{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:E66N2ADXHA3WTSEVGOSYSVXZGD","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":"ca548c0ccc8c369ebbd65c2df174a0b630bc30d7bb58bd1720ce501cffb7ffd8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-30T15:37:37Z","title_canon_sha256":"7fedbcbf8c5af3941de69f601ff4f3854bb84bd49cceb610f0d2e66c067f053f"},"schema_version":"1.0","source":{"id":"2506.23970","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2506.23970","created_at":"2026-07-05T11:29:30Z"},{"alias_kind":"arxiv_version","alias_value":"2506.23970v1","created_at":"2026-07-05T11:29:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.23970","created_at":"2026-07-05T11:29:30Z"},{"alias_kind":"pith_short_12","alias_value":"E66N2ADXHA3W","created_at":"2026-07-05T11:29:30Z"},{"alias_kind":"pith_short_16","alias_value":"E66N2ADXHA3WTSEV","created_at":"2026-07-05T11:29:30Z"},{"alias_kind":"pith_short_8","alias_value":"E66N2ADX","created_at":"2026-07-05T11:29:30Z"}],"graph_snapshots":[{"event_id":"sha256:e431d587fd818a1e3185b881ded42afef7f55d4b6782f49b0a66a237e3995a40","target":"graph","created_at":"2026-07-05T11:29:30Z","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/2506.23970/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A famous conjecture by Itai and Zehavi states that, for every $d$-vertex-connected graph $G$ and every vertex $r$ in $G$, there are $d$ spanning trees of $G$ such that, for every vertex $v$ in $G\\setminus \\{r\\}$, the paths between $r$ and $v$ in different trees are internally vertex-disjoint. We show that with high probability the Itai-Zehavi conjecture holds asymptotically for the Erd\\H{o}s-R\\'enyi random graph $G(n,p)$ when $np= \\omega(\\log n)$ and for random regular graphs $G(n,d)$ when $d= \\omega(\\log n)$. Moreover, we essentially confirm the conjecture up to a constant factor for sparser ","authors_text":"Adva Mond, Julien Portier, Lawrence Hollom, Lyuben Lichev, Yiting Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-30T15:37:37Z","title":"Approximate Itai-Zehavi conjecture for random graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.23970","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":"sha256:316b1afc7d1626f5b60c82d0e6fe5e00a08c63130fda2c226f355197cb234425","target":"record","created_at":"2026-07-05T11:29:30Z","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":"ca548c0ccc8c369ebbd65c2df174a0b630bc30d7bb58bd1720ce501cffb7ffd8","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.CO","submitted_at":"2025-06-30T15:37:37Z","title_canon_sha256":"7fedbcbf8c5af3941de69f601ff4f3854bb84bd49cceb610f0d2e66c067f053f"},"schema_version":"1.0","source":{"id":"2506.23970","kind":"arxiv","version":1}},"canonical_sha256":"27bcdd0077383769c89533a58956f930fb5b02e9ccacf87146eec286f2d66634","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27bcdd0077383769c89533a58956f930fb5b02e9ccacf87146eec286f2d66634","first_computed_at":"2026-07-05T11:29:30.945217Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:29:30.945217Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G3HpAqd0ZX9WDwd4mluPZjNn02Zt7MrtpA7XK2ozPjhX6ahevpfF11c//QMtLNM05BOAgQ2csRHV7XTRxFk3Aw==","signature_status":"signed_v1","signed_at":"2026-07-05T11:29:30.945649Z","signed_message":"canonical_sha256_bytes"},"source_id":"2506.23970","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:316b1afc7d1626f5b60c82d0e6fe5e00a08c63130fda2c226f355197cb234425","sha256:e431d587fd818a1e3185b881ded42afef7f55d4b6782f49b0a66a237e3995a40"],"state_sha256":"c014b01e8cc28c226c7eab81ce03c77e24edb75970629a48be5dab9dec6792b1"}