{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:5MGQ6HSS2UBECBVGAB65BY5AHG","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":"9802da3c48784b2b5ca39e5eba82096b8f1c8591e681457e0180c20541e75d9e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-04-11T19:25:41Z","title_canon_sha256":"949d5983dec6f5444890ca83ab5b39e7836f3b3c7a203847ff445cee17542d11"},"schema_version":"1.0","source":{"id":"2504.08935","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2504.08935","created_at":"2026-05-18T03:09:45Z"},{"alias_kind":"arxiv_version","alias_value":"2504.08935v4","created_at":"2026-05-18T03:09:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.08935","created_at":"2026-05-18T03:09:45Z"},{"alias_kind":"pith_short_12","alias_value":"5MGQ6HSS2UBE","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_16","alias_value":"5MGQ6HSS2UBECBVG","created_at":"2026-05-18T12:33:37Z"},{"alias_kind":"pith_short_8","alias_value":"5MGQ6HSS","created_at":"2026-05-18T12:33:37Z"}],"graph_snapshots":[{"event_id":"sha256:3b28e5bbaba0edcfd2019f01e00ba3f023354ae28ee3c7f0d4bdf971310d313d","target":"graph","created_at":"2026-05-18T03:09:45Z","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 introduce and study derivatives in first-passage percolation with edge weights given by i.i.d. random variables supported on ${a,b}$. We show that the variance of the passage time can be expressed in terms of these derivatives. We further analyze their structure and establish several fundamental properties and bounds.","authors_text":"Dan Stefanica, Ivan Matic, Rados Radoicic","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-04-11T19:25:41Z","title":"Higher-order derivatives of first-passage percolation with respect to the environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.08935","kind":"arxiv","version":4},"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":"sha256:5d2b5fcd613b5955ec99a804a8cd5799b6958b0117883661f990480b32b147e3","target":"record","created_at":"2026-05-18T03:09:45Z","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":"9802da3c48784b2b5ca39e5eba82096b8f1c8591e681457e0180c20541e75d9e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-04-11T19:25:41Z","title_canon_sha256":"949d5983dec6f5444890ca83ab5b39e7836f3b3c7a203847ff445cee17542d11"},"schema_version":"1.0","source":{"id":"2504.08935","kind":"arxiv","version":4}},"canonical_sha256":"eb0d0f1e52d5024106a6007dd0e3a0399117959fd1219ce7a06cefbb651d6aba","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb0d0f1e52d5024106a6007dd0e3a0399117959fd1219ce7a06cefbb651d6aba","first_computed_at":"2026-05-18T03:09:45.707758Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:09:45.707758Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"730EV58U96c3aNUjWXx/iy+lVssuXxKdtBtgZFLupyi8yn2qIVfaBcYn8G55Q0FLNlLsw+DgIJmFFWBddzIhCg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:09:45.708689Z","signed_message":"canonical_sha256_bytes"},"source_id":"2504.08935","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5d2b5fcd613b5955ec99a804a8cd5799b6958b0117883661f990480b32b147e3","sha256:3b28e5bbaba0edcfd2019f01e00ba3f023354ae28ee3c7f0d4bdf971310d313d"],"state_sha256":"039e227404676cb7d466092eaeda5e0d1a6c216225cb8884c052823a671cc220"}