{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IDDLKA44RGPWMFXW5QHWNDEZVH","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":"df2b9669ba5594f58ff98c15bc3b7fba50ac96d3cfde7fb2890c406997fbe3a9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-09-05T14:36:30Z","title_canon_sha256":"30c9db38d15d8045f47293d060e201f4046cad2adc90a0c69bedd42cda69c55a"},"schema_version":"1.0","source":{"id":"2509.05143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.05143","created_at":"2026-07-05T12:05:36Z"},{"alias_kind":"arxiv_version","alias_value":"2509.05143v1","created_at":"2026-07-05T12:05:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.05143","created_at":"2026-07-05T12:05:36Z"},{"alias_kind":"pith_short_12","alias_value":"IDDLKA44RGPW","created_at":"2026-07-05T12:05:36Z"},{"alias_kind":"pith_short_16","alias_value":"IDDLKA44RGPWMFXW","created_at":"2026-07-05T12:05:36Z"},{"alias_kind":"pith_short_8","alias_value":"IDDLKA44","created_at":"2026-07-05T12:05:36Z"}],"graph_snapshots":[{"event_id":"sha256:5a7a7c5a53091adc63281930b0c65051b42c68cd6def0a1f2216106404a46849","target":"graph","created_at":"2026-07-05T12:05:36Z","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/2509.05143/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study network robustness under correlated failures modeled by colors, where each color represents a class of edges or vertices that may fail simultaneously. An edge-colored graph is said to be edge-color-avoiding $k$-edge-connected if it remains $k$-edge-connected after the removal of all edges of any single color. We characterize the graphs that admit such a coloring and show that, when $k = 1$, one can determine in polynomial time both the minimum number of colors required and a coloring achieving it; while the problem becomes NP-hard for $k \\ge 2$. We also investigate the problem of orie","authors_text":"J\\'ozsef Pint\\'er, Kitti Varga","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-09-05T14:36:30Z","title":"Color-avoiding connected colorings and orientations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.05143","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":"sha256:3f6bb1038def4e41868615543e9aaca8df1dc98dd56c572553e2038bfb339254","target":"record","created_at":"2026-07-05T12:05:36Z","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":"df2b9669ba5594f58ff98c15bc3b7fba50ac96d3cfde7fb2890c406997fbe3a9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2025-09-05T14:36:30Z","title_canon_sha256":"30c9db38d15d8045f47293d060e201f4046cad2adc90a0c69bedd42cda69c55a"},"schema_version":"1.0","source":{"id":"2509.05143","kind":"arxiv","version":1}},"canonical_sha256":"40c6b5039c899f6616f6ec0f668c99a9fc10356b5c5eebc3b965cd3439b360e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40c6b5039c899f6616f6ec0f668c99a9fc10356b5c5eebc3b965cd3439b360e0","first_computed_at":"2026-07-05T12:05:36.763018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:05:36.763018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sRp9EyMS2INPhxAO6mM9sAlajv+CT3ILvE86OVrLg+2m8LCfgN6wEC2Do05BC6IVnDK0fyR0o7C7XPQbdz7uBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:05:36.763392Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.05143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f6bb1038def4e41868615543e9aaca8df1dc98dd56c572553e2038bfb339254","sha256:5a7a7c5a53091adc63281930b0c65051b42c68cd6def0a1f2216106404a46849"],"state_sha256":"86b184407d978790a7edf84135c08cd4a84919108e0decc312f65cf14fc925de"}