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In particular, $\\mathsf{ZF + AD + V = L(\\mathbb{R})}$ proves that for every nontrivial forcing $\\mathbb{P} \\in L_\\Theta(\\mathbb{R})$, $1_{\\mathbb{P}} \\Vdash_{\\mathbb{P}} \\neg\\mathsf{AD}$."},"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":"1903.07005","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2019-03-16T23:57:53Z","cross_cats_sorted":[],"title_canon_sha256":"0c8f185d55e4583d02a7ed8d365eb1063a5e7c4eb711ce3cbf6c1efb0ef188f2","abstract_canon_sha256":"c53669ef4fe113f09bed88eea9c8751bf1adcd104fbe5521aa672fad77839b62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:04.574624Z","signature_b64":"sm6AMBlyK6J5ifGHKa26TBvPXVIDxz2aWiyrAyvtv0Lxpsxd/FMJzmW6ZLaA/kbAxUgFrzWPPFb2aiI2wWKnCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"964c837967ef50b28652d1402653238dc741ea872ca33b1ca634931ac15539d9","last_reissued_at":"2026-05-17T23:51:04.574070Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:04.574070Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Destruction of the Axiom of Determinacy by Forcings on $\\mathbb{R}$ when $\\Theta$ is Regular","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Stephen Jackson, William Chan","submitted_at":"2019-03-16T23:57:53Z","abstract_excerpt":"$\\mathsf{ZF + AD}$ proves that for all nontrivial forcings $\\mathbb{P}$ on a wellorderable set of cardinality less than $\\Theta$, $1_{\\mathbb{P}} \\Vdash_{\\mathbb{P}} \\neg\\mathsf{AD}$. $\\mathsf{ZF + AD} + \\Theta$ is regular proves that for all nontrivial forcing $\\mathbb{P}$ which is a surjective image of $\\mathbb{R}$, $1_{\\mathbb{P}} \\Vdash_{\\mathbb{P}} \\neg\\mathsf{AD}$. In particular, $\\mathsf{ZF + AD + V = L(\\mathbb{R})}$ proves that for every nontrivial forcing $\\mathbb{P} \\in L_\\Theta(\\mathbb{R})$, $1_{\\mathbb{P}} \\Vdash_{\\mathbb{P}} \\neg\\mathsf{AD}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.07005","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1903.07005","created_at":"2026-05-17T23:51:04.574155+00:00"},{"alias_kind":"arxiv_version","alias_value":"1903.07005v1","created_at":"2026-05-17T23:51:04.574155+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1903.07005","created_at":"2026-05-17T23:51:04.574155+00:00"},{"alias_kind":"pith_short_12","alias_value":"SZGIG6LH55IL","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_16","alias_value":"SZGIG6LH55ILFBSS","created_at":"2026-05-18T12:33:27.125529+00:00"},{"alias_kind":"pith_short_8","alias_value":"SZGIG6LH","created_at":"2026-05-18T12:33:27.125529+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/SZGIG6LH55ILFBSS2FACMUZDRX","json":"https://pith.science/pith/SZGIG6LH55ILFBSS2FACMUZDRX.json","graph_json":"https://pith.science/api/pith-number/SZGIG6LH55ILFBSS2FACMUZDRX/graph.json","events_json":"https://pith.science/api/pith-number/SZGIG6LH55ILFBSS2FACMUZDRX/events.json","paper":"https://pith.science/paper/SZGIG6LH"},"agent_actions":{"view_html":"https://pith.science/pith/SZGIG6LH55ILFBSS2FACMUZDRX","download_json":"https://pith.science/pith/SZGIG6LH55ILFBSS2FACMUZDRX.json","view_paper":"https://pith.science/paper/SZGIG6LH","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1903.07005&json=true","fetch_graph":"https://pith.science/api/pith-number/SZGIG6LH55ILFBSS2FACMUZDRX/graph.json","fetch_events":"https://pith.science/api/pith-number/SZGIG6LH55ILFBSS2FACMUZDRX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SZGIG6LH55ILFBSS2FACMUZDRX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SZGIG6LH55ILFBSS2FACMUZDRX/action/storage_attestation","attest_author":"https://pith.science/pith/SZGIG6LH55ILFBSS2FACMUZDRX/action/author_attestation","sign_citation":"https://pith.science/pith/SZGIG6LH55ILFBSS2FACMUZDRX/action/citation_signature","submit_replication":"https://pith.science/pith/SZGIG6LH55ILFBSS2FACMUZDRX/action/replication_record"}},"created_at":"2026-05-17T23:51:04.574155+00:00","updated_at":"2026-05-17T23:51:04.574155+00:00"}