{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:L7XCWCPGNZKUEPRSSPVPM74EFE","merge_version":"pith-open-graph-merge-v1","event_count":3,"valid_event_count":3,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"478d3d9ab802b866ef05d9a199caa1ef659e37a67d09a53d33364b513e175e15","cross_cats_sorted":["cs.IR","cs.PF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-30T12:45:49Z","title_canon_sha256":"fb599aeabf833885a220b60b1ee7b9dad3076b805233bf50508f5a5fea332282"},"schema_version":"1.0","source":{"id":"2607.28136","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.28136","created_at":"2026-07-31T01:35:50Z"},{"alias_kind":"arxiv_version","alias_value":"2607.28136v1","created_at":"2026-07-31T01:35:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.28136","created_at":"2026-07-31T01:35:50Z"},{"alias_kind":"pith_short_12","alias_value":"L7XCWCPGNZKU","created_at":"2026-07-31T01:35:50Z"},{"alias_kind":"pith_short_16","alias_value":"L7XCWCPGNZKUEPRS","created_at":"2026-07-31T01:35:50Z"},{"alias_kind":"pith_short_8","alias_value":"L7XCWCPG","created_at":"2026-07-31T01:35:50Z"}],"graph_snapshots":[{"event_id":"sha256:4498f9305fbae5aec14149a9f226be4105d0902f29516dda585ae36c4e3840db","target":"graph","created_at":"2026-07-31T01:35:50Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.28136/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study static, computation-friendly, lossless compression formats for graphs, focusing on memory locality and operational efficiency of $k^2$-trees. We observe that their traditional level-wise layouts suffer from poor cache performance due to weak locality, especially in operations such as matrix-vector and matrix-matrix operations. To address this limitation, we propose four depth-first representations of $k^2$-trees: a plain depth-first layout (EDF-1), a balanced-parenthesis representation (BP), and their compressed variants (CEDF and CBP). We further introduce a linear-tim","authors_text":"Francesco Tosoni, Gabriel Carmona, Giovanni Manzini, Paolo Ferragina","cross_cats":["cs.IR","cs.PF"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-30T12:45:49Z","title":"Extended Depth-First Representations of $k^2$-trees"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.28136","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":"sha256:379f833f061821e4522e8e0b68b5d0df0a96dc731030e73e79aca6510c61f4ba","target":"record","created_at":"2026-07-31T01:35:50Z","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":"478d3d9ab802b866ef05d9a199caa1ef659e37a67d09a53d33364b513e175e15","cross_cats_sorted":["cs.IR","cs.PF"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2026-07-30T12:45:49Z","title_canon_sha256":"fb599aeabf833885a220b60b1ee7b9dad3076b805233bf50508f5a5fea332282"},"schema_version":"1.0","source":{"id":"2607.28136","kind":"arxiv","version":1}},"canonical_sha256":"5fee2b09e66e55423e3293eaf67f84293ef66f95f32a16b7a0e249f3f91c3a10","receipt":{"builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5fee2b09e66e55423e3293eaf67f84293ef66f95f32a16b7a0e249f3f91c3a10","first_computed_at":"2026-07-31T01:35:50.811618Z","kind":"pith_receipt","last_reissued_at":"2026-07-31T01:35:50.811618Z","receipt_version":"0.3","signature_status":"unsigned_v0"},"source_id":"2607.28136","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:379f833f061821e4522e8e0b68b5d0df0a96dc731030e73e79aca6510c61f4ba","sha256:4498f9305fbae5aec14149a9f226be4105d0902f29516dda585ae36c4e3840db","sha256:9042902f4e7e21c8a6fd0ab62673b11acc4a638fd377a8859ce56efacce54c3c"],"state_sha256":"e8b7fa1b0f6b930b18cce159403048fc8dada301994e8dd249364a4e4b1c65db"}