{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:6YW64KNZI744YAHN64GDD6IT4F","short_pith_number":"pith:6YW64KNZ","canonical_record":{"source":{"id":"2506.02363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-06-03T01:47:52Z","cross_cats_sorted":[],"title_canon_sha256":"abc56b50762186b07fa3c90dc9aa202aa521805ee948b5c877df98e7fa1c5d02","abstract_canon_sha256":"44faa6c98f189293ab3339c6caf02f0e030ab1b8be8399223e9c8b5482b127fc"},"schema_version":"1.0"},"canonical_sha256":"f62dee29b947f9cc00edf70c31f913e14fcebded8ba691b1957fe3a4b2cb2c7d","source":{"kind":"arxiv","id":"2506.02363","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02363","created_at":"2026-07-05T11:14:37Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02363v1","created_at":"2026-07-05T11:14:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02363","created_at":"2026-07-05T11:14:37Z"},{"alias_kind":"pith_short_12","alias_value":"6YW64KNZI744","created_at":"2026-07-05T11:14:37Z"},{"alias_kind":"pith_short_16","alias_value":"6YW64KNZI744YAHN","created_at":"2026-07-05T11:14:37Z"},{"alias_kind":"pith_short_8","alias_value":"6YW64KNZ","created_at":"2026-07-05T11:14:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:6YW64KNZI744YAHN64GDD6IT4F","target":"record","payload":{"canonical_record":{"source":{"id":"2506.02363","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-06-03T01:47:52Z","cross_cats_sorted":[],"title_canon_sha256":"abc56b50762186b07fa3c90dc9aa202aa521805ee948b5c877df98e7fa1c5d02","abstract_canon_sha256":"44faa6c98f189293ab3339c6caf02f0e030ab1b8be8399223e9c8b5482b127fc"},"schema_version":"1.0"},"canonical_sha256":"f62dee29b947f9cc00edf70c31f913e14fcebded8ba691b1957fe3a4b2cb2c7d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:14:37.491255Z","signature_b64":"Jfn5cXr7na1LoOisjkgCyNEEaoR2jISYoLPdRJtSzJXobFPzZBMUYmrl0py1z2QHls29Bvqi7e7LOIN3qE2gAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f62dee29b947f9cc00edf70c31f913e14fcebded8ba691b1957fe3a4b2cb2c7d","last_reissued_at":"2026-07-05T11:14:37.490821Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:14:37.490821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2506.02363","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:14:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XYzksF2uVn0AkN1zJT2TYFGOAOjC7brA3pvTLQh4/sJsoC8C28HU7lP++Le0qNGFp2hKj2SNYggwp2R5tq46Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:16:20.014517Z"},"content_sha256":"6b6baadb117272e65325f97b63c1028c3a9aa67ade7b94f2694933e9e23704c6","schema_version":"1.0","event_id":"sha256:6b6baadb117272e65325f97b63c1028c3a9aa67ade7b94f2694933e9e23704c6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:6YW64KNZI744YAHN64GDD6IT4F","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Function-on-function Differential Regression","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"stat.ME","authors_text":"Fang Yao, Tongyu Li","submitted_at":"2025-06-03T01:47:52Z","abstract_excerpt":"Function-on-function regression has been a topic of substantial interest due to its broad applicability, where the relation between functional predictor and response is concerned. In this article, we propose a new framework for modeling the regression mapping that extends beyond integral type, motivated by the prevalence of physical phenomena governed by differential relations, which is referred to as function-on-function differential regression. However, a key challenge lies in representing the differential regression operator, unlike functions that can be expressed by expansions. As a main c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02363","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.02363/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:14:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Plc4kj6UpBrjEP1LoiDB7v6WiKrj/+eL2+ycxzegJDruE6FYthV+U0yczJwvyHKgqM9WCOUQK9fdgzZ/A9DcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T04:16:20.015020Z"},"content_sha256":"6e54f316af5c3d4b96610696fc87704f1edf160c461a52ccab6a5d7b320c1f1b","schema_version":"1.0","event_id":"sha256:6e54f316af5c3d4b96610696fc87704f1edf160c461a52ccab6a5d7b320c1f1b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6YW64KNZI744YAHN64GDD6IT4F/bundle.json","state_url":"https://pith.science/pith/6YW64KNZI744YAHN64GDD6IT4F/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6YW64KNZI744YAHN64GDD6IT4F/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":"2026-08-09T04:16:20Z","links":{"resolver":"https://pith.science/pith/6YW64KNZI744YAHN64GDD6IT4F","bundle":"https://pith.science/pith/6YW64KNZI744YAHN64GDD6IT4F/bundle.json","state":"https://pith.science/pith/6YW64KNZI744YAHN64GDD6IT4F/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6YW64KNZI744YAHN64GDD6IT4F/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6YW64KNZI744YAHN64GDD6IT4F","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":"44faa6c98f189293ab3339c6caf02f0e030ab1b8be8399223e9c8b5482b127fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-06-03T01:47:52Z","title_canon_sha256":"abc56b50762186b07fa3c90dc9aa202aa521805ee948b5c877df98e7fa1c5d02"},"schema_version":"1.0","source":{"id":"2506.02363","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.02363","created_at":"2026-07-05T11:14:37Z"},{"alias_kind":"arxiv_version","alias_value":"2506.02363v1","created_at":"2026-07-05T11:14:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.02363","created_at":"2026-07-05T11:14:37Z"},{"alias_kind":"pith_short_12","alias_value":"6YW64KNZI744","created_at":"2026-07-05T11:14:37Z"},{"alias_kind":"pith_short_16","alias_value":"6YW64KNZI744YAHN","created_at":"2026-07-05T11:14:37Z"},{"alias_kind":"pith_short_8","alias_value":"6YW64KNZ","created_at":"2026-07-05T11:14:37Z"}],"graph_snapshots":[{"event_id":"sha256:6e54f316af5c3d4b96610696fc87704f1edf160c461a52ccab6a5d7b320c1f1b","target":"graph","created_at":"2026-07-05T11:14:37Z","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/2506.02363/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Function-on-function regression has been a topic of substantial interest due to its broad applicability, where the relation between functional predictor and response is concerned. In this article, we propose a new framework for modeling the regression mapping that extends beyond integral type, motivated by the prevalence of physical phenomena governed by differential relations, which is referred to as function-on-function differential regression. However, a key challenge lies in representing the differential regression operator, unlike functions that can be expressed by expansions. As a main c","authors_text":"Fang Yao, Tongyu Li","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-06-03T01:47:52Z","title":"Function-on-function Differential Regression"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.02363","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":"sha256:6b6baadb117272e65325f97b63c1028c3a9aa67ade7b94f2694933e9e23704c6","target":"record","created_at":"2026-07-05T11:14:37Z","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":"44faa6c98f189293ab3339c6caf02f0e030ab1b8be8399223e9c8b5482b127fc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2025-06-03T01:47:52Z","title_canon_sha256":"abc56b50762186b07fa3c90dc9aa202aa521805ee948b5c877df98e7fa1c5d02"},"schema_version":"1.0","source":{"id":"2506.02363","kind":"arxiv","version":1}},"canonical_sha256":"f62dee29b947f9cc00edf70c31f913e14fcebded8ba691b1957fe3a4b2cb2c7d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f62dee29b947f9cc00edf70c31f913e14fcebded8ba691b1957fe3a4b2cb2c7d","first_computed_at":"2026-07-05T11:14:37.490821Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:14:37.490821Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Jfn5cXr7na1LoOisjkgCyNEEaoR2jISYoLPdRJtSzJXobFPzZBMUYmrl0py1z2QHls29Bvqi7e7LOIN3qE2gAA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:14:37.491255Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.02363","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b6baadb117272e65325f97b63c1028c3a9aa67ade7b94f2694933e9e23704c6","sha256:6e54f316af5c3d4b96610696fc87704f1edf160c461a52ccab6a5d7b320c1f1b"],"state_sha256":"359d112a4e499c2e1b422b80f6fb9eb942024704e1f8586492c6f03fb3afc59a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8yau0EGqYaf6KoFJANJI4pFfjJUBK0HrSmRa7FuCZNeO66ptQR7n3wZO7tZ6eT3EMsa89W4iW059TT7QzrGdCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T04:16:20.021411Z","bundle_sha256":"26e2a0cf82e6ff6b9dd2d5fe2c37c0751468af2bbc67f3f42f4eb8c9b41ec880"}}