{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5CIR2OA6IK6R2R7RFFOZD5C7QM","short_pith_number":"pith:5CIR2OA6","canonical_record":{"source":{"id":"1511.01054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-03T19:51:24Z","cross_cats_sorted":[],"title_canon_sha256":"d7f0883d60d236c0a152df1f9dda02667d40890801a3246d5a6cde18fe5766bc","abstract_canon_sha256":"2ae1aa7028361d38e5035027459afe4012a46e35a20d35e3ff4cbc2fc1d32282"},"schema_version":"1.0"},"canonical_sha256":"e8911d381e42bd1d47f1295d91f45f832e84c9b6c1017f820b3b12f424832752","source":{"kind":"arxiv","id":"1511.01054","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01054","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01054v1","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01054","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"pith_short_12","alias_value":"5CIR2OA6IK6R","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5CIR2OA6IK6R2R7R","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5CIR2OA6","created_at":"2026-05-18T12:29:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5CIR2OA6IK6R2R7RFFOZD5C7QM","target":"record","payload":{"canonical_record":{"source":{"id":"1511.01054","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-03T19:51:24Z","cross_cats_sorted":[],"title_canon_sha256":"d7f0883d60d236c0a152df1f9dda02667d40890801a3246d5a6cde18fe5766bc","abstract_canon_sha256":"2ae1aa7028361d38e5035027459afe4012a46e35a20d35e3ff4cbc2fc1d32282"},"schema_version":"1.0"},"canonical_sha256":"e8911d381e42bd1d47f1295d91f45f832e84c9b6c1017f820b3b12f424832752","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:55.324202Z","signature_b64":"9/4aoskFv4w2acdTIY86iLLWEjgL062KdwtDmBwoXIvU9nmRsFK7856M9j06JgcWa2OY5V9oR4e101sCmn8UCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8911d381e42bd1d47f1295d91f45f832e84c9b6c1017f820b3b12f424832752","last_reissued_at":"2026-05-18T01:27:55.323109Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:55.323109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.01054","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":"2026-05-18T01:27:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XcdHVlhDNPu8QjFTt7M6kQw0XvvfrcSmFs0Q8u/tQTsiHZZrdoqr9TfovktFqhr0/HW/PX4tyUitgYh/2e9zCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:31:37.045265Z"},"content_sha256":"065acfe8cb7ef548d21016a8e79671cb27d7fa018b1a3754964947e93e81fab5","schema_version":"1.0","event_id":"sha256:065acfe8cb7ef548d21016a8e79671cb27d7fa018b1a3754964947e93e81fab5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5CIR2OA6IK6R2R7RFFOZD5C7QM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"No Maximal Models from Looking Down","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Will Boney","submitted_at":"2015-11-03T19:51:24Z","abstract_excerpt":"In [Sh893], Shelah proves that (on a stationary set of cardinals) an AEC has not too many models or every model has extensions of arbitrary cardinality. We show that, if we assume limited amalgamation, then the second condition holds for a larger class of cardinals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01054","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":"2026-05-18T01:27:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aGBjT4nI+SoWlkAN4BjNd99mry5SkbBkhgcvdLcJHwzuZyhnrKTiKliAeQGNKXJJYN9aJjxNoj0Ti5MFYZP6AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T22:31:37.046043Z"},"content_sha256":"80bb7dbac3faaaf8e2013781ce18f75164c325eda9c1f8c20849674624f8e6e1","schema_version":"1.0","event_id":"sha256:80bb7dbac3faaaf8e2013781ce18f75164c325eda9c1f8c20849674624f8e6e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5CIR2OA6IK6R2R7RFFOZD5C7QM/bundle.json","state_url":"https://pith.science/pith/5CIR2OA6IK6R2R7RFFOZD5C7QM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5CIR2OA6IK6R2R7RFFOZD5C7QM/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":"2026-05-25T22:31:37Z","links":{"resolver":"https://pith.science/pith/5CIR2OA6IK6R2R7RFFOZD5C7QM","bundle":"https://pith.science/pith/5CIR2OA6IK6R2R7RFFOZD5C7QM/bundle.json","state":"https://pith.science/pith/5CIR2OA6IK6R2R7RFFOZD5C7QM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5CIR2OA6IK6R2R7RFFOZD5C7QM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5CIR2OA6IK6R2R7RFFOZD5C7QM","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":"2ae1aa7028361d38e5035027459afe4012a46e35a20d35e3ff4cbc2fc1d32282","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-03T19:51:24Z","title_canon_sha256":"d7f0883d60d236c0a152df1f9dda02667d40890801a3246d5a6cde18fe5766bc"},"schema_version":"1.0","source":{"id":"1511.01054","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.01054","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"arxiv_version","alias_value":"1511.01054v1","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.01054","created_at":"2026-05-18T01:27:55Z"},{"alias_kind":"pith_short_12","alias_value":"5CIR2OA6IK6R","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5CIR2OA6IK6R2R7R","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5CIR2OA6","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:80bb7dbac3faaaf8e2013781ce18f75164c325eda9c1f8c20849674624f8e6e1","target":"graph","created_at":"2026-05-18T01:27:55Z","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":"In [Sh893], Shelah proves that (on a stationary set of cardinals) an AEC has not too many models or every model has extensions of arbitrary cardinality. We show that, if we assume limited amalgamation, then the second condition holds for a larger class of cardinals.","authors_text":"Will Boney","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-03T19:51:24Z","title":"No Maximal Models from Looking Down"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.01054","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":"sha256:065acfe8cb7ef548d21016a8e79671cb27d7fa018b1a3754964947e93e81fab5","target":"record","created_at":"2026-05-18T01:27:55Z","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":"2ae1aa7028361d38e5035027459afe4012a46e35a20d35e3ff4cbc2fc1d32282","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-11-03T19:51:24Z","title_canon_sha256":"d7f0883d60d236c0a152df1f9dda02667d40890801a3246d5a6cde18fe5766bc"},"schema_version":"1.0","source":{"id":"1511.01054","kind":"arxiv","version":1}},"canonical_sha256":"e8911d381e42bd1d47f1295d91f45f832e84c9b6c1017f820b3b12f424832752","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8911d381e42bd1d47f1295d91f45f832e84c9b6c1017f820b3b12f424832752","first_computed_at":"2026-05-18T01:27:55.323109Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:55.323109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9/4aoskFv4w2acdTIY86iLLWEjgL062KdwtDmBwoXIvU9nmRsFK7856M9j06JgcWa2OY5V9oR4e101sCmn8UCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:55.324202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.01054","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:065acfe8cb7ef548d21016a8e79671cb27d7fa018b1a3754964947e93e81fab5","sha256:80bb7dbac3faaaf8e2013781ce18f75164c325eda9c1f8c20849674624f8e6e1"],"state_sha256":"5117f3da52899069b0b132a595017a0c3ab8b2da0867a0098cf9b444af76c3a7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7s1L+02vQIG3jfRY2iJVT86eVu/MedxX7JnqX33CLYPKu+nNKU6fIo0iCyZl79syVjxlrWNgdLGJlN8z5XHHDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T22:31:37.049982Z","bundle_sha256":"43a25b359c202118aa923d93d0c638029b6a90a2405123fea967da5006c23e75"}}