{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:PAEEKLVIVECJGLQ2DZBFNQSKUJ","short_pith_number":"pith:PAEEKLVI","canonical_record":{"source":{"id":"1302.7270","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-02-28T18:08:25Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"58d226901c3c56fecf9f34b0bfd816f58bd8d03abbf8ab6155864ba4e0d41d33","abstract_canon_sha256":"1663bfa86c16638e5363b710154756537326dba2478e2213f7c69edd8726c526"},"schema_version":"1.0"},"canonical_sha256":"7808452ea8a904932e1a1e4256c24aa264b0174a64b8a258dc98a65d99b25ddc","source":{"kind":"arxiv","id":"1302.7270","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.7270","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"arxiv_version","alias_value":"1302.7270v2","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7270","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"pith_short_12","alias_value":"PAEEKLVIVECJ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PAEEKLVIVECJGLQ2","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PAEEKLVI","created_at":"2026-05-18T12:27:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:PAEEKLVIVECJGLQ2DZBFNQSKUJ","target":"record","payload":{"canonical_record":{"source":{"id":"1302.7270","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-02-28T18:08:25Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"58d226901c3c56fecf9f34b0bfd816f58bd8d03abbf8ab6155864ba4e0d41d33","abstract_canon_sha256":"1663bfa86c16638e5363b710154756537326dba2478e2213f7c69edd8726c526"},"schema_version":"1.0"},"canonical_sha256":"7808452ea8a904932e1a1e4256c24aa264b0174a64b8a258dc98a65d99b25ddc","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:22.032537Z","signature_b64":"AKbiRe4yaKQAV3UNR2Q+xKeOpFKWrwLp/lBGG5ehE47r7b7MukU7q3PDKCwrtDfN1pcvkSjEZohqeEfo8csNBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7808452ea8a904932e1a1e4256c24aa264b0174a64b8a258dc98a65d99b25ddc","last_reissued_at":"2026-05-18T02:58:22.032052Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:22.032052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.7270","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":"2026-05-18T02:58:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qx7a8Ub6nlDQ0u96BFxx7FfdBGpAPHKyEJ+1VyAtI/w6ct8nLzQtHjcvXsI+iC+0vuReP9I9TVBqNfDlHTAODg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:14:56.871104Z"},"content_sha256":"c7c7dcc1e8aeb61b8405f657b0c09c53b074ff2ac4f548d9b9550afdbc64123e","schema_version":"1.0","event_id":"sha256:c7c7dcc1e8aeb61b8405f657b0c09c53b074ff2ac4f548d9b9550afdbc64123e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:PAEEKLVIVECJGLQ2DZBFNQSKUJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A polynomial-time approximation scheme for Euclidean Steiner forest","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.CG","authors_text":"Claire Mathieu, Glencora Borradaile, Philip Klein","submitted_at":"2013-02-28T18:08:25Z","abstract_excerpt":"We give a randomized O(n polylog n)-time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed eps > 0 and given n terminals in the plane with connection requests between some pairs of terminals, our scheme finds a (1 + eps)-approximation to the minimum-length forest that connects every requested pair of terminals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7270","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":"2026-05-18T02:58:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Um4vp3ocduLz/E9/R5HPqo30RjJCvdAsP7dOfIzuSRoLKDIUFv7dTt8wzxmZtPz+C2m0w9IRwKbkRf4hFuU0CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T23:14:56.871464Z"},"content_sha256":"e3c1af35c4c8a3dfbf4589a056c68b1f288e2902fb7217c23f949faf557e9c7b","schema_version":"1.0","event_id":"sha256:e3c1af35c4c8a3dfbf4589a056c68b1f288e2902fb7217c23f949faf557e9c7b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PAEEKLVIVECJGLQ2DZBFNQSKUJ/bundle.json","state_url":"https://pith.science/pith/PAEEKLVIVECJGLQ2DZBFNQSKUJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PAEEKLVIVECJGLQ2DZBFNQSKUJ/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":"2026-06-23T23:14:56Z","links":{"resolver":"https://pith.science/pith/PAEEKLVIVECJGLQ2DZBFNQSKUJ","bundle":"https://pith.science/pith/PAEEKLVIVECJGLQ2DZBFNQSKUJ/bundle.json","state":"https://pith.science/pith/PAEEKLVIVECJGLQ2DZBFNQSKUJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PAEEKLVIVECJGLQ2DZBFNQSKUJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:PAEEKLVIVECJGLQ2DZBFNQSKUJ","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":"1663bfa86c16638e5363b710154756537326dba2478e2213f7c69edd8726c526","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-02-28T18:08:25Z","title_canon_sha256":"58d226901c3c56fecf9f34b0bfd816f58bd8d03abbf8ab6155864ba4e0d41d33"},"schema_version":"1.0","source":{"id":"1302.7270","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.7270","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"arxiv_version","alias_value":"1302.7270v2","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7270","created_at":"2026-05-18T02:58:22Z"},{"alias_kind":"pith_short_12","alias_value":"PAEEKLVIVECJ","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_16","alias_value":"PAEEKLVIVECJGLQ2","created_at":"2026-05-18T12:27:54Z"},{"alias_kind":"pith_short_8","alias_value":"PAEEKLVI","created_at":"2026-05-18T12:27:54Z"}],"graph_snapshots":[{"event_id":"sha256:e3c1af35c4c8a3dfbf4589a056c68b1f288e2902fb7217c23f949faf557e9c7b","target":"graph","created_at":"2026-05-18T02:58:22Z","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 give a randomized O(n polylog n)-time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed eps > 0 and given n terminals in the plane with connection requests between some pairs of terminals, our scheme finds a (1 + eps)-approximation to the minimum-length forest that connects every requested pair of terminals.","authors_text":"Claire Mathieu, Glencora Borradaile, Philip Klein","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-02-28T18:08:25Z","title":"A polynomial-time approximation scheme for Euclidean Steiner forest"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7270","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:c7c7dcc1e8aeb61b8405f657b0c09c53b074ff2ac4f548d9b9550afdbc64123e","target":"record","created_at":"2026-05-18T02:58:22Z","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":"1663bfa86c16638e5363b710154756537326dba2478e2213f7c69edd8726c526","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.CG","submitted_at":"2013-02-28T18:08:25Z","title_canon_sha256":"58d226901c3c56fecf9f34b0bfd816f58bd8d03abbf8ab6155864ba4e0d41d33"},"schema_version":"1.0","source":{"id":"1302.7270","kind":"arxiv","version":2}},"canonical_sha256":"7808452ea8a904932e1a1e4256c24aa264b0174a64b8a258dc98a65d99b25ddc","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7808452ea8a904932e1a1e4256c24aa264b0174a64b8a258dc98a65d99b25ddc","first_computed_at":"2026-05-18T02:58:22.032052Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:22.032052Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AKbiRe4yaKQAV3UNR2Q+xKeOpFKWrwLp/lBGG5ehE47r7b7MukU7q3PDKCwrtDfN1pcvkSjEZohqeEfo8csNBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:22.032537Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.7270","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c7c7dcc1e8aeb61b8405f657b0c09c53b074ff2ac4f548d9b9550afdbc64123e","sha256:e3c1af35c4c8a3dfbf4589a056c68b1f288e2902fb7217c23f949faf557e9c7b"],"state_sha256":"541e3277476cbdd3708f774955c84e49088218dbf01cb68350204b4a673f459a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SVaWMG6IXQmQb5Plgl428gI+OtX8fuXawfih78sv8qbS8bLpTmM85Msj7lsTwIHUJz0qAc5/vQ13kROTd6KJAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T23:14:56.873406Z","bundle_sha256":"a39e41d780676ae21214170f35526f9dcc6b68b8bf4a1204671442805840f421"}}