{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:DGZYURS5XXQCFEY5VOS3PWJJVQ","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":"6592bcf1f315497122db1b61753758e42541bc429e3ed13938cd5acd514e43be","cross_cats_sorted":["cs.IT","cs.NA","math.IT","math.NA"],"license":"","primary_cat":"cs.DS","submitted_at":"2008-02-20T14:24:39Z","title_canon_sha256":"51f08f5cd686a375eac0e85621deb0c04ec230611380474df3750bb484f07d0a"},"schema_version":"1.0","source":{"id":"0802.2856","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0802.2856","created_at":"2026-06-03T22:06:04Z"},{"alias_kind":"arxiv_version","alias_value":"0802.2856v2","created_at":"2026-06-03T22:06:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.2856","created_at":"2026-06-03T22:06:04Z"},{"alias_kind":"pith_short_12","alias_value":"DGZYURS5XXQC","created_at":"2026-06-03T22:06:04Z"},{"alias_kind":"pith_short_16","alias_value":"DGZYURS5XXQCFEY5","created_at":"2026-06-03T22:06:04Z"},{"alias_kind":"pith_short_8","alias_value":"DGZYURS5","created_at":"2026-06-03T22:06:04Z"}],"graph_snapshots":[{"event_id":"sha256:eedf701007be921780947b4da09707124e20afe460660bc62eb1c110e4ba4e42","target":"graph","created_at":"2026-06-03T22:06:04Z","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/0802.2856/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Monotone systems of polynomial equations (MSPEs) are systems of fixed-point equations $X_1 = f_1(X_1, ..., X_n),$ $..., X_n = f_n(X_1, ..., X_n)$ where each $f_i$ is a polynomial with positive real coefficients. The question of computing the least non-negative solution of a given MSPE $\\vec X = \\vec f(\\vec X)$ arises naturally in the analysis of stochastic models such as stochastic context-free grammars, probabilistic pushdown automata, and back-button processes. Etessami and Yannakakis have recently adapted Newton's iterative method to MSPEs. In a previous paper we have proved the existence o","authors_text":"Javier Esparza, Michael Luttenberger, Stefan Kiefer","cross_cats":["cs.IT","cs.NA","math.IT","math.NA"],"headline":"","license":"","primary_cat":"cs.DS","submitted_at":"2008-02-20T14:24:39Z","title":"Convergence Thresholds of Newton's Method for Monotone Polynomial Equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.2856","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:f052c2291bd52bf9361947bad63c448644704e186c32c5ab03e5ee24e2bb2d3f","target":"record","created_at":"2026-06-03T22:06:04Z","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":"6592bcf1f315497122db1b61753758e42541bc429e3ed13938cd5acd514e43be","cross_cats_sorted":["cs.IT","cs.NA","math.IT","math.NA"],"license":"","primary_cat":"cs.DS","submitted_at":"2008-02-20T14:24:39Z","title_canon_sha256":"51f08f5cd686a375eac0e85621deb0c04ec230611380474df3750bb484f07d0a"},"schema_version":"1.0","source":{"id":"0802.2856","kind":"arxiv","version":2}},"canonical_sha256":"19b38a465dbde022931daba5b7d929ac188692a6aecb2317c68a5a1882dc44e3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"19b38a465dbde022931daba5b7d929ac188692a6aecb2317c68a5a1882dc44e3","first_computed_at":"2026-06-03T22:06:04.581506Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-03T22:06:04.581506Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nEsQN3HEpYjRqP151aZ379mLv3/PpRvYUVAxVX9VdYTkP13/Uf8YfEIZqvPVq5gDL7MEBEWilBrSojZAzBBNBA==","signature_status":"signed_v1","signed_at":"2026-06-03T22:06:04.581951Z","signed_message":"canonical_sha256_bytes"},"source_id":"0802.2856","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f052c2291bd52bf9361947bad63c448644704e186c32c5ab03e5ee24e2bb2d3f","sha256:eedf701007be921780947b4da09707124e20afe460660bc62eb1c110e4ba4e42"],"state_sha256":"72f4cad96891adbc7b8862a0f31d70621d7804b84930805328cd4d3665108d3d"}