{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:O2NVDY6WVNAJYMLNSELX6HDBUO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"693cb3a04a09898ae41b6ed276bc29a890a6bf11a4c0384576d996aa64e76c45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-06-05T15:17:59Z","title_canon_sha256":"85ce81b3195b33628d4ac4a88ee7f3086f5a6591b9d61279e812c6d9eff05985"},"schema_version":"1.0","source":{"id":"1106.0908","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1106.0908","created_at":"2026-05-18T04:20:37Z"},{"alias_kind":"arxiv_version","alias_value":"1106.0908v1","created_at":"2026-05-18T04:20:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.0908","created_at":"2026-05-18T04:20:37Z"},{"alias_kind":"pith_short_12","alias_value":"O2NVDY6WVNAJ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"O2NVDY6WVNAJYMLN","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"O2NVDY6W","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:0711999323631f14b6e32f52b179eb68c27b93f25317c539e3980e6f1029fbbf","target":"graph","created_at":"2026-05-18T04:20:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Assuming that $0^#$ exists, we prove that there is a structure that can effectively interpret its own jump. In particular, we get a structure $\\mathcal A$ such that \\[ Sp({\\mathcal A}) = \\{{\\bf x}':{\\bf x}\\in Sp ({\\mathcal A})\\}, \\] where $Sp ({\\mathcal A})$ is the set of Turing degrees which compute a copy of $\\mathcal A$.\n  It turns out that, more interesting than the result itself, is its unexpected complexity. We prove that higher-order arithmetic, which is the union of full $n$th-order arithmetic for all $n$, cannot prove the existence of such a structure.","authors_text":"Antonio Montalban","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-06-05T15:17:59Z","title":"A fixed point for the jump operator on structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0908","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a81d6c81c303286d688d757f139928843ac460660fae8b9619279cc1201555b7","target":"record","created_at":"2026-05-18T04:20:37Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"693cb3a04a09898ae41b6ed276bc29a890a6bf11a4c0384576d996aa64e76c45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2011-06-05T15:17:59Z","title_canon_sha256":"85ce81b3195b33628d4ac4a88ee7f3086f5a6591b9d61279e812c6d9eff05985"},"schema_version":"1.0","source":{"id":"1106.0908","kind":"arxiv","version":1}},"canonical_sha256":"769b51e3d6ab409c316d91177f1c61a3a9e154ce62771a2d2bdf56482023d2c4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"769b51e3d6ab409c316d91177f1c61a3a9e154ce62771a2d2bdf56482023d2c4","first_computed_at":"2026-05-18T04:20:37.079085Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:20:37.079085Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rsHLpCJ1HYU4k9EokzKvUfmoyZD7wyg2uZY9WWG4EktNLJrTCS9/WQSV58SIneEiaggvlsKEX+gqcVYbgAhDBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:20:37.079842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.0908","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a81d6c81c303286d688d757f139928843ac460660fae8b9619279cc1201555b7","sha256:0711999323631f14b6e32f52b179eb68c27b93f25317c539e3980e6f1029fbbf"],"state_sha256":"ee8edfe6804f4b4143a665c76c9fc59f9f6662b59578a74504c816b84c45e711"}