{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BJWXIQRW455YYRFRJTTM66PEMJ","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":"ca869226e7af9c7d898c33fc873f2c9327a5c1a9e87165e53fd9a2f7ad0ddd69","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T07:09:47Z","title_canon_sha256":"ae17cdccfc5b4cbd23ecfb15e8d8a634fdd32ad4b7f9e17caa634dd665babf71"},"schema_version":"1.0","source":{"id":"1310.0911","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0911","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0911v2","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0911","created_at":"2026-05-18T03:05:01Z"},{"alias_kind":"pith_short_12","alias_value":"BJWXIQRW455Y","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BJWXIQRW455YYRFR","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BJWXIQRW","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:13bc81f6001415a9a382d2da0f5dd5fd0f83083d92f29629422a0643ee58453d","target":"graph","created_at":"2026-05-18T03:05:01Z","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"},"paper":{"abstract_excerpt":"In this paper we provide the small-time heat kernel asymptotics at the cut locus in three relevant cases: generic low-dimensional Riemannian manifolds, generic 3D contact sub-Riemannian manifolds (close to the starting point) and generic 4D quasi-contact sub-Riemannian manifolds (close to a generic starting point). As a byproduct, we show that, for generic low-dimensional Riemannian manifolds, the only singularities of the exponential map, as a Lagragian map, that can arise along a minimizing geodesic are $A_3$ and $A_5$ (in the classification of Arnol'd's school). We show that in the non-gene","authors_text":"Davide Barilari, Gr\\'egoire Charlot, Robert W. Neel, Ugo Boscain","cross_cats":["math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T07:09:47Z","title":"On the heat diffusion for generic Riemannian and sub-Riemannian structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0911","kind":"arxiv","version":2},"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":"sha256:367f023b7b80cff1414caaf3d9a72b5b2e74fc62ed6cfd062b5c96b2810f7d19","target":"record","created_at":"2026-05-18T03:05:01Z","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":"ca869226e7af9c7d898c33fc873f2c9327a5c1a9e87165e53fd9a2f7ad0ddd69","cross_cats_sorted":["math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2013-10-03T07:09:47Z","title_canon_sha256":"ae17cdccfc5b4cbd23ecfb15e8d8a634fdd32ad4b7f9e17caa634dd665babf71"},"schema_version":"1.0","source":{"id":"1310.0911","kind":"arxiv","version":2}},"canonical_sha256":"0a6d744236e77b8c44b14ce6cf79e4626075ab859f4263f0737a0569ab9161e6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a6d744236e77b8c44b14ce6cf79e4626075ab859f4263f0737a0569ab9161e6","first_computed_at":"2026-05-18T03:05:01.141869Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:01.141869Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MI1aGrMokWHHUC+VrSC86ub9PH8UphpaQR8n01jCXKX0zS96yp6kVQntlJu8VTvPFYHYOXjqluMTByngxADFDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:01.142444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0911","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:367f023b7b80cff1414caaf3d9a72b5b2e74fc62ed6cfd062b5c96b2810f7d19","sha256:13bc81f6001415a9a382d2da0f5dd5fd0f83083d92f29629422a0643ee58453d"],"state_sha256":"d791ffa5951ee0d26ecd2cea765cc5507e858c6837c51b9220de8700f348d050"}