{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:3EI2ZKH43Q3AXQ4FM4VXLPVPP5","short_pith_number":"pith:3EI2ZKH4","schema_version":"1.0","canonical_sha256":"d911aca8fcdc360bc385672b75beaf7f441303c4f1a1d05bd54515eb504172a0","source":{"kind":"arxiv","id":"1312.2222","version":2},"attestation_state":"computed","paper":{"title":"A Stability Result for Sparse Convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CO","math.IT"],"primary_cat":"cs.DM","authors_text":"Peter Jung, Philipp Walk","submitted_at":"2013-12-08T14:59:27Z","abstract_excerpt":"We will establish in this note a stability result for sparse convolutions on torsion-free additive (discrete) abelian groups. Sparse convolutions on torsion-free groups are free of cancellations and hence admit stability, i.e. injectivity with a universal lower bound $\\alpha=\\alpha(s,f)$, only depending on the cardinality $s$ and $f$ of the supports of both input sequences. More precisely, we show that $\\alpha$ depends only on $s$ and $f$ and not on the ambient dimension. This statement follows from a reduction argument which involves a compression into a small set preserving the additive stru"},"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":"1312.2222","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2013-12-08T14:59:27Z","cross_cats_sorted":["cs.IT","math.CO","math.IT"],"title_canon_sha256":"478cac8d753ba9e90f723d677294fb0f90b627a3ec28ff9a8f73087ed71fc6c2","abstract_canon_sha256":"95c52ca5935c7820095797abae82a6295540c64a85f84e8947491bb3a5eb59d4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:39.314865Z","signature_b64":"0gnBiHZdy+b+PnjRQ9aHKq8O+vLvhKX+0aBGDmFXDkAL+6Ek51jkn3OB/XurH5jmWVErm7rhS5penCD7bz1uDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d911aca8fcdc360bc385672b75beaf7f441303c4f1a1d05bd54515eb504172a0","last_reissued_at":"2026-05-18T02:54:39.314210Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:39.314210Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Stability Result for Sparse Convolutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.CO","math.IT"],"primary_cat":"cs.DM","authors_text":"Peter Jung, Philipp Walk","submitted_at":"2013-12-08T14:59:27Z","abstract_excerpt":"We will establish in this note a stability result for sparse convolutions on torsion-free additive (discrete) abelian groups. Sparse convolutions on torsion-free groups are free of cancellations and hence admit stability, i.e. injectivity with a universal lower bound $\\alpha=\\alpha(s,f)$, only depending on the cardinality $s$ and $f$ of the supports of both input sequences. More precisely, we show that $\\alpha$ depends only on $s$ and $f$ and not on the ambient dimension. This statement follows from a reduction argument which involves a compression into a small set preserving the additive stru"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2222","kind":"arxiv","version":2},"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":"1312.2222","created_at":"2026-05-18T02:54:39.314298+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.2222v2","created_at":"2026-05-18T02:54:39.314298+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2222","created_at":"2026-05-18T02:54:39.314298+00:00"},{"alias_kind":"pith_short_12","alias_value":"3EI2ZKH43Q3A","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"3EI2ZKH43Q3AXQ4F","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"3EI2ZKH4","created_at":"2026-05-18T12:27:32.513160+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/3EI2ZKH43Q3AXQ4FM4VXLPVPP5","json":"https://pith.science/pith/3EI2ZKH43Q3AXQ4FM4VXLPVPP5.json","graph_json":"https://pith.science/api/pith-number/3EI2ZKH43Q3AXQ4FM4VXLPVPP5/graph.json","events_json":"https://pith.science/api/pith-number/3EI2ZKH43Q3AXQ4FM4VXLPVPP5/events.json","paper":"https://pith.science/paper/3EI2ZKH4"},"agent_actions":{"view_html":"https://pith.science/pith/3EI2ZKH43Q3AXQ4FM4VXLPVPP5","download_json":"https://pith.science/pith/3EI2ZKH43Q3AXQ4FM4VXLPVPP5.json","view_paper":"https://pith.science/paper/3EI2ZKH4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.2222&json=true","fetch_graph":"https://pith.science/api/pith-number/3EI2ZKH43Q3AXQ4FM4VXLPVPP5/graph.json","fetch_events":"https://pith.science/api/pith-number/3EI2ZKH43Q3AXQ4FM4VXLPVPP5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3EI2ZKH43Q3AXQ4FM4VXLPVPP5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3EI2ZKH43Q3AXQ4FM4VXLPVPP5/action/storage_attestation","attest_author":"https://pith.science/pith/3EI2ZKH43Q3AXQ4FM4VXLPVPP5/action/author_attestation","sign_citation":"https://pith.science/pith/3EI2ZKH43Q3AXQ4FM4VXLPVPP5/action/citation_signature","submit_replication":"https://pith.science/pith/3EI2ZKH43Q3AXQ4FM4VXLPVPP5/action/replication_record"}},"created_at":"2026-05-18T02:54:39.314298+00:00","updated_at":"2026-05-18T02:54:39.314298+00:00"}