{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:3V66TWAIBS664IMYQ7UBJKYWR6","short_pith_number":"pith:3V66TWAI","schema_version":"1.0","canonical_sha256":"dd7de9d8080cbdee219887e814ab168fac4415a2070a5bf299e9a238e7b308f7","source":{"kind":"arxiv","id":"1501.03056","version":1},"attestation_state":"computed","paper":{"title":"Non-Abelian Analogs of Lattice Rounding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.CO","math.NT"],"primary_cat":"math.GR","authors_text":"Evgeni Begelfor, Ramarathnam Venkatesan, Stephen D. Miller","submitted_at":"2015-01-13T15:54:05Z","abstract_excerpt":"Lattice rounding in Euclidean space can be viewed as finding the nearest point in the orbit of an action by a discrete group, relative to the norm inherited from the ambient space. Using this point of view, we initiate the study of non-abelian analogs of lattice rounding involving matrix groups. In one direction, we give an algorithm for solving a normed word problem when the inputs are random products over a basis set, and give theoretical justification for its success. In another direction, we prove a general inapproximability result which essentially rules out strong approximation algorithm"},"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":"1501.03056","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-01-13T15:54:05Z","cross_cats_sorted":["cs.CR","math.CO","math.NT"],"title_canon_sha256":"487526e9c4a3ff4586e9fd072cac9f35333b9a38a27b356219d3b0b63166bd93","abstract_canon_sha256":"05de39c20c85afead8cb67c60a11a47c6260c74f00bd5acd4f1d09c00d0b7062"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:30.609788Z","signature_b64":"cVYjJ2vQKWHDxhtCrGqmf0brtONe/KTyntq85mWmv01Yd2cqozN7rk7Uz7zOUHP16sWm9MmBDu1lAd5NSvt8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd7de9d8080cbdee219887e814ab168fac4415a2070a5bf299e9a238e7b308f7","last_reissued_at":"2026-05-18T02:29:30.609360Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:30.609360Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Non-Abelian Analogs of Lattice Rounding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CR","math.CO","math.NT"],"primary_cat":"math.GR","authors_text":"Evgeni Begelfor, Ramarathnam Venkatesan, Stephen D. Miller","submitted_at":"2015-01-13T15:54:05Z","abstract_excerpt":"Lattice rounding in Euclidean space can be viewed as finding the nearest point in the orbit of an action by a discrete group, relative to the norm inherited from the ambient space. Using this point of view, we initiate the study of non-abelian analogs of lattice rounding involving matrix groups. In one direction, we give an algorithm for solving a normed word problem when the inputs are random products over a basis set, and give theoretical justification for its success. In another direction, we prove a general inapproximability result which essentially rules out strong approximation algorithm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.03056","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":"1501.03056","created_at":"2026-05-18T02:29:30.609431+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.03056v1","created_at":"2026-05-18T02:29:30.609431+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.03056","created_at":"2026-05-18T02:29:30.609431+00:00"},{"alias_kind":"pith_short_12","alias_value":"3V66TWAIBS66","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"3V66TWAIBS664IMY","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"3V66TWAI","created_at":"2026-05-18T12:29:02.477457+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":0,"sample":[{"citing_arxiv_id":"2605.05015","citing_title":"Dephasing Effects on the Dynamical Evolution of Quantum Correlations and Coherence in Neutrino Oscillations","ref_index":60,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3V66TWAIBS664IMYQ7UBJKYWR6","json":"https://pith.science/pith/3V66TWAIBS664IMYQ7UBJKYWR6.json","graph_json":"https://pith.science/api/pith-number/3V66TWAIBS664IMYQ7UBJKYWR6/graph.json","events_json":"https://pith.science/api/pith-number/3V66TWAIBS664IMYQ7UBJKYWR6/events.json","paper":"https://pith.science/paper/3V66TWAI"},"agent_actions":{"view_html":"https://pith.science/pith/3V66TWAIBS664IMYQ7UBJKYWR6","download_json":"https://pith.science/pith/3V66TWAIBS664IMYQ7UBJKYWR6.json","view_paper":"https://pith.science/paper/3V66TWAI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.03056&json=true","fetch_graph":"https://pith.science/api/pith-number/3V66TWAIBS664IMYQ7UBJKYWR6/graph.json","fetch_events":"https://pith.science/api/pith-number/3V66TWAIBS664IMYQ7UBJKYWR6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3V66TWAIBS664IMYQ7UBJKYWR6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3V66TWAIBS664IMYQ7UBJKYWR6/action/storage_attestation","attest_author":"https://pith.science/pith/3V66TWAIBS664IMYQ7UBJKYWR6/action/author_attestation","sign_citation":"https://pith.science/pith/3V66TWAIBS664IMYQ7UBJKYWR6/action/citation_signature","submit_replication":"https://pith.science/pith/3V66TWAIBS664IMYQ7UBJKYWR6/action/replication_record"}},"created_at":"2026-05-18T02:29:30.609431+00:00","updated_at":"2026-05-18T02:29:30.609431+00:00"}