{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:UBZATLOY36ABZQMEA6HIWAYIAU","short_pith_number":"pith:UBZATLOY","canonical_record":{"source":{"id":"2502.00135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-31T19:40:12Z","cross_cats_sorted":[],"title_canon_sha256":"a08209a3f43f536582d45c9d0288e3e0f37c8927e502e31dad8dde273b4ba885","abstract_canon_sha256":"8de5fc64467daa1cd1f6951565452b587b0ab2ed67acf9c4b66b6aa649e558a3"},"schema_version":"1.0"},"canonical_sha256":"a07209add8df801cc184078e8b030805290c2a65584db4395ca5f573b7835551","source":{"kind":"arxiv","id":"2502.00135","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.00135","created_at":"2026-07-05T10:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"2502.00135v1","created_at":"2026-07-05T10:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.00135","created_at":"2026-07-05T10:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"UBZATLOY36AB","created_at":"2026-07-05T10:08:03Z"},{"alias_kind":"pith_short_16","alias_value":"UBZATLOY36ABZQME","created_at":"2026-07-05T10:08:03Z"},{"alias_kind":"pith_short_8","alias_value":"UBZATLOY","created_at":"2026-07-05T10:08:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:UBZATLOY36ABZQMEA6HIWAYIAU","target":"record","payload":{"canonical_record":{"source":{"id":"2502.00135","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-31T19:40:12Z","cross_cats_sorted":[],"title_canon_sha256":"a08209a3f43f536582d45c9d0288e3e0f37c8927e502e31dad8dde273b4ba885","abstract_canon_sha256":"8de5fc64467daa1cd1f6951565452b587b0ab2ed67acf9c4b66b6aa649e558a3"},"schema_version":"1.0"},"canonical_sha256":"a07209add8df801cc184078e8b030805290c2a65584db4395ca5f573b7835551","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:08:03.420845Z","signature_b64":"8ZyoOLkRpoDh6wMSdHJNGeDge8ZM8aSRO6EskDukWbDG6VqkCSmJDcRvyokrgq9PpjxWUDTeJodHLVZ5/S+GAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a07209add8df801cc184078e8b030805290c2a65584db4395ca5f573b7835551","last_reissued_at":"2026-07-05T10:08:03.420460Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:08:03.420460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2502.00135","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":"2026-07-05T10:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XLNUprmIgtkD0EJaWwz/bX18C7FD1040jzQ7tf40NS3xwI2qg6julLU8Im13wJKOfz6ZsRwI5TOGSSOe5SIvAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T01:25:13.768978Z"},"content_sha256":"915fb8edf8207d02218f540dd2276dc71cdc68ddea4c93987dcd53a5097d75c2","schema_version":"1.0","event_id":"sha256:915fb8edf8207d02218f540dd2276dc71cdc68ddea4c93987dcd53a5097d75c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:UBZATLOY36ABZQMEA6HIWAYIAU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rainbow Erd\\H{o}s-S\\'os Conjectures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dylan King, Nicholas Crawford, Sam Spiro","submitted_at":"2025-01-31T19:40:12Z","abstract_excerpt":"An edge colored graph is said to contain rainbow-$F$ if $F$ is a subgraph and every edge receives a different color. In 2007, Keevash, Mubayi, Sudakov, and Verstra\\\"ete introduced the \\emph{rainbow extremal number} $\\mathrm{ex}^*(n,F)$, a variant on the classical Tur\\'an problem, asking for the maximum number of edges in a $n$-vertex properly edge-colored graph which does not contain a rainbow-$F$. In the following years many authors have studied the asymptotic behavior of $\\mathrm{ex}^*(n,F)$ when $F$ is bipartite. In the particular case that $F$ is a tree $T$, the infamous Erd\\\"os-S\\'os conj"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.00135","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/2502.00135/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":"2026-07-05T10:08:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Bq5FvzsIiuWs5q8CNINijTwwiFmi1vp7eZZiJz9n8MJeoZ5Aeaq3GjxZA7BlKHrGO1qW1gToY2cxe9hQWNljCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-24T01:25:13.769493Z"},"content_sha256":"5c076c324716b7a0c8a50ea95d71f5ee3a06ed0cdd2fa41e1bef14afef4c3b9d","schema_version":"1.0","event_id":"sha256:5c076c324716b7a0c8a50ea95d71f5ee3a06ed0cdd2fa41e1bef14afef4c3b9d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UBZATLOY36ABZQMEA6HIWAYIAU/bundle.json","state_url":"https://pith.science/pith/UBZATLOY36ABZQMEA6HIWAYIAU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UBZATLOY36ABZQMEA6HIWAYIAU/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":"2026-08-24T01:25:13Z","links":{"resolver":"https://pith.science/pith/UBZATLOY36ABZQMEA6HIWAYIAU","bundle":"https://pith.science/pith/UBZATLOY36ABZQMEA6HIWAYIAU/bundle.json","state":"https://pith.science/pith/UBZATLOY36ABZQMEA6HIWAYIAU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UBZATLOY36ABZQMEA6HIWAYIAU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:UBZATLOY36ABZQMEA6HIWAYIAU","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":"8de5fc64467daa1cd1f6951565452b587b0ab2ed67acf9c4b66b6aa649e558a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-31T19:40:12Z","title_canon_sha256":"a08209a3f43f536582d45c9d0288e3e0f37c8927e502e31dad8dde273b4ba885"},"schema_version":"1.0","source":{"id":"2502.00135","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.00135","created_at":"2026-07-05T10:08:03Z"},{"alias_kind":"arxiv_version","alias_value":"2502.00135v1","created_at":"2026-07-05T10:08:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.00135","created_at":"2026-07-05T10:08:03Z"},{"alias_kind":"pith_short_12","alias_value":"UBZATLOY36AB","created_at":"2026-07-05T10:08:03Z"},{"alias_kind":"pith_short_16","alias_value":"UBZATLOY36ABZQME","created_at":"2026-07-05T10:08:03Z"},{"alias_kind":"pith_short_8","alias_value":"UBZATLOY","created_at":"2026-07-05T10:08:03Z"}],"graph_snapshots":[{"event_id":"sha256:5c076c324716b7a0c8a50ea95d71f5ee3a06ed0cdd2fa41e1bef14afef4c3b9d","target":"graph","created_at":"2026-07-05T10:08:03Z","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/2502.00135/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"An edge colored graph is said to contain rainbow-$F$ if $F$ is a subgraph and every edge receives a different color. In 2007, Keevash, Mubayi, Sudakov, and Verstra\\\"ete introduced the \\emph{rainbow extremal number} $\\mathrm{ex}^*(n,F)$, a variant on the classical Tur\\'an problem, asking for the maximum number of edges in a $n$-vertex properly edge-colored graph which does not contain a rainbow-$F$. In the following years many authors have studied the asymptotic behavior of $\\mathrm{ex}^*(n,F)$ when $F$ is bipartite. In the particular case that $F$ is a tree $T$, the infamous Erd\\\"os-S\\'os conj","authors_text":"Dylan King, Nicholas Crawford, Sam Spiro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-31T19:40:12Z","title":"Rainbow Erd\\H{o}s-S\\'os Conjectures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.00135","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":"sha256:915fb8edf8207d02218f540dd2276dc71cdc68ddea4c93987dcd53a5097d75c2","target":"record","created_at":"2026-07-05T10:08:03Z","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":"8de5fc64467daa1cd1f6951565452b587b0ab2ed67acf9c4b66b6aa649e558a3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-01-31T19:40:12Z","title_canon_sha256":"a08209a3f43f536582d45c9d0288e3e0f37c8927e502e31dad8dde273b4ba885"},"schema_version":"1.0","source":{"id":"2502.00135","kind":"arxiv","version":1}},"canonical_sha256":"a07209add8df801cc184078e8b030805290c2a65584db4395ca5f573b7835551","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a07209add8df801cc184078e8b030805290c2a65584db4395ca5f573b7835551","first_computed_at":"2026-07-05T10:08:03.420460Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:08:03.420460Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8ZyoOLkRpoDh6wMSdHJNGeDge8ZM8aSRO6EskDukWbDG6VqkCSmJDcRvyokrgq9PpjxWUDTeJodHLVZ5/S+GAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:08:03.420845Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.00135","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:915fb8edf8207d02218f540dd2276dc71cdc68ddea4c93987dcd53a5097d75c2","sha256:5c076c324716b7a0c8a50ea95d71f5ee3a06ed0cdd2fa41e1bef14afef4c3b9d"],"state_sha256":"43743b399d30eea3443d8aa8e995505f20061944ce1128704300eed56e51311a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yECl8aq+HlT6fHh6X9DNMeh1Nf9KUyF1M3EwdO/ItDrIKjcXeHGGKpTaWTQy20AZf6qNvp9Z5hkRSL42IJanAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-24T01:25:13.773963Z","bundle_sha256":"938d5f7e55bb406e110e6e6dc26487a9b379305af189625012bd824e29feb58b"}}