{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:7RBABMUHSHRO6G3MW6MTN6RM6P","short_pith_number":"pith:7RBABMUH","canonical_record":{"source":{"id":"1103.0804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-03-03T23:48:57Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"959b4cd66ab75a8f7c70ca025e0acc3aa1db6978bddc8bec18e690087db26cec","abstract_canon_sha256":"f823829459956390b62aead9ab88e5779e39643592189a5ec41008d4c9096bcc"},"schema_version":"1.0"},"canonical_sha256":"fc4200b28791e2ef1b6cb79936fa2cf3f16f71f0ccfc697794e6127b66ef37a4","source":{"kind":"arxiv","id":"1103.0804","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0804","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0804v1","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0804","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"pith_short_12","alias_value":"7RBABMUHSHRO","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7RBABMUHSHRO6G3M","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7RBABMUH","created_at":"2026-05-18T12:26:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:7RBABMUHSHRO6G3MW6MTN6RM6P","target":"record","payload":{"canonical_record":{"source":{"id":"1103.0804","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-03-03T23:48:57Z","cross_cats_sorted":["math.GR","math.GT"],"title_canon_sha256":"959b4cd66ab75a8f7c70ca025e0acc3aa1db6978bddc8bec18e690087db26cec","abstract_canon_sha256":"f823829459956390b62aead9ab88e5779e39643592189a5ec41008d4c9096bcc"},"schema_version":"1.0"},"canonical_sha256":"fc4200b28791e2ef1b6cb79936fa2cf3f16f71f0ccfc697794e6127b66ef37a4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:26.232233Z","signature_b64":"oNi03gGdMJf0g68qrZTGCaDjPFlYAdyHTab/HVqE5xWl3nJXJZfQwcM5IQsFN3DSfsnH5XMmeHH13/c0tGheDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc4200b28791e2ef1b6cb79936fa2cf3f16f71f0ccfc697794e6127b66ef37a4","last_reissued_at":"2026-05-18T04:27:26.231690Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:26.231690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1103.0804","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":"2026-05-18T04:27:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kUe0fZHj07UeFd7SsWY42G6UdL2RSBaicE67+2xRLpv1eQpxnRXdc9+I26ZJ/n5Oy/kPU7bgCeSCcymhtzkuAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:56:34.659396Z"},"content_sha256":"cb19a38ea07dbf1612c272f804a6dd6a4aa900a8d4ab3a41b063261510b4543e","schema_version":"1.0","event_id":"sha256:cb19a38ea07dbf1612c272f804a6dd6a4aa900a8d4ab3a41b063261510b4543e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:7RBABMUHSHRO6G3MW6MTN6RM6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant extension properties of coset spaces of locally compact groups and approximate slices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR","math.GT"],"primary_cat":"math.GN","authors_text":"Sergey A. Antonyan","submitted_at":"2011-03-03T23:48:57Z","abstract_excerpt":"We prove that for a compact subgroup $H$ of a locally compact Hausdorff group $G$, the following properties are mutually equivalent: (1) $G/H$ is a manifold, (2) $G/H$ is finite-dimensional and locally connected, (3) $G/H$ is locally contractible, (4) $G/H$ is an ANE for paracompact spaces, (5) $G/H$ is a metrizable $G$-ANE for paracompact proper $G$-spaces having a paracompact orbit space. A new version of the Approximate slice theorem is also proven in the light of these results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0804","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":"2026-05-18T04:27:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cIQIvN1RU4BuqcUG5liDS4Eb9KP8YwMyDCb0djr0J1/YJAql7TrZyzoVIybfkSr2W2XcEbNW8JtEg70DaBMtAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T10:56:34.659737Z"},"content_sha256":"f19ea66ab0a397d54ab3385709da350db3cd2c1380c73bf91914d1db0dd1f711","schema_version":"1.0","event_id":"sha256:f19ea66ab0a397d54ab3385709da350db3cd2c1380c73bf91914d1db0dd1f711"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7RBABMUHSHRO6G3MW6MTN6RM6P/bundle.json","state_url":"https://pith.science/pith/7RBABMUHSHRO6G3MW6MTN6RM6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7RBABMUHSHRO6G3MW6MTN6RM6P/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":"2026-06-27T10:56:34Z","links":{"resolver":"https://pith.science/pith/7RBABMUHSHRO6G3MW6MTN6RM6P","bundle":"https://pith.science/pith/7RBABMUHSHRO6G3MW6MTN6RM6P/bundle.json","state":"https://pith.science/pith/7RBABMUHSHRO6G3MW6MTN6RM6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7RBABMUHSHRO6G3MW6MTN6RM6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7RBABMUHSHRO6G3MW6MTN6RM6P","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":"f823829459956390b62aead9ab88e5779e39643592189a5ec41008d4c9096bcc","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-03-03T23:48:57Z","title_canon_sha256":"959b4cd66ab75a8f7c70ca025e0acc3aa1db6978bddc8bec18e690087db26cec"},"schema_version":"1.0","source":{"id":"1103.0804","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.0804","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"arxiv_version","alias_value":"1103.0804v1","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.0804","created_at":"2026-05-18T04:27:26Z"},{"alias_kind":"pith_short_12","alias_value":"7RBABMUHSHRO","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7RBABMUHSHRO6G3M","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7RBABMUH","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:f19ea66ab0a397d54ab3385709da350db3cd2c1380c73bf91914d1db0dd1f711","target":"graph","created_at":"2026-05-18T04:27:26Z","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 that for a compact subgroup $H$ of a locally compact Hausdorff group $G$, the following properties are mutually equivalent: (1) $G/H$ is a manifold, (2) $G/H$ is finite-dimensional and locally connected, (3) $G/H$ is locally contractible, (4) $G/H$ is an ANE for paracompact spaces, (5) $G/H$ is a metrizable $G$-ANE for paracompact proper $G$-spaces having a paracompact orbit space. A new version of the Approximate slice theorem is also proven in the light of these results.","authors_text":"Sergey A. Antonyan","cross_cats":["math.GR","math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-03-03T23:48:57Z","title":"Equivariant extension properties of coset spaces of locally compact groups and approximate slices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.0804","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:cb19a38ea07dbf1612c272f804a6dd6a4aa900a8d4ab3a41b063261510b4543e","target":"record","created_at":"2026-05-18T04:27:26Z","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":"f823829459956390b62aead9ab88e5779e39643592189a5ec41008d4c9096bcc","cross_cats_sorted":["math.GR","math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GN","submitted_at":"2011-03-03T23:48:57Z","title_canon_sha256":"959b4cd66ab75a8f7c70ca025e0acc3aa1db6978bddc8bec18e690087db26cec"},"schema_version":"1.0","source":{"id":"1103.0804","kind":"arxiv","version":1}},"canonical_sha256":"fc4200b28791e2ef1b6cb79936fa2cf3f16f71f0ccfc697794e6127b66ef37a4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc4200b28791e2ef1b6cb79936fa2cf3f16f71f0ccfc697794e6127b66ef37a4","first_computed_at":"2026-05-18T04:27:26.231690Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:27:26.231690Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oNi03gGdMJf0g68qrZTGCaDjPFlYAdyHTab/HVqE5xWl3nJXJZfQwcM5IQsFN3DSfsnH5XMmeHH13/c0tGheDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:27:26.232233Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.0804","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb19a38ea07dbf1612c272f804a6dd6a4aa900a8d4ab3a41b063261510b4543e","sha256:f19ea66ab0a397d54ab3385709da350db3cd2c1380c73bf91914d1db0dd1f711"],"state_sha256":"cb5e12a715a570ed616457d310e7889d15c94c6ebca5567cf97e4721c8d7abd0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DU+O8tk3iiK1vxT7QzwvQFFEzb1/hbXLAHQDaByrxT7zNqVjPWMgQmmUbFfGXNl+5rYyE070DbtoM8bcm+5WBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T10:56:34.661529Z","bundle_sha256":"1d5747f1a5a9f704d273d629309e06875aae90a57fe760eed775d4949578985d"}}