{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:4FXCLJXCDXIHGC5RDOSPM2ZDTJ","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":"0bd9c6a78b5bfbcd0382d8d9cf792d24519c2c53cef03caaf53a194e31f304d3","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2009-02-20T18:07:28Z","title_canon_sha256":"68392a2d348c048d5a704d6a4739321765e8058f6c57d60a72f13ace4583058e"},"schema_version":"1.0","source":{"id":"0902.3635","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0902.3635","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"arxiv_version","alias_value":"0902.3635v1","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0902.3635","created_at":"2026-05-18T03:13:22Z"},{"alias_kind":"pith_short_12","alias_value":"4FXCLJXCDXIH","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"4FXCLJXCDXIHGC5R","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"4FXCLJXC","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:d44fe24984bca36074275898441cf9f8be395e0d71c40527854e9f45250fa46e","target":"graph","created_at":"2026-05-18T03:13:22Z","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":"Using a human-oriented formal example proof of the (lim+) theorem, i.e. that the sum of limits is the limit of the sum, which is of value for reference on its own, we exhibit a non-permutability of beta-steps and delta+-steps (according to Smullyan's classification), which is not visible with non-liberalized delta-rules and not serious with further liberalized delta-rules, such as the delta++-rule. Besides a careful presentation of the search for a proof of (lim+) with several pedagogical intentions, the main subject is to explain why the order of beta-steps plays such a practically important ","authors_text":"Claus-Peter Wirth","cross_cats":["cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2009-02-20T18:07:28Z","title":"lim+, delta+, and Non-Permutability of beta-Steps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3635","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":"sha256:0a002102bd54f0713ad2e5e08e483d7881232c370b15e2c06b8b0d5003fb56a0","target":"record","created_at":"2026-05-18T03:13:22Z","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":"0bd9c6a78b5bfbcd0382d8d9cf792d24519c2c53cef03caaf53a194e31f304d3","cross_cats_sorted":["cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.AI","submitted_at":"2009-02-20T18:07:28Z","title_canon_sha256":"68392a2d348c048d5a704d6a4739321765e8058f6c57d60a72f13ace4583058e"},"schema_version":"1.0","source":{"id":"0902.3635","kind":"arxiv","version":1}},"canonical_sha256":"e16e25a6e21dd0730bb11ba4f66b239a601a66260d83285069ed7655508760ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e16e25a6e21dd0730bb11ba4f66b239a601a66260d83285069ed7655508760ee","first_computed_at":"2026-05-18T03:13:22.198701Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:22.198701Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XRQnCvov5SyRuPcV5aaDZyuB1nXL7GQStVl7JmpAoNGqYZwFGPCCAyts4tbAUCSn/3m77ajqdVioWaDacSz3DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:22.199412Z","signed_message":"canonical_sha256_bytes"},"source_id":"0902.3635","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0a002102bd54f0713ad2e5e08e483d7881232c370b15e2c06b8b0d5003fb56a0","sha256:d44fe24984bca36074275898441cf9f8be395e0d71c40527854e9f45250fa46e"],"state_sha256":"697244dd98670c0ff160eb093564fd850eb4e87fba34cb6c28749c6736e2f618"}