{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:SMAQZB2HYSAQTYK7C772AN263Q","short_pith_number":"pith:SMAQZB2H","canonical_record":{"source":{"id":"1502.08035","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-27T19:41:32Z","cross_cats_sorted":[],"title_canon_sha256":"a77a93c1496dc4d2ee6391a47e9d2c9432e471a61946e3fe709c4becfb2d80c0","abstract_canon_sha256":"005f2e079a192f9d7f5446c419d9b8c9677d7a4818c1e5646830c68eb410465f"},"schema_version":"1.0"},"canonical_sha256":"93010c8747c48109e15f17ffa0375edc166ec76c718b6b621ecfcb5bc477db50","source":{"kind":"arxiv","id":"1502.08035","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.08035","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"1502.08035v2","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.08035","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"SMAQZB2HYSAQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SMAQZB2HYSAQTYK7","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SMAQZB2H","created_at":"2026-05-18T12:29:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:SMAQZB2HYSAQTYK7C772AN263Q","target":"record","payload":{"canonical_record":{"source":{"id":"1502.08035","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-27T19:41:32Z","cross_cats_sorted":[],"title_canon_sha256":"a77a93c1496dc4d2ee6391a47e9d2c9432e471a61946e3fe709c4becfb2d80c0","abstract_canon_sha256":"005f2e079a192f9d7f5446c419d9b8c9677d7a4818c1e5646830c68eb410465f"},"schema_version":"1.0"},"canonical_sha256":"93010c8747c48109e15f17ffa0375edc166ec76c718b6b621ecfcb5bc477db50","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:39.891707Z","signature_b64":"zec9zM3Pa1kD5rbcSqK3rJ+vprzbQhAYKIeF9PBACWRPwZtKAqqrE7aqzqCLQ3nvJla8lfDjAaOMEMatWSbZAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93010c8747c48109e15f17ffa0375edc166ec76c718b6b621ecfcb5bc477db50","last_reissued_at":"2026-05-18T02:25:39.891249Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:39.891249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.08035","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4LyEEFfbf3muap8k49WCpn973Y9jSSPy74hKIzBrnGe6gzjw3d9wX6xhoTZo8s59UV+CnHqtFvgUembw9WqFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:00:21.071900Z"},"content_sha256":"1070b05ec0c5ff848af54d96e8e32d0af7f8480b85fbbd3a69e5816ce20edb46","schema_version":"1.0","event_id":"sha256:1070b05ec0c5ff848af54d96e8e32d0af7f8480b85fbbd3a69e5816ce20edb46"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:SMAQZB2HYSAQTYK7C772AN263Q","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The open quadrant problem: A topological proof","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Carlos Ueno, J.M. Gamboa, Jose F. Fernando","submitted_at":"2015-02-27T19:41:32Z","abstract_excerpt":"In this work we present a new polynomial map $f:=(f_1,f_2):{\\mathbb R}^2\\to{\\mathbb R}^2$ whose image is the open quadrant $\\{x>0,y>0\\}\\subset{\\mathbb R}^2$. The proof of this fact involves arguments of topological nature that avoid hard computer calculations. In addition each polynomial $f_i\\in{\\mathbb R}[{\\tt x},{\\tt y}]$ has degree $\\leq16$ and only $11$ monomials, becoming the simplest known map solving the open quadrant problem."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.08035","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:25:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fihWT1FSwWJTNnfAsy2FUlFoXC8Xu12Vox36F/pyRxug/brTakJCTJsxFDTMdmBEF+hzYj5/1i71jxL8PUbCAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T16:00:21.072241Z"},"content_sha256":"ef15db67b1245f39782fe5f752f152331a49399e7855fb42b8901cc5ac2041fc","schema_version":"1.0","event_id":"sha256:ef15db67b1245f39782fe5f752f152331a49399e7855fb42b8901cc5ac2041fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SMAQZB2HYSAQTYK7C772AN263Q/bundle.json","state_url":"https://pith.science/pith/SMAQZB2HYSAQTYK7C772AN263Q/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SMAQZB2HYSAQTYK7C772AN263Q/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T16:00:21Z","links":{"resolver":"https://pith.science/pith/SMAQZB2HYSAQTYK7C772AN263Q","bundle":"https://pith.science/pith/SMAQZB2HYSAQTYK7C772AN263Q/bundle.json","state":"https://pith.science/pith/SMAQZB2HYSAQTYK7C772AN263Q/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SMAQZB2HYSAQTYK7C772AN263Q/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SMAQZB2HYSAQTYK7C772AN263Q","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":"005f2e079a192f9d7f5446c419d9b8c9677d7a4818c1e5646830c68eb410465f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-27T19:41:32Z","title_canon_sha256":"a77a93c1496dc4d2ee6391a47e9d2c9432e471a61946e3fe709c4becfb2d80c0"},"schema_version":"1.0","source":{"id":"1502.08035","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.08035","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"arxiv_version","alias_value":"1502.08035v2","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.08035","created_at":"2026-05-18T02:25:39Z"},{"alias_kind":"pith_short_12","alias_value":"SMAQZB2HYSAQ","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SMAQZB2HYSAQTYK7","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SMAQZB2H","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:ef15db67b1245f39782fe5f752f152331a49399e7855fb42b8901cc5ac2041fc","target":"graph","created_at":"2026-05-18T02:25:39Z","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":"In this work we present a new polynomial map $f:=(f_1,f_2):{\\mathbb R}^2\\to{\\mathbb R}^2$ whose image is the open quadrant $\\{x>0,y>0\\}\\subset{\\mathbb R}^2$. The proof of this fact involves arguments of topological nature that avoid hard computer calculations. In addition each polynomial $f_i\\in{\\mathbb R}[{\\tt x},{\\tt y}]$ has degree $\\leq16$ and only $11$ monomials, becoming the simplest known map solving the open quadrant problem.","authors_text":"Carlos Ueno, J.M. Gamboa, Jose F. Fernando","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-27T19:41:32Z","title":"The open quadrant problem: A topological proof"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.08035","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":"sha256:1070b05ec0c5ff848af54d96e8e32d0af7f8480b85fbbd3a69e5816ce20edb46","target":"record","created_at":"2026-05-18T02:25:39Z","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":"005f2e079a192f9d7f5446c419d9b8c9677d7a4818c1e5646830c68eb410465f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-02-27T19:41:32Z","title_canon_sha256":"a77a93c1496dc4d2ee6391a47e9d2c9432e471a61946e3fe709c4becfb2d80c0"},"schema_version":"1.0","source":{"id":"1502.08035","kind":"arxiv","version":2}},"canonical_sha256":"93010c8747c48109e15f17ffa0375edc166ec76c718b6b621ecfcb5bc477db50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93010c8747c48109e15f17ffa0375edc166ec76c718b6b621ecfcb5bc477db50","first_computed_at":"2026-05-18T02:25:39.891249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:25:39.891249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zec9zM3Pa1kD5rbcSqK3rJ+vprzbQhAYKIeF9PBACWRPwZtKAqqrE7aqzqCLQ3nvJla8lfDjAaOMEMatWSbZAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:25:39.891707Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.08035","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1070b05ec0c5ff848af54d96e8e32d0af7f8480b85fbbd3a69e5816ce20edb46","sha256:ef15db67b1245f39782fe5f752f152331a49399e7855fb42b8901cc5ac2041fc"],"state_sha256":"dd3a5695bf1cda2ebdfed3a4d64678a20c263cb9f65391d58c776f912ba26ef6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"siB8kLJThye60yVZ2ik4yAs90SwQSONwUwWtMxk3SLpXMyHeBvBCN0HHXnZ2Jm6huMxB4Wovy7/6swSkNLNNBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T16:00:21.074180Z","bundle_sha256":"0816ce285e745f62d320e8e6b1def4637fa95f5d061449b123465cc51941f4de"}}