{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RBORJMAKBSSXGUM6VDV5PSIDQX","short_pith_number":"pith:RBORJMAK","canonical_record":{"source":{"id":"1501.06946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-01-27T22:08:45Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"bc7916722439656d0c6338b058fc868a1c491d5912a079c3446ac02a3bf66c44","abstract_canon_sha256":"2353370bc0185b02582ab12a59e2fb8f90cb5f9799e1a60506b099c293a89c7b"},"schema_version":"1.0"},"canonical_sha256":"885d14b00a0ca573519ea8ebd7c90385f4ce9b9b56f57210533ac2c47a2ce60c","source":{"kind":"arxiv","id":"1501.06946","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06946","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06946v1","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06946","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"RBORJMAKBSSX","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RBORJMAKBSSXGUM6","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RBORJMAK","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RBORJMAKBSSXGUM6VDV5PSIDQX","target":"record","payload":{"canonical_record":{"source":{"id":"1501.06946","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-01-27T22:08:45Z","cross_cats_sorted":["cs.DS"],"title_canon_sha256":"bc7916722439656d0c6338b058fc868a1c491d5912a079c3446ac02a3bf66c44","abstract_canon_sha256":"2353370bc0185b02582ab12a59e2fb8f90cb5f9799e1a60506b099c293a89c7b"},"schema_version":"1.0"},"canonical_sha256":"885d14b00a0ca573519ea8ebd7c90385f4ce9b9b56f57210533ac2c47a2ce60c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:30.720670Z","signature_b64":"bBF0fuskgVbc+Gh/Fjv4xZAtZCX9orRsWcF3WZDLIy+i9BMJeiPj5H7hJWzIAgOXPsk+OEQlGQT0JWt7SJbmBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"885d14b00a0ca573519ea8ebd7c90385f4ce9b9b56f57210533ac2c47a2ce60c","last_reissued_at":"2026-05-18T02:28:30.720092Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:30.720092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1501.06946","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YAcvSSppEiWjn2txeFC5vnndHWrpdxty/7qoATN2nEGIfRkPz+U4CwUAOrBMf1nXo6+46SmssI+4MdSE91DrCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:27:58.554586Z"},"content_sha256":"0ea54dfc2f9c5c50bb4296f4e080c2587c352969f3f3d5cc433753ef43018f13","schema_version":"1.0","event_id":"sha256:0ea54dfc2f9c5c50bb4296f4e080c2587c352969f3f3d5cc433753ef43018f13"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RBORJMAKBSSXGUM6VDV5PSIDQX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New Bounds on Optimal Sorting Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"cs.DM","authors_text":"Mike M\\\"uller, Thorsten Ehlers","submitted_at":"2015-01-27T22:08:45Z","abstract_excerpt":"We present new parallel sorting networks for $17$ to $20$ inputs. For $17, 19,$ and $20$ inputs these new networks are faster (i.e., they require less computation steps) than the previously known best networks. Therefore, we improve upon the known upper bounds for minimal depth sorting networks on $17, 19,$ and $20$ channels. Furthermore, we show that our sorting network for $17$ inputs is optimal in the sense that no sorting network using less layers exists. This solves the main open problem of [D. Bundala & J. Za\\'vodn\\'y. Optimal sorting networks, Proc. LATA 2014]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06946","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:28:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zGJsHCEfBdFEkLP54XQ0J4G9SS0alJ/jL+zvZ+gXxy21sNx5bSCYwcbZu/t2ApTPd4LWgHg1e4gxHfczcBADDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T18:27:58.555280Z"},"content_sha256":"2aaae4c6236357b740de2521af4b305c024135591484a84c134cb3f60cd27b90","schema_version":"1.0","event_id":"sha256:2aaae4c6236357b740de2521af4b305c024135591484a84c134cb3f60cd27b90"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBORJMAKBSSXGUM6VDV5PSIDQX/bundle.json","state_url":"https://pith.science/pith/RBORJMAKBSSXGUM6VDV5PSIDQX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBORJMAKBSSXGUM6VDV5PSIDQX/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-27T18:27:58Z","links":{"resolver":"https://pith.science/pith/RBORJMAKBSSXGUM6VDV5PSIDQX","bundle":"https://pith.science/pith/RBORJMAKBSSXGUM6VDV5PSIDQX/bundle.json","state":"https://pith.science/pith/RBORJMAKBSSXGUM6VDV5PSIDQX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBORJMAKBSSXGUM6VDV5PSIDQX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RBORJMAKBSSXGUM6VDV5PSIDQX","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":"2353370bc0185b02582ab12a59e2fb8f90cb5f9799e1a60506b099c293a89c7b","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-01-27T22:08:45Z","title_canon_sha256":"bc7916722439656d0c6338b058fc868a1c491d5912a079c3446ac02a3bf66c44"},"schema_version":"1.0","source":{"id":"1501.06946","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.06946","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"1501.06946v1","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06946","created_at":"2026-05-18T02:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"RBORJMAKBSSX","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RBORJMAKBSSXGUM6","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RBORJMAK","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:2aaae4c6236357b740de2521af4b305c024135591484a84c134cb3f60cd27b90","target":"graph","created_at":"2026-05-18T02:28:30Z","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":"We present new parallel sorting networks for $17$ to $20$ inputs. For $17, 19,$ and $20$ inputs these new networks are faster (i.e., they require less computation steps) than the previously known best networks. Therefore, we improve upon the known upper bounds for minimal depth sorting networks on $17, 19,$ and $20$ channels. Furthermore, we show that our sorting network for $17$ inputs is optimal in the sense that no sorting network using less layers exists. This solves the main open problem of [D. Bundala & J. Za\\'vodn\\'y. Optimal sorting networks, Proc. LATA 2014].","authors_text":"Mike M\\\"uller, Thorsten Ehlers","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-01-27T22:08:45Z","title":"New Bounds on Optimal Sorting Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06946","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":"sha256:0ea54dfc2f9c5c50bb4296f4e080c2587c352969f3f3d5cc433753ef43018f13","target":"record","created_at":"2026-05-18T02:28:30Z","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":"2353370bc0185b02582ab12a59e2fb8f90cb5f9799e1a60506b099c293a89c7b","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-01-27T22:08:45Z","title_canon_sha256":"bc7916722439656d0c6338b058fc868a1c491d5912a079c3446ac02a3bf66c44"},"schema_version":"1.0","source":{"id":"1501.06946","kind":"arxiv","version":1}},"canonical_sha256":"885d14b00a0ca573519ea8ebd7c90385f4ce9b9b56f57210533ac2c47a2ce60c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"885d14b00a0ca573519ea8ebd7c90385f4ce9b9b56f57210533ac2c47a2ce60c","first_computed_at":"2026-05-18T02:28:30.720092Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:30.720092Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bBF0fuskgVbc+Gh/Fjv4xZAtZCX9orRsWcF3WZDLIy+i9BMJeiPj5H7hJWzIAgOXPsk+OEQlGQT0JWt7SJbmBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:30.720670Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.06946","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0ea54dfc2f9c5c50bb4296f4e080c2587c352969f3f3d5cc433753ef43018f13","sha256:2aaae4c6236357b740de2521af4b305c024135591484a84c134cb3f60cd27b90"],"state_sha256":"7ff4f308bbfea65d3f2058346cea064e64f9523a805eea5616b6b14d66430ce7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D9iw1lNapWgrMiHL2buOIWhuPVIBN3jZokRXNyxFtlGzIVX/ZYbYCsfKv33z+VrciF8p/IXUzeBKz/NJD6UaBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T18:27:58.559046Z","bundle_sha256":"8e2f739eea982d57488d94b495da62ef526e027836a27be80c0fcf359f02e9f3"}}