{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:3YZ44Y3HQ5VCDMVGKRMPHGYZAP","short_pith_number":"pith:3YZ44Y3H","schema_version":"1.0","canonical_sha256":"de33ce6367876a21b2a65458f39b1903f2b75c6b2155a53eab895f7d0e1f9ca2","source":{"kind":"arxiv","id":"2507.12676","version":1},"attestation_state":"computed","paper":{"title":"Spaces of left-preorders on free products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Iv\\'an Ch\\'ercoles Cuesta","submitted_at":"2025-07-16T23:26:30Z","abstract_excerpt":"Using dynamical techniques we show that there are no isolated elements on the space of left-preorders on a free product of two groups. As a consequence, when the groups are finitely generated, this space is either empty or a Cantor set. For any subgroup of a free product having finite Kurosh rank, we develop similar results for the subspace consisting on the set of left-preorders relative to that subgroup. We provide a generating set for a certain intersection of subgroups of a free product."},"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":"2507.12676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2025-07-16T23:26:30Z","cross_cats_sorted":[],"title_canon_sha256":"77e0c3686bb4fb492cdad45338b51c63929973ac869e198e14f8faf212260e54","abstract_canon_sha256":"418691aafea70de159b8a61ac9531d9e688f3dbdf33ea5182629052ac171b9c8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:38:37.102073Z","signature_b64":"aZjecRJerbVvKbwpZ3Yk6fgy6XIPuPSXU1ifWsX2aPVqAaVzCvbFt4+lFPfrpeQthTArk3QEXRrpJkexyrP5AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"de33ce6367876a21b2a65458f39b1903f2b75c6b2155a53eab895f7d0e1f9ca2","last_reissued_at":"2026-07-05T11:38:37.101613Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:38:37.101613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Spaces of left-preorders on free products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Iv\\'an Ch\\'ercoles Cuesta","submitted_at":"2025-07-16T23:26:30Z","abstract_excerpt":"Using dynamical techniques we show that there are no isolated elements on the space of left-preorders on a free product of two groups. As a consequence, when the groups are finitely generated, this space is either empty or a Cantor set. For any subgroup of a free product having finite Kurosh rank, we develop similar results for the subspace consisting on the set of left-preorders relative to that subgroup. We provide a generating set for a certain intersection of subgroups of a free product."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.12676","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/2507.12676/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":"2507.12676","created_at":"2026-07-05T11:38:37.101681+00:00"},{"alias_kind":"arxiv_version","alias_value":"2507.12676v1","created_at":"2026-07-05T11:38:37.101681+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2507.12676","created_at":"2026-07-05T11:38:37.101681+00:00"},{"alias_kind":"pith_short_12","alias_value":"3YZ44Y3HQ5VC","created_at":"2026-07-05T11:38:37.101681+00:00"},{"alias_kind":"pith_short_16","alias_value":"3YZ44Y3HQ5VCDMVG","created_at":"2026-07-05T11:38:37.101681+00:00"},{"alias_kind":"pith_short_8","alias_value":"3YZ44Y3H","created_at":"2026-07-05T11:38:37.101681+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/3YZ44Y3HQ5VCDMVGKRMPHGYZAP","json":"https://pith.science/pith/3YZ44Y3HQ5VCDMVGKRMPHGYZAP.json","graph_json":"https://pith.science/api/pith-number/3YZ44Y3HQ5VCDMVGKRMPHGYZAP/graph.json","events_json":"https://pith.science/api/pith-number/3YZ44Y3HQ5VCDMVGKRMPHGYZAP/events.json","paper":"https://pith.science/paper/3YZ44Y3H"},"agent_actions":{"view_html":"https://pith.science/pith/3YZ44Y3HQ5VCDMVGKRMPHGYZAP","download_json":"https://pith.science/pith/3YZ44Y3HQ5VCDMVGKRMPHGYZAP.json","view_paper":"https://pith.science/paper/3YZ44Y3H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2507.12676&json=true","fetch_graph":"https://pith.science/api/pith-number/3YZ44Y3HQ5VCDMVGKRMPHGYZAP/graph.json","fetch_events":"https://pith.science/api/pith-number/3YZ44Y3HQ5VCDMVGKRMPHGYZAP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3YZ44Y3HQ5VCDMVGKRMPHGYZAP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3YZ44Y3HQ5VCDMVGKRMPHGYZAP/action/storage_attestation","attest_author":"https://pith.science/pith/3YZ44Y3HQ5VCDMVGKRMPHGYZAP/action/author_attestation","sign_citation":"https://pith.science/pith/3YZ44Y3HQ5VCDMVGKRMPHGYZAP/action/citation_signature","submit_replication":"https://pith.science/pith/3YZ44Y3HQ5VCDMVGKRMPHGYZAP/action/replication_record"}},"created_at":"2026-07-05T11:38:37.101681+00:00","updated_at":"2026-07-05T11:38:37.101681+00:00"}