{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:DCI4VT6ACRVK7WJK2UBFP2R7XD","short_pith_number":"pith:DCI4VT6A","schema_version":"1.0","canonical_sha256":"1891cacfc0146aafd92ad50257ea3fb8ce6b07728f019be1f25fde230cc20fdd","source":{"kind":"arxiv","id":"1610.08620","version":2},"attestation_state":"computed","paper":{"title":"Weak prediction principles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Omer Ben-Neria, Shimon Garti, Yair Hayut","submitted_at":"2016-10-27T05:25:30Z","abstract_excerpt":"We prove the consistency of the failure of the weak diamond $\\Phi_\\lambda$ at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond $\\Psi_\\lambda$ is equivalent to the statement $2^{<\\lambda}<2^\\lambda$ and hence holds at every strongly inaccessible cardinal."},"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":"1610.08620","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2016-10-27T05:25:30Z","cross_cats_sorted":[],"title_canon_sha256":"9a824a4cbfa78c978ccd7f2002718b8a0efd27fa60611b16af7c9ce67890c01f","abstract_canon_sha256":"e6b9af7d80b11700f42eb7ef75098ed7eb18a99b6521493f02daa028cc7784db"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:44.602642Z","signature_b64":"/3KYfhAVbsahxcPb2YUeJrYKLmJ6DylXI19pjXoGOoqk18hlj03Vhre2eKcaKkkajwVQYnTWRLSTaNp6at6BAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1891cacfc0146aafd92ad50257ea3fb8ce6b07728f019be1f25fde230cc20fdd","last_reissued_at":"2026-05-17T23:51:44.602015Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:44.602015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak prediction principles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Omer Ben-Neria, Shimon Garti, Yair Hayut","submitted_at":"2016-10-27T05:25:30Z","abstract_excerpt":"We prove the consistency of the failure of the weak diamond $\\Phi_\\lambda$ at strongly inaccessible cardinals. On the other hand, we show that the very weak diamond $\\Psi_\\lambda$ is equivalent to the statement $2^{<\\lambda}<2^\\lambda$ and hence holds at every strongly inaccessible cardinal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.08620","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":"1610.08620","created_at":"2026-05-17T23:51:44.602104+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.08620v2","created_at":"2026-05-17T23:51:44.602104+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.08620","created_at":"2026-05-17T23:51:44.602104+00:00"},{"alias_kind":"pith_short_12","alias_value":"DCI4VT6ACRVK","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_16","alias_value":"DCI4VT6ACRVK7WJK","created_at":"2026-05-18T12:30:12.583610+00:00"},{"alias_kind":"pith_short_8","alias_value":"DCI4VT6A","created_at":"2026-05-18T12:30:12.583610+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/DCI4VT6ACRVK7WJK2UBFP2R7XD","json":"https://pith.science/pith/DCI4VT6ACRVK7WJK2UBFP2R7XD.json","graph_json":"https://pith.science/api/pith-number/DCI4VT6ACRVK7WJK2UBFP2R7XD/graph.json","events_json":"https://pith.science/api/pith-number/DCI4VT6ACRVK7WJK2UBFP2R7XD/events.json","paper":"https://pith.science/paper/DCI4VT6A"},"agent_actions":{"view_html":"https://pith.science/pith/DCI4VT6ACRVK7WJK2UBFP2R7XD","download_json":"https://pith.science/pith/DCI4VT6ACRVK7WJK2UBFP2R7XD.json","view_paper":"https://pith.science/paper/DCI4VT6A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.08620&json=true","fetch_graph":"https://pith.science/api/pith-number/DCI4VT6ACRVK7WJK2UBFP2R7XD/graph.json","fetch_events":"https://pith.science/api/pith-number/DCI4VT6ACRVK7WJK2UBFP2R7XD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DCI4VT6ACRVK7WJK2UBFP2R7XD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DCI4VT6ACRVK7WJK2UBFP2R7XD/action/storage_attestation","attest_author":"https://pith.science/pith/DCI4VT6ACRVK7WJK2UBFP2R7XD/action/author_attestation","sign_citation":"https://pith.science/pith/DCI4VT6ACRVK7WJK2UBFP2R7XD/action/citation_signature","submit_replication":"https://pith.science/pith/DCI4VT6ACRVK7WJK2UBFP2R7XD/action/replication_record"}},"created_at":"2026-05-17T23:51:44.602104+00:00","updated_at":"2026-05-17T23:51:44.602104+00:00"}