{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VT34Y5JKNA4NCS4YMDEBPENTAY","short_pith_number":"pith:VT34Y5JK","canonical_record":{"source":{"id":"1301.5114","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-22T09:07:36Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"08db8c538e3b6eb0589ea2c0f29b893c44134ab55db32d94cc2e4dd11d4fb4aa","abstract_canon_sha256":"6a2cd163b3b47aad9b0e7d600b321919b9c34d7bcbad5d3e3de7b5647fdff235"},"schema_version":"1.0"},"canonical_sha256":"acf7cc752a6838d14b9860c81791b30636aa9a40af7c2571637c937af0ac4e42","source":{"kind":"arxiv","id":"1301.5114","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5114","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5114v4","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5114","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"VT34Y5JKNA4N","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VT34Y5JKNA4NCS4Y","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VT34Y5JK","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VT34Y5JKNA4NCS4YMDEBPENTAY","target":"record","payload":{"canonical_record":{"source":{"id":"1301.5114","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-22T09:07:36Z","cross_cats_sorted":["math.GN"],"title_canon_sha256":"08db8c538e3b6eb0589ea2c0f29b893c44134ab55db32d94cc2e4dd11d4fb4aa","abstract_canon_sha256":"6a2cd163b3b47aad9b0e7d600b321919b9c34d7bcbad5d3e3de7b5647fdff235"},"schema_version":"1.0"},"canonical_sha256":"acf7cc752a6838d14b9860c81791b30636aa9a40af7c2571637c937af0ac4e42","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:56.901845Z","signature_b64":"fObR0UBKBc3AnzDNLsx3QZEy1wGQ8Kkp1/eIzammE56o8b4K+nZGg+CGc1JDcBmEpZwNTso9R6CXzCM0rc72Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"acf7cc752a6838d14b9860c81791b30636aa9a40af7c2571637c937af0ac4e42","last_reissued_at":"2026-05-18T03:17:56.901268Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:56.901268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.5114","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:17:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V9XB2R1sK+9gWsYnD7NZBnDHLUJFr9d2HvWhEi6vciDtusbPhsKttQmmhhoQMSaF0KLUIYj+de0+posRahRoDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T08:12:35.864250Z"},"content_sha256":"a736d1142cbbd46b5085308dddca8d58193a7383e8485224eb3d75a0364b8884","schema_version":"1.0","event_id":"sha256:a736d1142cbbd46b5085308dddca8d58193a7383e8485224eb3d75a0364b8884"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VT34Y5JKNA4NCS4YMDEBPENTAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Transitive actions of locally compact groups on locally contractible spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"Karl H. Hofmann, Linus Kramer","submitted_at":"2013-01-22T09:07:36Z","abstract_excerpt":"Suppose that $X=G/K$ is the quotient of a locally compact group by a closed subgroup. If $X$ is locally contractible and connected, we prove that $X$ is a manifold. If the $G$-action is faithful, then $G$ is a Lie group."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5114","kind":"arxiv","version":4},"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":"2026-05-18T03:17:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RNVwP7St4BNgEU3hN3UtOYhlPvToqlYRA0B1W1xTT8Nqmtf9JhrJKHNIfX8pFl47J16guhrkPPfQgO8jiVFjBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-22T08:12:35.865005Z"},"content_sha256":"1fbd8cdaec5a3ec18e89fefd21548aa378d9fdbd97a10dd55803b73d15a0b90e","schema_version":"1.0","event_id":"sha256:1fbd8cdaec5a3ec18e89fefd21548aa378d9fdbd97a10dd55803b73d15a0b90e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VT34Y5JKNA4NCS4YMDEBPENTAY/bundle.json","state_url":"https://pith.science/pith/VT34Y5JKNA4NCS4YMDEBPENTAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VT34Y5JKNA4NCS4YMDEBPENTAY/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":"2026-05-22T08:12:35Z","links":{"resolver":"https://pith.science/pith/VT34Y5JKNA4NCS4YMDEBPENTAY","bundle":"https://pith.science/pith/VT34Y5JKNA4NCS4YMDEBPENTAY/bundle.json","state":"https://pith.science/pith/VT34Y5JKNA4NCS4YMDEBPENTAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VT34Y5JKNA4NCS4YMDEBPENTAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VT34Y5JKNA4NCS4YMDEBPENTAY","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":"6a2cd163b3b47aad9b0e7d600b321919b9c34d7bcbad5d3e3de7b5647fdff235","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-22T09:07:36Z","title_canon_sha256":"08db8c538e3b6eb0589ea2c0f29b893c44134ab55db32d94cc2e4dd11d4fb4aa"},"schema_version":"1.0","source":{"id":"1301.5114","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5114","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5114v4","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5114","created_at":"2026-05-18T03:17:56Z"},{"alias_kind":"pith_short_12","alias_value":"VT34Y5JKNA4N","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VT34Y5JKNA4NCS4Y","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VT34Y5JK","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:1fbd8cdaec5a3ec18e89fefd21548aa378d9fdbd97a10dd55803b73d15a0b90e","target":"graph","created_at":"2026-05-18T03:17:56Z","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":"Suppose that $X=G/K$ is the quotient of a locally compact group by a closed subgroup. If $X$ is locally contractible and connected, we prove that $X$ is a manifold. If the $G$-action is faithful, then $G$ is a Lie group.","authors_text":"Karl H. Hofmann, Linus Kramer","cross_cats":["math.GN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-22T09:07:36Z","title":"Transitive actions of locally compact groups on locally contractible spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5114","kind":"arxiv","version":4},"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:a736d1142cbbd46b5085308dddca8d58193a7383e8485224eb3d75a0364b8884","target":"record","created_at":"2026-05-18T03:17:56Z","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":"6a2cd163b3b47aad9b0e7d600b321919b9c34d7bcbad5d3e3de7b5647fdff235","cross_cats_sorted":["math.GN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-01-22T09:07:36Z","title_canon_sha256":"08db8c538e3b6eb0589ea2c0f29b893c44134ab55db32d94cc2e4dd11d4fb4aa"},"schema_version":"1.0","source":{"id":"1301.5114","kind":"arxiv","version":4}},"canonical_sha256":"acf7cc752a6838d14b9860c81791b30636aa9a40af7c2571637c937af0ac4e42","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"acf7cc752a6838d14b9860c81791b30636aa9a40af7c2571637c937af0ac4e42","first_computed_at":"2026-05-18T03:17:56.901268Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:56.901268Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fObR0UBKBc3AnzDNLsx3QZEy1wGQ8Kkp1/eIzammE56o8b4K+nZGg+CGc1JDcBmEpZwNTso9R6CXzCM0rc72Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:56.901845Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5114","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a736d1142cbbd46b5085308dddca8d58193a7383e8485224eb3d75a0364b8884","sha256:1fbd8cdaec5a3ec18e89fefd21548aa378d9fdbd97a10dd55803b73d15a0b90e"],"state_sha256":"2c84428da92721398b137dc8d68907c24d6833287c975f26353bef55927c56eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xonoyn1Uc/4/ldANbWGxbBM38KmwBFusU3YiStrcUnPjIN9H33NCs0KjPLHPUSQTWvKoDPqjCUqiWqen0UuYDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-22T08:12:35.868619Z","bundle_sha256":"da5aa1d0b0b33c99ab9d60461588e3fa09f0d489df53610f8142bf30d6528f55"}}