{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:AAOK37HDKTWFA2GBFCVKR7FKHH","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":"efbbc04aacf19dbd60a7e12236e578f60f565e0417979c50472bf2141d446ab8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-06-18T16:10:04Z","title_canon_sha256":"8d5ebdabd4e167ce55ec88c5490f9bb6e5ff914d17902225bae5da92a7f6ac96"},"schema_version":"1.0","source":{"id":"2606.20429","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.20429","created_at":"2026-06-19T16:13:12Z"},{"alias_kind":"arxiv_version","alias_value":"2606.20429v1","created_at":"2026-06-19T16:13:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.20429","created_at":"2026-06-19T16:13:12Z"},{"alias_kind":"pith_short_12","alias_value":"AAOK37HDKTWF","created_at":"2026-06-19T16:13:12Z"},{"alias_kind":"pith_short_16","alias_value":"AAOK37HDKTWFA2GB","created_at":"2026-06-19T16:13:12Z"},{"alias_kind":"pith_short_8","alias_value":"AAOK37HD","created_at":"2026-06-19T16:13:12Z"}],"graph_snapshots":[{"event_id":"sha256:18c399cfb758fd9c6ab98415673923f107e94ed142979c79aa6c5783cc405028","target":"graph","created_at":"2026-06-19T16:13:12Z","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/2606.20429/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the $G$-Daugavet property ($G$-DPr, for short) for Banach spaces endowed with an action of a group $G$ by surjective linear isometries. This notion provides a common framework for the classical Daugavet property and the alternative Daugavet property, which correspond respectively to the trivial action and to the scalar action of $S_{\\mathbb{K}}$. We establish several characterizations of the $G$-DPr in terms of $G$-slices and closed convex $G$-invariant hulls, recovering the usual slice descriptions of the DPr and the aDPr as particular cases. We show that the presence of a group ","authors_text":"Helena del R\\'io, Sheldon Dantas, Tom\\'a\\v{s} Raunig","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-06-18T16:10:04Z","title":"A group action approach to the Daugavet property"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.20429","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:e0e9f844d78ebceca4328247981291896818f8489c6d8596af76a03e662df554","target":"record","created_at":"2026-06-19T16:13:12Z","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":"efbbc04aacf19dbd60a7e12236e578f60f565e0417979c50472bf2141d446ab8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.FA","submitted_at":"2026-06-18T16:10:04Z","title_canon_sha256":"8d5ebdabd4e167ce55ec88c5490f9bb6e5ff914d17902225bae5da92a7f6ac96"},"schema_version":"1.0","source":{"id":"2606.20429","kind":"arxiv","version":1}},"canonical_sha256":"001cadfce354ec5068c128aaa8fcaa39c706714814246ea8695dbab26eac76cc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"001cadfce354ec5068c128aaa8fcaa39c706714814246ea8695dbab26eac76cc","first_computed_at":"2026-06-19T16:13:12.233782Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:13:12.233782Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6v6P93v7Htl1YpWsHuEjgyxJNcLq6JBKv5VYln4w5AWWw8q48kG3VSv5tML2TI4M4Z3Ca3qnQhVqbhSdahf5CQ==","signature_status":"signed_v1","signed_at":"2026-06-19T16:13:12.234177Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.20429","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e0e9f844d78ebceca4328247981291896818f8489c6d8596af76a03e662df554","sha256:18c399cfb758fd9c6ab98415673923f107e94ed142979c79aa6c5783cc405028"],"state_sha256":"b256ebd1e2cd57d09251d32febb1987824bb4655c5d478b1a7c44cd27bfb7af6"}