{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:VSJTXZHP3HJQEYA6FSES4M7SAW","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":"c7af59d80eca7a2d81da2d601d8bd11fa2ea91af73c9f2c6c0b7d9f00d5f2346","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-06-24T12:31:38Z","title_canon_sha256":"9c11957755d78a643adb60d9d505457cb9501dd0b9ddb736fbc6337ff76a4bd5"},"schema_version":"1.0","source":{"id":"2206.12245","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.12245","created_at":"2026-07-05T04:34:34Z"},{"alias_kind":"arxiv_version","alias_value":"2206.12245v1","created_at":"2026-07-05T04:34:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.12245","created_at":"2026-07-05T04:34:34Z"},{"alias_kind":"pith_short_12","alias_value":"VSJTXZHP3HJQ","created_at":"2026-07-05T04:34:34Z"},{"alias_kind":"pith_short_16","alias_value":"VSJTXZHP3HJQEYA6","created_at":"2026-07-05T04:34:34Z"},{"alias_kind":"pith_short_8","alias_value":"VSJTXZHP","created_at":"2026-07-05T04:34:34Z"}],"graph_snapshots":[{"event_id":"sha256:9e249749a3abe4e3f9a958092c722e0c7646489a6ccf27689a22df068a560a0e","target":"graph","created_at":"2026-07-05T04:34:34Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2206.12245/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum $k$-Edge-Connected Spanning Subgraph problem ($k$-ECSS), as well as nonuniform demands such as the Survivable Network Design problem. A weakness of these formulations, though, is that we are not able to ask for fault-tolerance larger than the connectivity. We introduce and study new variants of these problems under a notion of relative fault-tolerance. Informally, we require not that two nodes are connected if there are a bounded number ","authors_text":"Ama Koranteng, Guy Kortsarz, Michael Dinitz","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-06-24T12:31:38Z","title":"Relative Survivable Network Design"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.12245","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":"sha256:9c71aeac84e37ac0d937325c558b54f1b4bc798063e632ac3cccd154c85501f7","target":"record","created_at":"2026-07-05T04:34:34Z","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":"c7af59d80eca7a2d81da2d601d8bd11fa2ea91af73c9f2c6c0b7d9f00d5f2346","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2022-06-24T12:31:38Z","title_canon_sha256":"9c11957755d78a643adb60d9d505457cb9501dd0b9ddb736fbc6337ff76a4bd5"},"schema_version":"1.0","source":{"id":"2206.12245","kind":"arxiv","version":1}},"canonical_sha256":"ac933be4efd9d302601e2c892e33f205b58be9b02e0cbd03679f6ea54b237b7b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ac933be4efd9d302601e2c892e33f205b58be9b02e0cbd03679f6ea54b237b7b","first_computed_at":"2026-07-05T04:34:34.479538Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:34:34.479538Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gSIEAL2B+Jnk8dSL49XJkLGJkHpHeqs4GaNTLUavcJzuRSCIkli34ww5/TdTWb+MJ6swwzQNv67N6mruIcR8AA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:34:34.480003Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.12245","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9c71aeac84e37ac0d937325c558b54f1b4bc798063e632ac3cccd154c85501f7","sha256:9e249749a3abe4e3f9a958092c722e0c7646489a6ccf27689a22df068a560a0e"],"state_sha256":"539aad929989c99e92ac703ea0a1575b4e52207a97a26ffe2c79513810a885e5"}