{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:HBHYQPQNPYX5XLSTTEWHJMGU6O","short_pith_number":"pith:HBHYQPQN","canonical_record":{"source":{"id":"2409.16541","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-25T01:30:16Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"c0f2ea3b543545210ac5850a04dc35c1089c23b04377b5bf4c921e607cf16c4f","abstract_canon_sha256":"3e9f2835d99b7c2c4ee0f2d4238d342e7c7ed65824f009f7283f00bce047632a"},"schema_version":"1.0"},"canonical_sha256":"384f883e0d7e2fdbae53992c74b0d4f3828e96d606062afed5d2eec10b3868b5","source":{"kind":"arxiv","id":"2409.16541","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.16541","created_at":"2026-07-05T10:41:15Z"},{"alias_kind":"arxiv_version","alias_value":"2409.16541v2","created_at":"2026-07-05T10:41:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.16541","created_at":"2026-07-05T10:41:15Z"},{"alias_kind":"pith_short_12","alias_value":"HBHYQPQNPYX5","created_at":"2026-07-05T10:41:15Z"},{"alias_kind":"pith_short_16","alias_value":"HBHYQPQNPYX5XLST","created_at":"2026-07-05T10:41:15Z"},{"alias_kind":"pith_short_8","alias_value":"HBHYQPQN","created_at":"2026-07-05T10:41:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:HBHYQPQNPYX5XLSTTEWHJMGU6O","target":"record","payload":{"canonical_record":{"source":{"id":"2409.16541","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-25T01:30:16Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"c0f2ea3b543545210ac5850a04dc35c1089c23b04377b5bf4c921e607cf16c4f","abstract_canon_sha256":"3e9f2835d99b7c2c4ee0f2d4238d342e7c7ed65824f009f7283f00bce047632a"},"schema_version":"1.0"},"canonical_sha256":"384f883e0d7e2fdbae53992c74b0d4f3828e96d606062afed5d2eec10b3868b5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:41:15.507955Z","signature_b64":"3JBdhCLEyyT+7bjl+Zou2gxATO5ovGawme0Qcq3ZUzPvTJotwwtxzThfmTYYEWYl79bY2GS5hghz+CIxXFrxDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"384f883e0d7e2fdbae53992c74b0d4f3828e96d606062afed5d2eec10b3868b5","last_reissued_at":"2026-07-05T10:41:15.507471Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:41:15.507471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.16541","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:41:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pxr6NHmp6zK/BVz2goZpF+9QU9vBpu85tQCTQkx3ZVAgDEoVwb2UR+wRURdW6qkul6Gqlp2C4N1I0UF18Me4BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T10:39:13.082468Z"},"content_sha256":"67db5d608b414c78d7913909e60eaa1f5a2b6f5c90b6035dfd2810e616ced697","schema_version":"1.0","event_id":"sha256:67db5d608b414c78d7913909e60eaa1f5a2b6f5c90b6035dfd2810e616ced697"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:HBHYQPQNPYX5XLSTTEWHJMGU6O","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Monge-Kantorovich Fitting With Sobolev Budgets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"cs.LG","authors_text":"Forest Kobayashi, Jonathan Hayase, Young-Heon Kim","submitted_at":"2024-09-25T01:30:16Z","abstract_excerpt":"Given $m < n$, we consider the problem of ``best'' approximating an $n\\text{-d}$ probability measure $\\rho$ via an $m\\text{-d}$ measure $\\nu$ such that $\\mathrm{supp}\\ \\nu$ has bounded total ``complexity.'' When $\\rho$ is concentrated near an $m\\text{-d}$ set we may interpret this as a manifold learning problem with noisy data. However, we do not restrict our analysis to this case, as the more general formulation has broader applications.\n  We quantify $\\nu$'s performance in approximating $\\rho$ via the Monge-Kantorovich (also called Wasserstein) $p$-cost $\\mathbb{W}_p^p(\\rho, \\nu)$, and const"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.16541","kind":"arxiv","version":2},"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/2409.16541/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":"2026-07-05T10:41:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C7pBScDvx7LLfxiTxs6a4Z22iDLCcIcZZzrFL0XD3QVFRgMNl3ywSt6/XWogsOwxmocSt06F/C7MAr4QK/95BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-20T10:39:13.083315Z"},"content_sha256":"de40de89a79fbb2d18add2b5f24f65e7c5b65fd87095381fa94b2a53c56c3764","schema_version":"1.0","event_id":"sha256:de40de89a79fbb2d18add2b5f24f65e7c5b65fd87095381fa94b2a53c56c3764"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HBHYQPQNPYX5XLSTTEWHJMGU6O/bundle.json","state_url":"https://pith.science/pith/HBHYQPQNPYX5XLSTTEWHJMGU6O/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HBHYQPQNPYX5XLSTTEWHJMGU6O/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":"2026-08-20T10:39:13Z","links":{"resolver":"https://pith.science/pith/HBHYQPQNPYX5XLSTTEWHJMGU6O","bundle":"https://pith.science/pith/HBHYQPQNPYX5XLSTTEWHJMGU6O/bundle.json","state":"https://pith.science/pith/HBHYQPQNPYX5XLSTTEWHJMGU6O/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HBHYQPQNPYX5XLSTTEWHJMGU6O/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:HBHYQPQNPYX5XLSTTEWHJMGU6O","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":"3e9f2835d99b7c2c4ee0f2d4238d342e7c7ed65824f009f7283f00bce047632a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-25T01:30:16Z","title_canon_sha256":"c0f2ea3b543545210ac5850a04dc35c1089c23b04377b5bf4c921e607cf16c4f"},"schema_version":"1.0","source":{"id":"2409.16541","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.16541","created_at":"2026-07-05T10:41:15Z"},{"alias_kind":"arxiv_version","alias_value":"2409.16541v2","created_at":"2026-07-05T10:41:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.16541","created_at":"2026-07-05T10:41:15Z"},{"alias_kind":"pith_short_12","alias_value":"HBHYQPQNPYX5","created_at":"2026-07-05T10:41:15Z"},{"alias_kind":"pith_short_16","alias_value":"HBHYQPQNPYX5XLST","created_at":"2026-07-05T10:41:15Z"},{"alias_kind":"pith_short_8","alias_value":"HBHYQPQN","created_at":"2026-07-05T10:41:15Z"}],"graph_snapshots":[{"event_id":"sha256:de40de89a79fbb2d18add2b5f24f65e7c5b65fd87095381fa94b2a53c56c3764","target":"graph","created_at":"2026-07-05T10:41:15Z","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/2409.16541/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given $m < n$, we consider the problem of ``best'' approximating an $n\\text{-d}$ probability measure $\\rho$ via an $m\\text{-d}$ measure $\\nu$ such that $\\mathrm{supp}\\ \\nu$ has bounded total ``complexity.'' When $\\rho$ is concentrated near an $m\\text{-d}$ set we may interpret this as a manifold learning problem with noisy data. However, we do not restrict our analysis to this case, as the more general formulation has broader applications.\n  We quantify $\\nu$'s performance in approximating $\\rho$ via the Monge-Kantorovich (also called Wasserstein) $p$-cost $\\mathbb{W}_p^p(\\rho, \\nu)$, and const","authors_text":"Forest Kobayashi, Jonathan Hayase, Young-Heon Kim","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-25T01:30:16Z","title":"Monge-Kantorovich Fitting With Sobolev Budgets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.16541","kind":"arxiv","version":2},"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":"sha256:67db5d608b414c78d7913909e60eaa1f5a2b6f5c90b6035dfd2810e616ced697","target":"record","created_at":"2026-07-05T10:41:15Z","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":"3e9f2835d99b7c2c4ee0f2d4238d342e7c7ed65824f009f7283f00bce047632a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LG","submitted_at":"2024-09-25T01:30:16Z","title_canon_sha256":"c0f2ea3b543545210ac5850a04dc35c1089c23b04377b5bf4c921e607cf16c4f"},"schema_version":"1.0","source":{"id":"2409.16541","kind":"arxiv","version":2}},"canonical_sha256":"384f883e0d7e2fdbae53992c74b0d4f3828e96d606062afed5d2eec10b3868b5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"384f883e0d7e2fdbae53992c74b0d4f3828e96d606062afed5d2eec10b3868b5","first_computed_at":"2026-07-05T10:41:15.507471Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:41:15.507471Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3JBdhCLEyyT+7bjl+Zou2gxATO5ovGawme0Qcq3ZUzPvTJotwwtxzThfmTYYEWYl79bY2GS5hghz+CIxXFrxDQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:41:15.507955Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.16541","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67db5d608b414c78d7913909e60eaa1f5a2b6f5c90b6035dfd2810e616ced697","sha256:de40de89a79fbb2d18add2b5f24f65e7c5b65fd87095381fa94b2a53c56c3764"],"state_sha256":"2d2d541a279ac7f23728a2ec9289e9ee19c5f8e37a690f18f30fe93e5b283c8f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4GnYTN4kq+ji2R5GNT98WhXKkfFJQz5+j1lOurlJ+n0A4Ida0uwVdGY3ii1QT6Ocx3gni9+9AW+u5M8nIeNrBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-20T10:39:13.089492Z","bundle_sha256":"461bde52a94c900741ab9102eca11a44a4d922eb5aee437b7a8fe7f33758755d"}}