{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:M5GJK5NUJDOA74THMT7RZSBPDI","short_pith_number":"pith:M5GJK5NU","canonical_record":{"source":{"id":"2407.20307","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-07-29T16:16:34Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"48009707a9738ec952fdd1c8b3779fbcb2c257fb059eabbd9c294ea1bdec4404","abstract_canon_sha256":"bee1728b4f436f8ec3f47064439f856a95ca9af610f922adcbdc1cf2063ee37d"},"schema_version":"1.0"},"canonical_sha256":"674c9575b448dc0ff26764ff1cc82f1a2609489a665757c0b420a51db9a1231e","source":{"kind":"arxiv","id":"2407.20307","version":5},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.20307","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"2407.20307v5","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.20307","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"M5GJK5NUJDOA","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_16","alias_value":"M5GJK5NUJDOA74TH","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_8","alias_value":"M5GJK5NU","created_at":"2026-05-21T01:05:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:M5GJK5NUJDOA74THMT7RZSBPDI","target":"record","payload":{"canonical_record":{"source":{"id":"2407.20307","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-07-29T16:16:34Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"48009707a9738ec952fdd1c8b3779fbcb2c257fb059eabbd9c294ea1bdec4404","abstract_canon_sha256":"bee1728b4f436f8ec3f47064439f856a95ca9af610f922adcbdc1cf2063ee37d"},"schema_version":"1.0"},"canonical_sha256":"674c9575b448dc0ff26764ff1cc82f1a2609489a665757c0b420a51db9a1231e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-21T01:05:02.751220Z","signature_b64":"6FtBn5AV3dtWjwEM1Rrs7/dJzdl2/qpaQ1J8o4ixZmNYFiVjShtRi+qB7mpke5P2A9CRh5Wi+jcGsvIvyxsmBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"674c9575b448dc0ff26764ff1cc82f1a2609489a665757c0b420a51db9a1231e","last_reissued_at":"2026-05-21T01:05:02.750230Z","signature_status":"signed_v1","first_computed_at":"2026-05-21T01:05:02.750230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2407.20307","source_version":5,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-21T01:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s5dYKHh1Jbuwqhl5/+noc1s+CnA5d65oF3sjFZFxaIXYzITB+RIbJ7wWspfjsXT7y2BirhgVyWWtJaf7LL8DBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:48:42.681856Z"},"content_sha256":"cd82df21ee422ffbf047e16f1f1a44557a410e9059978186ba7b6edd38e0d4ee","schema_version":"1.0","event_id":"sha256:cd82df21ee422ffbf047e16f1f1a44557a410e9059978186ba7b6edd38e0d4ee"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:M5GJK5NUJDOA74THMT7RZSBPDI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fra\\\"{i}ss\\'{e}'s Conjecture and big Ramsey degrees of structures admitting finite monomorphic decomposition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.LO","authors_text":"Dragan Ma\\v{s}ulovi\\'c, Veljko Tolji\\'c","submitted_at":"2024-07-29T16:16:34Z","abstract_excerpt":"In this paper we show that a countable structure admitting a finite monomorphic decomposition has finite big Ramsey degrees if and only if so does every monomorphic part in its minimal monomorphic decomposition. The necessary prerequisite for this result is the characterization of monomorphic structures with finite big Ramsey degrees: a countable monomorphic structure has finite big Ramsey degrees if and only if it is chainable by a chain with finite big Ramsey degrees. Interestingly, both characterizations require deep structural properties of chains. Fra\\\"{i}ss\\'{e}'s Conjecture (actually, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.20307","kind":"arxiv","version":5},"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/2407.20307/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":"2026-05-21T01:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SE8kCdGi3bC7BFrO/aSKd6a5QanBR7N49a0W6J7RDhWfy1QXSFudgLyx1b10cxA76s87jBM8rj3y5AC9HcGEAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T06:48:42.682279Z"},"content_sha256":"23502f216a3d984d775113890824a4f97d87e6104983b4a81fedc5a09bd65af5","schema_version":"1.0","event_id":"sha256:23502f216a3d984d775113890824a4f97d87e6104983b4a81fedc5a09bd65af5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M5GJK5NUJDOA74THMT7RZSBPDI/bundle.json","state_url":"https://pith.science/pith/M5GJK5NUJDOA74THMT7RZSBPDI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M5GJK5NUJDOA74THMT7RZSBPDI/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":"2026-05-31T06:48:42Z","links":{"resolver":"https://pith.science/pith/M5GJK5NUJDOA74THMT7RZSBPDI","bundle":"https://pith.science/pith/M5GJK5NUJDOA74THMT7RZSBPDI/bundle.json","state":"https://pith.science/pith/M5GJK5NUJDOA74THMT7RZSBPDI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M5GJK5NUJDOA74THMT7RZSBPDI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:M5GJK5NUJDOA74THMT7RZSBPDI","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":"bee1728b4f436f8ec3f47064439f856a95ca9af610f922adcbdc1cf2063ee37d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-07-29T16:16:34Z","title_canon_sha256":"48009707a9738ec952fdd1c8b3779fbcb2c257fb059eabbd9c294ea1bdec4404"},"schema_version":"1.0","source":{"id":"2407.20307","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2407.20307","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"2407.20307v5","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2407.20307","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"M5GJK5NUJDOA","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_16","alias_value":"M5GJK5NUJDOA74TH","created_at":"2026-05-21T01:05:02Z"},{"alias_kind":"pith_short_8","alias_value":"M5GJK5NU","created_at":"2026-05-21T01:05:02Z"}],"graph_snapshots":[{"event_id":"sha256:23502f216a3d984d775113890824a4f97d87e6104983b4a81fedc5a09bd65af5","target":"graph","created_at":"2026-05-21T01:05:02Z","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/2407.20307/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper we show that a countable structure admitting a finite monomorphic decomposition has finite big Ramsey degrees if and only if so does every monomorphic part in its minimal monomorphic decomposition. The necessary prerequisite for this result is the characterization of monomorphic structures with finite big Ramsey degrees: a countable monomorphic structure has finite big Ramsey degrees if and only if it is chainable by a chain with finite big Ramsey degrees. Interestingly, both characterizations require deep structural properties of chains. Fra\\\"{i}ss\\'{e}'s Conjecture (actually, i","authors_text":"Dragan Ma\\v{s}ulovi\\'c, Veljko Tolji\\'c","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-07-29T16:16:34Z","title":"Fra\\\"{i}ss\\'{e}'s Conjecture and big Ramsey degrees of structures admitting finite monomorphic decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.20307","kind":"arxiv","version":5},"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:cd82df21ee422ffbf047e16f1f1a44557a410e9059978186ba7b6edd38e0d4ee","target":"record","created_at":"2026-05-21T01:05:02Z","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":"bee1728b4f436f8ec3f47064439f856a95ca9af610f922adcbdc1cf2063ee37d","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2024-07-29T16:16:34Z","title_canon_sha256":"48009707a9738ec952fdd1c8b3779fbcb2c257fb059eabbd9c294ea1bdec4404"},"schema_version":"1.0","source":{"id":"2407.20307","kind":"arxiv","version":5}},"canonical_sha256":"674c9575b448dc0ff26764ff1cc82f1a2609489a665757c0b420a51db9a1231e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"674c9575b448dc0ff26764ff1cc82f1a2609489a665757c0b420a51db9a1231e","first_computed_at":"2026-05-21T01:05:02.750230Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:05:02.750230Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6FtBn5AV3dtWjwEM1Rrs7/dJzdl2/qpaQ1J8o4ixZmNYFiVjShtRi+qB7mpke5P2A9CRh5Wi+jcGsvIvyxsmBA==","signature_status":"signed_v1","signed_at":"2026-05-21T01:05:02.751220Z","signed_message":"canonical_sha256_bytes"},"source_id":"2407.20307","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd82df21ee422ffbf047e16f1f1a44557a410e9059978186ba7b6edd38e0d4ee","sha256:23502f216a3d984d775113890824a4f97d87e6104983b4a81fedc5a09bd65af5"],"state_sha256":"29d2a84dd2cd3c288d819f8af3cfb147ef011acce24a8020e102d2f103b8ac51"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ul4RV8BrzCpU1Xxqw/X5wP/b7jH9XLSaI0piVQ2wSvsnNom9lirnFCe5kefXnr2wDLT6YPA1Bt3erPr7tr5QDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T06:48:42.685516Z","bundle_sha256":"5854d582b51435b95b9565f39bf35b0aa988cd0567a1d12c0931b1bf3e82af0e"}}