{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:J4CL575WWFHNT2MTOURYRA2IOD","short_pith_number":"pith:J4CL575W","canonical_record":{"source":{"id":"1903.09358","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2019-03-22T05:03:14Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"ba500ec51ce4dafb565be1369d485e307cacca7c738323368a1f6770a1c51efd","abstract_canon_sha256":"49da633015adc54800eea7a006016bf65507f812cc9e9c80ce3ee4ba3a69c443"},"schema_version":"1.0"},"canonical_sha256":"4f04beffb6b14ed9e993752388834870e57e9f6054c71e9922d6fbe12612d85b","source":{"kind":"arxiv","id":"1903.09358","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09358","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09358v1","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09358","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"pith_short_12","alias_value":"J4CL575WWFHN","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"J4CL575WWFHNT2MT","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"J4CL575W","created_at":"2026-05-18T12:33:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:J4CL575WWFHNT2MTOURYRA2IOD","target":"record","payload":{"canonical_record":{"source":{"id":"1903.09358","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2019-03-22T05:03:14Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"ba500ec51ce4dafb565be1369d485e307cacca7c738323368a1f6770a1c51efd","abstract_canon_sha256":"49da633015adc54800eea7a006016bf65507f812cc9e9c80ce3ee4ba3a69c443"},"schema_version":"1.0"},"canonical_sha256":"4f04beffb6b14ed9e993752388834870e57e9f6054c71e9922d6fbe12612d85b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:39.851084Z","signature_b64":"Y9w9zlLt4x0ZvfXQRd6NKHkGSuYY3lXUcQbwTR7Q/3z5DlM+FnsuXmAq5ni6pc9Wyxp+VajEdRFXimbMPYuWDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4f04beffb6b14ed9e993752388834870e57e9f6054c71e9922d6fbe12612d85b","last_reissued_at":"2026-05-17T23:50:39.850626Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:39.850626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1903.09358","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":"2026-05-17T23:50:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8U7it6AJf0qgNA2l66GskFSoYSEbBtNWrMf1v/ZL56HoNqXGZOyZNnCMreMdp7iEShwrNL27ict0HWZPwmi0Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:36:31.091645Z"},"content_sha256":"ee84e0dbcce326742e789e96533647480ced4285bd42caaca49180886e5b57a5","schema_version":"1.0","event_id":"sha256:ee84e0dbcce326742e789e96533647480ced4285bd42caaca49180886e5b57a5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:J4CL575WWFHNT2MTOURYRA2IOD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient Algorithms for Geometric Partial Matching","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DS","authors_text":"Allen Xiao, Hsien-Chih Chang, Pankaj K. Agarwal","submitted_at":"2019-03-22T05:03:14Z","abstract_excerpt":"Let $A$ and $B$ be two point sets in the plane of sizes $r$ and $n$ respectively (assume $r \\leq n$), and let $k$ be a parameter. A matching between $A$ and $B$ is a family of pairs in $A \\times B$ so that any point of $A \\cup B$ appears in at most one pair. Given two positive integers $p$ and $q$, we define the cost of matching $M$ to be $c(M) = \\sum_{(a, b) \\in M}\\|{a-b}\\|_p^q$ where $\\|{\\cdot}\\|_p$ is the $L_p$-norm. The geometric partial matching problem asks to find the minimum-cost size-$k$ matching between $A$ and $B$.\n  We present efficient algorithms for geometric partial matching pro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09358","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":""},"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":"2026-05-17T23:50:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CLsnKzQw4DK3fzok/dtffncbKkXvq6WmAhHDH/ruK8byy+Ehti6FB2IEdWGDMATwKNGqU5LUKWJvhomJ/891Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T05:36:31.092094Z"},"content_sha256":"157943dd0fafc9442c981ea7663146a270b9167f38b879c5a58f8aad36bf7938","schema_version":"1.0","event_id":"sha256:157943dd0fafc9442c981ea7663146a270b9167f38b879c5a58f8aad36bf7938"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J4CL575WWFHNT2MTOURYRA2IOD/bundle.json","state_url":"https://pith.science/pith/J4CL575WWFHNT2MTOURYRA2IOD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J4CL575WWFHNT2MTOURYRA2IOD/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":"2026-08-04T05:36:31Z","links":{"resolver":"https://pith.science/pith/J4CL575WWFHNT2MTOURYRA2IOD","bundle":"https://pith.science/pith/J4CL575WWFHNT2MTOURYRA2IOD/bundle.json","state":"https://pith.science/pith/J4CL575WWFHNT2MTOURYRA2IOD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J4CL575WWFHNT2MTOURYRA2IOD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:J4CL575WWFHNT2MTOURYRA2IOD","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":"49da633015adc54800eea7a006016bf65507f812cc9e9c80ce3ee4ba3a69c443","cross_cats_sorted":["cs.CG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2019-03-22T05:03:14Z","title_canon_sha256":"ba500ec51ce4dafb565be1369d485e307cacca7c738323368a1f6770a1c51efd"},"schema_version":"1.0","source":{"id":"1903.09358","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1903.09358","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"arxiv_version","alias_value":"1903.09358v1","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.09358","created_at":"2026-05-17T23:50:39Z"},{"alias_kind":"pith_short_12","alias_value":"J4CL575WWFHN","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_16","alias_value":"J4CL575WWFHNT2MT","created_at":"2026-05-18T12:33:18Z"},{"alias_kind":"pith_short_8","alias_value":"J4CL575W","created_at":"2026-05-18T12:33:18Z"}],"graph_snapshots":[{"event_id":"sha256:157943dd0fafc9442c981ea7663146a270b9167f38b879c5a58f8aad36bf7938","target":"graph","created_at":"2026-05-17T23:50:39Z","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":"Let $A$ and $B$ be two point sets in the plane of sizes $r$ and $n$ respectively (assume $r \\leq n$), and let $k$ be a parameter. A matching between $A$ and $B$ is a family of pairs in $A \\times B$ so that any point of $A \\cup B$ appears in at most one pair. Given two positive integers $p$ and $q$, we define the cost of matching $M$ to be $c(M) = \\sum_{(a, b) \\in M}\\|{a-b}\\|_p^q$ where $\\|{\\cdot}\\|_p$ is the $L_p$-norm. The geometric partial matching problem asks to find the minimum-cost size-$k$ matching between $A$ and $B$.\n  We present efficient algorithms for geometric partial matching pro","authors_text":"Allen Xiao, Hsien-Chih Chang, Pankaj K. Agarwal","cross_cats":["cs.CG"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2019-03-22T05:03:14Z","title":"Efficient Algorithms for Geometric Partial Matching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.09358","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:ee84e0dbcce326742e789e96533647480ced4285bd42caaca49180886e5b57a5","target":"record","created_at":"2026-05-17T23:50:39Z","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":"49da633015adc54800eea7a006016bf65507f812cc9e9c80ce3ee4ba3a69c443","cross_cats_sorted":["cs.CG"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2019-03-22T05:03:14Z","title_canon_sha256":"ba500ec51ce4dafb565be1369d485e307cacca7c738323368a1f6770a1c51efd"},"schema_version":"1.0","source":{"id":"1903.09358","kind":"arxiv","version":1}},"canonical_sha256":"4f04beffb6b14ed9e993752388834870e57e9f6054c71e9922d6fbe12612d85b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4f04beffb6b14ed9e993752388834870e57e9f6054c71e9922d6fbe12612d85b","first_computed_at":"2026-05-17T23:50:39.850626Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:39.850626Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Y9w9zlLt4x0ZvfXQRd6NKHkGSuYY3lXUcQbwTR7Q/3z5DlM+FnsuXmAq5ni6pc9Wyxp+VajEdRFXimbMPYuWDw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:39.851084Z","signed_message":"canonical_sha256_bytes"},"source_id":"1903.09358","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee84e0dbcce326742e789e96533647480ced4285bd42caaca49180886e5b57a5","sha256:157943dd0fafc9442c981ea7663146a270b9167f38b879c5a58f8aad36bf7938"],"state_sha256":"d2419dd5d747d45e3c16fc1509c38aea8bdd6df8f0bc60a9e7d4c397d10ac2e6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RuLgYNvnNuERc4woP3gmhtGuSgMVeb74r7g0O+fDPa+VFR4xZ2/ehxbkuLRrAcOhOOGnqV5TCtKwg+7HrI6NBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T05:36:31.096785Z","bundle_sha256":"08b7f913ca4587c796cd3213725be86fb05b1763072f2c95bbbbdef26898b883"}}