{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:TGY2QHLWK6O56A7EFUSOFJ27GR","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":"f5d4962b5ec387360ad1fa2b9edeea84004fc50fbead5fd8091e35cfe836fe5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-04-04T17:09:41Z","title_canon_sha256":"2781a1a77675d7cc501f53818a94e0b9b4c519d8946f0192519e0a77931cacb8"},"schema_version":"1.0","source":{"id":"1204.1003","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.1003","created_at":"2026-05-18T02:43:54Z"},{"alias_kind":"arxiv_version","alias_value":"1204.1003v2","created_at":"2026-05-18T02:43:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.1003","created_at":"2026-05-18T02:43:54Z"},{"alias_kind":"pith_short_12","alias_value":"TGY2QHLWK6O5","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_16","alias_value":"TGY2QHLWK6O56A7E","created_at":"2026-05-18T12:27:23Z"},{"alias_kind":"pith_short_8","alias_value":"TGY2QHLW","created_at":"2026-05-18T12:27:23Z"}],"graph_snapshots":[{"event_id":"sha256:692cdb155c4df1b58259212efff22fe73694b9699bf8f7308c5beb3a7d689528","target":"graph","created_at":"2026-05-18T02:43:54Z","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 discuss the extension of inequality R_A >= c/a * r_b + b/a * r_c to the plane of triangle ABC. Based on the obtained extension, in regard to all three vertices of the triangle, we get the extension of Erdos-Mordell inequality, and some inequalities of Erdos-Mordell type.","authors_text":"Branislav Popkonstantinovic, Branko Malesevic, Maja Petrovic, Marija Obradovic","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-04-04T17:09:41Z","title":"On the Extension of the Erdos-Mordell Type Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.1003","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":"sha256:0cf3e34a29d63ddd73fce13645a8db5a0cd61bfdc8630116a8153b3104dd0b00","target":"record","created_at":"2026-05-18T02:43:54Z","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":"f5d4962b5ec387360ad1fa2b9edeea84004fc50fbead5fd8091e35cfe836fe5a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2012-04-04T17:09:41Z","title_canon_sha256":"2781a1a77675d7cc501f53818a94e0b9b4c519d8946f0192519e0a77931cacb8"},"schema_version":"1.0","source":{"id":"1204.1003","kind":"arxiv","version":2}},"canonical_sha256":"99b1a81d76579ddf03e42d24e2a75f3476abc55f44bfedc427384d50ed671bb7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"99b1a81d76579ddf03e42d24e2a75f3476abc55f44bfedc427384d50ed671bb7","first_computed_at":"2026-05-18T02:43:54.553185Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:54.553185Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lpTLj1JUs8jbZ0Nsv46RVegldTLcXB+n10BfPK4AhE51vPqfaudnSiy8kYLR0+Ivv8v1pu33G9V4FhwCi4JiDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:54.553571Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.1003","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0cf3e34a29d63ddd73fce13645a8db5a0cd61bfdc8630116a8153b3104dd0b00","sha256:692cdb155c4df1b58259212efff22fe73694b9699bf8f7308c5beb3a7d689528"],"state_sha256":"cc1f878f2cf5f73a67c85d540df7786dca77b1116e86a0f722973eeb0757b5bd"}