{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6BE5RO6NHGALLFHM4PKECAGCW6","short_pith_number":"pith:6BE5RO6N","canonical_record":{"source":{"id":"1409.8272","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-29T19:59:21Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c56d4b5f7d2983a2e5ecf0e6a10aa71a377d27edc8ee9d5c07251f8313939cd4","abstract_canon_sha256":"cc954270c8ec1ef1ab18426478b2d9b61774d963127b8f6be2f8b115b87da41a"},"schema_version":"1.0"},"canonical_sha256":"f049d8bbcd3980b594ece3d44100c2b7baac35a41dc130505dd1b267eaecd828","source":{"kind":"arxiv","id":"1409.8272","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8272","created_at":"2026-05-18T02:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8272v2","created_at":"2026-05-18T02:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8272","created_at":"2026-05-18T02:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"6BE5RO6NHGAL","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6BE5RO6NHGALLFHM","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6BE5RO6N","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6BE5RO6NHGALLFHM4PKECAGCW6","target":"record","payload":{"canonical_record":{"source":{"id":"1409.8272","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-29T19:59:21Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"c56d4b5f7d2983a2e5ecf0e6a10aa71a377d27edc8ee9d5c07251f8313939cd4","abstract_canon_sha256":"cc954270c8ec1ef1ab18426478b2d9b61774d963127b8f6be2f8b115b87da41a"},"schema_version":"1.0"},"canonical_sha256":"f049d8bbcd3980b594ece3d44100c2b7baac35a41dc130505dd1b267eaecd828","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:17.636926Z","signature_b64":"D3X/rpwlDYUwspN4kAJJhB51N9JeGPnc2QJ6RZfeEcn2cCFxSfXsvtrbkTojkykZT4MM7WpTAPGMwIaQEr0QCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f049d8bbcd3980b594ece3d44100c2b7baac35a41dc130505dd1b267eaecd828","last_reissued_at":"2026-05-18T02:40:17.636261Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:17.636261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.8272","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":"2026-05-18T02:40:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bEoArBYNJG+comRiYgCFMZfzkN9nXkJFXSZPc3+VEp6hR4II91CvzB1aXTdIf8++jAiaGf78CvCe3jwMrio6Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:32:26.827905Z"},"content_sha256":"aace7b3b9039aad72c9f2ec266adb49b5349db81d3af75e1beebbf99b61e985c","schema_version":"1.0","event_id":"sha256:aace7b3b9039aad72c9f2ec266adb49b5349db81d3af75e1beebbf99b61e985c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6BE5RO6NHGALLFHM4PKECAGCW6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Semidefinite approximations of conical hulls of measured sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OC","authors_text":"Juli\\'an Romero, Mauricio Velasco","submitted_at":"2014-09-29T19:59:21Z","abstract_excerpt":"Let $C$ be a proper convex cone generated by a compact set which supports a measure $\\mu$. A construction due to A.Barvinok, E.Veomett and J.B. Lasserre produces, using $\\mu$, a sequence $(P_k)_{k\\in \\mathbb{N}}$ of nested spectrahedral cones which contains the cone $C^*$ dual to $C$. We prove convergence results for such sequences of spectrahedra and provide tools for bounding the distance between $P_k$ and $C^*$. These tools are especially useful on cones with enough symmetries and allow us to determine bounds for several cones of interest. We compute such upper bounds for semidefinite appro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8272","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":"2026-05-18T02:40:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"livF2jFCYAqoe0H5w4QDJlRXZafZLVBA3XpBp2q6xsd18fm9G/SKPQQDMVnMSlalGh9f2SS9/1SxrKfct8ApDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T23:32:26.828643Z"},"content_sha256":"312c5768db4d67e3065775f81b3c0946065a3a4b6d177a694301d4e03cb9643c","schema_version":"1.0","event_id":"sha256:312c5768db4d67e3065775f81b3c0946065a3a4b6d177a694301d4e03cb9643c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6BE5RO6NHGALLFHM4PKECAGCW6/bundle.json","state_url":"https://pith.science/pith/6BE5RO6NHGALLFHM4PKECAGCW6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6BE5RO6NHGALLFHM4PKECAGCW6/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":"2026-06-11T23:32:26Z","links":{"resolver":"https://pith.science/pith/6BE5RO6NHGALLFHM4PKECAGCW6","bundle":"https://pith.science/pith/6BE5RO6NHGALLFHM4PKECAGCW6/bundle.json","state":"https://pith.science/pith/6BE5RO6NHGALLFHM4PKECAGCW6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6BE5RO6NHGALLFHM4PKECAGCW6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6BE5RO6NHGALLFHM4PKECAGCW6","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":"cc954270c8ec1ef1ab18426478b2d9b61774d963127b8f6be2f8b115b87da41a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-29T19:59:21Z","title_canon_sha256":"c56d4b5f7d2983a2e5ecf0e6a10aa71a377d27edc8ee9d5c07251f8313939cd4"},"schema_version":"1.0","source":{"id":"1409.8272","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8272","created_at":"2026-05-18T02:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8272v2","created_at":"2026-05-18T02:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8272","created_at":"2026-05-18T02:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"6BE5RO6NHGAL","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6BE5RO6NHGALLFHM","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6BE5RO6N","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:312c5768db4d67e3065775f81b3c0946065a3a4b6d177a694301d4e03cb9643c","target":"graph","created_at":"2026-05-18T02:40:17Z","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":"Let $C$ be a proper convex cone generated by a compact set which supports a measure $\\mu$. A construction due to A.Barvinok, E.Veomett and J.B. Lasserre produces, using $\\mu$, a sequence $(P_k)_{k\\in \\mathbb{N}}$ of nested spectrahedral cones which contains the cone $C^*$ dual to $C$. We prove convergence results for such sequences of spectrahedra and provide tools for bounding the distance between $P_k$ and $C^*$. These tools are especially useful on cones with enough symmetries and allow us to determine bounds for several cones of interest. We compute such upper bounds for semidefinite appro","authors_text":"Juli\\'an Romero, Mauricio Velasco","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-29T19:59:21Z","title":"Semidefinite approximations of conical hulls of measured sets"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8272","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:aace7b3b9039aad72c9f2ec266adb49b5349db81d3af75e1beebbf99b61e985c","target":"record","created_at":"2026-05-18T02:40:17Z","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":"cc954270c8ec1ef1ab18426478b2d9b61774d963127b8f6be2f8b115b87da41a","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2014-09-29T19:59:21Z","title_canon_sha256":"c56d4b5f7d2983a2e5ecf0e6a10aa71a377d27edc8ee9d5c07251f8313939cd4"},"schema_version":"1.0","source":{"id":"1409.8272","kind":"arxiv","version":2}},"canonical_sha256":"f049d8bbcd3980b594ece3d44100c2b7baac35a41dc130505dd1b267eaecd828","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f049d8bbcd3980b594ece3d44100c2b7baac35a41dc130505dd1b267eaecd828","first_computed_at":"2026-05-18T02:40:17.636261Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:17.636261Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"D3X/rpwlDYUwspN4kAJJhB51N9JeGPnc2QJ6RZfeEcn2cCFxSfXsvtrbkTojkykZT4MM7WpTAPGMwIaQEr0QCg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:17.636926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8272","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aace7b3b9039aad72c9f2ec266adb49b5349db81d3af75e1beebbf99b61e985c","sha256:312c5768db4d67e3065775f81b3c0946065a3a4b6d177a694301d4e03cb9643c"],"state_sha256":"3a5d6a227b3825c5fd69d15d60fe0adf97caf01b8c3e3845f17b9585e744a026"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F5uJ3kZvep331ZVpkhjVawfHqb62LQ3ITbxOrXDkHgBGcPHA2S7mVrbgwXuamNn1xDlkiFVUzOtvxhdJTPVVBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T23:32:26.832851Z","bundle_sha256":"b516ea4e1cee0cbe61ceb74ef3d9eb072f59648be6c97ab5c162b26ac44ef5fa"}}