{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NM2AL4Z7ECL6JKUJGUEIJKWPST","short_pith_number":"pith:NM2AL4Z7","canonical_record":{"source":{"id":"1503.09014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-31T12:05:12Z","cross_cats_sorted":[],"title_canon_sha256":"a8a3a2db9102c4c1bf774d5cd670428b9b679cc8126c2b824f590a91d7e694a6","abstract_canon_sha256":"a7bbf838f123d106b8083a0c233c051692902fefde416530024794a49ea8f4b7"},"schema_version":"1.0"},"canonical_sha256":"6b3405f33f2097e4aa89350884aacf94e2a0e04ef6a39db448574cac70da2877","source":{"kind":"arxiv","id":"1503.09014","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.09014","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"arxiv_version","alias_value":"1503.09014v1","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.09014","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"pith_short_12","alias_value":"NM2AL4Z7ECL6","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NM2AL4Z7ECL6JKUJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NM2AL4Z7","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NM2AL4Z7ECL6JKUJGUEIJKWPST","target":"record","payload":{"canonical_record":{"source":{"id":"1503.09014","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-31T12:05:12Z","cross_cats_sorted":[],"title_canon_sha256":"a8a3a2db9102c4c1bf774d5cd670428b9b679cc8126c2b824f590a91d7e694a6","abstract_canon_sha256":"a7bbf838f123d106b8083a0c233c051692902fefde416530024794a49ea8f4b7"},"schema_version":"1.0"},"canonical_sha256":"6b3405f33f2097e4aa89350884aacf94e2a0e04ef6a39db448574cac70da2877","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:51.635000Z","signature_b64":"crX96bqh6VlAg2dqVc3set9gltq2fXWN0YVmvrnEuNvzyZcnriCZwzWRNRIwNAf5TJ3g+0V4F/rOp5gCmfPXDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6b3405f33f2097e4aa89350884aacf94e2a0e04ef6a39db448574cac70da2877","last_reissued_at":"2026-05-18T02:19:51.634440Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:51.634440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1503.09014","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":"2026-05-18T02:19:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"//5+lXboU8OGUi5eHledBK28pwneHvUoDqrm9UCcsEuDqjFQA83VBVqHH/ScfKQlIn42/OUshuTDEBkSs496DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:37:10.366977Z"},"content_sha256":"92ac30be991c3168baf3d9bac14b41ed497acb310db3b7f6f8b2dc6dd59f7270","schema_version":"1.0","event_id":"sha256:92ac30be991c3168baf3d9bac14b41ed497acb310db3b7f6f8b2dc6dd59f7270"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NM2AL4Z7ECL6JKUJGUEIJKWPST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Finding a maximal element of a convex set through its characteristic cone: An application to finding a strictly complementary solution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Kaoru Tone, Mahmood Mehdiloozad, Mohammad Bagher Ahmadi, Rahim Askarpour","submitted_at":"2015-03-31T12:05:12Z","abstract_excerpt":"In order to express a polyhedron as the (Minkowski) sum of a polytope and a polyhedral cone, Motzkin (1936) made a transition from the polyhedron to a polyhedral cone. Based on his excellent idea, we represent a set by a characteristic cone. By using this representation, we then reach four main results: (i) expressing a closed convex set containing no line as the direct sum of the convex hull of its extreme points and conical hull of its extreme directions, (ii) establishing a convex programming (CP) based framework for determining a maximal element-an element with the maximum number of positi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.09014","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":"2026-05-18T02:19:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tWQJ2PUes4x+X7r5zMqGXHWHUWKFYe5gnvQKYnfiz3qMcoL/rgLkWTtHt6baJrKyoKOi+CU07ByK7VqhYv7ODA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T23:37:10.367354Z"},"content_sha256":"9919a166eb42bc51a6f58921d35c6bda9bf4af4f0d2d4c20fb0d06803bbe9bbe","schema_version":"1.0","event_id":"sha256:9919a166eb42bc51a6f58921d35c6bda9bf4af4f0d2d4c20fb0d06803bbe9bbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NM2AL4Z7ECL6JKUJGUEIJKWPST/bundle.json","state_url":"https://pith.science/pith/NM2AL4Z7ECL6JKUJGUEIJKWPST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NM2AL4Z7ECL6JKUJGUEIJKWPST/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":"2026-05-30T23:37:10Z","links":{"resolver":"https://pith.science/pith/NM2AL4Z7ECL6JKUJGUEIJKWPST","bundle":"https://pith.science/pith/NM2AL4Z7ECL6JKUJGUEIJKWPST/bundle.json","state":"https://pith.science/pith/NM2AL4Z7ECL6JKUJGUEIJKWPST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NM2AL4Z7ECL6JKUJGUEIJKWPST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NM2AL4Z7ECL6JKUJGUEIJKWPST","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":"a7bbf838f123d106b8083a0c233c051692902fefde416530024794a49ea8f4b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-31T12:05:12Z","title_canon_sha256":"a8a3a2db9102c4c1bf774d5cd670428b9b679cc8126c2b824f590a91d7e694a6"},"schema_version":"1.0","source":{"id":"1503.09014","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.09014","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"arxiv_version","alias_value":"1503.09014v1","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.09014","created_at":"2026-05-18T02:19:51Z"},{"alias_kind":"pith_short_12","alias_value":"NM2AL4Z7ECL6","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"NM2AL4Z7ECL6JKUJ","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"NM2AL4Z7","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:9919a166eb42bc51a6f58921d35c6bda9bf4af4f0d2d4c20fb0d06803bbe9bbe","target":"graph","created_at":"2026-05-18T02:19:51Z","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 order to express a polyhedron as the (Minkowski) sum of a polytope and a polyhedral cone, Motzkin (1936) made a transition from the polyhedron to a polyhedral cone. Based on his excellent idea, we represent a set by a characteristic cone. By using this representation, we then reach four main results: (i) expressing a closed convex set containing no line as the direct sum of the convex hull of its extreme points and conical hull of its extreme directions, (ii) establishing a convex programming (CP) based framework for determining a maximal element-an element with the maximum number of positi","authors_text":"Kaoru Tone, Mahmood Mehdiloozad, Mohammad Bagher Ahmadi, Rahim Askarpour","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-31T12:05:12Z","title":"Finding a maximal element of a convex set through its characteristic cone: An application to finding a strictly complementary solution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.09014","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":"sha256:92ac30be991c3168baf3d9bac14b41ed497acb310db3b7f6f8b2dc6dd59f7270","target":"record","created_at":"2026-05-18T02:19:51Z","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":"a7bbf838f123d106b8083a0c233c051692902fefde416530024794a49ea8f4b7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2015-03-31T12:05:12Z","title_canon_sha256":"a8a3a2db9102c4c1bf774d5cd670428b9b679cc8126c2b824f590a91d7e694a6"},"schema_version":"1.0","source":{"id":"1503.09014","kind":"arxiv","version":1}},"canonical_sha256":"6b3405f33f2097e4aa89350884aacf94e2a0e04ef6a39db448574cac70da2877","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b3405f33f2097e4aa89350884aacf94e2a0e04ef6a39db448574cac70da2877","first_computed_at":"2026-05-18T02:19:51.634440Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:51.634440Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"crX96bqh6VlAg2dqVc3set9gltq2fXWN0YVmvrnEuNvzyZcnriCZwzWRNRIwNAf5TJ3g+0V4F/rOp5gCmfPXDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:51.635000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.09014","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92ac30be991c3168baf3d9bac14b41ed497acb310db3b7f6f8b2dc6dd59f7270","sha256:9919a166eb42bc51a6f58921d35c6bda9bf4af4f0d2d4c20fb0d06803bbe9bbe"],"state_sha256":"eb8b0ac05402c250ec9c9a3e810a2ea2a210235e8d8aef8e825ea8f3e9074486"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Eq/LBBWkRw5mQsOx7mbglHeogYlWlWYF09ZDdMOse8I0yE6CyMW8aqOh7JuCdWjd1myqXPX4NRrc89HLlxaTBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T23:37:10.369467Z","bundle_sha256":"668e5d8b214e17d4aa4c179925eab045d97dbda05eaf08ab5b735544d98d457a"}}