{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:26DREUDOEOGTV2BTWBKXI4AM3G","short_pith_number":"pith:26DREUDO","canonical_record":{"source":{"id":"1303.6659","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-03-26T20:52:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"fe46286c21cd763daecc6d08353f4e1098ae44f879076676b528c6d30da7e3f8","abstract_canon_sha256":"05c7c3a8555d55bf934315e733952e0194a9e3283d4062aaba00a6e3d5fade3a"},"schema_version":"1.0"},"canonical_sha256":"d78712506e238d3ae833b05574700cd9a8081928178d9d51f96556c5dc85ec5d","source":{"kind":"arxiv","id":"1303.6659","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6659","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6659v3","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6659","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"26DREUDOEOGT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"26DREUDOEOGTV2BT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"26DREUDO","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:26DREUDOEOGTV2BTWBKXI4AM3G","target":"record","payload":{"canonical_record":{"source":{"id":"1303.6659","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-03-26T20:52:07Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"fe46286c21cd763daecc6d08353f4e1098ae44f879076676b528c6d30da7e3f8","abstract_canon_sha256":"05c7c3a8555d55bf934315e733952e0194a9e3283d4062aaba00a6e3d5fade3a"},"schema_version":"1.0"},"canonical_sha256":"d78712506e238d3ae833b05574700cd9a8081928178d9d51f96556c5dc85ec5d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:26:03.224041Z","signature_b64":"fRdUMBH8m6KOqwt8U1m1Gf/tlpWtgmeMmXFkb9qbhaoBIw7NztJALnNImFrq2OR/LI8m8sHiP/ou2hz55YkiDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d78712506e238d3ae833b05574700cd9a8081928178d9d51f96556c5dc85ec5d","last_reissued_at":"2026-05-18T01:26:03.223577Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:26:03.223577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.6659","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eY7H5uXamNhZyPA2Cr+d5kVKt+5+pL9qI3C/I2oC1/RK2f7uUV/YgePfL/nA92zcMWtge0DKbflWywjYTDs0Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:58:54.844743Z"},"content_sha256":"f3fc95337ad090c3660a0bf12ee4c85d382f6f3be993d1f5a1d00f417f9f6a8c","schema_version":"1.0","event_id":"sha256:f3fc95337ad090c3660a0bf12ee4c85d382f6f3be993d1f5a1d00f417f9f6a8c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:26DREUDOEOGTV2BTWBKXI4AM3G","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The traveling salesman problem for lines, balls and planes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"cs.CG","authors_text":"Adrian Dumitrescu, Csaba D. T\\'oth","submitted_at":"2013-03-26T20:52:07Z","abstract_excerpt":"We revisit the traveling salesman problem with neighborhoods (TSPN) and propose several new approximation algorithms. These constitute either first approximations (for hyperplanes, lines, and balls in $\\mathbb{R}^d$, for $d\\geq 3$) or improvements over previous approximations achievable in comparable times (for unit disks in the plane).\n  \\smallskip (I) Given a set of $n$ hyperplanes in $\\mathbb{R}^d$, a TSP tour whose length is at most $O(1)$ times the optimal can be computed in $O(n)$ time, when $d$ is constant.\n  \\smallskip (II) Given a set of $n$ lines in $\\mathbb{R}^d$, a TSP tour whose l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6659","kind":"arxiv","version":3},"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":"2026-05-18T01:26:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IIxZOtVw185wi7DsMmEiZx0Xw2riIAf8Nmd5S1+8tzxvT7JM3m5dTAJQ4NYh5ow8og1CM8vuRfaAH3Gk94icDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:58:54.845366Z"},"content_sha256":"ee2e0a688beeba2c842b9eea1c269fd3423c9ca1cfa842938dc8e854c2cc9186","schema_version":"1.0","event_id":"sha256:ee2e0a688beeba2c842b9eea1c269fd3423c9ca1cfa842938dc8e854c2cc9186"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/26DREUDOEOGTV2BTWBKXI4AM3G/bundle.json","state_url":"https://pith.science/pith/26DREUDOEOGTV2BTWBKXI4AM3G/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/26DREUDOEOGTV2BTWBKXI4AM3G/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":"2026-05-30T15:58:54Z","links":{"resolver":"https://pith.science/pith/26DREUDOEOGTV2BTWBKXI4AM3G","bundle":"https://pith.science/pith/26DREUDOEOGTV2BTWBKXI4AM3G/bundle.json","state":"https://pith.science/pith/26DREUDOEOGTV2BTWBKXI4AM3G/state.json","well_known_bundle":"https://pith.science/.well-known/pith/26DREUDOEOGTV2BTWBKXI4AM3G/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:26DREUDOEOGTV2BTWBKXI4AM3G","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":"05c7c3a8555d55bf934315e733952e0194a9e3283d4062aaba00a6e3d5fade3a","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-03-26T20:52:07Z","title_canon_sha256":"fe46286c21cd763daecc6d08353f4e1098ae44f879076676b528c6d30da7e3f8"},"schema_version":"1.0","source":{"id":"1303.6659","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.6659","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"arxiv_version","alias_value":"1303.6659v3","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.6659","created_at":"2026-05-18T01:26:03Z"},{"alias_kind":"pith_short_12","alias_value":"26DREUDOEOGT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"26DREUDOEOGTV2BT","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"26DREUDO","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:ee2e0a688beeba2c842b9eea1c269fd3423c9ca1cfa842938dc8e854c2cc9186","target":"graph","created_at":"2026-05-18T01:26:03Z","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":"We revisit the traveling salesman problem with neighborhoods (TSPN) and propose several new approximation algorithms. These constitute either first approximations (for hyperplanes, lines, and balls in $\\mathbb{R}^d$, for $d\\geq 3$) or improvements over previous approximations achievable in comparable times (for unit disks in the plane).\n  \\smallskip (I) Given a set of $n$ hyperplanes in $\\mathbb{R}^d$, a TSP tour whose length is at most $O(1)$ times the optimal can be computed in $O(n)$ time, when $d$ is constant.\n  \\smallskip (II) Given a set of $n$ lines in $\\mathbb{R}^d$, a TSP tour whose l","authors_text":"Adrian Dumitrescu, Csaba D. T\\'oth","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-03-26T20:52:07Z","title":"The traveling salesman problem for lines, balls and planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6659","kind":"arxiv","version":3},"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:f3fc95337ad090c3660a0bf12ee4c85d382f6f3be993d1f5a1d00f417f9f6a8c","target":"record","created_at":"2026-05-18T01:26:03Z","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":"05c7c3a8555d55bf934315e733952e0194a9e3283d4062aaba00a6e3d5fade3a","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-03-26T20:52:07Z","title_canon_sha256":"fe46286c21cd763daecc6d08353f4e1098ae44f879076676b528c6d30da7e3f8"},"schema_version":"1.0","source":{"id":"1303.6659","kind":"arxiv","version":3}},"canonical_sha256":"d78712506e238d3ae833b05574700cd9a8081928178d9d51f96556c5dc85ec5d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d78712506e238d3ae833b05574700cd9a8081928178d9d51f96556c5dc85ec5d","first_computed_at":"2026-05-18T01:26:03.223577Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:26:03.223577Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fRdUMBH8m6KOqwt8U1m1Gf/tlpWtgmeMmXFkb9qbhaoBIw7NztJALnNImFrq2OR/LI8m8sHiP/ou2hz55YkiDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:26:03.224041Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.6659","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f3fc95337ad090c3660a0bf12ee4c85d382f6f3be993d1f5a1d00f417f9f6a8c","sha256:ee2e0a688beeba2c842b9eea1c269fd3423c9ca1cfa842938dc8e854c2cc9186"],"state_sha256":"6fb97e84ef6fd44727a7e770bc59b5a270b8a456b8080abcfc960be375c20197"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6qrsPu2nXvIyPLHlSXcgsczoAgxm8Br48c1QIHb/glH6UwI6vDNcDmXIhoGeqrfcuo/6GRR9Ky3CnUW602w/DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:58:54.848833Z","bundle_sha256":"056ec9f264d5265cddb003972e15955b58b379cbf6c20b549b0d27a6a1da2349"}}