{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:4TCR3L7TWXDYHWOCRTZM7IZSZG","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":"87dd11d89abfbec9d1424dc219f5193111e3685f62622225cb5584db8ec3c0a2","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-18T13:21:11Z","title_canon_sha256":"4f1cc319f6ce23309f13f2e158d9fe4729ad5700eba0b34d9273940314326958"},"schema_version":"1.0","source":{"id":"2607.16817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.16817","created_at":"2026-07-21T01:21:00Z"},{"alias_kind":"arxiv_version","alias_value":"2607.16817v1","created_at":"2026-07-21T01:21:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.16817","created_at":"2026-07-21T01:21:00Z"},{"alias_kind":"pith_short_12","alias_value":"4TCR3L7TWXDY","created_at":"2026-07-21T01:21:00Z"},{"alias_kind":"pith_short_16","alias_value":"4TCR3L7TWXDYHWOC","created_at":"2026-07-21T01:21:00Z"},{"alias_kind":"pith_short_8","alias_value":"4TCR3L7T","created_at":"2026-07-21T01:21:00Z"}],"graph_snapshots":[{"event_id":"sha256:97312ee049c8cdc6f791ded8e4a71b227752cf4bf6ffe636b6d446f34097d2cf","target":"graph","created_at":"2026-07-21T01:21:00Z","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/2607.16817/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that forward ideal sub-Finslerian manifolds support interpolation inequalities for optimal transport, extending the results of Barilari and Rizzi, arXiv:1705.05380, from the sub-Riemannian to the sub-Finslerian setting. A key role is played by the introduction of sub-Finslerian Jacobi fields and the establishment of optimal transport theory on sub-Finslerian manifolds. By combining this transport framework with sub-Finslerian Jacobian estimates, we characterize the generalized distortion coefficients. As an application, we deduce several fundamental geometric inequaliti","authors_text":"Haowei Lin","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-18T13:21:11Z","title":"Sub-Finslerian Interpolation Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.16817","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:bf7add5c55e3745f05a268eb8838fb2c09829ab674628cb95e61d503ecc26c83","target":"record","created_at":"2026-07-21T01:21:00Z","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":"87dd11d89abfbec9d1424dc219f5193111e3685f62622225cb5584db8ec3c0a2","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2026-07-18T13:21:11Z","title_canon_sha256":"4f1cc319f6ce23309f13f2e158d9fe4729ad5700eba0b34d9273940314326958"},"schema_version":"1.0","source":{"id":"2607.16817","kind":"arxiv","version":1}},"canonical_sha256":"e4c51daff3b5c783d9c28cf2cfa332c9827d8bb45d61399d29a8b481721e44c0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e4c51daff3b5c783d9c28cf2cfa332c9827d8bb45d61399d29a8b481721e44c0","first_computed_at":"2026-07-21T01:21:00.390340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-21T01:21:00.390340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5rjPAos7xv0aSSf/8RXJXcoVWWri/b8BPmzXXWY/gpb51WCOU+XJ4iQj67vir64eWXBPxYc5VTTgbOkS/P29Dg==","signature_status":"signed_v1","signed_at":"2026-07-21T01:21:00.391171Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.16817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bf7add5c55e3745f05a268eb8838fb2c09829ab674628cb95e61d503ecc26c83","sha256:97312ee049c8cdc6f791ded8e4a71b227752cf4bf6ffe636b6d446f34097d2cf"],"state_sha256":"5fdb96e6bf6e594efa49929f2b328bad88de18ecb1b1133e0d75f9fcd9970e7c"}