{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:6S6YPYQPHYISXL7XC33IXDSBHH","short_pith_number":"pith:6S6YPYQP","canonical_record":{"source":{"id":"2509.07232","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-09-08T21:20:07Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"fb5b8ab8100c3b220b4ec438f443fa720d6dc0f231fdca1cb0d9f501474ecf3f","abstract_canon_sha256":"ae8cec26fbe01d1bbe37b3bf3f4abbb36d036a856f296b717f618ceab06c421d"},"schema_version":"1.0"},"canonical_sha256":"f4bd87e20f3e112baff716f68b8e4139cb6214b42a053a1dd2644a881fc0687c","source":{"kind":"arxiv","id":"2509.07232","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.07232","created_at":"2026-07-05T12:07:18Z"},{"alias_kind":"arxiv_version","alias_value":"2509.07232v1","created_at":"2026-07-05T12:07:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07232","created_at":"2026-07-05T12:07:18Z"},{"alias_kind":"pith_short_12","alias_value":"6S6YPYQPHYIS","created_at":"2026-07-05T12:07:18Z"},{"alias_kind":"pith_short_16","alias_value":"6S6YPYQPHYISXL7X","created_at":"2026-07-05T12:07:18Z"},{"alias_kind":"pith_short_8","alias_value":"6S6YPYQP","created_at":"2026-07-05T12:07:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:6S6YPYQPHYISXL7XC33IXDSBHH","target":"record","payload":{"canonical_record":{"source":{"id":"2509.07232","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-09-08T21:20:07Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"fb5b8ab8100c3b220b4ec438f443fa720d6dc0f231fdca1cb0d9f501474ecf3f","abstract_canon_sha256":"ae8cec26fbe01d1bbe37b3bf3f4abbb36d036a856f296b717f618ceab06c421d"},"schema_version":"1.0"},"canonical_sha256":"f4bd87e20f3e112baff716f68b8e4139cb6214b42a053a1dd2644a881fc0687c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:07:18.039486Z","signature_b64":"X6amx3j/QkovzdHWr9HaELkTDH6k4lsCti7FuAWuxq2wxN6hEN5rpu1/V4PTBz+YS7bnQZ+1kdDD/v4DArcCDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4bd87e20f3e112baff716f68b8e4139cb6214b42a053a1dd2644a881fc0687c","last_reissued_at":"2026-07-05T12:07:18.038951Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:07:18.038951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2509.07232","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":"2026-07-05T12:07:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1x/7Bn2icHlfLjhf9ZKtdlGdMcsrKhnGAsL0wc6zJeEbYLwYyWx5rdbyOC6HqRmI1LXID9h/Inkt8Lku+iXTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:48:19.144929Z"},"content_sha256":"f02a1b77a0d0ddfe8939f50f1ca38f33e47fcc8340d2150811c43d391b2072a8","schema_version":"1.0","event_id":"sha256:f02a1b77a0d0ddfe8939f50f1ca38f33e47fcc8340d2150811c43d391b2072a8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:6S6YPYQPHYISXL7XC33IXDSBHH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the exact region between Chatterjee's rank correlation and Spearman's footrule","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Marcus Rockel","submitted_at":"2025-09-08T21:20:07Z","abstract_excerpt":"Chatterjee's rank correlation \\(\\xi\\) has emerged as a popular measure quantifying the strength of directed functional dependence between random variables $X$ and $Y$. If $X$ and $Y$ are continuous, $\\xi$ equals Spearman's footrule~\\(\\psi\\) for the Markov product of the copula induced by $(X,Y)$ and its transpose. We analyze the relationship between these two measures more in depth by studying the attainable region of possible pairs \\((\\xi, \\psi)\\) over all bivariate copulas. In particular, we show that for given $\\xi$, the maximal possible value of $\\psi$ is uniquely attained by a Fr\\'echet c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07232","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/2509.07232/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":"2026-07-05T12:07:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zB43aHFeuWQpZyERfq6RYURfnRKezYJrn2GybJvJNUTnIZePdOR9YWm1jNgcORUfar2rWxQlqOOYW0Xwrqn9Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-18T18:48:19.146777Z"},"content_sha256":"495f1aacdf9560b70eb2036b5832f79d35e348976224dd89f2029c821849e522","schema_version":"1.0","event_id":"sha256:495f1aacdf9560b70eb2036b5832f79d35e348976224dd89f2029c821849e522"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6S6YPYQPHYISXL7XC33IXDSBHH/bundle.json","state_url":"https://pith.science/pith/6S6YPYQPHYISXL7XC33IXDSBHH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6S6YPYQPHYISXL7XC33IXDSBHH/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":"2026-08-18T18:48:19Z","links":{"resolver":"https://pith.science/pith/6S6YPYQPHYISXL7XC33IXDSBHH","bundle":"https://pith.science/pith/6S6YPYQPHYISXL7XC33IXDSBHH/bundle.json","state":"https://pith.science/pith/6S6YPYQPHYISXL7XC33IXDSBHH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6S6YPYQPHYISXL7XC33IXDSBHH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:6S6YPYQPHYISXL7XC33IXDSBHH","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":"ae8cec26fbe01d1bbe37b3bf3f4abbb36d036a856f296b717f618ceab06c421d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-09-08T21:20:07Z","title_canon_sha256":"fb5b8ab8100c3b220b4ec438f443fa720d6dc0f231fdca1cb0d9f501474ecf3f"},"schema_version":"1.0","source":{"id":"2509.07232","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.07232","created_at":"2026-07-05T12:07:18Z"},{"alias_kind":"arxiv_version","alias_value":"2509.07232v1","created_at":"2026-07-05T12:07:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07232","created_at":"2026-07-05T12:07:18Z"},{"alias_kind":"pith_short_12","alias_value":"6S6YPYQPHYIS","created_at":"2026-07-05T12:07:18Z"},{"alias_kind":"pith_short_16","alias_value":"6S6YPYQPHYISXL7X","created_at":"2026-07-05T12:07:18Z"},{"alias_kind":"pith_short_8","alias_value":"6S6YPYQP","created_at":"2026-07-05T12:07:18Z"}],"graph_snapshots":[{"event_id":"sha256:495f1aacdf9560b70eb2036b5832f79d35e348976224dd89f2029c821849e522","target":"graph","created_at":"2026-07-05T12:07:18Z","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/2509.07232/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Chatterjee's rank correlation \\(\\xi\\) has emerged as a popular measure quantifying the strength of directed functional dependence between random variables $X$ and $Y$. If $X$ and $Y$ are continuous, $\\xi$ equals Spearman's footrule~\\(\\psi\\) for the Markov product of the copula induced by $(X,Y)$ and its transpose. We analyze the relationship between these two measures more in depth by studying the attainable region of possible pairs \\((\\xi, \\psi)\\) over all bivariate copulas. In particular, we show that for given $\\xi$, the maximal possible value of $\\psi$ is uniquely attained by a Fr\\'echet c","authors_text":"Marcus Rockel","cross_cats":["stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-09-08T21:20:07Z","title":"On the exact region between Chatterjee's rank correlation and Spearman's footrule"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07232","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:f02a1b77a0d0ddfe8939f50f1ca38f33e47fcc8340d2150811c43d391b2072a8","target":"record","created_at":"2026-07-05T12:07:18Z","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":"ae8cec26fbe01d1bbe37b3bf3f4abbb36d036a856f296b717f618ceab06c421d","cross_cats_sorted":["stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2025-09-08T21:20:07Z","title_canon_sha256":"fb5b8ab8100c3b220b4ec438f443fa720d6dc0f231fdca1cb0d9f501474ecf3f"},"schema_version":"1.0","source":{"id":"2509.07232","kind":"arxiv","version":1}},"canonical_sha256":"f4bd87e20f3e112baff716f68b8e4139cb6214b42a053a1dd2644a881fc0687c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4bd87e20f3e112baff716f68b8e4139cb6214b42a053a1dd2644a881fc0687c","first_computed_at":"2026-07-05T12:07:18.038951Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:07:18.038951Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"X6amx3j/QkovzdHWr9HaELkTDH6k4lsCti7FuAWuxq2wxN6hEN5rpu1/V4PTBz+YS7bnQZ+1kdDD/v4DArcCDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:07:18.039486Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.07232","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f02a1b77a0d0ddfe8939f50f1ca38f33e47fcc8340d2150811c43d391b2072a8","sha256:495f1aacdf9560b70eb2036b5832f79d35e348976224dd89f2029c821849e522"],"state_sha256":"9d56335023c3a923f3299b9b60750bfc1290af3887996e3a6e6acd5dc5deba26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TrYFNYo2smAe8O5v9mHSXFFL2tf1YBhd/Mo5a+b4yeucNQZ4BlPBHhT1cc8JZJtE8g21BPkkp3my3veHrqQPAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-18T18:48:19.159393Z","bundle_sha256":"d8d3365b0f08e6a6aa37652b057fa9869d4ac8037bc8660c2ca8b61fa4db4d95"}}