{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:TNDQRWVYG3ZGE2WEM6QBDEC6CB","short_pith_number":"pith:TNDQRWVY","canonical_record":{"source":{"id":"1112.3523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-12-15T14:41:45Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"416f62555d39b7b26f8b8bb0c75724ae024024f9bd12ffc41d3697522fce2f91","abstract_canon_sha256":"9ef905e9d69fdae5853aabf4fac6146505154b20fc0fc176ebb84fa5bbd82749"},"schema_version":"1.0"},"canonical_sha256":"9b4708dab836f2626ac467a011905e107444e4d8673c623a88fb57653e810a86","source":{"kind":"arxiv","id":"1112.3523","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3523","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3523v1","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3523","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"TNDQRWVYG3ZG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNDQRWVYG3ZGE2WE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNDQRWVY","created_at":"2026-05-18T12:26:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:TNDQRWVYG3ZGE2WEM6QBDEC6CB","target":"record","payload":{"canonical_record":{"source":{"id":"1112.3523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-12-15T14:41:45Z","cross_cats_sorted":["cs.CG"],"title_canon_sha256":"416f62555d39b7b26f8b8bb0c75724ae024024f9bd12ffc41d3697522fce2f91","abstract_canon_sha256":"9ef905e9d69fdae5853aabf4fac6146505154b20fc0fc176ebb84fa5bbd82749"},"schema_version":"1.0"},"canonical_sha256":"9b4708dab836f2626ac467a011905e107444e4d8673c623a88fb57653e810a86","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:18.391382Z","signature_b64":"AEZ26dAZqXQfOx1IEGd06dhTUVEby5PHztH86pY4gdXT2FvJZW+rE+DVmEbPsU2hFhk9ChSlXq8rFDKkGQJnBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b4708dab836f2626ac467a011905e107444e4d8673c623a88fb57653e810a86","last_reissued_at":"2026-05-18T04:06:18.390785Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:18.390785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.3523","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":"2026-05-18T04:06:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8hm/dwDD1PWgdtCaxc8XnW7qS3xZAY17CHQ+ccBbCA3KM3ygtaXHz/kQTvs4LmU+RuziiKWMoU3qAVPkERfUCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:01:37.018587Z"},"content_sha256":"0db7205c206803ede17422c14abe8a2b1ec83f20e3e4fdac11fb9fe6c3652325","schema_version":"1.0","event_id":"sha256:0db7205c206803ede17422c14abe8a2b1ec83f20e3e4fdac11fb9fe6c3652325"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:TNDQRWVYG3ZGE2WEM6QBDEC6CB","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximating the Edge Length of 2-Edge Connected Planar Geometric Graphs on a Set of Points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"cs.DM","authors_text":"Danny Krizanc, Evangelos Kranakis, Ladislav Stacho, Oscar Morales-Ponce, Stefan Dobrev","submitted_at":"2011-12-15T14:41:45Z","abstract_excerpt":"Given a set $P$ of $n$ points in the plane, we solve the problems of constructing a geometric planar graph spanning $P$ 1) of minimum degree 2, and 2) which is 2-edge connected, respectively, and has max edge length bounded by a factor of 2 times the optimal; we also show that the factor 2 is best possible given appropriate connectivity conditions on the set $P$, respectively. First, we construct in $O(n\\log{n})$ time a geometric planar graph of minimum degree 2 and max edge length bounded by 2 times the optimal. This is then used to construct in $O(n\\log n)$ time a 2-edge connected geometric "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3523","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":"2026-05-18T04:06:18Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HQnHddCjPBiId+lzGlup4OfLUxdMAPrpVxoTdU/+dW+21Fg2nfremoFPzmx3926gJNgZjFV2G0oUKFC8+oJMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T15:01:37.019269Z"},"content_sha256":"fcdb5b39cdcbf9b8731883fb13edda42efb54caf3c634e41fe76aaec4e965133","schema_version":"1.0","event_id":"sha256:fcdb5b39cdcbf9b8731883fb13edda42efb54caf3c634e41fe76aaec4e965133"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TNDQRWVYG3ZGE2WEM6QBDEC6CB/bundle.json","state_url":"https://pith.science/pith/TNDQRWVYG3ZGE2WEM6QBDEC6CB/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TNDQRWVYG3ZGE2WEM6QBDEC6CB/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":"2026-05-27T15:01:37Z","links":{"resolver":"https://pith.science/pith/TNDQRWVYG3ZGE2WEM6QBDEC6CB","bundle":"https://pith.science/pith/TNDQRWVYG3ZGE2WEM6QBDEC6CB/bundle.json","state":"https://pith.science/pith/TNDQRWVYG3ZGE2WEM6QBDEC6CB/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TNDQRWVYG3ZGE2WEM6QBDEC6CB/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:TNDQRWVYG3ZGE2WEM6QBDEC6CB","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":"9ef905e9d69fdae5853aabf4fac6146505154b20fc0fc176ebb84fa5bbd82749","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-12-15T14:41:45Z","title_canon_sha256":"416f62555d39b7b26f8b8bb0c75724ae024024f9bd12ffc41d3697522fce2f91"},"schema_version":"1.0","source":{"id":"1112.3523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.3523","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"arxiv_version","alias_value":"1112.3523v1","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.3523","created_at":"2026-05-18T04:06:18Z"},{"alias_kind":"pith_short_12","alias_value":"TNDQRWVYG3ZG","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"TNDQRWVYG3ZGE2WE","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"TNDQRWVY","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:fcdb5b39cdcbf9b8731883fb13edda42efb54caf3c634e41fe76aaec4e965133","target":"graph","created_at":"2026-05-18T04:06:18Z","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":"Given a set $P$ of $n$ points in the plane, we solve the problems of constructing a geometric planar graph spanning $P$ 1) of minimum degree 2, and 2) which is 2-edge connected, respectively, and has max edge length bounded by a factor of 2 times the optimal; we also show that the factor 2 is best possible given appropriate connectivity conditions on the set $P$, respectively. First, we construct in $O(n\\log{n})$ time a geometric planar graph of minimum degree 2 and max edge length bounded by 2 times the optimal. This is then used to construct in $O(n\\log n)$ time a 2-edge connected geometric ","authors_text":"Danny Krizanc, Evangelos Kranakis, Ladislav Stacho, Oscar Morales-Ponce, Stefan Dobrev","cross_cats":["cs.CG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-12-15T14:41:45Z","title":"Approximating the Edge Length of 2-Edge Connected Planar Geometric Graphs on a Set of Points"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3523","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":"sha256:0db7205c206803ede17422c14abe8a2b1ec83f20e3e4fdac11fb9fe6c3652325","target":"record","created_at":"2026-05-18T04:06:18Z","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":"9ef905e9d69fdae5853aabf4fac6146505154b20fc0fc176ebb84fa5bbd82749","cross_cats_sorted":["cs.CG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-12-15T14:41:45Z","title_canon_sha256":"416f62555d39b7b26f8b8bb0c75724ae024024f9bd12ffc41d3697522fce2f91"},"schema_version":"1.0","source":{"id":"1112.3523","kind":"arxiv","version":1}},"canonical_sha256":"9b4708dab836f2626ac467a011905e107444e4d8673c623a88fb57653e810a86","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9b4708dab836f2626ac467a011905e107444e4d8673c623a88fb57653e810a86","first_computed_at":"2026-05-18T04:06:18.390785Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:18.390785Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AEZ26dAZqXQfOx1IEGd06dhTUVEby5PHztH86pY4gdXT2FvJZW+rE+DVmEbPsU2hFhk9ChSlXq8rFDKkGQJnBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:18.391382Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.3523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0db7205c206803ede17422c14abe8a2b1ec83f20e3e4fdac11fb9fe6c3652325","sha256:fcdb5b39cdcbf9b8731883fb13edda42efb54caf3c634e41fe76aaec4e965133"],"state_sha256":"6676ac5b607870433a9ab03d7a58210d86a76a2b4bdb2861453470e644fed4be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3hXIpkSDBy8n54X62rh97OMcp/M4PS9KItHGVJUpYpvpqRwc42OhrKJtwvNAWMKFBPCjdaZEFNknhfYEocOODw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T15:01:37.025441Z","bundle_sha256":"27e5f3f6a271be94714eebf163bc6b90461e9639573aebc3f67aad1b44b8a0d8"}}