{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:Z7QROZA2SODYG6QLA3QRYW55CV","short_pith_number":"pith:Z7QROZA2","canonical_record":{"source":{"id":"1212.6107","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-26T01:26:31Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"caa02d37e25842d9069b1834283ea8f7b7f25de065a26af7db6b712eab7dcd21","abstract_canon_sha256":"9d3a02f61564a0802f54697cfb641e1df8749735b37295cb7aefdf9994930549"},"schema_version":"1.0"},"canonical_sha256":"cfe117641a9387837a0b06e11c5bbd156648c27cde1f6a42d1c197f7fa30a3aa","source":{"kind":"arxiv","id":"1212.6107","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6107","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6107v1","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6107","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"Z7QROZA2SODY","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z7QROZA2SODYG6QL","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z7QROZA2","created_at":"2026-05-18T12:27:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:Z7QROZA2SODYG6QLA3QRYW55CV","target":"record","payload":{"canonical_record":{"source":{"id":"1212.6107","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-26T01:26:31Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"caa02d37e25842d9069b1834283ea8f7b7f25de065a26af7db6b712eab7dcd21","abstract_canon_sha256":"9d3a02f61564a0802f54697cfb641e1df8749735b37295cb7aefdf9994930549"},"schema_version":"1.0"},"canonical_sha256":"cfe117641a9387837a0b06e11c5bbd156648c27cde1f6a42d1c197f7fa30a3aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:42.748309Z","signature_b64":"PwHsBubYjTlgmNnHEv1aai2Re9J6MCjs2X0XT64m/wrGvAF1x2RPHK8MN9rOtpc/X+FY0aJC1Nw44zyRM+sUAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfe117641a9387837a0b06e11c5bbd156648c27cde1f6a42d1c197f7fa30a3aa","last_reissued_at":"2026-05-18T03:37:42.747682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:42.747682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1212.6107","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LaLaK0tKFwuuLcYrFNia2GC+YaGMPa3l6Uepowtdz4ADaP9LyxB9oCaj/fVrwmtSBNPE7EuSmGCZdq9o6QQXBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T02:29:03.041488Z"},"content_sha256":"eca2291bf7418493bf4a937e663403caf25cdf5719030f0cf53753c239cc78fc","schema_version":"1.0","event_id":"sha256:eca2291bf7418493bf4a937e663403caf25cdf5719030f0cf53753c239cc78fc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:Z7QROZA2SODYG6QLA3QRYW55CV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A solution of a tropical linear vector equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.OC","authors_text":"Nikolai Krivulin","submitted_at":"2012-12-26T01:26:31Z","abstract_excerpt":"A linear vector equation is considered defined in terms of idempotent mathematics. To solve the equation, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces and reduces the solution of the equation to that of a tropical optimization problem. Based on the approach, existence and uniqueness conditions are established for the solution, and a general solution to the equation is given."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6107","kind":"arxiv","version":1},"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":"2026-05-18T03:37:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O5RpsMTUXJxTtbToVQrQ/vy4CTolFnQmZOJ7qJierZLWmttvvHSFWr4D2GEauSy9irV5t3IfQtbKn16i5zwSAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T02:29:03.041834Z"},"content_sha256":"e82fc133da9aa19225ef8bea5033b0faae51d9a72aba1d7a91ff9b94b6c49e05","schema_version":"1.0","event_id":"sha256:e82fc133da9aa19225ef8bea5033b0faae51d9a72aba1d7a91ff9b94b6c49e05"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z7QROZA2SODYG6QLA3QRYW55CV/bundle.json","state_url":"https://pith.science/pith/Z7QROZA2SODYG6QLA3QRYW55CV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z7QROZA2SODYG6QLA3QRYW55CV/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":"2026-07-04T02:29:03Z","links":{"resolver":"https://pith.science/pith/Z7QROZA2SODYG6QLA3QRYW55CV","bundle":"https://pith.science/pith/Z7QROZA2SODYG6QLA3QRYW55CV/bundle.json","state":"https://pith.science/pith/Z7QROZA2SODYG6QLA3QRYW55CV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z7QROZA2SODYG6QLA3QRYW55CV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z7QROZA2SODYG6QLA3QRYW55CV","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":"9d3a02f61564a0802f54697cfb641e1df8749735b37295cb7aefdf9994930549","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-26T01:26:31Z","title_canon_sha256":"caa02d37e25842d9069b1834283ea8f7b7f25de065a26af7db6b712eab7dcd21"},"schema_version":"1.0","source":{"id":"1212.6107","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1212.6107","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"arxiv_version","alias_value":"1212.6107v1","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1212.6107","created_at":"2026-05-18T03:37:42Z"},{"alias_kind":"pith_short_12","alias_value":"Z7QROZA2SODY","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z7QROZA2SODYG6QL","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z7QROZA2","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:e82fc133da9aa19225ef8bea5033b0faae51d9a72aba1d7a91ff9b94b6c49e05","target":"graph","created_at":"2026-05-18T03:37:42Z","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":"A linear vector equation is considered defined in terms of idempotent mathematics. To solve the equation, we apply an approach that is based on the analysis of distances between vectors in idempotent vector spaces and reduces the solution of the equation to that of a tropical optimization problem. Based on the approach, existence and uniqueness conditions are established for the solution, and a general solution to the equation is given.","authors_text":"Nikolai Krivulin","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-26T01:26:31Z","title":"A solution of a tropical linear vector equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.6107","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:eca2291bf7418493bf4a937e663403caf25cdf5719030f0cf53753c239cc78fc","target":"record","created_at":"2026-05-18T03:37:42Z","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":"9d3a02f61564a0802f54697cfb641e1df8749735b37295cb7aefdf9994930549","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2012-12-26T01:26:31Z","title_canon_sha256":"caa02d37e25842d9069b1834283ea8f7b7f25de065a26af7db6b712eab7dcd21"},"schema_version":"1.0","source":{"id":"1212.6107","kind":"arxiv","version":1}},"canonical_sha256":"cfe117641a9387837a0b06e11c5bbd156648c27cde1f6a42d1c197f7fa30a3aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfe117641a9387837a0b06e11c5bbd156648c27cde1f6a42d1c197f7fa30a3aa","first_computed_at":"2026-05-18T03:37:42.747682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:42.747682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PwHsBubYjTlgmNnHEv1aai2Re9J6MCjs2X0XT64m/wrGvAF1x2RPHK8MN9rOtpc/X+FY0aJC1Nw44zyRM+sUAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:42.748309Z","signed_message":"canonical_sha256_bytes"},"source_id":"1212.6107","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eca2291bf7418493bf4a937e663403caf25cdf5719030f0cf53753c239cc78fc","sha256:e82fc133da9aa19225ef8bea5033b0faae51d9a72aba1d7a91ff9b94b6c49e05"],"state_sha256":"6e2ec16bcbc537bce7e3ffbe1e83360c38af873e971ec9dfc41bd82b957d88b0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RK+DtO+QJf9SCzhfhZMafIAwVf6ZMImzSKIIyKlL7HkDPsDbN+HJVC1ZtL11+INE9IABSRPLmi11lbDY8ZXsDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T02:29:03.043729Z","bundle_sha256":"165e36fde0247fc0d11ef4abfc03d463c80104b54616d69e7a9f95ff7adb77d6"}}