{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:SFMZFF5SWEEBVICMCJSJHADQZW","short_pith_number":"pith:SFMZFF5S","canonical_record":{"source":{"id":"2606.02389","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T15:37:05Z","cross_cats_sorted":[],"title_canon_sha256":"69fb577a7fd405427a2c8cd0722489d20e6306c99db3a55efd6ce6e0803f8ab5","abstract_canon_sha256":"52453e32b362c7410879555e4fe3ab7e3df16e2bc1e91423fa9be1724acaec45"},"schema_version":"1.0"},"canonical_sha256":"91599297b2b1081aa04c1264938070cd86874d22de0da61bc85c46ab2c90493f","source":{"kind":"arxiv","id":"2606.02389","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02389","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02389v1","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02389","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"SFMZFF5SWEEB","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"pith_short_16","alias_value":"SFMZFF5SWEEBVICM","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"pith_short_8","alias_value":"SFMZFF5S","created_at":"2026-06-02T03:04:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:SFMZFF5SWEEBVICMCJSJHADQZW","target":"record","payload":{"canonical_record":{"source":{"id":"2606.02389","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T15:37:05Z","cross_cats_sorted":[],"title_canon_sha256":"69fb577a7fd405427a2c8cd0722489d20e6306c99db3a55efd6ce6e0803f8ab5","abstract_canon_sha256":"52453e32b362c7410879555e4fe3ab7e3df16e2bc1e91423fa9be1724acaec45"},"schema_version":"1.0"},"canonical_sha256":"91599297b2b1081aa04c1264938070cd86874d22de0da61bc85c46ab2c90493f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T03:04:57.874455Z","signature_b64":"PSlkmYq/VTQwvl7LP8qs+7BFyMej46kOWng8sPb8+ZHlw5J9iJoi80gE9G//csDbSDMYNnOcqNa/Q7OrVLXzDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"91599297b2b1081aa04c1264938070cd86874d22de0da61bc85c46ab2c90493f","last_reissued_at":"2026-06-02T03:04:57.874075Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T03:04:57.874075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.02389","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T03:04:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zmuQYTzrcRhi+JAI8xPFWdPNGrapBK3y51OyY6Lxu2v91+b13MLfdLRVVUYQo8CcsBWqO/TIzvYQDQICh5BSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T05:19:54.328756Z"},"content_sha256":"a44669f542ca3c4bd382fe5b29fd848b1d23c9c1e95caaf5f441b437eef71e1c","schema_version":"1.0","event_id":"sha256:a44669f542ca3c4bd382fe5b29fd848b1d23c9c1e95caaf5f441b437eef71e1c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:SFMZFF5SWEEBVICMCJSJHADQZW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A degree version of the Burr-Erd\\H{o}s conjecture on trees","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jasmin Katz, Jozef Skokan, Mat\\'ias Pavez-Sign\\'e","submitted_at":"2026-06-01T15:37:05Z","abstract_excerpt":"An old conjecture of Burr and Erd\\H os states that the Ramsey number of any $n$-vertex tree $T$ is at most $2n-2$. In 2012, Schelp asked whether a degree version of the Burr--Erd\\H{o}s conjecture holds. More precisely, Schelp asked if is it true that for any $\\varepsilon>0$ and $\\Delta\\ge 2$, if $G$ is a graph on $N\\ge (2+\\varepsilon)n$ vertices and minimum degree $\\delta(G)\\ge \\lfloor 3N/4\\rfloor$, then every blue/red colouring of the edges of $G$ yields a monochromatic copy of each $n$-vertex tree with maximum degree at most $\\Delta$. We prove this conjecture in a strong form, showing that i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02389","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.02389/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-06-02T03:04:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fc2BRdlzENUJzJHBCxD8sOxecEN/x1YM03Cy/NK5j3qoH3mYxDRYxj9UBjkaFQdpaswUACsAZ+5viOo3+i8aBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T05:19:54.329133Z"},"content_sha256":"3230fe2ca3ec3d85399d3a7644535b07f37e8d9a753ed8a303c5f85dcab62d8a","schema_version":"1.0","event_id":"sha256:3230fe2ca3ec3d85399d3a7644535b07f37e8d9a753ed8a303c5f85dcab62d8a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SFMZFF5SWEEBVICMCJSJHADQZW/bundle.json","state_url":"https://pith.science/pith/SFMZFF5SWEEBVICMCJSJHADQZW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SFMZFF5SWEEBVICMCJSJHADQZW/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-29T05:19:54Z","links":{"resolver":"https://pith.science/pith/SFMZFF5SWEEBVICMCJSJHADQZW","bundle":"https://pith.science/pith/SFMZFF5SWEEBVICMCJSJHADQZW/bundle.json","state":"https://pith.science/pith/SFMZFF5SWEEBVICMCJSJHADQZW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SFMZFF5SWEEBVICMCJSJHADQZW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SFMZFF5SWEEBVICMCJSJHADQZW","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":"52453e32b362c7410879555e4fe3ab7e3df16e2bc1e91423fa9be1724acaec45","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T15:37:05Z","title_canon_sha256":"69fb577a7fd405427a2c8cd0722489d20e6306c99db3a55efd6ce6e0803f8ab5"},"schema_version":"1.0","source":{"id":"2606.02389","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.02389","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"arxiv_version","alias_value":"2606.02389v1","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.02389","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"pith_short_12","alias_value":"SFMZFF5SWEEB","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"pith_short_16","alias_value":"SFMZFF5SWEEBVICM","created_at":"2026-06-02T03:04:57Z"},{"alias_kind":"pith_short_8","alias_value":"SFMZFF5S","created_at":"2026-06-02T03:04:57Z"}],"graph_snapshots":[{"event_id":"sha256:3230fe2ca3ec3d85399d3a7644535b07f37e8d9a753ed8a303c5f85dcab62d8a","target":"graph","created_at":"2026-06-02T03:04:57Z","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/2606.02389/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An old conjecture of Burr and Erd\\H os states that the Ramsey number of any $n$-vertex tree $T$ is at most $2n-2$. In 2012, Schelp asked whether a degree version of the Burr--Erd\\H{o}s conjecture holds. More precisely, Schelp asked if is it true that for any $\\varepsilon>0$ and $\\Delta\\ge 2$, if $G$ is a graph on $N\\ge (2+\\varepsilon)n$ vertices and minimum degree $\\delta(G)\\ge \\lfloor 3N/4\\rfloor$, then every blue/red colouring of the edges of $G$ yields a monochromatic copy of each $n$-vertex tree with maximum degree at most $\\Delta$. We prove this conjecture in a strong form, showing that i","authors_text":"Jasmin Katz, Jozef Skokan, Mat\\'ias Pavez-Sign\\'e","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T15:37:05Z","title":"A degree version of the Burr-Erd\\H{o}s conjecture on trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.02389","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:a44669f542ca3c4bd382fe5b29fd848b1d23c9c1e95caaf5f441b437eef71e1c","target":"record","created_at":"2026-06-02T03:04:57Z","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":"52453e32b362c7410879555e4fe3ab7e3df16e2bc1e91423fa9be1724acaec45","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-06-01T15:37:05Z","title_canon_sha256":"69fb577a7fd405427a2c8cd0722489d20e6306c99db3a55efd6ce6e0803f8ab5"},"schema_version":"1.0","source":{"id":"2606.02389","kind":"arxiv","version":1}},"canonical_sha256":"91599297b2b1081aa04c1264938070cd86874d22de0da61bc85c46ab2c90493f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"91599297b2b1081aa04c1264938070cd86874d22de0da61bc85c46ab2c90493f","first_computed_at":"2026-06-02T03:04:57.874075Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-02T03:04:57.874075Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PSlkmYq/VTQwvl7LP8qs+7BFyMej46kOWng8sPb8+ZHlw5J9iJoi80gE9G//csDbSDMYNnOcqNa/Q7OrVLXzDg==","signature_status":"signed_v1","signed_at":"2026-06-02T03:04:57.874455Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.02389","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a44669f542ca3c4bd382fe5b29fd848b1d23c9c1e95caaf5f441b437eef71e1c","sha256:3230fe2ca3ec3d85399d3a7644535b07f37e8d9a753ed8a303c5f85dcab62d8a"],"state_sha256":"5408aaee302789870dfe9f3ce517bcbb9c3151814c522f07b2eadb4c381b1568"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B69lpCdG68TqTcAAYk8D3yhvftsmMG9ddvOMnP1AUp/wAF5qYW64ebXOVTAwYrp9k4N0j+rwQykzBq4LylbjAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T05:19:54.331130Z","bundle_sha256":"1821b86a5902cc5df8f9fc1ad7058f60ad41217b405580f8770fd99679538da6"}}