{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:YW76WBJFJBPPDUMIHPGIODIDH2","short_pith_number":"pith:YW76WBJF","canonical_record":{"source":{"id":"1404.0948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T15:02:11Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"7a085ee97e0ed342d6d53fdae7a2c2c26d0c46c17d4e988a59f2f5d78fc283e4","abstract_canon_sha256":"a2ed50f1180912515f03adc46ae3c96500c7f76b88d6f9856a3007d4ffecddaf"},"schema_version":"1.0"},"canonical_sha256":"c5bfeb0525485ef1d1883bcc870d033eb588e5bb37afa3ace2c98ff48b64f25a","source":{"kind":"arxiv","id":"1404.0948","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0948","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0948v2","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0948","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"pith_short_12","alias_value":"YW76WBJFJBPP","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YW76WBJFJBPPDUMI","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YW76WBJF","created_at":"2026-05-18T12:28:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:YW76WBJFJBPPDUMIHPGIODIDH2","target":"record","payload":{"canonical_record":{"source":{"id":"1404.0948","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T15:02:11Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"7a085ee97e0ed342d6d53fdae7a2c2c26d0c46c17d4e988a59f2f5d78fc283e4","abstract_canon_sha256":"a2ed50f1180912515f03adc46ae3c96500c7f76b88d6f9856a3007d4ffecddaf"},"schema_version":"1.0"},"canonical_sha256":"c5bfeb0525485ef1d1883bcc870d033eb588e5bb37afa3ace2c98ff48b64f25a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:26.402332Z","signature_b64":"eIvFXRXeN37G0uzA1UL2BiW9uLrqUx3f8olpoqVvzPttZyuGHy2HZ9gkVe1JO2c6F0KR73UnXHx9eF5rnORdAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5bfeb0525485ef1d1883bcc870d033eb588e5bb37afa3ace2c98ff48b64f25a","last_reissued_at":"2026-05-18T00:56:26.401700Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:26.401700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.0948","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C2fFPMI2JBw5afc48xsuGaEqBFWVJiIqkNl69fOxtiv6toEYzoPGF9yd4LrcQ1Z4q1VlIK0YWUy6aVK6+zZADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:51:00.636426Z"},"content_sha256":"2f3b48a14f17c2ddadeb25e24fb97d4369804343ace70628cc27bc2c01324bb8","schema_version":"1.0","event_id":"sha256:2f3b48a14f17c2ddadeb25e24fb97d4369804343ace70628cc27bc2c01324bb8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:YW76WBJFJBPPDUMIHPGIODIDH2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Quest for Optimal Sorting Networks: Efficient Generation of Two-Layer Prefixes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"cs.DS","authors_text":"Luis Cruz-Filipe, Michael Codish, Peter Schneider-Kamp","submitted_at":"2014-04-03T15:02:11Z","abstract_excerpt":"Previous work identifying depth-optimal $n$-channel sorting networks for $9\\leq n \\leq 16$ is based on exploiting symmetries of the first two layers. However, the naive generate-and-test approach typically applied does not scale. This paper revisits the problem of generating two-layer prefixes modulo symmetries. An improved notion of symmetry is provided and a novel technique based on regular languages and graph isomorphism is shown to generate the set of non-symmetric representations. An empirical evaluation demonstrates that the new method outperforms the generate-and-test approach by orders"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0948","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zn1Jm7QFamHmfotrqVYaJkmGlwjfu/PG8XgXIKvqp4SWY+FIVguHjMSvo4St5mibXrTTbHWSk31J3CR5ysSXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T21:51:00.637123Z"},"content_sha256":"f5b025442603ae17f778d373f5d75da19d85c14abd7e4062e195f49b17793ca7","schema_version":"1.0","event_id":"sha256:f5b025442603ae17f778d373f5d75da19d85c14abd7e4062e195f49b17793ca7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YW76WBJFJBPPDUMIHPGIODIDH2/bundle.json","state_url":"https://pith.science/pith/YW76WBJFJBPPDUMIHPGIODIDH2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YW76WBJFJBPPDUMIHPGIODIDH2/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":"2026-05-28T21:51:00Z","links":{"resolver":"https://pith.science/pith/YW76WBJFJBPPDUMIHPGIODIDH2","bundle":"https://pith.science/pith/YW76WBJFJBPPDUMIHPGIODIDH2/bundle.json","state":"https://pith.science/pith/YW76WBJFJBPPDUMIHPGIODIDH2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YW76WBJFJBPPDUMIHPGIODIDH2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:YW76WBJFJBPPDUMIHPGIODIDH2","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":"a2ed50f1180912515f03adc46ae3c96500c7f76b88d6f9856a3007d4ffecddaf","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T15:02:11Z","title_canon_sha256":"7a085ee97e0ed342d6d53fdae7a2c2c26d0c46c17d4e988a59f2f5d78fc283e4"},"schema_version":"1.0","source":{"id":"1404.0948","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.0948","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"arxiv_version","alias_value":"1404.0948v2","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.0948","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"pith_short_12","alias_value":"YW76WBJFJBPP","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_16","alias_value":"YW76WBJFJBPPDUMI","created_at":"2026-05-18T12:28:59Z"},{"alias_kind":"pith_short_8","alias_value":"YW76WBJF","created_at":"2026-05-18T12:28:59Z"}],"graph_snapshots":[{"event_id":"sha256:f5b025442603ae17f778d373f5d75da19d85c14abd7e4062e195f49b17793ca7","target":"graph","created_at":"2026-05-18T00:56:26Z","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":"Previous work identifying depth-optimal $n$-channel sorting networks for $9\\leq n \\leq 16$ is based on exploiting symmetries of the first two layers. However, the naive generate-and-test approach typically applied does not scale. This paper revisits the problem of generating two-layer prefixes modulo symmetries. An improved notion of symmetry is provided and a novel technique based on regular languages and graph isomorphism is shown to generate the set of non-symmetric representations. An empirical evaluation demonstrates that the new method outperforms the generate-and-test approach by orders","authors_text":"Luis Cruz-Filipe, Michael Codish, Peter Schneider-Kamp","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T15:02:11Z","title":"The Quest for Optimal Sorting Networks: Efficient Generation of Two-Layer Prefixes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.0948","kind":"arxiv","version":2},"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":"sha256:2f3b48a14f17c2ddadeb25e24fb97d4369804343ace70628cc27bc2c01324bb8","target":"record","created_at":"2026-05-18T00:56:26Z","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":"a2ed50f1180912515f03adc46ae3c96500c7f76b88d6f9856a3007d4ffecddaf","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-04-03T15:02:11Z","title_canon_sha256":"7a085ee97e0ed342d6d53fdae7a2c2c26d0c46c17d4e988a59f2f5d78fc283e4"},"schema_version":"1.0","source":{"id":"1404.0948","kind":"arxiv","version":2}},"canonical_sha256":"c5bfeb0525485ef1d1883bcc870d033eb588e5bb37afa3ace2c98ff48b64f25a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5bfeb0525485ef1d1883bcc870d033eb588e5bb37afa3ace2c98ff48b64f25a","first_computed_at":"2026-05-18T00:56:26.401700Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:26.401700Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eIvFXRXeN37G0uzA1UL2BiW9uLrqUx3f8olpoqVvzPttZyuGHy2HZ9gkVe1JO2c6F0KR73UnXHx9eF5rnORdAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:26.402332Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.0948","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2f3b48a14f17c2ddadeb25e24fb97d4369804343ace70628cc27bc2c01324bb8","sha256:f5b025442603ae17f778d373f5d75da19d85c14abd7e4062e195f49b17793ca7"],"state_sha256":"ed68eaf5ecfdc2b9234a8bc4bd7cf07bfe393511ccf591e4753949c322286751"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vz7tRBsL1GjceWscX1rBSGpFXA1PSYUt6wyZBi86h/5Kvn3Qo4CPXiCMfI7TUMt0kMhmHAMinehJ+8FaQH8SBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T21:51:00.641110Z","bundle_sha256":"dfacf47f457c9c5979df75dcfff2b58f6b8fcd3bfac0e780934fdbed454662cb"}}