{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:I4XNQTIYKPY4DOW3URCMFMDBKY","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":"b211cd0687ce5092a149ea219f0302323fe567a08bbcdd7c647d41b5f88e4ea4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T09:45:41Z","title_canon_sha256":"0e35c148afc391573d471dca540c120b00f3c89f23a6ce5ca96d5779784f7c24"},"schema_version":"1.0","source":{"id":"2606.30055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.30055","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"arxiv_version","alias_value":"2606.30055v1","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30055","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"pith_short_12","alias_value":"I4XNQTIYKPY4","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"pith_short_16","alias_value":"I4XNQTIYKPY4DOW3","created_at":"2026-06-30T02:17:47Z"},{"alias_kind":"pith_short_8","alias_value":"I4XNQTIY","created_at":"2026-06-30T02:17:47Z"}],"graph_snapshots":[{"event_id":"sha256:f42c01601d746cc3ca9d8d3b00143265ca4ea01ab305650d30520b9745227d54","target":"graph","created_at":"2026-06-30T02:17:47Z","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/2606.30055/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove~\\cite[Conjecture 2.12]{BGS20} on the signature tail asymptotics of pure rough paths and extend it to arbitrary reasonable tensor norms. In more details, let \\[ \\mathbf X_t=\\exp(tl) \\,\\text{ with }\\, l=l_1+\\cdots+l_m\\,\\text{ and }\\, l_r\\in\\mathcal L_r(V), \\] be a pure $m$-rough path over a finite dimensional real or complex Banach space, and equip the tensor powers of $V$ with arbitrary reasonable tensor algebra norms. We prove that \\[ \\limsup_{n\\to\\infty}\\left(\\left(\\frac{n}{m}\\right)!\\left\\|\\pi_n(\\exp l)\\right\\|_n\\right)^{m/n}=\\|l_m\\|_m . \\] In particular, this identifies the signatu","authors_text":"Nannan Li, Xing Gao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T09:45:41Z","title":"Exact Signature Tail Asymptotics for Pure Rough Paths"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30055","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":"sha256:468acd14c4cfd08db06b1132a64b14bdb0ad88f550e9c3b29dc187dead350e04","target":"record","created_at":"2026-06-30T02:17:47Z","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":"b211cd0687ce5092a149ea219f0302323fe567a08bbcdd7c647d41b5f88e4ea4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2026-06-29T09:45:41Z","title_canon_sha256":"0e35c148afc391573d471dca540c120b00f3c89f23a6ce5ca96d5779784f7c24"},"schema_version":"1.0","source":{"id":"2606.30055","kind":"arxiv","version":1}},"canonical_sha256":"472ed84d1853f1c1badba444c2b061563785982dc0a1a91aa6f863368112e3a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"472ed84d1853f1c1badba444c2b061563785982dc0a1a91aa6f863368112e3a5","first_computed_at":"2026-06-30T02:17:47.687633Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T02:17:47.687633Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ur1bgvSPEEZempUIk/7r74/XxTgN1mUJx+19gNsF3i8UGuRw9bs3IlZaOGa+Y7xta2FGvKFeB8V+9IsDc80uAQ==","signature_status":"signed_v1","signed_at":"2026-06-30T02:17:47.688162Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.30055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:468acd14c4cfd08db06b1132a64b14bdb0ad88f550e9c3b29dc187dead350e04","sha256:f42c01601d746cc3ca9d8d3b00143265ca4ea01ab305650d30520b9745227d54"],"state_sha256":"d73fb7a753389b288c62a94ba48ce5daeb21b3413482de632d72b4c032a7f58d"}