{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:OJSNNKZX2Q2T6GOU2B5CSU4YIM","short_pith_number":"pith:OJSNNKZX","canonical_record":{"source":{"id":"1210.3111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T02:59:36Z","cross_cats_sorted":[],"title_canon_sha256":"b061815f0cc437d55f2a03ff0f6be76e39b7eb4fd3382a1d295f9aa998810854","abstract_canon_sha256":"c7ee34795ba187b4247a005cdda08371481beb7fda8c1d9185d8290a52354950"},"schema_version":"1.0"},"canonical_sha256":"7264d6ab37d4353f19d4d07a295398432d4b269646cdd921927382d7ba159214","source":{"kind":"arxiv","id":"1210.3111","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3111","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3111v2","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3111","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"pith_short_12","alias_value":"OJSNNKZX2Q2T","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OJSNNKZX2Q2T6GOU","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OJSNNKZX","created_at":"2026-05-18T12:27:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:OJSNNKZX2Q2T6GOU2B5CSU4YIM","target":"record","payload":{"canonical_record":{"source":{"id":"1210.3111","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T02:59:36Z","cross_cats_sorted":[],"title_canon_sha256":"b061815f0cc437d55f2a03ff0f6be76e39b7eb4fd3382a1d295f9aa998810854","abstract_canon_sha256":"c7ee34795ba187b4247a005cdda08371481beb7fda8c1d9185d8290a52354950"},"schema_version":"1.0"},"canonical_sha256":"7264d6ab37d4353f19d4d07a295398432d4b269646cdd921927382d7ba159214","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:30:25.562661Z","signature_b64":"UDV5tPilgXW4PEmS88pOBONegpXAD9KCe9vV9rKAYCEBxIbJSD3UNlIS3ucIjx48njoDrdsrKVdZou8oprhDCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7264d6ab37d4353f19d4d07a295398432d4b269646cdd921927382d7ba159214","last_reissued_at":"2026-05-18T03:30:25.561963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:30:25.561963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1210.3111","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":"2026-05-18T03:30:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SIPv+t85aWOiu0IELM3e+7qiPTFXR98X4HKWtg1xscB/1CoHO7bLrh6p8uoUB+wCOEPh7BHJSxDq8cup2rUiBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:20:47.276991Z"},"content_sha256":"4d36071e03e750a4ea01f8ea9fd857b1ee3e613da39c4cd0e3d9eb40167074f0","schema_version":"1.0","event_id":"sha256:4d36071e03e750a4ea01f8ea9fd857b1ee3e613da39c4cd0e3d9eb40167074f0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:OJSNNKZX2Q2T6GOU2B5CSU4YIM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Free boundary regularity in the optimal partial transport problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Emanuel Indrei","submitted_at":"2012-10-11T02:59:36Z","abstract_excerpt":"In the optimal partial transport problem, one is asked to transport a fraction $0<m \\leq \\min\\{||f||_{L^1}, ||g||_{L^1}\\}$ of the mass of $f=f \\chi_\\Omega$ onto $g=g\\chi_\\Lambda$ while minimizing a transportation cost. If $f$ and $g$ are bounded away from zero and infinity on strictly convex domains $\\Omega$ and $\\Lambda$, respectively, and if the cost is quadratic, then away from $\\partial(\\Omega \\cap \\Lambda)$ the free boundaries of the active regions are shown to be $C_{loc}^{1,\\alpha}$ hypersurfaces up to a possible singular set. This improves and generalizes a result of Caffarelli and McC"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3111","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":""},"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":"2026-05-18T03:30:25Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NrBFWxJYdlirWc7Vttqp1RiTqqvaPRG98sCDslJNq0ad1OS6mgHqqdoozmWIY/52OTs9FNltw+os3ILUZ8WCAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T06:20:47.277335Z"},"content_sha256":"0fda019e8acdc726288f36746c58a27eea27991e48cf976f9966465da0c0d4a3","schema_version":"1.0","event_id":"sha256:0fda019e8acdc726288f36746c58a27eea27991e48cf976f9966465da0c0d4a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OJSNNKZX2Q2T6GOU2B5CSU4YIM/bundle.json","state_url":"https://pith.science/pith/OJSNNKZX2Q2T6GOU2B5CSU4YIM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OJSNNKZX2Q2T6GOU2B5CSU4YIM/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":"2026-06-20T06:20:47Z","links":{"resolver":"https://pith.science/pith/OJSNNKZX2Q2T6GOU2B5CSU4YIM","bundle":"https://pith.science/pith/OJSNNKZX2Q2T6GOU2B5CSU4YIM/bundle.json","state":"https://pith.science/pith/OJSNNKZX2Q2T6GOU2B5CSU4YIM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OJSNNKZX2Q2T6GOU2B5CSU4YIM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:OJSNNKZX2Q2T6GOU2B5CSU4YIM","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":"c7ee34795ba187b4247a005cdda08371481beb7fda8c1d9185d8290a52354950","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T02:59:36Z","title_canon_sha256":"b061815f0cc437d55f2a03ff0f6be76e39b7eb4fd3382a1d295f9aa998810854"},"schema_version":"1.0","source":{"id":"1210.3111","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1210.3111","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"arxiv_version","alias_value":"1210.3111v2","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.3111","created_at":"2026-05-18T03:30:25Z"},{"alias_kind":"pith_short_12","alias_value":"OJSNNKZX2Q2T","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"OJSNNKZX2Q2T6GOU","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"OJSNNKZX","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:0fda019e8acdc726288f36746c58a27eea27991e48cf976f9966465da0c0d4a3","target":"graph","created_at":"2026-05-18T03:30:25Z","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":"In the optimal partial transport problem, one is asked to transport a fraction $0<m \\leq \\min\\{||f||_{L^1}, ||g||_{L^1}\\}$ of the mass of $f=f \\chi_\\Omega$ onto $g=g\\chi_\\Lambda$ while minimizing a transportation cost. If $f$ and $g$ are bounded away from zero and infinity on strictly convex domains $\\Omega$ and $\\Lambda$, respectively, and if the cost is quadratic, then away from $\\partial(\\Omega \\cap \\Lambda)$ the free boundaries of the active regions are shown to be $C_{loc}^{1,\\alpha}$ hypersurfaces up to a possible singular set. This improves and generalizes a result of Caffarelli and McC","authors_text":"Emanuel Indrei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T02:59:36Z","title":"Free boundary regularity in the optimal partial transport problem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.3111","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":"sha256:4d36071e03e750a4ea01f8ea9fd857b1ee3e613da39c4cd0e3d9eb40167074f0","target":"record","created_at":"2026-05-18T03:30:25Z","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":"c7ee34795ba187b4247a005cdda08371481beb7fda8c1d9185d8290a52354950","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-10-11T02:59:36Z","title_canon_sha256":"b061815f0cc437d55f2a03ff0f6be76e39b7eb4fd3382a1d295f9aa998810854"},"schema_version":"1.0","source":{"id":"1210.3111","kind":"arxiv","version":2}},"canonical_sha256":"7264d6ab37d4353f19d4d07a295398432d4b269646cdd921927382d7ba159214","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7264d6ab37d4353f19d4d07a295398432d4b269646cdd921927382d7ba159214","first_computed_at":"2026-05-18T03:30:25.561963Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:30:25.561963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UDV5tPilgXW4PEmS88pOBONegpXAD9KCe9vV9rKAYCEBxIbJSD3UNlIS3ucIjx48njoDrdsrKVdZou8oprhDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:30:25.562661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1210.3111","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4d36071e03e750a4ea01f8ea9fd857b1ee3e613da39c4cd0e3d9eb40167074f0","sha256:0fda019e8acdc726288f36746c58a27eea27991e48cf976f9966465da0c0d4a3"],"state_sha256":"841598827f3841905ccb49114f9eb96e274ed3d361a289544f28476c7cc7e56a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q3uPTkzyeb7szsBngJ/lkl29l6d1UK6HD+u/uIO7Y9UY/fs7m+sLYE28h7nlM6Dqp3LkAnLETzg+3CwUyuRADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T06:20:47.279216Z","bundle_sha256":"25dd2b89b1e3b446b8f55669020a30a410addda0a66ed95eafbb2acb51a15bb1"}}