{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:S3XCD7D6ZQ6LDTI4QY2R37KY5V","short_pith_number":"pith:S3XCD7D6","canonical_record":{"source":{"id":"1504.03394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-14T00:23:42Z","cross_cats_sorted":[],"title_canon_sha256":"2a2d69fcaefbef534ceb43c3f3cbe14d9841744cc85d5f74b196353d96b64785","abstract_canon_sha256":"ff9a3d2d64d6aa92a4806dfa96470e7c4a43a73c501583789bbb5a7e26e8851d"},"schema_version":"1.0"},"canonical_sha256":"96ee21fc7ecc3cb1cd1c86351dfd58ed5c4d600bd35de1ff33a59c707c3f90d4","source":{"kind":"arxiv","id":"1504.03394","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03394","created_at":"2026-05-18T02:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03394v1","created_at":"2026-05-18T02:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03394","created_at":"2026-05-18T02:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"S3XCD7D6ZQ6L","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S3XCD7D6ZQ6LDTI4","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S3XCD7D6","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:S3XCD7D6ZQ6LDTI4QY2R37KY5V","target":"record","payload":{"canonical_record":{"source":{"id":"1504.03394","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-14T00:23:42Z","cross_cats_sorted":[],"title_canon_sha256":"2a2d69fcaefbef534ceb43c3f3cbe14d9841744cc85d5f74b196353d96b64785","abstract_canon_sha256":"ff9a3d2d64d6aa92a4806dfa96470e7c4a43a73c501583789bbb5a7e26e8851d"},"schema_version":"1.0"},"canonical_sha256":"96ee21fc7ecc3cb1cd1c86351dfd58ed5c4d600bd35de1ff33a59c707c3f90d4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:57.916394Z","signature_b64":"CK+Y0Tx3ZZwYvXnLLyWzi/VmY2vA6PTul0MgYTpi91m/jnh/R28v5u8bylFgkF++MxIaFIiRiMF9IWGeMenhAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"96ee21fc7ecc3cb1cd1c86351dfd58ed5c4d600bd35de1ff33a59c707c3f90d4","last_reissued_at":"2026-05-18T02:18:57.915862Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:57.915862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.03394","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":"2026-05-18T02:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pJUmE6aRf230A8/53qB4pM3KO1jsXSo1qwxjZR0n5tEq/evEvYybEsKNVEr5tFRtNkfD2TSLX8UdhdYRcjm8CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:26:33.111705Z"},"content_sha256":"776f98ac5437c1329f106b13a58f49c4ea12f3e0ab9514b6097c936ff555ae19","schema_version":"1.0","event_id":"sha256:776f98ac5437c1329f106b13a58f49c4ea12f3e0ab9514b6097c936ff555ae19"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:S3XCD7D6ZQ6LDTI4QY2R37KY5V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Properness conditions for actions and coactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"John Quigg, Magnus B. Landstad, S. Kaliszewski","submitted_at":"2015-04-14T00:23:42Z","abstract_excerpt":"Three properness conditions for actions of locally compact groups on C*-algebras are studied, as well as their dual analogues for coactions. To motivate the properness conditions for actions, the commutative cases (actions on spaces) are surveyed; here the conditions are known: proper, locally proper, and pointwise properness, although the latter property has not been so well studied in the literature. The basic theory of these properness conditions is summarized, with somewhat more attention paid to pointwise properness. C*-characterizations of the properties are proved, and applications to C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03394","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":"2026-05-18T02:18:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f9wR6yaoWuJyqSYf6bEKU/NylvBBZH9oDLuwur/905wFuyjc54IeH8c1R564npQMdKmfbYDuXOEQB31yT6ymBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T22:26:33.112047Z"},"content_sha256":"8965b6121148a8586d6bd835902e20f92fd284038e94a1b21846a4cadfc4ddd0","schema_version":"1.0","event_id":"sha256:8965b6121148a8586d6bd835902e20f92fd284038e94a1b21846a4cadfc4ddd0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S3XCD7D6ZQ6LDTI4QY2R37KY5V/bundle.json","state_url":"https://pith.science/pith/S3XCD7D6ZQ6LDTI4QY2R37KY5V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S3XCD7D6ZQ6LDTI4QY2R37KY5V/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":"2026-06-01T22:26:33Z","links":{"resolver":"https://pith.science/pith/S3XCD7D6ZQ6LDTI4QY2R37KY5V","bundle":"https://pith.science/pith/S3XCD7D6ZQ6LDTI4QY2R37KY5V/bundle.json","state":"https://pith.science/pith/S3XCD7D6ZQ6LDTI4QY2R37KY5V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S3XCD7D6ZQ6LDTI4QY2R37KY5V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:S3XCD7D6ZQ6LDTI4QY2R37KY5V","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":"ff9a3d2d64d6aa92a4806dfa96470e7c4a43a73c501583789bbb5a7e26e8851d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-14T00:23:42Z","title_canon_sha256":"2a2d69fcaefbef534ceb43c3f3cbe14d9841744cc85d5f74b196353d96b64785"},"schema_version":"1.0","source":{"id":"1504.03394","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.03394","created_at":"2026-05-18T02:18:57Z"},{"alias_kind":"arxiv_version","alias_value":"1504.03394v1","created_at":"2026-05-18T02:18:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.03394","created_at":"2026-05-18T02:18:57Z"},{"alias_kind":"pith_short_12","alias_value":"S3XCD7D6ZQ6L","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"S3XCD7D6ZQ6LDTI4","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"S3XCD7D6","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:8965b6121148a8586d6bd835902e20f92fd284038e94a1b21846a4cadfc4ddd0","target":"graph","created_at":"2026-05-18T02:18:57Z","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":"Three properness conditions for actions of locally compact groups on C*-algebras are studied, as well as their dual analogues for coactions. To motivate the properness conditions for actions, the commutative cases (actions on spaces) are surveyed; here the conditions are known: proper, locally proper, and pointwise properness, although the latter property has not been so well studied in the literature. The basic theory of these properness conditions is summarized, with somewhat more attention paid to pointwise properness. C*-characterizations of the properties are proved, and applications to C","authors_text":"John Quigg, Magnus B. Landstad, S. Kaliszewski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-14T00:23:42Z","title":"Properness conditions for actions and coactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.03394","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":"sha256:776f98ac5437c1329f106b13a58f49c4ea12f3e0ab9514b6097c936ff555ae19","target":"record","created_at":"2026-05-18T02:18:57Z","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":"ff9a3d2d64d6aa92a4806dfa96470e7c4a43a73c501583789bbb5a7e26e8851d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-04-14T00:23:42Z","title_canon_sha256":"2a2d69fcaefbef534ceb43c3f3cbe14d9841744cc85d5f74b196353d96b64785"},"schema_version":"1.0","source":{"id":"1504.03394","kind":"arxiv","version":1}},"canonical_sha256":"96ee21fc7ecc3cb1cd1c86351dfd58ed5c4d600bd35de1ff33a59c707c3f90d4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96ee21fc7ecc3cb1cd1c86351dfd58ed5c4d600bd35de1ff33a59c707c3f90d4","first_computed_at":"2026-05-18T02:18:57.915862Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:57.915862Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CK+Y0Tx3ZZwYvXnLLyWzi/VmY2vA6PTul0MgYTpi91m/jnh/R28v5u8bylFgkF++MxIaFIiRiMF9IWGeMenhAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:57.916394Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.03394","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:776f98ac5437c1329f106b13a58f49c4ea12f3e0ab9514b6097c936ff555ae19","sha256:8965b6121148a8586d6bd835902e20f92fd284038e94a1b21846a4cadfc4ddd0"],"state_sha256":"8f07c48ee51ab3f903d4837ce8d48d02f72448694fed2b23bf82ca06b95c2faa"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sbLtCF2DRzArlbT8kun3lMVbzmTCiUy23tMRX8LnO//iWwduGGEw9upoavHj+uAT7tJE6l6M4gYSFZ/PjfbgBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T22:26:33.114157Z","bundle_sha256":"59a4412eec2671e1a9aebe85e781d5164d0dfe2283e7bc445b03f2eaf9cdcc4b"}}