{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:QNJQVYTQREECF3KITBND427KZD","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":"fc06140bed85e2992489a5f929db8eb64cb6d4aafc353088fac531cebc095884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-05-30T12:41:30Z","title_canon_sha256":"04a2f09c9b94770cc176893de989b8977017e8069ffccbddca2e836cefe218d6"},"schema_version":"1.0","source":{"id":"1005.5523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.5523","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"arxiv_version","alias_value":"1005.5523v1","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.5523","created_at":"2026-05-18T03:29:28Z"},{"alias_kind":"pith_short_12","alias_value":"QNJQVYTQREEC","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_16","alias_value":"QNJQVYTQREECF3KI","created_at":"2026-05-18T12:26:12Z"},{"alias_kind":"pith_short_8","alias_value":"QNJQVYTQ","created_at":"2026-05-18T12:26:12Z"}],"graph_snapshots":[{"event_id":"sha256:18cca429338b77baf432fb8ab2b52dd3ecae3df91c476fff24ea08db96bccc9b","target":"graph","created_at":"2026-05-18T03:29:28Z","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 characterize those valued fields for which the image of the valuation ring under every polynomial in several variables contains an element of maximal value, or zero.","authors_text":"Florian Pop, Franz-Viktor Kuhlmann, Salih Azgin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-05-30T12:41:30Z","title":"Characterization of Extremal Valued Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.5523","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":"sha256:347386e0b5e1b77789f2bb8f5d7b941c5a57a8661f0da3803a0671744e52077a","target":"record","created_at":"2026-05-18T03:29:28Z","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":"fc06140bed85e2992489a5f929db8eb64cb6d4aafc353088fac531cebc095884","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2010-05-30T12:41:30Z","title_canon_sha256":"04a2f09c9b94770cc176893de989b8977017e8069ffccbddca2e836cefe218d6"},"schema_version":"1.0","source":{"id":"1005.5523","kind":"arxiv","version":1}},"canonical_sha256":"83530ae270890822ed48985a3e6beac8c2bd3873611f3f422b8a269bd86c4454","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"83530ae270890822ed48985a3e6beac8c2bd3873611f3f422b8a269bd86c4454","first_computed_at":"2026-05-18T03:29:28.042485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:29:28.042485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tIa0CBl2XA/SbmfjHCxMLENbQk6G1Xgx4CKwgPsT5x6XoJ8DCiGXgDwYa5V95Wa2fyWWoUI20IKK1WStsQlDDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:29:28.043199Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.5523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:347386e0b5e1b77789f2bb8f5d7b941c5a57a8661f0da3803a0671744e52077a","sha256:18cca429338b77baf432fb8ab2b52dd3ecae3df91c476fff24ea08db96bccc9b"],"state_sha256":"aff95c2726c5f182fa558eb982df849c1c010e2182e069bc3492021af285b0b5"}