{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7ZISS3T3X2DFXR6JHWMJ4VS4SY","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":"d1c16113ffb5f9d58168298f21aac54ac4726b717887f59c93440a0f4b11cdb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-21T07:00:17Z","title_canon_sha256":"dbbcba4244fa403e0d68d6b263b995b6474fab0cd3fc7f09eb2391b81f551725"},"schema_version":"1.0","source":{"id":"2605.22065","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22065","created_at":"2026-05-22T01:04:23Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22065v1","created_at":"2026-05-22T01:04:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22065","created_at":"2026-05-22T01:04:23Z"},{"alias_kind":"pith_short_12","alias_value":"7ZISS3T3X2DF","created_at":"2026-05-22T01:04:23Z"},{"alias_kind":"pith_short_16","alias_value":"7ZISS3T3X2DFXR6J","created_at":"2026-05-22T01:04:23Z"},{"alias_kind":"pith_short_8","alias_value":"7ZISS3T3","created_at":"2026-05-22T01:04:23Z"}],"graph_snapshots":[{"event_id":"sha256:1210492a3d535ec8aecb74c9637fe855e183cffcc84eeda25873667b9d5976f4","target":"graph","created_at":"2026-05-22T01:04:23Z","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/2605.22065/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We provide a complete description of the automorphism group $\\Aut (W)$ of a Coxeter group $W$ admitting a star-shaped finite Coxeter diagram. We prove that each automorphism decomposes as a product of inner and diagram automorphisms, along with three additional types: transvections and two families of partial conjugations. Furthermore, we investigate the natural short exact sequence $1 \\to \\Inn (W) \\to \\Aut (W) \\to \\Out (W) \\to 1$. Using Moussong's criteria for hyperbolicity, we show that these groups possess the $R_\\infty$-property. Finally, we establish rigidity properties for these groups u","authors_text":"A Rameswar Patro, Arijit Mahato, Tushar Kanta Naik","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-21T07:00:17Z","title":"Symmetry and Rigidity of Star-Shaped Coxeter Systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22065","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:d567fbea6096e976aa8243ca4f8adb78431138c2e9e7ebb88d70d642e35cf457","target":"record","created_at":"2026-05-22T01:04:23Z","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":"d1c16113ffb5f9d58168298f21aac54ac4726b717887f59c93440a0f4b11cdb3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2026-05-21T07:00:17Z","title_canon_sha256":"dbbcba4244fa403e0d68d6b263b995b6474fab0cd3fc7f09eb2391b81f551725"},"schema_version":"1.0","source":{"id":"2605.22065","kind":"arxiv","version":1}},"canonical_sha256":"fe51296e7bbe865bc7c93d989e565c96374356342f00cbde782446880a66819a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe51296e7bbe865bc7c93d989e565c96374356342f00cbde782446880a66819a","first_computed_at":"2026-05-22T01:04:23.427259Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:23.427259Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YrKy3oh067v0s5JoXlCfFuaxSnz3Wp3/h+65LnSzCll+mBme8GTIrlOCKRhX1NKy+gaE3omDCCIHO6DIEQrpDw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:23.428117Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22065","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d567fbea6096e976aa8243ca4f8adb78431138c2e9e7ebb88d70d642e35cf457","sha256:1210492a3d535ec8aecb74c9637fe855e183cffcc84eeda25873667b9d5976f4"],"state_sha256":"64d12fca0a4532fdfbb26075d7109535b4ce5051e74e6748b88ff9d3f0125b94"}