{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:C2XUTJQCPNPTSCEFYZEONXAL7R","short_pith_number":"pith:C2XUTJQC","canonical_record":{"source":{"id":"2605.24141","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GN","submitted_at":"2026-05-22T19:03:36Z","cross_cats_sorted":[],"title_canon_sha256":"4ccf3c54fe5df9743a3d62b3263881d94c63482d89008c42aecb09b47950808f","abstract_canon_sha256":"adde0e095355c68448b565f08d6986b7b45243de735f322ad5507e40b0c50656"},"schema_version":"1.0"},"canonical_sha256":"16af49a6027b5f390885c648e6dc0bfc5b8b0c68398ff863d9a6f534f83ef320","source":{"kind":"arxiv","id":"2605.24141","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24141","created_at":"2026-05-26T01:02:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24141v1","created_at":"2026-05-26T01:02:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24141","created_at":"2026-05-26T01:02:48Z"},{"alias_kind":"pith_short_12","alias_value":"C2XUTJQCPNPT","created_at":"2026-05-26T01:02:48Z"},{"alias_kind":"pith_short_16","alias_value":"C2XUTJQCPNPTSCEF","created_at":"2026-05-26T01:02:48Z"},{"alias_kind":"pith_short_8","alias_value":"C2XUTJQC","created_at":"2026-05-26T01:02:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:C2XUTJQCPNPTSCEFYZEONXAL7R","target":"record","payload":{"canonical_record":{"source":{"id":"2605.24141","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GN","submitted_at":"2026-05-22T19:03:36Z","cross_cats_sorted":[],"title_canon_sha256":"4ccf3c54fe5df9743a3d62b3263881d94c63482d89008c42aecb09b47950808f","abstract_canon_sha256":"adde0e095355c68448b565f08d6986b7b45243de735f322ad5507e40b0c50656"},"schema_version":"1.0"},"canonical_sha256":"16af49a6027b5f390885c648e6dc0bfc5b8b0c68398ff863d9a6f534f83ef320","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-26T01:02:48.402170Z","signature_b64":"u/Go/g8h/Vx9vSvjSd1JM/ZYY6zxQFNuulVCA7q/BZvy2JfP4Eg7FLtmMUfunj/Hu0WWiZ0WcRxG2RfeO4bqBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16af49a6027b5f390885c648e6dc0bfc5b8b0c68398ff863d9a6f534f83ef320","last_reissued_at":"2026-05-26T01:02:48.401370Z","signature_status":"signed_v1","first_computed_at":"2026-05-26T01:02:48.401370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.24141","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":"2026-05-26T01:02:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmP8019484igH2yVUatXkoeKGLmAW7cbXBotVKFdwJwYc6H6Ln1ZCT4itLZnvNUfHqgFVh5M4xyNCA81TmcZBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T15:16:54.499695Z"},"content_sha256":"0d1f622723711b747e8a3aff339d5a03c436feec21edbf8df1c29afac1ad8a50","schema_version":"1.0","event_id":"sha256:0d1f622723711b747e8a3aff339d5a03c436feec21edbf8df1c29afac1ad8a50"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:C2XUTJQCPNPTSCEFYZEONXAL7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Equivariant homotopy dense subsets in the realm of uniform G-ANR spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.GN","authors_text":"Luis A. Mart\\'inez-S\\'anchez, Sergey A. Antonyan","submitted_at":"2026-05-22T19:03:36Z","abstract_excerpt":"Let $G$ be a compact group. The existence of certain $G$-homotopy dense subsets in a metrizable $G$-space $X$ plays a fundamental role, as it is equivalent to $X$ being a $G$-ANR. From this perspective, the present paper develops several applications of this class of $G$-subsets.\n  In particular, we prove that for a compact $G$-space $X$ and a metric space $Y$, the mapping space $C(X,Y)$ is a $G$-UA(N)R if and only if $Y$ is a UA(N)R in the sense of Michael. This result is significant because it enables the construction of examples of Lawson metric $G$-semilattices for which the property of be"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24141","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.24141/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-05-26T01:02:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eKD1RDphQXWUCQFdevnkBPRnxW5W7alnXNkw4JxcxQEBh5q+NaqtPqJ44a5f1K8R43sJwC9SSr0gPPzY8UMRBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T15:16:54.500082Z"},"content_sha256":"d3f548f651ba1c34444093d8be570787a7df8683a10244e6e6b4c8f414e4dc4a","schema_version":"1.0","event_id":"sha256:d3f548f651ba1c34444093d8be570787a7df8683a10244e6e6b4c8f414e4dc4a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C2XUTJQCPNPTSCEFYZEONXAL7R/bundle.json","state_url":"https://pith.science/pith/C2XUTJQCPNPTSCEFYZEONXAL7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C2XUTJQCPNPTSCEFYZEONXAL7R/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":"2026-06-10T15:16:54Z","links":{"resolver":"https://pith.science/pith/C2XUTJQCPNPTSCEFYZEONXAL7R","bundle":"https://pith.science/pith/C2XUTJQCPNPTSCEFYZEONXAL7R/bundle.json","state":"https://pith.science/pith/C2XUTJQCPNPTSCEFYZEONXAL7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C2XUTJQCPNPTSCEFYZEONXAL7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:C2XUTJQCPNPTSCEFYZEONXAL7R","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":"adde0e095355c68448b565f08d6986b7b45243de735f322ad5507e40b0c50656","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GN","submitted_at":"2026-05-22T19:03:36Z","title_canon_sha256":"4ccf3c54fe5df9743a3d62b3263881d94c63482d89008c42aecb09b47950808f"},"schema_version":"1.0","source":{"id":"2605.24141","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.24141","created_at":"2026-05-26T01:02:48Z"},{"alias_kind":"arxiv_version","alias_value":"2605.24141v1","created_at":"2026-05-26T01:02:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.24141","created_at":"2026-05-26T01:02:48Z"},{"alias_kind":"pith_short_12","alias_value":"C2XUTJQCPNPT","created_at":"2026-05-26T01:02:48Z"},{"alias_kind":"pith_short_16","alias_value":"C2XUTJQCPNPTSCEF","created_at":"2026-05-26T01:02:48Z"},{"alias_kind":"pith_short_8","alias_value":"C2XUTJQC","created_at":"2026-05-26T01:02:48Z"}],"graph_snapshots":[{"event_id":"sha256:d3f548f651ba1c34444093d8be570787a7df8683a10244e6e6b4c8f414e4dc4a","target":"graph","created_at":"2026-05-26T01:02:48Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.24141/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G$ be a compact group. The existence of certain $G$-homotopy dense subsets in a metrizable $G$-space $X$ plays a fundamental role, as it is equivalent to $X$ being a $G$-ANR. From this perspective, the present paper develops several applications of this class of $G$-subsets.\n  In particular, we prove that for a compact $G$-space $X$ and a metric space $Y$, the mapping space $C(X,Y)$ is a $G$-UA(N)R if and only if $Y$ is a UA(N)R in the sense of Michael. This result is significant because it enables the construction of examples of Lawson metric $G$-semilattices for which the property of be","authors_text":"Luis A. Mart\\'inez-S\\'anchez, Sergey A. Antonyan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GN","submitted_at":"2026-05-22T19:03:36Z","title":"Equivariant homotopy dense subsets in the realm of uniform G-ANR spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.24141","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":"sha256:0d1f622723711b747e8a3aff339d5a03c436feec21edbf8df1c29afac1ad8a50","target":"record","created_at":"2026-05-26T01:02:48Z","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":"adde0e095355c68448b565f08d6986b7b45243de735f322ad5507e40b0c50656","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.GN","submitted_at":"2026-05-22T19:03:36Z","title_canon_sha256":"4ccf3c54fe5df9743a3d62b3263881d94c63482d89008c42aecb09b47950808f"},"schema_version":"1.0","source":{"id":"2605.24141","kind":"arxiv","version":1}},"canonical_sha256":"16af49a6027b5f390885c648e6dc0bfc5b8b0c68398ff863d9a6f534f83ef320","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16af49a6027b5f390885c648e6dc0bfc5b8b0c68398ff863d9a6f534f83ef320","first_computed_at":"2026-05-26T01:02:48.401370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-26T01:02:48.401370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u/Go/g8h/Vx9vSvjSd1JM/ZYY6zxQFNuulVCA7q/BZvy2JfP4Eg7FLtmMUfunj/Hu0WWiZ0WcRxG2RfeO4bqBA==","signature_status":"signed_v1","signed_at":"2026-05-26T01:02:48.402170Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.24141","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d1f622723711b747e8a3aff339d5a03c436feec21edbf8df1c29afac1ad8a50","sha256:d3f548f651ba1c34444093d8be570787a7df8683a10244e6e6b4c8f414e4dc4a"],"state_sha256":"ca4471a46742884cd6dceb778d3fcb4b4b999c2ae4b74fa25865002bb93d090e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wx5+06GyeTU9uQhspi3MrDXQjF6wR7ryyW2a/iWYSNmiPJS4GJVb2ybY8hTWyRTxKglfDyhzt4JRVV9S9W8YBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T15:16:54.502119Z","bundle_sha256":"5a77dcf3588759a89277bd8e20eae58ce6aa38f95c5e08ff6bfa71330a530778"}}