{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:PHDVFAFDLIRJTUWFV6ZRS7IKW3","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":"c22c59342b4194462c33c3958c0d71cbd0d2ca1e7bc6b74f9668a4a579c1b6be","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2024-12-22T13:56:01Z","title_canon_sha256":"d545542e53961cad8de5a500b777b4e101e796e51da8c38518b2760a3dbf174e"},"schema_version":"1.0","source":{"id":"2501.01970","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.01970","created_at":"2026-07-05T11:44:00Z"},{"alias_kind":"arxiv_version","alias_value":"2501.01970v3","created_at":"2026-07-05T11:44:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01970","created_at":"2026-07-05T11:44:00Z"},{"alias_kind":"pith_short_12","alias_value":"PHDVFAFDLIRJ","created_at":"2026-07-05T11:44:00Z"},{"alias_kind":"pith_short_16","alias_value":"PHDVFAFDLIRJTUWF","created_at":"2026-07-05T11:44:00Z"},{"alias_kind":"pith_short_8","alias_value":"PHDVFAFD","created_at":"2026-07-05T11:44:00Z"}],"graph_snapshots":[{"event_id":"sha256:2e0876f77d039b9af7e1859620552c5854b7fb26e4bc180b8239c4c4e3a65411","target":"graph","created_at":"2026-07-05T11:44:00Z","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/2501.01970/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This manuscript investigates the curvature and topological properties of certain $\\infty$-Einstein Finsler metrics on Finsler metric measure spaces. By imposing symmetry conditions, we construct a series of special metrics and analyze their equivalence on special manifolds. Provided a Ricci curvature bound, we establish a linear growth lower bound estimate for the S-curvature and the distortion, revealing the interplay between curvature and measure on $\\infty$-Einstein Finsler manifolds. Furthermore, by introducing scalar curvature and imposing a linear growth lower bound condition, we derive ","authors_text":"Bin Shen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2024-12-22T13:56:01Z","title":"Bounds of Scalar curvature, S-curvature and distortion on $\\infty$-Einstein Finsler manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01970","kind":"arxiv","version":3},"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:a608938ca773ea80b75c3ad2a42611a5c9d7c26affc442637a10216ae129653f","target":"record","created_at":"2026-07-05T11:44:00Z","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":"c22c59342b4194462c33c3958c0d71cbd0d2ca1e7bc6b74f9668a4a579c1b6be","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.DG","submitted_at":"2024-12-22T13:56:01Z","title_canon_sha256":"d545542e53961cad8de5a500b777b4e101e796e51da8c38518b2760a3dbf174e"},"schema_version":"1.0","source":{"id":"2501.01970","kind":"arxiv","version":3}},"canonical_sha256":"79c75280a35a2299d2c5afb3197d0ab6efbcde1b69b3656fce239e8b6f5ab6b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"79c75280a35a2299d2c5afb3197d0ab6efbcde1b69b3656fce239e8b6f5ab6b9","first_computed_at":"2026-07-05T11:44:00.133880Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:44:00.133880Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hOU15kv/r0tX3ytfc09YvW0kHTN59e1zx3ngF2e3xhgkpNlFo29SBC0uAGSuVrbVTwR8hueDBnflO5oyjx3/Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:44:00.134384Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.01970","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a608938ca773ea80b75c3ad2a42611a5c9d7c26affc442637a10216ae129653f","sha256:2e0876f77d039b9af7e1859620552c5854b7fb26e4bc180b8239c4c4e3a65411"],"state_sha256":"deeed39e594f2bfd5f3bbdde1559e9ee1877fc2d0bf6c23cb9ee8cd04e4ce83c"}