{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:BBA5QSFNOXP4MAEYST5K7PK44D","short_pith_number":"pith:BBA5QSFN","canonical_record":{"source":{"id":"1411.6408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-24T11:00:09Z","cross_cats_sorted":[],"title_canon_sha256":"54038f049d98b95da25bd3553eb71f30c82b23b565ceb3a1b554b0e443df2b5b","abstract_canon_sha256":"4225fc4cc6dc2b8b2f2ccebc11412bef3963e6cb195704339f03a8283a11ab94"},"schema_version":"1.0"},"canonical_sha256":"0841d848ad75dfc6009894faafbd5ce0cf7a83647a7e46c23b05c5676c07abee","source":{"kind":"arxiv","id":"1411.6408","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6408","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6408v1","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6408","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"pith_short_12","alias_value":"BBA5QSFNOXP4","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BBA5QSFNOXP4MAEY","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BBA5QSFN","created_at":"2026-05-18T12:28:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:BBA5QSFNOXP4MAEYST5K7PK44D","target":"record","payload":{"canonical_record":{"source":{"id":"1411.6408","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-24T11:00:09Z","cross_cats_sorted":[],"title_canon_sha256":"54038f049d98b95da25bd3553eb71f30c82b23b565ceb3a1b554b0e443df2b5b","abstract_canon_sha256":"4225fc4cc6dc2b8b2f2ccebc11412bef3963e6cb195704339f03a8283a11ab94"},"schema_version":"1.0"},"canonical_sha256":"0841d848ad75dfc6009894faafbd5ce0cf7a83647a7e46c23b05c5676c07abee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:26.269250Z","signature_b64":"V/OOXdoPuD7sBbLylh+mXLjo2D71tu12pf3NvBiwBj9wOHYVuwHqflpusJwARoGTuVKpKuEUME5zaeAHagzeDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0841d848ad75dfc6009894faafbd5ce0cf7a83647a7e46c23b05c5676c07abee","last_reissued_at":"2026-05-18T00:56:26.268622Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:26.268622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.6408","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":"2026-05-18T00:56:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WveGPenlC/bUubGuvmyLxVGQN+AZYXR7iIAMsaYdJGlCUJ6zQHlRhnIK8TsulGQ+xclgXYHQDyet28Ru8XScDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:02:58.466657Z"},"content_sha256":"3f3dcdaae339fc60103713db5385481d95f86e347f535e9203278ba09847d5c8","schema_version":"1.0","event_id":"sha256:3f3dcdaae339fc60103713db5385481d95f86e347f535e9203278ba09847d5c8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:BBA5QSFNOXP4MAEYST5K7PK44D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Sorting Networks: the End Game","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Lu\\'is Cruz-Filipe, Michael Codish, Peter Schneider-Kamp","submitted_at":"2014-11-24T11:00:09Z","abstract_excerpt":"This paper studies properties of the back end of a sorting network and illustrates the utility of these in the search for networks of optimal size or depth. All previous works focus on properties of the front end of networks and on how to apply these to break symmetries in the search. The new properties help shed understanding on how sorting networks sort and speed-up solvers for both optimal size and depth by an order of magnitude."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6408","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":"2026-05-18T00:56:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/TC0GxQnJT7e0AoQ8IaS8gylL1jAaiIgPcJxM6hILkYBiJaQ9Xp/j48upxqLgVU5BtKeW9IeC5luwRJ4dBAEBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T20:02:58.467367Z"},"content_sha256":"dcc7fb4406248c91920430ee9194a7b3f29c7199e532822422d17cd60f3c1515","schema_version":"1.0","event_id":"sha256:dcc7fb4406248c91920430ee9194a7b3f29c7199e532822422d17cd60f3c1515"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BBA5QSFNOXP4MAEYST5K7PK44D/bundle.json","state_url":"https://pith.science/pith/BBA5QSFNOXP4MAEYST5K7PK44D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BBA5QSFNOXP4MAEYST5K7PK44D/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":"2026-05-28T20:02:58Z","links":{"resolver":"https://pith.science/pith/BBA5QSFNOXP4MAEYST5K7PK44D","bundle":"https://pith.science/pith/BBA5QSFNOXP4MAEYST5K7PK44D/bundle.json","state":"https://pith.science/pith/BBA5QSFNOXP4MAEYST5K7PK44D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BBA5QSFNOXP4MAEYST5K7PK44D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:BBA5QSFNOXP4MAEYST5K7PK44D","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":"4225fc4cc6dc2b8b2f2ccebc11412bef3963e6cb195704339f03a8283a11ab94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-24T11:00:09Z","title_canon_sha256":"54038f049d98b95da25bd3553eb71f30c82b23b565ceb3a1b554b0e443df2b5b"},"schema_version":"1.0","source":{"id":"1411.6408","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.6408","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"arxiv_version","alias_value":"1411.6408v1","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.6408","created_at":"2026-05-18T00:56:26Z"},{"alias_kind":"pith_short_12","alias_value":"BBA5QSFNOXP4","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_16","alias_value":"BBA5QSFNOXP4MAEY","created_at":"2026-05-18T12:28:22Z"},{"alias_kind":"pith_short_8","alias_value":"BBA5QSFN","created_at":"2026-05-18T12:28:22Z"}],"graph_snapshots":[{"event_id":"sha256:dcc7fb4406248c91920430ee9194a7b3f29c7199e532822422d17cd60f3c1515","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":"This paper studies properties of the back end of a sorting network and illustrates the utility of these in the search for networks of optimal size or depth. All previous works focus on properties of the front end of networks and on how to apply these to break symmetries in the search. The new properties help shed understanding on how sorting networks sort and speed-up solvers for both optimal size and depth by an order of magnitude.","authors_text":"Lu\\'is Cruz-Filipe, Michael Codish, Peter Schneider-Kamp","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-24T11:00:09Z","title":"Sorting Networks: the End Game"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6408","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":"sha256:3f3dcdaae339fc60103713db5385481d95f86e347f535e9203278ba09847d5c8","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":"4225fc4cc6dc2b8b2f2ccebc11412bef3963e6cb195704339f03a8283a11ab94","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-11-24T11:00:09Z","title_canon_sha256":"54038f049d98b95da25bd3553eb71f30c82b23b565ceb3a1b554b0e443df2b5b"},"schema_version":"1.0","source":{"id":"1411.6408","kind":"arxiv","version":1}},"canonical_sha256":"0841d848ad75dfc6009894faafbd5ce0cf7a83647a7e46c23b05c5676c07abee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0841d848ad75dfc6009894faafbd5ce0cf7a83647a7e46c23b05c5676c07abee","first_computed_at":"2026-05-18T00:56:26.268622Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:26.268622Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V/OOXdoPuD7sBbLylh+mXLjo2D71tu12pf3NvBiwBj9wOHYVuwHqflpusJwARoGTuVKpKuEUME5zaeAHagzeDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:26.269250Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.6408","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f3dcdaae339fc60103713db5385481d95f86e347f535e9203278ba09847d5c8","sha256:dcc7fb4406248c91920430ee9194a7b3f29c7199e532822422d17cd60f3c1515"],"state_sha256":"48103d10cb8703fb1e03d2580f90d96533fdbf8a018c68ab486de2e14e35b561"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z73rI2n3tM8bbY/3v/E9hqNf1B59vgB1CexG53BmvGdWSpP499pOyavP/lAdORp+HWwh+HckAAGf0CnOC9pzAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:02:58.470783Z","bundle_sha256":"a3d02dfd9c8c7b8362679eb604bea9b150bf0f4c183592f6b10fc9aeff6e6891"}}