{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2009:MFCMILCTZ3FLENW26FH5UTWNGI","short_pith_number":"pith:MFCMILCT","schema_version":"1.0","canonical_sha256":"6144c42c53cecab236daf14fda4ecd32157443049d33d9eb7e72b698e576dce1","source":{"kind":"arxiv","id":"0903.3614","version":4},"attestation_state":"computed","paper":{"title":"Maximal failures of sequence locality in a.e.c","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Saharon Shelah","submitted_at":"2009-03-20T20:49:39Z","abstract_excerpt":"We are interested in examples of a.e.c. with amalgamation having some (extreme) behaviour concerning types. Note we deal with k being sequence-local, i.e. local for increasing chains of length a regular cardinal (for types, equality of all restrictions imply equality). . For any cardinal theta>= aleph_0 we construct an a.e.c. with amalgamation k with L.S.T.(k) = theta, |tau_K| = theta such that {kappa : kappa is a regular cardinal and K is not (2^kappa, kappa)-sequence-local} is maximal. In fact we have a direct characterization of this class of cardinals: the regular kappa such that there is "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0903.3614","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2009-03-20T20:49:39Z","cross_cats_sorted":[],"title_canon_sha256":"67369212b246a289b15741888cd1f34489ac4dde6366ba334d1c681389cd03ef","abstract_canon_sha256":"32abb80dcbe15419040fcebdb76420a930967d71547f6278fc958f9dc32a9959"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:42.152527Z","signature_b64":"lAqH+Z53AqiUrPGy8cNqwuUYkOCVHMIrSDJA5Ek56OizU0PEIkl7yHm3KVhSgxD4Shrune5m9Bs47x9tGHINCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6144c42c53cecab236daf14fda4ecd32157443049d33d9eb7e72b698e576dce1","last_reissued_at":"2026-05-17T23:54:42.149944Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:42.149944Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Maximal failures of sequence locality in a.e.c","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Saharon Shelah","submitted_at":"2009-03-20T20:49:39Z","abstract_excerpt":"We are interested in examples of a.e.c. with amalgamation having some (extreme) behaviour concerning types. Note we deal with k being sequence-local, i.e. local for increasing chains of length a regular cardinal (for types, equality of all restrictions imply equality). . For any cardinal theta>= aleph_0 we construct an a.e.c. with amalgamation k with L.S.T.(k) = theta, |tau_K| = theta such that {kappa : kappa is a regular cardinal and K is not (2^kappa, kappa)-sequence-local} is maximal. In fact we have a direct characterization of this class of cardinals: the regular kappa such that there is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0903.3614","kind":"arxiv","version":4},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0903.3614","created_at":"2026-05-17T23:54:42.150057+00:00"},{"alias_kind":"arxiv_version","alias_value":"0903.3614v4","created_at":"2026-05-17T23:54:42.150057+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0903.3614","created_at":"2026-05-17T23:54:42.150057+00:00"},{"alias_kind":"pith_short_12","alias_value":"MFCMILCTZ3FL","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_16","alias_value":"MFCMILCTZ3FLENW2","created_at":"2026-05-18T12:26:00.592388+00:00"},{"alias_kind":"pith_short_8","alias_value":"MFCMILCT","created_at":"2026-05-18T12:26:00.592388+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.07893","citing_title":"Examples of non-tame abstract elementary classes of abelian groups","ref_index":24,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MFCMILCTZ3FLENW26FH5UTWNGI","json":"https://pith.science/pith/MFCMILCTZ3FLENW26FH5UTWNGI.json","graph_json":"https://pith.science/api/pith-number/MFCMILCTZ3FLENW26FH5UTWNGI/graph.json","events_json":"https://pith.science/api/pith-number/MFCMILCTZ3FLENW26FH5UTWNGI/events.json","paper":"https://pith.science/paper/MFCMILCT"},"agent_actions":{"view_html":"https://pith.science/pith/MFCMILCTZ3FLENW26FH5UTWNGI","download_json":"https://pith.science/pith/MFCMILCTZ3FLENW26FH5UTWNGI.json","view_paper":"https://pith.science/paper/MFCMILCT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0903.3614&json=true","fetch_graph":"https://pith.science/api/pith-number/MFCMILCTZ3FLENW26FH5UTWNGI/graph.json","fetch_events":"https://pith.science/api/pith-number/MFCMILCTZ3FLENW26FH5UTWNGI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MFCMILCTZ3FLENW26FH5UTWNGI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MFCMILCTZ3FLENW26FH5UTWNGI/action/storage_attestation","attest_author":"https://pith.science/pith/MFCMILCTZ3FLENW26FH5UTWNGI/action/author_attestation","sign_citation":"https://pith.science/pith/MFCMILCTZ3FLENW26FH5UTWNGI/action/citation_signature","submit_replication":"https://pith.science/pith/MFCMILCTZ3FLENW26FH5UTWNGI/action/replication_record"}},"created_at":"2026-05-17T23:54:42.150057+00:00","updated_at":"2026-05-17T23:54:42.150057+00:00"}