{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3RZPVQZTJ4JQBZN4CGAISESKP4","short_pith_number":"pith:3RZPVQZT","canonical_record":{"source":{"id":"1403.4102","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2014-03-17T14:08:25Z","cross_cats_sorted":[],"title_canon_sha256":"6d022f8fdfb90771eb710bf15026ca32fbca0ea2b9f33237d3e87ef402820128","abstract_canon_sha256":"393409632a2fb98ab953f5a836166932323304f2072bdc66706547e8858977a8"},"schema_version":"1.0"},"canonical_sha256":"dc72fac3334f1300e5bc118089124a7f22df8f13194a725a66e688f8d7fb3295","source":{"kind":"arxiv","id":"1403.4102","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4102","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4102v3","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4102","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"pith_short_12","alias_value":"3RZPVQZTJ4JQ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3RZPVQZTJ4JQBZN4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3RZPVQZT","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3RZPVQZTJ4JQBZN4CGAISESKP4","target":"record","payload":{"canonical_record":{"source":{"id":"1403.4102","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2014-03-17T14:08:25Z","cross_cats_sorted":[],"title_canon_sha256":"6d022f8fdfb90771eb710bf15026ca32fbca0ea2b9f33237d3e87ef402820128","abstract_canon_sha256":"393409632a2fb98ab953f5a836166932323304f2072bdc66706547e8858977a8"},"schema_version":"1.0"},"canonical_sha256":"dc72fac3334f1300e5bc118089124a7f22df8f13194a725a66e688f8d7fb3295","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:55.302081Z","signature_b64":"LdMBJJPathXGsSnmjiQzoEVK5Rma1Vj6ea2IAe+DygXSyNxIKhc4/QVoC8drlpdqW8LNfJZGmK9IezSRk4yuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc72fac3334f1300e5bc118089124a7f22df8f13194a725a66e688f8d7fb3295","last_reissued_at":"2026-05-18T02:44:55.301392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:55.301392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.4102","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RMmNsjiALawXwf/NBZ2WP8QrVUcpPBKMX/k39Fv+ZHrn26P6NJJqSB8vapXsnhYWQQZVL3RauqnB065p2hKIDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:23:09.757352Z"},"content_sha256":"2a68b00c0d4188f7d4743fee21e32a4bdb27f68d129236a6b1cc1e2c3d1e0822","schema_version":"1.0","event_id":"sha256:2a68b00c0d4188f7d4743fee21e32a4bdb27f68d129236a6b1cc1e2c3d1e0822"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3RZPVQZTJ4JQBZN4CGAISESKP4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Derivative for the intersection local time of fractional Brownian Motions","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Litan Yan","submitted_at":"2014-03-17T14:08:25Z","abstract_excerpt":"Let $B^{H_1}$ and $\\tilde{B}^{H_2}$ be two independent fractional Brownian motions on ${\\mathbb R}$ with respective indices $H_i\\in (0,1)$ and $H_1\\leq H_2$. In this paper, we consider their intersection local time $\\ell_t(a)$. We show that $\\ell_t(a)$ is differentiable in the spatial variable if $\\frac1{H_1}+\\frac1{H_2}>3$, and we introduce the so-called {\\it hybrid quadratic covariation} $[f(B^{H_1}-\\tilde{B}^{H_2}),B^{H_1}]^{(HC)}$. When $H_1<\\frac12$, we construct a Banach space ${\\mathscr H}$ of measurable functions such that the quadratic covariation exists in $L^2(\\Omega)$ for all $f\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4102","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y7W0l15LNMMmJcWRDLwoGcFXvMzaXCunt1n7xK2fDYbgZVYvsKtnS9pz9w9LbRqHJWntsnYa+xh80mcgxwjOAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T21:23:09.757814Z"},"content_sha256":"f682a9949a5ec352bf52be0e6c43cfa316c8a4f4c94b2b294bb475cb70b875f0","schema_version":"1.0","event_id":"sha256:f682a9949a5ec352bf52be0e6c43cfa316c8a4f4c94b2b294bb475cb70b875f0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3RZPVQZTJ4JQBZN4CGAISESKP4/bundle.json","state_url":"https://pith.science/pith/3RZPVQZTJ4JQBZN4CGAISESKP4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3RZPVQZTJ4JQBZN4CGAISESKP4/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T21:23:09Z","links":{"resolver":"https://pith.science/pith/3RZPVQZTJ4JQBZN4CGAISESKP4","bundle":"https://pith.science/pith/3RZPVQZTJ4JQBZN4CGAISESKP4/bundle.json","state":"https://pith.science/pith/3RZPVQZTJ4JQBZN4CGAISESKP4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3RZPVQZTJ4JQBZN4CGAISESKP4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3RZPVQZTJ4JQBZN4CGAISESKP4","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":"393409632a2fb98ab953f5a836166932323304f2072bdc66706547e8858977a8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2014-03-17T14:08:25Z","title_canon_sha256":"6d022f8fdfb90771eb710bf15026ca32fbca0ea2b9f33237d3e87ef402820128"},"schema_version":"1.0","source":{"id":"1403.4102","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.4102","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"arxiv_version","alias_value":"1403.4102v3","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.4102","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"pith_short_12","alias_value":"3RZPVQZTJ4JQ","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3RZPVQZTJ4JQBZN4","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3RZPVQZT","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:f682a9949a5ec352bf52be0e6c43cfa316c8a4f4c94b2b294bb475cb70b875f0","target":"graph","created_at":"2026-05-18T02:44:55Z","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":"Let $B^{H_1}$ and $\\tilde{B}^{H_2}$ be two independent fractional Brownian motions on ${\\mathbb R}$ with respective indices $H_i\\in (0,1)$ and $H_1\\leq H_2$. In this paper, we consider their intersection local time $\\ell_t(a)$. We show that $\\ell_t(a)$ is differentiable in the spatial variable if $\\frac1{H_1}+\\frac1{H_2}>3$, and we introduce the so-called {\\it hybrid quadratic covariation} $[f(B^{H_1}-\\tilde{B}^{H_2}),B^{H_1}]^{(HC)}$. When $H_1<\\frac12$, we construct a Banach space ${\\mathscr H}$ of measurable functions such that the quadratic covariation exists in $L^2(\\Omega)$ for all $f\\in","authors_text":"Litan Yan","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2014-03-17T14:08:25Z","title":"Derivative for the intersection local time of fractional Brownian Motions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.4102","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":"sha256:2a68b00c0d4188f7d4743fee21e32a4bdb27f68d129236a6b1cc1e2c3d1e0822","target":"record","created_at":"2026-05-18T02:44:55Z","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":"393409632a2fb98ab953f5a836166932323304f2072bdc66706547e8858977a8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"math.PR","submitted_at":"2014-03-17T14:08:25Z","title_canon_sha256":"6d022f8fdfb90771eb710bf15026ca32fbca0ea2b9f33237d3e87ef402820128"},"schema_version":"1.0","source":{"id":"1403.4102","kind":"arxiv","version":3}},"canonical_sha256":"dc72fac3334f1300e5bc118089124a7f22df8f13194a725a66e688f8d7fb3295","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc72fac3334f1300e5bc118089124a7f22df8f13194a725a66e688f8d7fb3295","first_computed_at":"2026-05-18T02:44:55.301392Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:55.301392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LdMBJJPathXGsSnmjiQzoEVK5Rma1Vj6ea2IAe+DygXSyNxIKhc4/QVoC8drlpdqW8LNfJZGmK9IezSRk4yuAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:55.302081Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.4102","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2a68b00c0d4188f7d4743fee21e32a4bdb27f68d129236a6b1cc1e2c3d1e0822","sha256:f682a9949a5ec352bf52be0e6c43cfa316c8a4f4c94b2b294bb475cb70b875f0"],"state_sha256":"c98f50885a8c12bafcb3a6096dcb6b2a54c9bcee321262f809ac00439a73d0f0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SNOxZLeWiitMEhzhZdbgg0NXvz9X7OZNcVEFZugMCW9wDcMjV0oIhOg8gvhgVgo7zisyulw0D7ElGvE6D8SwAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T21:23:09.760080Z","bundle_sha256":"b4645a92fde260c350df61386e9c8848f431055ae4a87fca2ae98e74bbfb3e19"}}