical_record":{"source":{"id":"1702.08093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-26T21:57:36Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"577eddd99098b6edaec3b443d5b559fdd1c78fc2a0d1d952ab8ca7dfdb3cf210","abstract_canon_sha256":"dc3a21fe3838f5545dda1eb07bd20e33650a1e2c7b0a055a6cfaee3d11ef7b2a"},"schema_version":"1.0"},"canonical_sha256":"4bc3d835bc6690888db872952d8a58c2e1f1bc82da2c9d0eb0bf4d440f9c79a0","source":{"kind":"arxiv","id":"1702.08093","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08093","created_at":"2026-05-18T00:49:56Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08093v1","created_at":"2026-05-18T00:49:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08093","created_at":"2026-05-18T00:49:56Z"},{"alias_kind":"pith_short_12","alias_value":"JPB5QNN4M2II","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JPB5QNN4M2IIRDNY","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JPB5QNN4","created_at":"2026-05-18T12:31:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:JPB5QNN4M2IIRDNYOKKS3CSYYL","target":"record","payload":{"canonical_record":{"source":{"id":"1702.08093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-26T21:57:36Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"577eddd99098b6edaec3b443d5b559fdd1c78fc2a0d1d952ab8ca7dfdb3cf210","abstract_canon_sha256":"dc3a21fe3838f5545dda1eb07bd20e33650a1e2c7b0a055a6cfaee3d11ef7b2a"},"schema_version":"1.0"},"canonical_sha256":"4bc3d835bc6690888db872952d8a58c2e1f1bc82da2c9d0eb0bf4d440f9c79a0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:56.048913Z","signature_b64":"fxo0XCoyj0utdSHujkZYud2tg1TQ9ledbo0a9i1Q8kySZuJAUFP7QjXwMT/SJefDcQmN+2gge5h2Wh2mr7fxCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4bc3d835bc6690888db872952d8a58c2e1f1bc82da2c9d0eb0bf4d440f9c79a0","last_reissued_at":"2026-05-18T00:49:56.048230Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:56.048230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.08093","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":"2026-05-18T00:49:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xtZdR5+g3OkaCCIj9XcLm1I/42WDBIi3yD6Ky2LIfD3rRrM939Xl/3EveCCQm1R9VSHqP/6PP/K0CJEqP7lRDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:49:29.743274Z"},"content_sha256":"7fced46ef9c26f964ff30c20dd16e79c98c8a3a6d36379b837020081b098efbe","schema_version":"1.0","event_id":"sha256:7fced46ef9c26f964ff30c20dd16e79c98c8a3a6d36379b837020081b098efbe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:JPB5QNN4M2IIRDNYOKKS3CSYYL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Characterizing slices for proper actions of locally compact groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GN","authors_text":"Sergey A. Antonyan","submitted_at":"2017-02-26T21:57:36Z","abstract_excerpt":"In his seminal work \\cite{pal:61}, R. Palais extended a substantial part of the theory of compact transformation groups to the case of proper actions of locally compact groups. Here we extend to proper actions some other important results well known for compact group actions. In particular, we prove that if $H$ is a compact subgroup of a locally compact group $G$ and $S$ is a small (in the sense of Palais) $H$-slice in a proper $G$-space, then the action map $G\\times S\\to G(S)$ is open. This is applied to prove that the slicing map $f_S:G(S)\\to G/H$ is continuos and open, which provides an ext"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08093","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":"2026-05-18T00:49:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"np0cGDhv3aGMp43bFgmwQoE2UoqdIMMlcue/PiaUGUA6zCHK6v4hRK1Gf3wPlqhosxicJnybMpH1L7AmpfiZCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T21:49:29.743649Z"},"content_sha256":"9829d56b19fbf78c2e1270cee814a49f85d50d054281f687aeb8b686339637ab","schema_version":"1.0","event_id":"sha256:9829d56b19fbf78c2e1270cee814a49f85d50d054281f687aeb8b686339637ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JPB5QNN4M2IIRDNYOKKS3CSYYL/bundle.json","state_url":"https://pith.science/pith/JPB5QNN4M2IIRDNYOKKS3CSYYL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JPB5QNN4M2IIRDNYOKKS3CSYYL/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":"2026-06-26T21:49:29Z","links":{"resolver":"https://pith.science/pith/JPB5QNN4M2IIRDNYOKKS3CSYYL","bundle":"https://pith.science/pith/JPB5QNN4M2IIRDNYOKKS3CSYYL/bundle.json","state":"https://pith.science/pith/JPB5QNN4M2IIRDNYOKKS3CSYYL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JPB5QNN4M2IIRDNYOKKS3CSYYL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:JPB5QNN4M2IIRDNYOKKS3CSYYL","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":"dc3a21fe3838f5545dda1eb07bd20e33650a1e2c7b0a055a6cfaee3d11ef7b2a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-26T21:57:36Z","title_canon_sha256":"577eddd99098b6edaec3b443d5b559fdd1c78fc2a0d1d952ab8ca7dfdb3cf210"},"schema_version":"1.0","source":{"id":"1702.08093","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.08093","created_at":"2026-05-18T00:49:56Z"},{"alias_kind":"arxiv_version","alias_value":"1702.08093v1","created_at":"2026-05-18T00:49:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.08093","created_at":"2026-05-18T00:49:56Z"},{"alias_kind":"pith_short_12","alias_value":"JPB5QNN4M2II","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_16","alias_value":"JPB5QNN4M2IIRDNY","created_at":"2026-05-18T12:31:24Z"},{"alias_kind":"pith_short_8","alias_value":"JPB5QNN4","created_at":"2026-05-18T12:31:24Z"}],"graph_snapshots":[{"event_id":"sha256:9829d56b19fbf78c2e1270cee814a49f85d50d054281f687aeb8b686339637ab","target":"graph","created_at":"2026-05-18T00:49:56Z","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":"In his seminal work \\cite{pal:61}, R. Palais extended a substantial part of the theory of compact transformation groups to the case of proper actions of locally compact groups. Here we extend to proper actions some other important results well known for compact group actions. In particular, we prove that if $H$ is a compact subgroup of a locally compact group $G$ and $S$ is a small (in the sense of Palais) $H$-slice in a proper $G$-space, then the action map $G\\times S\\to G(S)$ is open. This is applied to prove that the slicing map $f_S:G(S)\\to G/H$ is continuos and open, which provides an ext","authors_text":"Sergey A. Antonyan","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-26T21:57:36Z","title":"Characterizing slices for proper actions of locally compact groups"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.08093","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":"sha256:7fced46ef9c26f964ff30c20dd16e79c98c8a3a6d36379b837020081b098efbe","target":"record","created_at":"2026-05-18T00:49:56Z","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":"dc3a21fe3838f5545dda1eb07bd20e33650a1e2c7b0a055a6cfaee3d11ef7b2a","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2017-02-26T21:57:36Z","title_canon_sha256":"577eddd99098b6edaec3b443d5b559fdd1c78fc2a0d1d952ab8ca7dfdb3cf210"},"schema_version":"1.0","source":{"id":"1702.08093","kind":"arxiv","version":1}},"canonical_sha256":"4bc3d835bc6690888db872952d8a58c2e1f1bc82da2c9d0eb0bf4d440f9c79a0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4bc3d835bc6690888db872952d8a58c2e1f1bc82da2c9d0eb0bf4d440f9c79a0","first_computed_at":"2026-05-18T00:49:56.048230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:56.048230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fxo0XCoyj0utdSHujkZYud2tg1TQ9ledbo0a9i1Q8kySZuJAUFP7QjXwMT/SJefDcQmN+2gge5h2Wh2mr7fxCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:56.048913Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.08093","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7fced46ef9c26f964ff30c20dd16e79c98c8a3a6d36379b837020081b098efbe","sha256:9829d56b19fbf78c2e1270cee814a49f85d50d054281f687aeb8b686339637ab"],"state_sha256":"c52d9bdf7da2ba8617cb90eb3309465b35852e29baa70c5b30a82e83f1cab6dc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/yUWpAeEsu9Hkh8Ne/m1K88DcNr+Y0eL5s7O9CBG4cml84kJAm20yb6HaNGyRYGyN3Gyke7QSwlMPhRsap9JDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T21:49:29.745619Z","bundle_sha256":"6cc97b09efebdd0644d99be7ea1ec70749e0635b411f6f6857fa4f6ca704cd3b"}}