{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:JBZ5GYUC3SNIP6QCB77EQFMNHO","short_pith_number":"pith:JBZ5GYUC","schema_version":"1.0","canonical_sha256":"4873d36282dc9a87fa020ffe48158d3b8007d140b260da50db4e949871579c5b","source":{"kind":"arxiv","id":"2506.03572","version":2},"attestation_state":"computed","paper":{"title":"Extendible cardinals, and Laver-generic large cardinal axioms for extendibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Saka\\'e Fuchino","submitted_at":"2025-06-04T04:39:33Z","abstract_excerpt":"We introduce (super-$C^{(\\infty)}$-)Laver-generic large cardinal axioms for extendibility ((super-$C^{(\\infty)}$-)LgLCAs for extendible, for short), and show that most of the previously known consequences of the (super-$C^{(\\infty)}$-)LgLCAs for ultrahuge, in particular, general forms of Resurrection Principles, Maximality Principles, and Absoluteness Theorems, already follow from (super-$C^{(\\infty)}$\\mbox{-)}LgLCAs for extendible.\n  The consistency of LgLCAs for extendible (for transfinitely iterable $\\Sigma_2$-definable classes of posets) follows from an extendible cardinal while the consis"},"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":"2506.03572","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2025-06-04T04:39:33Z","cross_cats_sorted":[],"title_canon_sha256":"5747880ca8e85d40f5f4890d4219ebaafb543f1fdb2192184ef407e4c00a1790","abstract_canon_sha256":"1db8c0a16388c90131930df166795115f195a7bb124e59af0b9c2bab89ccc3a8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:26:52.246133Z","signature_b64":"3NAyn5YaKRvU1P4OQ0LPIwobvdvH1D0lZJv/rYO0GQkbmbDL4yMzxRq90xpucA8m0i6XPRXLdgf8keRqn/GCAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4873d36282dc9a87fa020ffe48158d3b8007d140b260da50db4e949871579c5b","last_reissued_at":"2026-07-05T11:26:52.245639Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:26:52.245639Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extendible cardinals, and Laver-generic large cardinal axioms for extendibility","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Saka\\'e Fuchino","submitted_at":"2025-06-04T04:39:33Z","abstract_excerpt":"We introduce (super-$C^{(\\infty)}$-)Laver-generic large cardinal axioms for extendibility ((super-$C^{(\\infty)}$-)LgLCAs for extendible, for short), and show that most of the previously known consequences of the (super-$C^{(\\infty)}$-)LgLCAs for ultrahuge, in particular, general forms of Resurrection Principles, Maximality Principles, and Absoluteness Theorems, already follow from (super-$C^{(\\infty)}$\\mbox{-)}LgLCAs for extendible.\n  The consistency of LgLCAs for extendible (for transfinitely iterable $\\Sigma_2$-definable classes of posets) follows from an extendible cardinal while the consis"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.03572","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.03572/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2506.03572","created_at":"2026-07-05T11:26:52.245701+00:00"},{"alias_kind":"arxiv_version","alias_value":"2506.03572v2","created_at":"2026-07-05T11:26:52.245701+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2506.03572","created_at":"2026-07-05T11:26:52.245701+00:00"},{"alias_kind":"pith_short_12","alias_value":"JBZ5GYUC3SNI","created_at":"2026-07-05T11:26:52.245701+00:00"},{"alias_kind":"pith_short_16","alias_value":"JBZ5GYUC3SNIP6QC","created_at":"2026-07-05T11:26:52.245701+00:00"},{"alias_kind":"pith_short_8","alias_value":"JBZ5GYUC","created_at":"2026-07-05T11:26:52.245701+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/JBZ5GYUC3SNIP6QCB77EQFMNHO","json":"https://pith.science/pith/JBZ5GYUC3SNIP6QCB77EQFMNHO.json","graph_json":"https://pith.science/api/pith-number/JBZ5GYUC3SNIP6QCB77EQFMNHO/graph.json","events_json":"https://pith.science/api/pith-number/JBZ5GYUC3SNIP6QCB77EQFMNHO/events.json","paper":"https://pith.science/paper/JBZ5GYUC"},"agent_actions":{"view_html":"https://pith.science/pith/JBZ5GYUC3SNIP6QCB77EQFMNHO","download_json":"https://pith.science/pith/JBZ5GYUC3SNIP6QCB77EQFMNHO.json","view_paper":"https://pith.science/paper/JBZ5GYUC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2506.03572&json=true","fetch_graph":"https://pith.science/api/pith-number/JBZ5GYUC3SNIP6QCB77EQFMNHO/graph.json","fetch_events":"https://pith.science/api/pith-number/JBZ5GYUC3SNIP6QCB77EQFMNHO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JBZ5GYUC3SNIP6QCB77EQFMNHO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JBZ5GYUC3SNIP6QCB77EQFMNHO/action/storage_attestation","attest_author":"https://pith.science/pith/JBZ5GYUC3SNIP6QCB77EQFMNHO/action/author_attestation","sign_citation":"https://pith.science/pith/JBZ5GYUC3SNIP6QCB77EQFMNHO/action/citation_signature","submit_replication":"https://pith.science/pith/JBZ5GYUC3SNIP6QCB77EQFMNHO/action/replication_record"}},"created_at":"2026-07-05T11:26:52.245701+00:00","updated_at":"2026-07-05T11:26:52.245701+00:00"}