{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:GCHEFLYVFHXGDYMTSVSVJBLHD5","short_pith_number":"pith:GCHEFLYV","canonical_record":{"source":{"id":"1408.4188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-19T01:42:24Z","cross_cats_sorted":[],"title_canon_sha256":"725b4f75b9f6fe7a93f2f306425a91d8f569b95e93b337723b71baf24c00f627","abstract_canon_sha256":"eb4126b127c5350b038c0842b57a5f131f1aad65d3b548a657a04d729104f7c1"},"schema_version":"1.0"},"canonical_sha256":"308e42af1529ee61e19395655485671f7866b249d58b0620e65dc868b2b6929b","source":{"kind":"arxiv","id":"1408.4188","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4188","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4188v1","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4188","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"pith_short_12","alias_value":"GCHEFLYVFHXG","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GCHEFLYVFHXGDYMT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GCHEFLYV","created_at":"2026-05-18T12:28:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:GCHEFLYVFHXGDYMTSVSVJBLHD5","target":"record","payload":{"canonical_record":{"source":{"id":"1408.4188","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-19T01:42:24Z","cross_cats_sorted":[],"title_canon_sha256":"725b4f75b9f6fe7a93f2f306425a91d8f569b95e93b337723b71baf24c00f627","abstract_canon_sha256":"eb4126b127c5350b038c0842b57a5f131f1aad65d3b548a657a04d729104f7c1"},"schema_version":"1.0"},"canonical_sha256":"308e42af1529ee61e19395655485671f7866b249d58b0620e65dc868b2b6929b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:55.940546Z","signature_b64":"DAd5vAoiby4g2m87df3LBfonXb377LNQqq4b8/jKZI1gi1reyqY6ogjrVxYT3LKj1ZGRLTyQiw6DppYk3sQBAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"308e42af1529ee61e19395655485671f7866b249d58b0620e65dc868b2b6929b","last_reissued_at":"2026-05-18T02:44:55.940116Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:55.940116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1408.4188","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":"2026-05-18T02:44:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UgaPiwDcBfgSl0q4rPRDwt28RVJFn25zBUgvS+3p+VTf2zuF+P9+8+e22TrYoxgUUlHdiZEPC/g3KR+QH4mvDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:37:20.764588Z"},"content_sha256":"871bdae4eece5edf90e0fdf450d6fbc0afafa5c0e2820003cb597cd4a0a2671c","schema_version":"1.0","event_id":"sha256:871bdae4eece5edf90e0fdf450d6fbc0afafa5c0e2820003cb597cd4a0a2671c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:GCHEFLYVFHXGDYMTSVSVJBLHD5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Small universal families of graphs on $\\aleph_{\\omega+1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Charles Morgan, James Cummings, Mirna D\\v{z}amonja","submitted_at":"2014-08-19T01:42:24Z","abstract_excerpt":"We prove that it is consistent that $\\aleph_\\omega$ is strong limit, $2^{\\aleph_\\omega}$ is large and the  universality number for graphs on $\\aleph_{\\omega+1}$ is small. The proof uses Prikry forcing with interleaved  collapsing."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4188","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":""},"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":"2026-05-18T02:44:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"P/FrhFE08ti4fBvNjm++yQV6SlQw7SqfeN3BzevNQg2RtKrnpkNBwYXWi7lHxIqcK3O+0vM9hN15TGzBVxyxAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T08:37:20.764953Z"},"content_sha256":"eb15173adb7ac14f396564c44eb4e17388eb91e21c69803727226f5d595056ac","schema_version":"1.0","event_id":"sha256:eb15173adb7ac14f396564c44eb4e17388eb91e21c69803727226f5d595056ac"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GCHEFLYVFHXGDYMTSVSVJBLHD5/bundle.json","state_url":"https://pith.science/pith/GCHEFLYVFHXGDYMTSVSVJBLHD5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GCHEFLYVFHXGDYMTSVSVJBLHD5/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":"2026-05-30T08:37:20Z","links":{"resolver":"https://pith.science/pith/GCHEFLYVFHXGDYMTSVSVJBLHD5","bundle":"https://pith.science/pith/GCHEFLYVFHXGDYMTSVSVJBLHD5/bundle.json","state":"https://pith.science/pith/GCHEFLYVFHXGDYMTSVSVJBLHD5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GCHEFLYVFHXGDYMTSVSVJBLHD5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:GCHEFLYVFHXGDYMTSVSVJBLHD5","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":"eb4126b127c5350b038c0842b57a5f131f1aad65d3b548a657a04d729104f7c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-19T01:42:24Z","title_canon_sha256":"725b4f75b9f6fe7a93f2f306425a91d8f569b95e93b337723b71baf24c00f627"},"schema_version":"1.0","source":{"id":"1408.4188","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.4188","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"arxiv_version","alias_value":"1408.4188v1","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.4188","created_at":"2026-05-18T02:44:55Z"},{"alias_kind":"pith_short_12","alias_value":"GCHEFLYVFHXG","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_16","alias_value":"GCHEFLYVFHXGDYMT","created_at":"2026-05-18T12:28:30Z"},{"alias_kind":"pith_short_8","alias_value":"GCHEFLYV","created_at":"2026-05-18T12:28:30Z"}],"graph_snapshots":[{"event_id":"sha256:eb15173adb7ac14f396564c44eb4e17388eb91e21c69803727226f5d595056ac","target":"graph","created_at":"2026-05-18T02:44:55Z","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"},"paper":{"abstract_excerpt":"We prove that it is consistent that $\\aleph_\\omega$ is strong limit, $2^{\\aleph_\\omega}$ is large and the  universality number for graphs on $\\aleph_{\\omega+1}$ is small. The proof uses Prikry forcing with interleaved  collapsing.","authors_text":"Charles Morgan, James Cummings, Mirna D\\v{z}amonja","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-19T01:42:24Z","title":"Small universal families of graphs on $\\aleph_{\\omega+1}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4188","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":"sha256:871bdae4eece5edf90e0fdf450d6fbc0afafa5c0e2820003cb597cd4a0a2671c","target":"record","created_at":"2026-05-18T02:44:55Z","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":"eb4126b127c5350b038c0842b57a5f131f1aad65d3b548a657a04d729104f7c1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-08-19T01:42:24Z","title_canon_sha256":"725b4f75b9f6fe7a93f2f306425a91d8f569b95e93b337723b71baf24c00f627"},"schema_version":"1.0","source":{"id":"1408.4188","kind":"arxiv","version":1}},"canonical_sha256":"308e42af1529ee61e19395655485671f7866b249d58b0620e65dc868b2b6929b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"308e42af1529ee61e19395655485671f7866b249d58b0620e65dc868b2b6929b","first_computed_at":"2026-05-18T02:44:55.940116Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:55.940116Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DAd5vAoiby4g2m87df3LBfonXb377LNQqq4b8/jKZI1gi1reyqY6ogjrVxYT3LKj1ZGRLTyQiw6DppYk3sQBAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:55.940546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.4188","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:871bdae4eece5edf90e0fdf450d6fbc0afafa5c0e2820003cb597cd4a0a2671c","sha256:eb15173adb7ac14f396564c44eb4e17388eb91e21c69803727226f5d595056ac"],"state_sha256":"84c40d11dee0d231f3d244a52640ad5a6d02441e310af8f7e1b4afab3606cc3a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xkGIFBVaK3olHfWQwwXR+JrTRl+6VyxhQQjoxlGekXk4dy4CsTFbyBtjFkTyJgTV4CFEUD2O38AUJymDxDsSCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T08:37:20.766995Z","bundle_sha256":"6565b3282949852f96e56e602bc420d56b64b9bb745ec60356fca010a8861dbe"}}