{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UWY5M2K5PV2BFKS3X7MOLKMS3B","short_pith_number":"pith:UWY5M2K5","canonical_record":{"source":{"id":"1508.04717","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-19T17:47:10Z","cross_cats_sorted":[],"title_canon_sha256":"c44061be0a5089058ba3566ae6d8305f240e41921b8685fa2c409fbecefe5eff","abstract_canon_sha256":"ac29ed418732ef8ba6b403765ecc3fc5775148d2c5062d0ae43ef53ffca64ed2"},"schema_version":"1.0"},"canonical_sha256":"a5b1d6695d7d7412aa5bbfd8e5a992d86f57fa22eaf8c7c15682f9d1d3e20d6b","source":{"kind":"arxiv","id":"1508.04717","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04717","created_at":"2026-07-05T09:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04717v6","created_at":"2026-07-05T09:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04717","created_at":"2026-07-05T09:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"UWY5M2K5PV2B","created_at":"2026-07-05T09:05:52Z"},{"alias_kind":"pith_short_16","alias_value":"UWY5M2K5PV2BFKS3","created_at":"2026-07-05T09:05:52Z"},{"alias_kind":"pith_short_8","alias_value":"UWY5M2K5","created_at":"2026-07-05T09:05:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UWY5M2K5PV2BFKS3X7MOLKMS3B","target":"record","payload":{"canonical_record":{"source":{"id":"1508.04717","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-19T17:47:10Z","cross_cats_sorted":[],"title_canon_sha256":"c44061be0a5089058ba3566ae6d8305f240e41921b8685fa2c409fbecefe5eff","abstract_canon_sha256":"ac29ed418732ef8ba6b403765ecc3fc5775148d2c5062d0ae43ef53ffca64ed2"},"schema_version":"1.0"},"canonical_sha256":"a5b1d6695d7d7412aa5bbfd8e5a992d86f57fa22eaf8c7c15682f9d1d3e20d6b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:05:52.581714Z","signature_b64":"SmhPYiinJTmKoq0JNNpg56igLOML6uR4vzMYMXiHkE+8nQYjrjjLkBYmCUOSigpi4tabgMqKD5wJxMlJw3Y0Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a5b1d6695d7d7412aa5bbfd8e5a992d86f57fa22eaf8c7c15682f9d1d3e20d6b","last_reissued_at":"2026-07-05T09:05:52.581165Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:05:52.581165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.04717","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T09:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZVGCSZpUTpEyacZE3BwO5K7npHQZ/DBA4GqvIXLWhKPR+On74thsSgKb2WkaMeJFAM/FuRHkXptQnV11I5wtBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:44:42.289463Z"},"content_sha256":"141ea3b26e07767799948ead92d4d464c09e084725f3f865c8140065375c1017","schema_version":"1.0","event_id":"sha256:141ea3b26e07767799948ead92d4d464c09e084725f3f865c8140065375c1017"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UWY5M2K5PV2BFKS3X7MOLKMS3B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit Models in Strictly Stable Abstract Elementary Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Monica M. VanDieren, Will Boney","submitted_at":"2015-08-19T17:47:10Z","abstract_excerpt":"In this paper, we examine the locality condition for non-splitting and determine the level of uniqueness of limit models that can be recovered in some stable, but not superstable, abstract elementary classes. In particular we prove (note that no tameness is assumed):\n  Suppose that $\\mathcal{K}$ is an abstract elementary class satisfying\n  1. the joint embedding and amalgamation properties with no maximal model of cardinality $\\mu$.\n  2. stability in $\\mu$.\n  3. $\\kappa^*_\\mu(\\mathcal{K})<\\mu^+$.\n  4. continuity for non-$\\mu$-splitting (i.e. if $p\\in\\text{ga-S}(M)$ and $M$ is a limit model wit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04717","kind":"arxiv","version":6},"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/1508.04717/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":"2026-07-05T09:05:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"twlhvxk78f4Oh5NCEE07AMTLCHzNCEZ1mqDbWZ/lR3nUuiHjoJgkhDkgk+fItZ+iKLrcuZr26RKqfpBqzeTJBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T08:44:42.290078Z"},"content_sha256":"79548f97cb1f02fb7d74d1c91542909e880cc9a721a77e00196544abfd05e77b","schema_version":"1.0","event_id":"sha256:79548f97cb1f02fb7d74d1c91542909e880cc9a721a77e00196544abfd05e77b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UWY5M2K5PV2BFKS3X7MOLKMS3B/bundle.json","state_url":"https://pith.science/pith/UWY5M2K5PV2BFKS3X7MOLKMS3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UWY5M2K5PV2BFKS3X7MOLKMS3B/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":"2026-08-16T08:44:42Z","links":{"resolver":"https://pith.science/pith/UWY5M2K5PV2BFKS3X7MOLKMS3B","bundle":"https://pith.science/pith/UWY5M2K5PV2BFKS3X7MOLKMS3B/bundle.json","state":"https://pith.science/pith/UWY5M2K5PV2BFKS3X7MOLKMS3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UWY5M2K5PV2BFKS3X7MOLKMS3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UWY5M2K5PV2BFKS3X7MOLKMS3B","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":"ac29ed418732ef8ba6b403765ecc3fc5775148d2c5062d0ae43ef53ffca64ed2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-19T17:47:10Z","title_canon_sha256":"c44061be0a5089058ba3566ae6d8305f240e41921b8685fa2c409fbecefe5eff"},"schema_version":"1.0","source":{"id":"1508.04717","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04717","created_at":"2026-07-05T09:05:52Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04717v6","created_at":"2026-07-05T09:05:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04717","created_at":"2026-07-05T09:05:52Z"},{"alias_kind":"pith_short_12","alias_value":"UWY5M2K5PV2B","created_at":"2026-07-05T09:05:52Z"},{"alias_kind":"pith_short_16","alias_value":"UWY5M2K5PV2BFKS3","created_at":"2026-07-05T09:05:52Z"},{"alias_kind":"pith_short_8","alias_value":"UWY5M2K5","created_at":"2026-07-05T09:05:52Z"}],"graph_snapshots":[{"event_id":"sha256:79548f97cb1f02fb7d74d1c91542909e880cc9a721a77e00196544abfd05e77b","target":"graph","created_at":"2026-07-05T09:05:52Z","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/1508.04717/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we examine the locality condition for non-splitting and determine the level of uniqueness of limit models that can be recovered in some stable, but not superstable, abstract elementary classes. In particular we prove (note that no tameness is assumed):\n  Suppose that $\\mathcal{K}$ is an abstract elementary class satisfying\n  1. the joint embedding and amalgamation properties with no maximal model of cardinality $\\mu$.\n  2. stability in $\\mu$.\n  3. $\\kappa^*_\\mu(\\mathcal{K})<\\mu^+$.\n  4. continuity for non-$\\mu$-splitting (i.e. if $p\\in\\text{ga-S}(M)$ and $M$ is a limit model wit","authors_text":"Monica M. VanDieren, Will Boney","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-19T17:47:10Z","title":"Limit Models in Strictly Stable Abstract Elementary Classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04717","kind":"arxiv","version":6},"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":"sha256:141ea3b26e07767799948ead92d4d464c09e084725f3f865c8140065375c1017","target":"record","created_at":"2026-07-05T09:05:52Z","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":"ac29ed418732ef8ba6b403765ecc3fc5775148d2c5062d0ae43ef53ffca64ed2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-08-19T17:47:10Z","title_canon_sha256":"c44061be0a5089058ba3566ae6d8305f240e41921b8685fa2c409fbecefe5eff"},"schema_version":"1.0","source":{"id":"1508.04717","kind":"arxiv","version":6}},"canonical_sha256":"a5b1d6695d7d7412aa5bbfd8e5a992d86f57fa22eaf8c7c15682f9d1d3e20d6b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a5b1d6695d7d7412aa5bbfd8e5a992d86f57fa22eaf8c7c15682f9d1d3e20d6b","first_computed_at":"2026-07-05T09:05:52.581165Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:05:52.581165Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SmhPYiinJTmKoq0JNNpg56igLOML6uR4vzMYMXiHkE+8nQYjrjjLkBYmCUOSigpi4tabgMqKD5wJxMlJw3Y0Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:05:52.581714Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04717","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:141ea3b26e07767799948ead92d4d464c09e084725f3f865c8140065375c1017","sha256:79548f97cb1f02fb7d74d1c91542909e880cc9a721a77e00196544abfd05e77b"],"state_sha256":"7cd57dc6a51368e4bfb5db484df23dbf9147a3961efdb887747274014098c113"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VU4R7faQDDI68cRRiz+hb94hLWL7UjYusNG5XuRukdJPXlSFekRmtc9iJO9UULiUt09nh7tMhufl3NV88cogCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T08:44:42.293889Z","bundle_sha256":"6288a8ceb3cf70f647b1503ca50e5f9c7a7704469a809129c0885380d8f705ce"}}