{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:Z6V5UZQJDKJOPNFYAC5QPXHIOS","short_pith_number":"pith:Z6V5UZQJ","canonical_record":{"source":{"id":"2607.08103","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-09T04:42:28Z","cross_cats_sorted":[],"title_canon_sha256":"693001dbecf421587ed2712abd7dce183964a0a35e440e790f70705f4213fce7","abstract_canon_sha256":"13192ef2abb7e18826dca31717f026d43107b4a9afa3cb1c3ac0e8ad44c11042"},"schema_version":"1.0"},"canonical_sha256":"cfabda66091a92e7b4b800bb07dce874a96757a2b2522391e276fd97735872e2","source":{"kind":"arxiv","id":"2607.08103","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08103","created_at":"2026-07-10T01:19:26Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08103v1","created_at":"2026-07-10T01:19:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08103","created_at":"2026-07-10T01:19:26Z"},{"alias_kind":"pith_short_12","alias_value":"Z6V5UZQJDKJO","created_at":"2026-07-10T01:19:26Z"},{"alias_kind":"pith_short_16","alias_value":"Z6V5UZQJDKJOPNFY","created_at":"2026-07-10T01:19:26Z"},{"alias_kind":"pith_short_8","alias_value":"Z6V5UZQJ","created_at":"2026-07-10T01:19:26Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:Z6V5UZQJDKJOPNFYAC5QPXHIOS","target":"record","payload":{"canonical_record":{"source":{"id":"2607.08103","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-09T04:42:28Z","cross_cats_sorted":[],"title_canon_sha256":"693001dbecf421587ed2712abd7dce183964a0a35e440e790f70705f4213fce7","abstract_canon_sha256":"13192ef2abb7e18826dca31717f026d43107b4a9afa3cb1c3ac0e8ad44c11042"},"schema_version":"1.0"},"canonical_sha256":"cfabda66091a92e7b4b800bb07dce874a96757a2b2522391e276fd97735872e2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-10T01:19:26.094713Z","signature_b64":"Xo3EPmsPt7cy4eR3cHR2CJZyfFARuzGUvNFDVvsFVKOcB6giUKtAq+/JM7t1Las4bl3DkjnES4AiDB8RzkaCCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfabda66091a92e7b4b800bb07dce874a96757a2b2522391e276fd97735872e2","last_reissued_at":"2026-07-10T01:19:26.094170Z","signature_status":"signed_v1","first_computed_at":"2026-07-10T01:19:26.094170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2607.08103","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":"2026-07-10T01:19:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P1YkKnF5oM7uaOzmR8PwDAE8kKPYA4m6YpHUIN0YAM94gEk2Y6ED34b89c0xDr4ZqKnO5VxUXRYjITmRWESTDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:12:41.887324Z"},"content_sha256":"a50acb8a737d638f07c72c54eb29dac6b02ae3849822e2c842aa2a74d6343141","schema_version":"1.0","event_id":"sha256:a50acb8a737d638f07c72c54eb29dac6b02ae3849822e2c842aa2a74d6343141"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:Z6V5UZQJDKJOPNFYAC5QPXHIOS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stochastic Order Learning: An Approach to Rank Estimation Using Noisy Data","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.LG","authors_text":"Chaewon Lee, Chang-Su Kim, Seon-Ho Lee","submitted_at":"2026-07-09T04:42:28Z","abstract_excerpt":"Rank estimation under label noise poses a fundamental challenge, as ordinal annotations often exhibit structured uncertainty rather than simple label corruption. In this paper, we reformulate rank estimation with noisy ordinal labels as a stochastic ordering problem, in which each instance is inherently associated with multiple plausible ranks instead of a single deterministic label. Based on this view, we propose stochastic order learning (SOL), a learning framework that captures ordinal label uncertainty and learns an embedding space through two complementary objectives: a discriminative los"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08103","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/2607.08103/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":"2026-07-10T01:19:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MW3HeI7RXMHB03Xn5NgJPEtoBVbS92gisbAB3O5oWClGuCOfRSiL7P2zjYJNqusPnuzTi6RylTTkxWcT9CzrDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T21:12:41.887725Z"},"content_sha256":"a5b25915055fc90cc4ce64b3e016a983f55648c193144c0e40f43efcb48d7d20","schema_version":"1.0","event_id":"sha256:a5b25915055fc90cc4ce64b3e016a983f55648c193144c0e40f43efcb48d7d20"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z6V5UZQJDKJOPNFYAC5QPXHIOS/bundle.json","state_url":"https://pith.science/pith/Z6V5UZQJDKJOPNFYAC5QPXHIOS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z6V5UZQJDKJOPNFYAC5QPXHIOS/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":"2026-08-05T21:12:41Z","links":{"resolver":"https://pith.science/pith/Z6V5UZQJDKJOPNFYAC5QPXHIOS","bundle":"https://pith.science/pith/Z6V5UZQJDKJOPNFYAC5QPXHIOS/bundle.json","state":"https://pith.science/pith/Z6V5UZQJDKJOPNFYAC5QPXHIOS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z6V5UZQJDKJOPNFYAC5QPXHIOS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:Z6V5UZQJDKJOPNFYAC5QPXHIOS","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":"13192ef2abb7e18826dca31717f026d43107b4a9afa3cb1c3ac0e8ad44c11042","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-09T04:42:28Z","title_canon_sha256":"693001dbecf421587ed2712abd7dce183964a0a35e440e790f70705f4213fce7"},"schema_version":"1.0","source":{"id":"2607.08103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08103","created_at":"2026-07-10T01:19:26Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08103v1","created_at":"2026-07-10T01:19:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08103","created_at":"2026-07-10T01:19:26Z"},{"alias_kind":"pith_short_12","alias_value":"Z6V5UZQJDKJO","created_at":"2026-07-10T01:19:26Z"},{"alias_kind":"pith_short_16","alias_value":"Z6V5UZQJDKJOPNFY","created_at":"2026-07-10T01:19:26Z"},{"alias_kind":"pith_short_8","alias_value":"Z6V5UZQJ","created_at":"2026-07-10T01:19:26Z"}],"graph_snapshots":[{"event_id":"sha256:a5b25915055fc90cc4ce64b3e016a983f55648c193144c0e40f43efcb48d7d20","target":"graph","created_at":"2026-07-10T01:19:26Z","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/2607.08103/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Rank estimation under label noise poses a fundamental challenge, as ordinal annotations often exhibit structured uncertainty rather than simple label corruption. In this paper, we reformulate rank estimation with noisy ordinal labels as a stochastic ordering problem, in which each instance is inherently associated with multiple plausible ranks instead of a single deterministic label. Based on this view, we propose stochastic order learning (SOL), a learning framework that captures ordinal label uncertainty and learns an embedding space through two complementary objectives: a discriminative los","authors_text":"Chaewon Lee, Chang-Su Kim, Seon-Ho Lee","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-09T04:42:28Z","title":"Stochastic Order Learning: An Approach to Rank Estimation Using Noisy Data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08103","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:a50acb8a737d638f07c72c54eb29dac6b02ae3849822e2c842aa2a74d6343141","target":"record","created_at":"2026-07-10T01:19:26Z","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":"13192ef2abb7e18826dca31717f026d43107b4a9afa3cb1c3ac0e8ad44c11042","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.LG","submitted_at":"2026-07-09T04:42:28Z","title_canon_sha256":"693001dbecf421587ed2712abd7dce183964a0a35e440e790f70705f4213fce7"},"schema_version":"1.0","source":{"id":"2607.08103","kind":"arxiv","version":1}},"canonical_sha256":"cfabda66091a92e7b4b800bb07dce874a96757a2b2522391e276fd97735872e2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfabda66091a92e7b4b800bb07dce874a96757a2b2522391e276fd97735872e2","first_computed_at":"2026-07-10T01:19:26.094170Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-10T01:19:26.094170Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Xo3EPmsPt7cy4eR3cHR2CJZyfFARuzGUvNFDVvsFVKOcB6giUKtAq+/JM7t1Las4bl3DkjnES4AiDB8RzkaCCA==","signature_status":"signed_v1","signed_at":"2026-07-10T01:19:26.094713Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.08103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a50acb8a737d638f07c72c54eb29dac6b02ae3849822e2c842aa2a74d6343141","sha256:a5b25915055fc90cc4ce64b3e016a983f55648c193144c0e40f43efcb48d7d20"],"state_sha256":"f2758f48908f84d5e9072fa71b0ff613950bec229a3a29aa24c8590fe9d86627"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f/Tpmo0HWe++rgHTvsckH9IrUvk2RyZtDyJbXkrjtzEj5gz9tiAGL7oNGbpvz55w2FH0eAqg+bTdmzgOml1ZCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T21:12:41.891052Z","bundle_sha256":"57d3685fa0dfc30d98fe4e13ad5004a105adb9eb6d187a5979f6421f79e84a81"}}