{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:536NIKT6ZXLRB6TYISKA2G7GYM","short_pith_number":"pith:536NIKT6","canonical_record":{"source":{"id":"1512.02054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-07T14:14:41Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"f057d3e54494227372c4ec4cf8c9b131de56e1e1f945496e3538a3cbd2e101a7","abstract_canon_sha256":"eb295d431c664bddf50d0420564ee9fbddacfcdd719ba518a582ac64db7efcbb"},"schema_version":"1.0"},"canonical_sha256":"eefcd42a7ecdd710fa7844940d1be6c31119050fac3d1e922a044f9385cdbcfb","source":{"kind":"arxiv","id":"1512.02054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02054","created_at":"2026-05-18T00:40:19Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02054v1","created_at":"2026-05-18T00:40:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02054","created_at":"2026-05-18T00:40:19Z"},{"alias_kind":"pith_short_12","alias_value":"536NIKT6ZXLR","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"536NIKT6ZXLRB6TY","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"536NIKT6","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:536NIKT6ZXLRB6TYISKA2G7GYM","target":"record","payload":{"canonical_record":{"source":{"id":"1512.02054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-07T14:14:41Z","cross_cats_sorted":["math.OC"],"title_canon_sha256":"f057d3e54494227372c4ec4cf8c9b131de56e1e1f945496e3538a3cbd2e101a7","abstract_canon_sha256":"eb295d431c664bddf50d0420564ee9fbddacfcdd719ba518a582ac64db7efcbb"},"schema_version":"1.0"},"canonical_sha256":"eefcd42a7ecdd710fa7844940d1be6c31119050fac3d1e922a044f9385cdbcfb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:40:19.779095Z","signature_b64":"9zgoQJgBjpcjS/AmaZepKv9qufILZMVm+mLGjo+Lh4ZopnKU3F1OWg8Rpk/jcp21LWlr8HM0XBHbBINLN1h5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"eefcd42a7ecdd710fa7844940d1be6c31119050fac3d1e922a044f9385cdbcfb","last_reissued_at":"2026-05-18T00:40:19.778500Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:40:19.778500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.02054","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":"2026-05-18T00:40:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4K/n7hTjK4qRip+Nw7vtiNg0nfRfO6wDJ5c0e4V3TxUB4WAVBcCvRCABmVY0j2ucRQRPB1H7tpH7rvo7OKY2Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:25:33.643511Z"},"content_sha256":"ae640a0e0581c801754e8c5ee98cc1982ef5c4cb07a9a1dcbf254696bfecb922","schema_version":"1.0","event_id":"sha256:ae640a0e0581c801754e8c5ee98cc1982ef5c4cb07a9a1dcbf254696bfecb922"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:536NIKT6ZXLRB6TYISKA2G7GYM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Maximum Scatter TSP on a Regular Grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OC"],"primary_cat":"cs.DM","authors_text":"Isabella Hoffmann, J\\\"org Rambau, Sascha Kurz","submitted_at":"2015-12-07T14:14:41Z","abstract_excerpt":"In the maximum scatter traveling salesman problem the objective is to find a tour that maximizes the shortest distance between any two consecutive nodes. This model can be applied to manufacturing processes, particularly laser melting processes. We extend an algorithm by Arkin et al. that yields optimal solutions for nodes on a line to a regular $m \\times n$-grid. The new algorithm $\\textsc{Weave}(m,n)$ takes linear time to compute an optimal tour in some cases. It is asymptotically optimal and a $\\frac{\\sqrt{10}}{5}$-approximation for the $3\\times 4$-grid, which is the worst case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02054","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":"2026-05-18T00:40:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hgGZaiD5Au3sBoo9+m++q/zZmGLz95II4spmpse1WtnZbEUch5SQ8iklvmOyOcAWF7t3EgshvEqJ0bwDZHOnAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T13:25:33.644191Z"},"content_sha256":"520afd3530b88fa5de5ef9fe0484ef49e0baa0b42d1839d61f3570c8a1ff6e10","schema_version":"1.0","event_id":"sha256:520afd3530b88fa5de5ef9fe0484ef49e0baa0b42d1839d61f3570c8a1ff6e10"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/536NIKT6ZXLRB6TYISKA2G7GYM/bundle.json","state_url":"https://pith.science/pith/536NIKT6ZXLRB6TYISKA2G7GYM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/536NIKT6ZXLRB6TYISKA2G7GYM/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":"2026-05-25T13:25:33Z","links":{"resolver":"https://pith.science/pith/536NIKT6ZXLRB6TYISKA2G7GYM","bundle":"https://pith.science/pith/536NIKT6ZXLRB6TYISKA2G7GYM/bundle.json","state":"https://pith.science/pith/536NIKT6ZXLRB6TYISKA2G7GYM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/536NIKT6ZXLRB6TYISKA2G7GYM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:536NIKT6ZXLRB6TYISKA2G7GYM","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":"eb295d431c664bddf50d0420564ee9fbddacfcdd719ba518a582ac64db7efcbb","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-07T14:14:41Z","title_canon_sha256":"f057d3e54494227372c4ec4cf8c9b131de56e1e1f945496e3538a3cbd2e101a7"},"schema_version":"1.0","source":{"id":"1512.02054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.02054","created_at":"2026-05-18T00:40:19Z"},{"alias_kind":"arxiv_version","alias_value":"1512.02054v1","created_at":"2026-05-18T00:40:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.02054","created_at":"2026-05-18T00:40:19Z"},{"alias_kind":"pith_short_12","alias_value":"536NIKT6ZXLR","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"536NIKT6ZXLRB6TY","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"536NIKT6","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:520afd3530b88fa5de5ef9fe0484ef49e0baa0b42d1839d61f3570c8a1ff6e10","target":"graph","created_at":"2026-05-18T00:40:19Z","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 maximum scatter traveling salesman problem the objective is to find a tour that maximizes the shortest distance between any two consecutive nodes. This model can be applied to manufacturing processes, particularly laser melting processes. We extend an algorithm by Arkin et al. that yields optimal solutions for nodes on a line to a regular $m \\times n$-grid. The new algorithm $\\textsc{Weave}(m,n)$ takes linear time to compute an optimal tour in some cases. It is asymptotically optimal and a $\\frac{\\sqrt{10}}{5}$-approximation for the $3\\times 4$-grid, which is the worst case.","authors_text":"Isabella Hoffmann, J\\\"org Rambau, Sascha Kurz","cross_cats":["math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-07T14:14:41Z","title":"The Maximum Scatter TSP on a Regular Grid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02054","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:ae640a0e0581c801754e8c5ee98cc1982ef5c4cb07a9a1dcbf254696bfecb922","target":"record","created_at":"2026-05-18T00:40:19Z","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":"eb295d431c664bddf50d0420564ee9fbddacfcdd719ba518a582ac64db7efcbb","cross_cats_sorted":["math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-12-07T14:14:41Z","title_canon_sha256":"f057d3e54494227372c4ec4cf8c9b131de56e1e1f945496e3538a3cbd2e101a7"},"schema_version":"1.0","source":{"id":"1512.02054","kind":"arxiv","version":1}},"canonical_sha256":"eefcd42a7ecdd710fa7844940d1be6c31119050fac3d1e922a044f9385cdbcfb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eefcd42a7ecdd710fa7844940d1be6c31119050fac3d1e922a044f9385cdbcfb","first_computed_at":"2026-05-18T00:40:19.778500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:40:19.778500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9zgoQJgBjpcjS/AmaZepKv9qufILZMVm+mLGjo+Lh4ZopnKU3F1OWg8Rpk/jcp21LWlr8HM0XBHbBINLN1h5BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:40:19.779095Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.02054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae640a0e0581c801754e8c5ee98cc1982ef5c4cb07a9a1dcbf254696bfecb922","sha256:520afd3530b88fa5de5ef9fe0484ef49e0baa0b42d1839d61f3570c8a1ff6e10"],"state_sha256":"221547969b43bad87c5da470ca4cc1f8df02bf683a5b17db37b6ea9764582d6d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wDjNwJeeu8LVPnE8cKOtnq3AYCXCXq3MW6grHWWPc86KX7OgiogyBOt3wIsgaQG7WjOz5grTbLccmq2LMKnvAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T13:25:33.648244Z","bundle_sha256":"131f531f387e150da30bba092b4a9e9e91bf4e5af2b43dbb668fefd408c11e6b"}}