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We define the relation =^infty, notion of infinitary equational reasoning, and ->^infty, the standard notion of infinitary rewriting as follows:\n  =^infty := nu R. ( <-_root + ->_root + lift(R) )^*\n  ->^infty := mu R. nu S. ( ->_root + lift(R) )^* ; lift(S)\n  where\n  lift(R) := { (f(s_1,...,s_n), f(t_1,...,t_n)) | s_1 R t_1,...,s_n R t_n } + id ,\n  and where mu is the least fixed point operator and nu is the greatest fixed point operator.\n  The setup captures rewrite seq"},"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":"1505.01128","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2015-05-05T19:11:54Z","cross_cats_sorted":[],"title_canon_sha256":"a658718f8eb11d941cbaa8b6307c1facb27ea77e20ca9f26364a188dd6abbe1c","abstract_canon_sha256":"109cb599781c50a6e9e732f60a855aca00dceb558cabf27b9de1aed71d70aaa8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:16:51.816490Z","signature_b64":"TEGGaOzoXLFVNmDJFd4pKFKEdVZzfA5BHFc033dJRGiBzJUpVXL/4RFkRcdIpOm74kFxvlD9qXyYe1WnOA3+Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f0771d86622df8831a5844f9b82014634a0002b7b2715f5c18a5f83efc5eb4fb","last_reissued_at":"2026-05-18T02:16:51.815786Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:16:51.815786Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Coinductive Framework for Infinitary Rewriting and Equational Reasoning (Extended Version)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.LO","authors_text":"Alexandra Silva, Andrew Polonsky, Dimitri Hendriks, Helle Hvid Hansen, J\\\"org Endrullis","submitted_at":"2015-05-05T19:11:54Z","abstract_excerpt":"We present a coinductive framework for defining infinitary analogues of equational reasoning and rewriting in a uniform way. We define the relation =^infty, notion of infinitary equational reasoning, and ->^infty, the standard notion of infinitary rewriting as follows:\n  =^infty := nu R. ( <-_root + ->_root + lift(R) )^*\n  ->^infty := mu R. nu S. ( ->_root + lift(R) )^* ; lift(S)\n  where\n  lift(R) := { (f(s_1,...,s_n), f(t_1,...,t_n)) | s_1 R t_1,...,s_n R t_n } + id ,\n  and where mu is the least fixed point operator and nu is the greatest fixed point operator.\n  The setup captures rewrite seq"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01128","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":"1505.01128","created_at":"2026-05-18T02:16:51.815898+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.01128v1","created_at":"2026-05-18T02:16:51.815898+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.01128","created_at":"2026-05-18T02:16:51.815898+00:00"},{"alias_kind":"pith_short_12","alias_value":"6B3R3BTCFX4I","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6B3R3BTCFX4IGGSY","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6B3R3BTC","created_at":"2026-05-18T12:29:07.941421+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/6B3R3BTCFX4IGGSYIT43QIAUMN","json":"https://pith.science/pith/6B3R3BTCFX4IGGSYIT43QIAUMN.json","graph_json":"https://pith.science/api/pith-number/6B3R3BTCFX4IGGSYIT43QIAUMN/graph.json","events_json":"https://pith.science/api/pith-number/6B3R3BTCFX4IGGSYIT43QIAUMN/events.json","paper":"https://pith.science/paper/6B3R3BTC"},"agent_actions":{"view_html":"https://pith.science/pith/6B3R3BTCFX4IGGSYIT43QIAUMN","download_json":"https://pith.science/pith/6B3R3BTCFX4IGGSYIT43QIAUMN.json","view_paper":"https://pith.science/paper/6B3R3BTC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.01128&json=true","fetch_graph":"https://pith.science/api/pith-number/6B3R3BTCFX4IGGSYIT43QIAUMN/graph.json","fetch_events":"https://pith.science/api/pith-number/6B3R3BTCFX4IGGSYIT43QIAUMN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6B3R3BTCFX4IGGSYIT43QIAUMN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6B3R3BTCFX4IGGSYIT43QIAUMN/action/storage_attestation","attest_author":"https://pith.science/pith/6B3R3BTCFX4IGGSYIT43QIAUMN/action/author_attestation","sign_citation":"https://pith.science/pith/6B3R3BTCFX4IGGSYIT43QIAUMN/action/citation_signature","submit_replication":"https://pith.science/pith/6B3R3BTCFX4IGGSYIT43QIAUMN/action/replication_record"}},"created_at":"2026-05-18T02:16:51.815898+00:00","updated_at":"2026-05-18T02:16:51.815898+00:00"}