{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:A3XWDFC7CA2TZFQ6N2QILWQTZG","short_pith_number":"pith:A3XWDFC7","schema_version":"1.0","canonical_sha256":"06ef61945f10353c961e6ea085da13c9a1f26d8a68db6a6a229f96b5e86a7a8a","source":{"kind":"arxiv","id":"1508.02148","version":1},"attestation_state":"computed","paper":{"title":"On compact Ricci solitons in Finsler geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Behroz Bidabad, Mohamad Yar Ahmadi","submitted_at":"2015-08-10T07:28:51Z","abstract_excerpt":"Ricci solitons on Finsler spaces, previously developed by the present authors, are a generalization of Einstein spaces, which can be considered as a solution to the Ricci flow on compact Finsler manifolds. In the present work it is shown that on a Finslerian space, a forward complete shrinking Ricci soliton is compact if and only if it is bounded. Moreover, it is proved that a compact shrinking Finslerian Ricci soliton has finite fundamental group and hence the first de Rham cohomology group vanishes."},"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":"1508.02148","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2015-08-10T07:28:51Z","cross_cats_sorted":[],"title_canon_sha256":"4f97a05b0c1bebf872cdcdfa6fb7f5bfe8019a2ed92cd95a52ffc5f19a2433c4","abstract_canon_sha256":"cc4a9851b62f8cd3302406d6a0ba3f70ae596dec42ce7255c29efba3f82abf4d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:34.058242Z","signature_b64":"osGSPla1F5oY7Hnq5MpZ/V/eeWzDlQ3S1NuBVhMP/o8mLgJHvYl59kIoOKRnc4LbjHMoNxG2xMEifjoIox6oAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06ef61945f10353c961e6ea085da13c9a1f26d8a68db6a6a229f96b5e86a7a8a","last_reissued_at":"2026-05-18T01:35:34.057525Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:34.057525Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On compact Ricci solitons in Finsler geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Behroz Bidabad, Mohamad Yar Ahmadi","submitted_at":"2015-08-10T07:28:51Z","abstract_excerpt":"Ricci solitons on Finsler spaces, previously developed by the present authors, are a generalization of Einstein spaces, which can be considered as a solution to the Ricci flow on compact Finsler manifolds. In the present work it is shown that on a Finslerian space, a forward complete shrinking Ricci soliton is compact if and only if it is bounded. Moreover, it is proved that a compact shrinking Finslerian Ricci soliton has finite fundamental group and hence the first de Rham cohomology group vanishes."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02148","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":""},"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":"1508.02148","created_at":"2026-05-18T01:35:34.057643+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.02148v1","created_at":"2026-05-18T01:35:34.057643+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02148","created_at":"2026-05-18T01:35:34.057643+00:00"},{"alias_kind":"pith_short_12","alias_value":"A3XWDFC7CA2T","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_16","alias_value":"A3XWDFC7CA2TZFQ6","created_at":"2026-05-18T12:29:10.953037+00:00"},{"alias_kind":"pith_short_8","alias_value":"A3XWDFC7","created_at":"2026-05-18T12:29:10.953037+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/A3XWDFC7CA2TZFQ6N2QILWQTZG","json":"https://pith.science/pith/A3XWDFC7CA2TZFQ6N2QILWQTZG.json","graph_json":"https://pith.science/api/pith-number/A3XWDFC7CA2TZFQ6N2QILWQTZG/graph.json","events_json":"https://pith.science/api/pith-number/A3XWDFC7CA2TZFQ6N2QILWQTZG/events.json","paper":"https://pith.science/paper/A3XWDFC7"},"agent_actions":{"view_html":"https://pith.science/pith/A3XWDFC7CA2TZFQ6N2QILWQTZG","download_json":"https://pith.science/pith/A3XWDFC7CA2TZFQ6N2QILWQTZG.json","view_paper":"https://pith.science/paper/A3XWDFC7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.02148&json=true","fetch_graph":"https://pith.science/api/pith-number/A3XWDFC7CA2TZFQ6N2QILWQTZG/graph.json","fetch_events":"https://pith.science/api/pith-number/A3XWDFC7CA2TZFQ6N2QILWQTZG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/A3XWDFC7CA2TZFQ6N2QILWQTZG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/A3XWDFC7CA2TZFQ6N2QILWQTZG/action/storage_attestation","attest_author":"https://pith.science/pith/A3XWDFC7CA2TZFQ6N2QILWQTZG/action/author_attestation","sign_citation":"https://pith.science/pith/A3XWDFC7CA2TZFQ6N2QILWQTZG/action/citation_signature","submit_replication":"https://pith.science/pith/A3XWDFC7CA2TZFQ6N2QILWQTZG/action/replication_record"}},"created_at":"2026-05-18T01:35:34.057643+00:00","updated_at":"2026-05-18T01:35:34.057643+00:00"}