{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TY44EWEANJKUDLSVQVWV2EMEOL","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":"71e788ff6131bbcabac89e3d24a5ad73164312116c92861d0090f3f4c50894cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-28T07:12:58Z","title_canon_sha256":"a461b3ac4f4279a0332b0fe58e60b7edba679960b6e6f7ed6d3508c787d2c10d"},"schema_version":"1.0","source":{"id":"1609.08801","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08801","created_at":"2026-05-18T00:01:02Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08801v2","created_at":"2026-05-18T00:01:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08801","created_at":"2026-05-18T00:01:02Z"},{"alias_kind":"pith_short_12","alias_value":"TY44EWEANJKU","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"TY44EWEANJKUDLSV","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"TY44EWEA","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:4c28f596ef4cf7360568fa78075f490296d4c21c4ca9f821c1ecf3eb8bc58f8b","target":"graph","created_at":"2026-05-18T00:01:02Z","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":"This paper makes two main contributions: The first is the construction of a near-minimum spanning tree with constant average distortion. The second is a general equivalence theorem relating two refined notions of distortion: scaling distortion and prioritized distortion.\n  Minimum Spanning Trees of weighted graphs are fundamental objects in numerous applications. In particular in distributed networks, the minimum spanning tree of the network is often used to route messages between network nodes. Unfortunately, while being most efficient in the total cost of connecting all nodes, minimum spanni","authors_text":"Arnold Filtser, Ofer Neiman, Yair Bartal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-28T07:12:58Z","title":"On Notions of Distortion and an Almost Minimum Spanning Tree with Constant Average Distortion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08801","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":"sha256:7feb25dac85e931511d8e7ea98cd1266e4fe93c4933b9db3c5cadab109eb4a22","target":"record","created_at":"2026-05-18T00:01:02Z","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":"71e788ff6131bbcabac89e3d24a5ad73164312116c92861d0090f3f4c50894cc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2016-09-28T07:12:58Z","title_canon_sha256":"a461b3ac4f4279a0332b0fe58e60b7edba679960b6e6f7ed6d3508c787d2c10d"},"schema_version":"1.0","source":{"id":"1609.08801","kind":"arxiv","version":2}},"canonical_sha256":"9e39c258806a5541ae55856d5d118472f78ee20e9712af68f15874f1230bdcbb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9e39c258806a5541ae55856d5d118472f78ee20e9712af68f15874f1230bdcbb","first_computed_at":"2026-05-18T00:01:02.063886Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:02.063886Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iPBdrw/tyMM3yLWH2ZvljATeuadJDJqtK6AOF8OWlrdUAz477Tfx59NCQ9VBLjQ89eH9LtOJH2ptNIPSYp+gBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:02.064442Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08801","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7feb25dac85e931511d8e7ea98cd1266e4fe93c4933b9db3c5cadab109eb4a22","sha256:4c28f596ef4cf7360568fa78075f490296d4c21c4ca9f821c1ecf3eb8bc58f8b"],"state_sha256":"2cfd98f3f95d2f28382979d6dc91084b3ba9287a5a85317f78cfcd4648d7bfd5"}