{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:6ULASYGCSLT7ZLQOWT55Q3KJ5P","short_pith_number":"pith:6ULASYGC","schema_version":"1.0","canonical_sha256":"f5160960c292e7fcae0eb4fbd86d49ebfbe7b97b39589b0d1bd23dcc8ce6d6d5","source":{"kind":"arxiv","id":"1308.5586","version":1},"attestation_state":"computed","paper":{"title":"SLP compression for solutions of equations with constraints in free and hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.LO"],"primary_cat":"math.GR","authors_text":"Atefeh Mohajeri Moghaddam, Olga Kharlampovich, Volker Diekert","submitted_at":"2013-08-26T13:47:22Z","abstract_excerpt":"The paper is a part of an ongoing program which aims to show that the existential theory in free groups (hyperbolic groups or even toral relatively hyperbolic) is NP-complete. For that we study compression of solutions with straight-line programs (SLPs) as suggested originally by Plandowski and Rytter in the context of a single word equation. We review some basic results on SLPs and give full proofs in order to keep this fundamental part of the program self-contained. Next we study systems of equations with constraints in free groups and more generally in free products of abelian groups. We sh"},"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":"1308.5586","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2013-08-26T13:47:22Z","cross_cats_sorted":["cs.DM","cs.LO"],"title_canon_sha256":"551db9a04664d92a2272c8e4fe94b933d067bdf0617440988cd6a894a0ca153e","abstract_canon_sha256":"d5f6437772b00d60ba962ad8f94d147fc5e1d5489a6f881d169b30a69b64af85"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:15:04.047903Z","signature_b64":"8J8YYbxcyJyTI+fu0g4AhF4UGQb0VG0r1kzadEYKy2J/H9Z7jZagFtt0dIkppzJJ+XyP1IRDttOPiRocFJkQBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f5160960c292e7fcae0eb4fbd86d49ebfbe7b97b39589b0d1bd23dcc8ce6d6d5","last_reissued_at":"2026-05-18T03:15:04.046883Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:15:04.046883Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"SLP compression for solutions of equations with constraints in free and hyperbolic groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.LO"],"primary_cat":"math.GR","authors_text":"Atefeh Mohajeri Moghaddam, Olga Kharlampovich, Volker Diekert","submitted_at":"2013-08-26T13:47:22Z","abstract_excerpt":"The paper is a part of an ongoing program which aims to show that the existential theory in free groups (hyperbolic groups or even toral relatively hyperbolic) is NP-complete. For that we study compression of solutions with straight-line programs (SLPs) as suggested originally by Plandowski and Rytter in the context of a single word equation. We review some basic results on SLPs and give full proofs in order to keep this fundamental part of the program self-contained. Next we study systems of equations with constraints in free groups and more generally in free products of abelian groups. We sh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.5586","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":"1308.5586","created_at":"2026-05-18T03:15:04.047059+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.5586v1","created_at":"2026-05-18T03:15:04.047059+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.5586","created_at":"2026-05-18T03:15:04.047059+00:00"},{"alias_kind":"pith_short_12","alias_value":"6ULASYGCSLT7","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_16","alias_value":"6ULASYGCSLT7ZLQO","created_at":"2026-05-18T12:27:36.564083+00:00"},{"alias_kind":"pith_short_8","alias_value":"6ULASYGC","created_at":"2026-05-18T12:27:36.564083+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/6ULASYGCSLT7ZLQOWT55Q3KJ5P","json":"https://pith.science/pith/6ULASYGCSLT7ZLQOWT55Q3KJ5P.json","graph_json":"https://pith.science/api/pith-number/6ULASYGCSLT7ZLQOWT55Q3KJ5P/graph.json","events_json":"https://pith.science/api/pith-number/6ULASYGCSLT7ZLQOWT55Q3KJ5P/events.json","paper":"https://pith.science/paper/6ULASYGC"},"agent_actions":{"view_html":"https://pith.science/pith/6ULASYGCSLT7ZLQOWT55Q3KJ5P","download_json":"https://pith.science/pith/6ULASYGCSLT7ZLQOWT55Q3KJ5P.json","view_paper":"https://pith.science/paper/6ULASYGC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.5586&json=true","fetch_graph":"https://pith.science/api/pith-number/6ULASYGCSLT7ZLQOWT55Q3KJ5P/graph.json","fetch_events":"https://pith.science/api/pith-number/6ULASYGCSLT7ZLQOWT55Q3KJ5P/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6ULASYGCSLT7ZLQOWT55Q3KJ5P/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6ULASYGCSLT7ZLQOWT55Q3KJ5P/action/storage_attestation","attest_author":"https://pith.science/pith/6ULASYGCSLT7ZLQOWT55Q3KJ5P/action/author_attestation","sign_citation":"https://pith.science/pith/6ULASYGCSLT7ZLQOWT55Q3KJ5P/action/citation_signature","submit_replication":"https://pith.science/pith/6ULASYGCSLT7ZLQOWT55Q3KJ5P/action/replication_record"}},"created_at":"2026-05-18T03:15:04.047059+00:00","updated_at":"2026-05-18T03:15:04.047059+00:00"}