{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:DHHTGLASMZOE255UNZAWJ6TMFA","short_pith_number":"pith:DHHTGLAS","schema_version":"1.0","canonical_sha256":"19cf332c12665c4d77b46e4164fa6c282a4aeb57b099cb618529bd0f071bb311","source":{"kind":"arxiv","id":"1510.01724","version":2},"attestation_state":"computed","paper":{"title":"A long pseudo-comparison of premice in $L[x]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Farmer Schlutzenberg","submitted_at":"2015-10-06T19:45:48Z","abstract_excerpt":"We describe an obstacle to the analysis of $\\mathrm{HOD}^{L[x]}$ as a core model: Assuming sufficient large cardinals, for a Turing cone of reals $x$ there are premice $M,N$ in $\\mathrm{HC}^{L[x]}$ such that the pseudo-comparison of $L[M]$ with $L[N]$ succeeds, is computed in $L[x]$, and lasts through $\\omega_1^{L[x]}$ stages. Moreover, we can take $M=M_1|(\\delta^+)^{M_1}$ where $M_1$ is the minimal iterable proper class inner model with a Woodin cardinal, and $\\delta$ is that Woodin. We can take $N$ such that $L[N]$ is $M_1$-like and short-tree-iterable."},"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":"1510.01724","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2015-10-06T19:45:48Z","cross_cats_sorted":[],"title_canon_sha256":"7e721531f89e7ea22336b4863faecd4480e3d449c50ef2b0150630a8da3eb2d4","abstract_canon_sha256":"4066dcf9ec8f1463158a94cd48e9e7fd064770bc0e1878e1b0da99dd89c5301f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:46.060697Z","signature_b64":"yQvd/T1DvgVVyYJ+K7ZOru/wj5mMANR/Xc9EL4l1Ra+vTgRb3p3exFCtgEMEFIgXWK3BPXt83gr9gIw5GXwbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"19cf332c12665c4d77b46e4164fa6c282a4aeb57b099cb618529bd0f071bb311","last_reissued_at":"2026-05-18T00:00:46.060283Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:46.060283Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A long pseudo-comparison of premice in $L[x]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Farmer Schlutzenberg","submitted_at":"2015-10-06T19:45:48Z","abstract_excerpt":"We describe an obstacle to the analysis of $\\mathrm{HOD}^{L[x]}$ as a core model: Assuming sufficient large cardinals, for a Turing cone of reals $x$ there are premice $M,N$ in $\\mathrm{HC}^{L[x]}$ such that the pseudo-comparison of $L[M]$ with $L[N]$ succeeds, is computed in $L[x]$, and lasts through $\\omega_1^{L[x]}$ stages. Moreover, we can take $M=M_1|(\\delta^+)^{M_1}$ where $M_1$ is the minimal iterable proper class inner model with a Woodin cardinal, and $\\delta$ is that Woodin. We can take $N$ such that $L[N]$ is $M_1$-like and short-tree-iterable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01724","kind":"arxiv","version":2},"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":"1510.01724","created_at":"2026-05-18T00:00:46.060353+00:00"},{"alias_kind":"arxiv_version","alias_value":"1510.01724v2","created_at":"2026-05-18T00:00:46.060353+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.01724","created_at":"2026-05-18T00:00:46.060353+00:00"},{"alias_kind":"pith_short_12","alias_value":"DHHTGLASMZOE","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DHHTGLASMZOE255U","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DHHTGLAS","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DHHTGLASMZOE255UNZAWJ6TMFA","json":"https://pith.science/pith/DHHTGLASMZOE255UNZAWJ6TMFA.json","graph_json":"https://pith.science/api/pith-number/DHHTGLASMZOE255UNZAWJ6TMFA/graph.json","events_json":"https://pith.science/api/pith-number/DHHTGLASMZOE255UNZAWJ6TMFA/events.json","paper":"https://pith.science/paper/DHHTGLAS"},"agent_actions":{"view_html":"https://pith.science/pith/DHHTGLASMZOE255UNZAWJ6TMFA","download_json":"https://pith.science/pith/DHHTGLASMZOE255UNZAWJ6TMFA.json","view_paper":"https://pith.science/paper/DHHTGLAS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1510.01724&json=true","fetch_graph":"https://pith.science/api/pith-number/DHHTGLASMZOE255UNZAWJ6TMFA/graph.json","fetch_events":"https://pith.science/api/pith-number/DHHTGLASMZOE255UNZAWJ6TMFA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DHHTGLASMZOE255UNZAWJ6TMFA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DHHTGLASMZOE255UNZAWJ6TMFA/action/storage_attestation","attest_author":"https://pith.science/pith/DHHTGLASMZOE255UNZAWJ6TMFA/action/author_attestation","sign_citation":"https://pith.science/pith/DHHTGLASMZOE255UNZAWJ6TMFA/action/citation_signature","submit_replication":"https://pith.science/pith/DHHTGLASMZOE255UNZAWJ6TMFA/action/replication_record"}},"created_at":"2026-05-18T00:00:46.060353+00:00","updated_at":"2026-05-18T00:00:46.060353+00:00"}