{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:IILOEN5U5KVLFOFWRTENAW4G5F","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":"3330c69ab18f6d795605e0555b3651181656a816539c08f24a7ddc939ee827aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-02-14T18:20:45Z","title_canon_sha256":"b0ed40a39337131bc5a8266be99f44e30f5a408cb32467813b52c496fa09ffe5"},"schema_version":"1.0","source":{"id":"2502.10348","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2502.10348","created_at":"2026-07-05T10:14:32Z"},{"alias_kind":"arxiv_version","alias_value":"2502.10348v1","created_at":"2026-07-05T10:14:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2502.10348","created_at":"2026-07-05T10:14:32Z"},{"alias_kind":"pith_short_12","alias_value":"IILOEN5U5KVL","created_at":"2026-07-05T10:14:32Z"},{"alias_kind":"pith_short_16","alias_value":"IILOEN5U5KVLFOFW","created_at":"2026-07-05T10:14:32Z"},{"alias_kind":"pith_short_8","alias_value":"IILOEN5U","created_at":"2026-07-05T10:14:32Z"}],"graph_snapshots":[{"event_id":"sha256:98ac5481fdf2526d8dde7fd07b572edd310b7f88c232920770a1f19e83e3e05e","target":"graph","created_at":"2026-07-05T10:14:32Z","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/2502.10348/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we show new data structures maintaining approximate shortest paths in sparse directed graphs with polynomially bounded non-negative edge weights under edge insertions.\n  We give more efficient incremental $(1+\\epsilon)$-approximate APSP data structures that work against an adaptive adversary: a deterministic one with $\\tilde{O}(m^{3/2}n^{3/4})$ total update time and a randomized one with $\\tilde{O}(m^{4/3}n^{5/6})$ total update time. For sparse graphs, these both improve polynomially upon the best-known bound against an adaptive adversary. To achieve that, building on the ideas ","authors_text":"Adam G\\'orkiewicz, Adam Karczmarz","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-02-14T18:20:45Z","title":"On Incremental Approximate Shortest Paths in Directed Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.10348","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":"sha256:4b2a3dbfa4bfd78c033d8d0ccfcf945eed0c23258a3918f28724e8f619b328b1","target":"record","created_at":"2026-07-05T10:14:32Z","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":"3330c69ab18f6d795605e0555b3651181656a816539c08f24a7ddc939ee827aa","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.DS","submitted_at":"2025-02-14T18:20:45Z","title_canon_sha256":"b0ed40a39337131bc5a8266be99f44e30f5a408cb32467813b52c496fa09ffe5"},"schema_version":"1.0","source":{"id":"2502.10348","kind":"arxiv","version":1}},"canonical_sha256":"4216e237b4eaaab2b8b68cc8d05b86e940dbe4af6af0d04fb8cb6b29fcd44aca","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4216e237b4eaaab2b8b68cc8d05b86e940dbe4af6af0d04fb8cb6b29fcd44aca","first_computed_at":"2026-07-05T10:14:32.913734Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:14:32.913734Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CSgDdrPDUFbzI8QBo+LVC8ncealOzB7rkCLUTm6p0sKgtHEyfEeVD1tWdALPwVwxgxPTuejqiQPk4pxC/IjlBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:14:32.914227Z","signed_message":"canonical_sha256_bytes"},"source_id":"2502.10348","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b2a3dbfa4bfd78c033d8d0ccfcf945eed0c23258a3918f28724e8f619b328b1","sha256:98ac5481fdf2526d8dde7fd07b572edd310b7f88c232920770a1f19e83e3e05e"],"state_sha256":"18dc940b1effc0f4228b9f97ba3fad5db116e327a8e0f024b25581c0072d8b2b"}