{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:CABNLVRI2H4YLXOZAJ4YQJQGUK","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":"c3e256af20374c893a65180fdb24fe02f8005967b8a4315529e73655d2662bd5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T20:35:06Z","title_canon_sha256":"0da1ef15bbe5ce1c7fe506fde96151cca4dd33e4fb2f3d9e1bea480b46a8bd9a"},"schema_version":"1.0","source":{"id":"2605.29080","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29080","created_at":"2026-05-29T01:05:17Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29080v1","created_at":"2026-05-29T01:05:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29080","created_at":"2026-05-29T01:05:17Z"},{"alias_kind":"pith_short_12","alias_value":"CABNLVRI2H4Y","created_at":"2026-05-29T01:05:17Z"},{"alias_kind":"pith_short_16","alias_value":"CABNLVRI2H4YLXOZ","created_at":"2026-05-29T01:05:17Z"},{"alias_kind":"pith_short_8","alias_value":"CABNLVRI","created_at":"2026-05-29T01:05:17Z"}],"graph_snapshots":[{"event_id":"sha256:bb955f290fe4fcee0f578563ffaacf4f9e39e1ec0af5122ed365ea812b6d4434","target":"graph","created_at":"2026-05-29T01:05:17Z","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/2605.29080/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove that if an $n$-vertex graph $G$ is non-extremal and $T$ is a bounded degree tree on $n$ vertices, then $T\\subset G$ even when the minimum degree of $G$ is less than $n/2$ by a linear term. We avoid the use of the Regularity lemma, instead we apply a vertex decomposition theorem by the author, which does not require a tower-type lower bound for $n.$","authors_text":"B\\'ela Csaba","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T20:35:06Z","title":"A stability theorem for embedding bounded degree spanning trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29080","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:ccc583f1fb45a17808a8adf5ffbc9e5acec2cc71cc21958b9aaef9c7acb0b5ff","target":"record","created_at":"2026-05-29T01:05:17Z","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":"c3e256af20374c893a65180fdb24fe02f8005967b8a4315529e73655d2662bd5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-27T20:35:06Z","title_canon_sha256":"0da1ef15bbe5ce1c7fe506fde96151cca4dd33e4fb2f3d9e1bea480b46a8bd9a"},"schema_version":"1.0","source":{"id":"2605.29080","kind":"arxiv","version":1}},"canonical_sha256":"1002d5d628d1f985ddd90279882606a2816b6f32ff4a33e544fb4895455245fb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1002d5d628d1f985ddd90279882606a2816b6f32ff4a33e544fb4895455245fb","first_computed_at":"2026-05-29T01:05:17.282192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:05:17.282192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5wTZ+RnSpRoUgcJcAYf2Gfr81qyehUGgasW6ckaHfNU/Y+dn0JXYHz522RIGV7AWSjdTY6GcCPd2CW5E0u1sCg==","signature_status":"signed_v1","signed_at":"2026-05-29T01:05:17.283094Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.29080","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ccc583f1fb45a17808a8adf5ffbc9e5acec2cc71cc21958b9aaef9c7acb0b5ff","sha256:bb955f290fe4fcee0f578563ffaacf4f9e39e1ec0af5122ed365ea812b6d4434"],"state_sha256":"7af7f534fc27cbf7f3761cf4cfcccb5765df75e8b2371cb2e165d12d22e5b3fe"}