{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:XUTZBGUE6Z6QRQBLNSPS5GFS6P","short_pith_number":"pith:XUTZBGUE","canonical_record":{"source":{"id":"2101.02619","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2021-01-07T16:40:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0dcfc0881f9868dd54ecbaf4b644acd21c8739a4e5aaf3986f2b81c4d89761cf","abstract_canon_sha256":"83303b89dd40cca625bbf08991d771a0f8ea7814b779299f214a33280ef2476b"},"schema_version":"1.0"},"canonical_sha256":"bd27909a84f67d08c02b6c9f2e98b2f3ef0c2d291f3b612ba4f5596522d9a620","source":{"kind":"arxiv","id":"2101.02619","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.02619","created_at":"2026-07-05T02:05:15Z"},{"alias_kind":"arxiv_version","alias_value":"2101.02619v1","created_at":"2026-07-05T02:05:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.02619","created_at":"2026-07-05T02:05:15Z"},{"alias_kind":"pith_short_12","alias_value":"XUTZBGUE6Z6Q","created_at":"2026-07-05T02:05:15Z"},{"alias_kind":"pith_short_16","alias_value":"XUTZBGUE6Z6QRQBL","created_at":"2026-07-05T02:05:15Z"},{"alias_kind":"pith_short_8","alias_value":"XUTZBGUE","created_at":"2026-07-05T02:05:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:XUTZBGUE6Z6QRQBLNSPS5GFS6P","target":"record","payload":{"canonical_record":{"source":{"id":"2101.02619","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2021-01-07T16:40:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"0dcfc0881f9868dd54ecbaf4b644acd21c8739a4e5aaf3986f2b81c4d89761cf","abstract_canon_sha256":"83303b89dd40cca625bbf08991d771a0f8ea7814b779299f214a33280ef2476b"},"schema_version":"1.0"},"canonical_sha256":"bd27909a84f67d08c02b6c9f2e98b2f3ef0c2d291f3b612ba4f5596522d9a620","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:05:15.511818Z","signature_b64":"rp5+KT2x/WVqPWJzROr4d1tMnfh8ravTK3RQhvGY/ZfudquNibgo39sp0w8GgSW94vQDzrdBos6kcSUABFlUBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd27909a84f67d08c02b6c9f2e98b2f3ef0c2d291f3b612ba4f5596522d9a620","last_reissued_at":"2026-07-05T02:05:15.511475Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:05:15.511475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2101.02619","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":"2026-07-05T02:05:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Wftq95fuGv1auV2dxe6SUjkWUZa/uYkaaKAXciJWIEO7Luzhw8WrOHfvJtv7KG3YX+M/gJrqwpurRIHGtEA3DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:47:32.614392Z"},"content_sha256":"5bfa25b51f43931f6c5ae9785c46bb91675b0fb161a0bbe686af88c15d225b84","schema_version":"1.0","event_id":"sha256:5bfa25b51f43931f6c5ae9785c46bb91675b0fb161a0bbe686af88c15d225b84"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:XUTZBGUE6Z6QRQBLNSPS5GFS6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Definable Equivariant Retractions in Non-Archimedean Geometry","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.LO","authors_text":"Ehud Hrushovski, Martin Hils, Pierre Simon","submitted_at":"2021-01-07T16:40:11Z","abstract_excerpt":"For $G$ an algebraic group definable over a model of $\\operatorname{ACVF}$, or more generally a definable subgroup of an algebraic group, we study the stable completion $\\widehat{G}$ of $G$, as introduced by Loeser and the second author. For $G$ connected and stably dominated, assuming $G$ commutative or that the valued field is of equicharacteristic 0, we construct a pro-definable $G$-equivariant strong deformation retraction of $\\widehat{G}$ onto the generic type of $G$.\n  For $G=S$ a semiabelian variety, we construct a pro-definable $S$-equivariant strong deformation retraction of $\\widehat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.02619","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/2101.02619/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":"2026-07-05T02:05:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ryVf8ag3D8t/ttOW0Z9x/XqrwjTvYmBmgKo/gsJDmjVU+o/V6zs5u8eFY7N4QgcgKO5sqi1Xx3Y0x+ddjq1nAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T19:47:32.615488Z"},"content_sha256":"04eac6dbcef501e219fed68de33093b52a208af0e6f96d12ef49427ac444ac1a","schema_version":"1.0","event_id":"sha256:04eac6dbcef501e219fed68de33093b52a208af0e6f96d12ef49427ac444ac1a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XUTZBGUE6Z6QRQBLNSPS5GFS6P/bundle.json","state_url":"https://pith.science/pith/XUTZBGUE6Z6QRQBLNSPS5GFS6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XUTZBGUE6Z6QRQBLNSPS5GFS6P/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":"2026-08-08T19:47:32Z","links":{"resolver":"https://pith.science/pith/XUTZBGUE6Z6QRQBLNSPS5GFS6P","bundle":"https://pith.science/pith/XUTZBGUE6Z6QRQBLNSPS5GFS6P/bundle.json","state":"https://pith.science/pith/XUTZBGUE6Z6QRQBLNSPS5GFS6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XUTZBGUE6Z6QRQBLNSPS5GFS6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:XUTZBGUE6Z6QRQBLNSPS5GFS6P","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":"83303b89dd40cca625bbf08991d771a0f8ea7814b779299f214a33280ef2476b","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2021-01-07T16:40:11Z","title_canon_sha256":"0dcfc0881f9868dd54ecbaf4b644acd21c8739a4e5aaf3986f2b81c4d89761cf"},"schema_version":"1.0","source":{"id":"2101.02619","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2101.02619","created_at":"2026-07-05T02:05:15Z"},{"alias_kind":"arxiv_version","alias_value":"2101.02619v1","created_at":"2026-07-05T02:05:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2101.02619","created_at":"2026-07-05T02:05:15Z"},{"alias_kind":"pith_short_12","alias_value":"XUTZBGUE6Z6Q","created_at":"2026-07-05T02:05:15Z"},{"alias_kind":"pith_short_16","alias_value":"XUTZBGUE6Z6QRQBL","created_at":"2026-07-05T02:05:15Z"},{"alias_kind":"pith_short_8","alias_value":"XUTZBGUE","created_at":"2026-07-05T02:05:15Z"}],"graph_snapshots":[{"event_id":"sha256:04eac6dbcef501e219fed68de33093b52a208af0e6f96d12ef49427ac444ac1a","target":"graph","created_at":"2026-07-05T02:05:15Z","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/2101.02619/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"For $G$ an algebraic group definable over a model of $\\operatorname{ACVF}$, or more generally a definable subgroup of an algebraic group, we study the stable completion $\\widehat{G}$ of $G$, as introduced by Loeser and the second author. For $G$ connected and stably dominated, assuming $G$ commutative or that the valued field is of equicharacteristic 0, we construct a pro-definable $G$-equivariant strong deformation retraction of $\\widehat{G}$ onto the generic type of $G$.\n  For $G=S$ a semiabelian variety, we construct a pro-definable $S$-equivariant strong deformation retraction of $\\widehat","authors_text":"Ehud Hrushovski, Martin Hils, Pierre Simon","cross_cats":["math.AG"],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2021-01-07T16:40:11Z","title":"Definable Equivariant Retractions in Non-Archimedean Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2101.02619","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":"sha256:5bfa25b51f43931f6c5ae9785c46bb91675b0fb161a0bbe686af88c15d225b84","target":"record","created_at":"2026-07-05T02:05:15Z","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":"83303b89dd40cca625bbf08991d771a0f8ea7814b779299f214a33280ef2476b","cross_cats_sorted":["math.AG"],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.LO","submitted_at":"2021-01-07T16:40:11Z","title_canon_sha256":"0dcfc0881f9868dd54ecbaf4b644acd21c8739a4e5aaf3986f2b81c4d89761cf"},"schema_version":"1.0","source":{"id":"2101.02619","kind":"arxiv","version":1}},"canonical_sha256":"bd27909a84f67d08c02b6c9f2e98b2f3ef0c2d291f3b612ba4f5596522d9a620","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd27909a84f67d08c02b6c9f2e98b2f3ef0c2d291f3b612ba4f5596522d9a620","first_computed_at":"2026-07-05T02:05:15.511475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:05:15.511475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rp5+KT2x/WVqPWJzROr4d1tMnfh8ravTK3RQhvGY/ZfudquNibgo39sp0w8GgSW94vQDzrdBos6kcSUABFlUBg==","signature_status":"signed_v1","signed_at":"2026-07-05T02:05:15.511818Z","signed_message":"canonical_sha256_bytes"},"source_id":"2101.02619","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5bfa25b51f43931f6c5ae9785c46bb91675b0fb161a0bbe686af88c15d225b84","sha256:04eac6dbcef501e219fed68de33093b52a208af0e6f96d12ef49427ac444ac1a"],"state_sha256":"d3c8ecce573d8443517971f39e1a7968864593660474226569b8d89bf4ba5335"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZdbwKxtUo/PzsRnT1Y99rUHs/9hylc1X8cSuirAgcVPVb7w/EbH3KrPoGHdmtNOJ0kFr+wXmawGacXYOy38dAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T19:47:32.622839Z","bundle_sha256":"89b533d396334f3c854f0f2ed524f01f9fcaee2b823b26d9d616e35fede1e984"}}