{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:73UYCBMRX6KFMMSVUSIZUJTEKD","short_pith_number":"pith:73UYCBMR","canonical_record":{"source":{"id":"1603.06916","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-22T19:18:57Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"576096e3e43baaa42ca18cef3236c9c0a4d28007a0068586e064b7172f3b06bf","abstract_canon_sha256":"7e334b66ef3e81bb19db01ddff3c9f890ba80bb15ca103ed3dc638942af9984c"},"schema_version":"1.0"},"canonical_sha256":"fee9810591bf94563255a4919a266450cf9e70423f9730e92813c528fb3badb1","source":{"kind":"arxiv","id":"1603.06916","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06916","created_at":"2026-05-18T00:26:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06916v3","created_at":"2026-05-18T00:26:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06916","created_at":"2026-05-18T00:26:37Z"},{"alias_kind":"pith_short_12","alias_value":"73UYCBMRX6KF","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"73UYCBMRX6KFMMSV","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"73UYCBMR","created_at":"2026-05-18T12:30:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:73UYCBMRX6KFMMSVUSIZUJTEKD","target":"record","payload":{"canonical_record":{"source":{"id":"1603.06916","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-22T19:18:57Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"576096e3e43baaa42ca18cef3236c9c0a4d28007a0068586e064b7172f3b06bf","abstract_canon_sha256":"7e334b66ef3e81bb19db01ddff3c9f890ba80bb15ca103ed3dc638942af9984c"},"schema_version":"1.0"},"canonical_sha256":"fee9810591bf94563255a4919a266450cf9e70423f9730e92813c528fb3badb1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:37.922144Z","signature_b64":"HVchb2baYsNff/c/GSEw138mdqdW9Pa/gjwaTPRTPKXOpV4SmsSuhn/3+ytVM6dvEvGpV7wPZjATWyhcKJ+qDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fee9810591bf94563255a4919a266450cf9e70423f9730e92813c528fb3badb1","last_reissued_at":"2026-05-18T00:26:37.921335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:37.921335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.06916","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:26:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"o8A9k3bF4CLMMtEFmAYwOfEAfsuU7e6yLeL65nFQOZ2oZedtjkhKgIM5fV1+ufDNJ8Dy/G77VxX2AFx3lvgPCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:42:46.096823Z"},"content_sha256":"d94ad72eaa98f711fc1b90707280e90371b8c3d9eaa7b0aa1727a527f6d5c18f","schema_version":"1.0","event_id":"sha256:d94ad72eaa98f711fc1b90707280e90371b8c3d9eaa7b0aa1727a527f6d5c18f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:73UYCBMRX6KFMMSVUSIZUJTEKD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving generic nonarchimedean semidefinite programs using stochastic game algorithms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Mateusz Skomra, St\\'ephane Gaubert, Xavier Allamigeon","submitted_at":"2016-03-22T19:18:57Z","abstract_excerpt":"A general issue in computational optimization is to develop combinatorial algorithms for semidefinite programming. We address this issue when the base field is nonarchimedean. We provide a solution for a class of semidefinite feasibility problems given by generic matrices. Our approach is based on tropical geometry. It relies on tropical spectrahedra, which are defined as the images by the valuation of nonarchimedean spectrahedra. We establish a correspondence between generic tropical spectrahedra and zero-sum stochastic games with perfect information. The latter have been well studied in algo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06916","kind":"arxiv","version":3},"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":"2026-05-18T00:26:37Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nx1K3VkNpH1BT7TGRItZCR22nb3i0UkzHYCPbqgwccxw5qISLjAWKuy7fE/L4N4Q00DT6BTdCvVXNNVxHnObCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:42:46.097184Z"},"content_sha256":"5d8ab5890fc85ef5f71cb66ce86cddda71e72fbac37f9a165edf4ce483a766b2","schema_version":"1.0","event_id":"sha256:5d8ab5890fc85ef5f71cb66ce86cddda71e72fbac37f9a165edf4ce483a766b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/73UYCBMRX6KFMMSVUSIZUJTEKD/bundle.json","state_url":"https://pith.science/pith/73UYCBMRX6KFMMSVUSIZUJTEKD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/73UYCBMRX6KFMMSVUSIZUJTEKD/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":"2026-05-26T00:42:46Z","links":{"resolver":"https://pith.science/pith/73UYCBMRX6KFMMSVUSIZUJTEKD","bundle":"https://pith.science/pith/73UYCBMRX6KFMMSVUSIZUJTEKD/bundle.json","state":"https://pith.science/pith/73UYCBMRX6KFMMSVUSIZUJTEKD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/73UYCBMRX6KFMMSVUSIZUJTEKD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:73UYCBMRX6KFMMSVUSIZUJTEKD","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":"7e334b66ef3e81bb19db01ddff3c9f890ba80bb15ca103ed3dc638942af9984c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-22T19:18:57Z","title_canon_sha256":"576096e3e43baaa42ca18cef3236c9c0a4d28007a0068586e064b7172f3b06bf"},"schema_version":"1.0","source":{"id":"1603.06916","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.06916","created_at":"2026-05-18T00:26:37Z"},{"alias_kind":"arxiv_version","alias_value":"1603.06916v3","created_at":"2026-05-18T00:26:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.06916","created_at":"2026-05-18T00:26:37Z"},{"alias_kind":"pith_short_12","alias_value":"73UYCBMRX6KF","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"73UYCBMRX6KFMMSV","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"73UYCBMR","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:5d8ab5890fc85ef5f71cb66ce86cddda71e72fbac37f9a165edf4ce483a766b2","target":"graph","created_at":"2026-05-18T00:26:37Z","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 general issue in computational optimization is to develop combinatorial algorithms for semidefinite programming. We address this issue when the base field is nonarchimedean. We provide a solution for a class of semidefinite feasibility problems given by generic matrices. Our approach is based on tropical geometry. It relies on tropical spectrahedra, which are defined as the images by the valuation of nonarchimedean spectrahedra. We establish a correspondence between generic tropical spectrahedra and zero-sum stochastic games with perfect information. The latter have been well studied in algo","authors_text":"Mateusz Skomra, St\\'ephane Gaubert, Xavier Allamigeon","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-22T19:18:57Z","title":"Solving generic nonarchimedean semidefinite programs using stochastic game algorithms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06916","kind":"arxiv","version":3},"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:d94ad72eaa98f711fc1b90707280e90371b8c3d9eaa7b0aa1727a527f6d5c18f","target":"record","created_at":"2026-05-18T00:26:37Z","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":"7e334b66ef3e81bb19db01ddff3c9f890ba80bb15ca103ed3dc638942af9984c","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2016-03-22T19:18:57Z","title_canon_sha256":"576096e3e43baaa42ca18cef3236c9c0a4d28007a0068586e064b7172f3b06bf"},"schema_version":"1.0","source":{"id":"1603.06916","kind":"arxiv","version":3}},"canonical_sha256":"fee9810591bf94563255a4919a266450cf9e70423f9730e92813c528fb3badb1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fee9810591bf94563255a4919a266450cf9e70423f9730e92813c528fb3badb1","first_computed_at":"2026-05-18T00:26:37.921335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:37.921335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HVchb2baYsNff/c/GSEw138mdqdW9Pa/gjwaTPRTPKXOpV4SmsSuhn/3+ytVM6dvEvGpV7wPZjATWyhcKJ+qDw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:37.922144Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.06916","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d94ad72eaa98f711fc1b90707280e90371b8c3d9eaa7b0aa1727a527f6d5c18f","sha256:5d8ab5890fc85ef5f71cb66ce86cddda71e72fbac37f9a165edf4ce483a766b2"],"state_sha256":"78e42524ede53230a285393e014f85663b79ab96f9300317e5f39038b3a7b79f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O97AXJq2fH/+Umh7oD6A1s4m3GlcL8x6jh/D2FFITn0YCwi8a9Fr7oCU5y36wyk0YQcmUSiFYUamhtHxQvxzDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:42:46.099855Z","bundle_sha256":"386a4fc018e01ef8e267047957613d140e7efa83b0fcba528dfe0f6785e44be8"}}