{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3CZ7WLSPKN22C5OO624AQDU4VT","short_pith_number":"pith:3CZ7WLSP","schema_version":"1.0","canonical_sha256":"d8b3fb2e4f5375a175cef6b8080e9cacf8b59294223639d416f7bd0206ffb133","source":{"kind":"arxiv","id":"2509.00321","version":1},"attestation_state":"computed","paper":{"title":"On the connectedness of the boundary of hierarchically hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ravi Tomar","submitted_at":"2025-08-30T02:47:34Z","abstract_excerpt":"We prove that, under a mild assumption, any metrizable compactification of a one-ended proper geodesic metric space is connected. As a consequence, we deduce that the boundary, introduced by Durham--Hagen--Sisto, of a one-ended hierarchically hyperbolic space is connected. Moreover, we prove that the connectedness of the boundary of a hierarchically hyperbolic group is equivalent to the one-endedness of the group. As an application, we show that if, for $n\\geq 2$, $G_1=A_1\\ast\\dots\\ast A_n$ and $G_2=B_1\\ast\\dots\\ast B_n$ are free products of one-ended hierarchically hyperbolic groups, then the"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2509.00321","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-08-30T02:47:34Z","cross_cats_sorted":[],"title_canon_sha256":"789b306443ae980877fca9c0e83cae7666a77ff99a32433fb8079a6ee122b1db","abstract_canon_sha256":"7ec2914276bf89be1dde0716046be6c1287bd24e270cd2ad7892c5d6e1ac5282"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:02:13.681575Z","signature_b64":"EsmI7jumkw12XxuSatAK8nHH/AeVELCfprTSG7JE5RNKYN8kJ6MAFW45E0iC926z9LdXQRGLDEvG4JbYs7hJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8b3fb2e4f5375a175cef6b8080e9cacf8b59294223639d416f7bd0206ffb133","last_reissued_at":"2026-07-05T12:02:13.680935Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:02:13.680935Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the connectedness of the boundary of hierarchically hyperbolic spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ravi Tomar","submitted_at":"2025-08-30T02:47:34Z","abstract_excerpt":"We prove that, under a mild assumption, any metrizable compactification of a one-ended proper geodesic metric space is connected. As a consequence, we deduce that the boundary, introduced by Durham--Hagen--Sisto, of a one-ended hierarchically hyperbolic space is connected. Moreover, we prove that the connectedness of the boundary of a hierarchically hyperbolic group is equivalent to the one-endedness of the group. As an application, we show that if, for $n\\geq 2$, $G_1=A_1\\ast\\dots\\ast A_n$ and $G_2=B_1\\ast\\dots\\ast B_n$ are free products of one-ended hierarchically hyperbolic groups, then the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.00321","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/2509.00321/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2509.00321","created_at":"2026-07-05T12:02:13.681012+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.00321v1","created_at":"2026-07-05T12:02:13.681012+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.00321","created_at":"2026-07-05T12:02:13.681012+00:00"},{"alias_kind":"pith_short_12","alias_value":"3CZ7WLSPKN22","created_at":"2026-07-05T12:02:13.681012+00:00"},{"alias_kind":"pith_short_16","alias_value":"3CZ7WLSPKN22C5OO","created_at":"2026-07-05T12:02:13.681012+00:00"},{"alias_kind":"pith_short_8","alias_value":"3CZ7WLSP","created_at":"2026-07-05T12:02:13.681012+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3CZ7WLSPKN22C5OO624AQDU4VT","json":"https://pith.science/pith/3CZ7WLSPKN22C5OO624AQDU4VT.json","graph_json":"https://pith.science/api/pith-number/3CZ7WLSPKN22C5OO624AQDU4VT/graph.json","events_json":"https://pith.science/api/pith-number/3CZ7WLSPKN22C5OO624AQDU4VT/events.json","paper":"https://pith.science/paper/3CZ7WLSP"},"agent_actions":{"view_html":"https://pith.science/pith/3CZ7WLSPKN22C5OO624AQDU4VT","download_json":"https://pith.science/pith/3CZ7WLSPKN22C5OO624AQDU4VT.json","view_paper":"https://pith.science/paper/3CZ7WLSP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.00321&json=true","fetch_graph":"https://pith.science/api/pith-number/3CZ7WLSPKN22C5OO624AQDU4VT/graph.json","fetch_events":"https://pith.science/api/pith-number/3CZ7WLSPKN22C5OO624AQDU4VT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3CZ7WLSPKN22C5OO624AQDU4VT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3CZ7WLSPKN22C5OO624AQDU4VT/action/storage_attestation","attest_author":"https://pith.science/pith/3CZ7WLSPKN22C5OO624AQDU4VT/action/author_attestation","sign_citation":"https://pith.science/pith/3CZ7WLSPKN22C5OO624AQDU4VT/action/citation_signature","submit_replication":"https://pith.science/pith/3CZ7WLSPKN22C5OO624AQDU4VT/action/replication_record"}},"created_at":"2026-07-05T12:02:13.681012+00:00","updated_at":"2026-07-05T12:02:13.681012+00:00"}