{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:QVSI4YIHGHX6GDX7QRQN4VLFHW","short_pith_number":"pith:QVSI4YIH","canonical_record":{"source":{"id":"0907.1158","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-07-07T07:48:18Z","cross_cats_sorted":[],"title_canon_sha256":"652777f70ccae1b099acd87f4532e8ec2d4524aefdc067c207f9ffc639319e97","abstract_canon_sha256":"ddf5e01bf4dd7db717e3a6e43c361478e57f70181d40ced527a21243c70860a9"},"schema_version":"1.0"},"canonical_sha256":"85648e610731efe30eff8460de55653d8932d230cb7f6815d41fcd70c15e065c","source":{"kind":"arxiv","id":"0907.1158","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.1158","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"arxiv_version","alias_value":"0907.1158v2","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.1158","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"pith_short_12","alias_value":"QVSI4YIHGHX6","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QVSI4YIHGHX6GDX7","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QVSI4YIH","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:QVSI4YIHGHX6GDX7QRQN4VLFHW","target":"record","payload":{"canonical_record":{"source":{"id":"0907.1158","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-07-07T07:48:18Z","cross_cats_sorted":[],"title_canon_sha256":"652777f70ccae1b099acd87f4532e8ec2d4524aefdc067c207f9ffc639319e97","abstract_canon_sha256":"ddf5e01bf4dd7db717e3a6e43c361478e57f70181d40ced527a21243c70860a9"},"schema_version":"1.0"},"canonical_sha256":"85648e610731efe30eff8460de55653d8932d230cb7f6815d41fcd70c15e065c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:08.815826Z","signature_b64":"boFXqQGAE4rj31InoTAbOrFJvoF4I+Y4pNYa6O+wca3Cx/8/5rk1hTGfwyhCTL6PrXAqEOOBYkp39m03ni00AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"85648e610731efe30eff8460de55653d8932d230cb7f6815d41fcd70c15e065c","last_reissued_at":"2026-05-18T03:56:08.814928Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:08.814928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0907.1158","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":"2026-05-18T03:56:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IkFFS6eqGAvcSOdJM+hjWtWDAMzHA8U4iN5g0VPQvpexm4puGqX2ljl8Lu3u7xOMq/G/w2XrRjFn5YJY95tCBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:14:46.526511Z"},"content_sha256":"ef49c10af81a3f6e0119252fa4a5adbd2871c92b12a1931c47cf1508ed877587","schema_version":"1.0","event_id":"sha256:ef49c10af81a3f6e0119252fa4a5adbd2871c92b12a1931c47cf1508ed877587"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:QVSI4YIHGHX6GDX7QRQN4VLFHW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Davis' Convexity Theorem and Extremal Ellipsoids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Hans-Peter Schr\\\"ocker, Matthias J. Weber","submitted_at":"2009-07-07T07:48:18Z","abstract_excerpt":"We give a variety of uniqueness results for minimal ellipsoids circumscribing and maximal ellipsoids inscribed into a convex body. Uniqueness follows from a convexity or concavity criterion on the function used to measure the size of the ellipsoid. Simple examples with non-unique minimal or maximal ellipsoids conclude this article."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1158","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":"2026-05-18T03:56:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ez2LvkbNxfuNJ0eRh2FJVhjQWZPQr53Fb4f4ECNzxncbCdBJoPaK/ei/YM9jfPgh5lIKoTFyjGcl5IM/XXsHAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T08:14:46.527219Z"},"content_sha256":"3fd44770d0ebff0efc049c2fd7f81bcb546cc4f902afe1999fffa002f2c89db4","schema_version":"1.0","event_id":"sha256:3fd44770d0ebff0efc049c2fd7f81bcb546cc4f902afe1999fffa002f2c89db4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QVSI4YIHGHX6GDX7QRQN4VLFHW/bundle.json","state_url":"https://pith.science/pith/QVSI4YIHGHX6GDX7QRQN4VLFHW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QVSI4YIHGHX6GDX7QRQN4VLFHW/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":"2026-06-25T08:14:46Z","links":{"resolver":"https://pith.science/pith/QVSI4YIHGHX6GDX7QRQN4VLFHW","bundle":"https://pith.science/pith/QVSI4YIHGHX6GDX7QRQN4VLFHW/bundle.json","state":"https://pith.science/pith/QVSI4YIHGHX6GDX7QRQN4VLFHW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QVSI4YIHGHX6GDX7QRQN4VLFHW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:QVSI4YIHGHX6GDX7QRQN4VLFHW","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":"ddf5e01bf4dd7db717e3a6e43c361478e57f70181d40ced527a21243c70860a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-07-07T07:48:18Z","title_canon_sha256":"652777f70ccae1b099acd87f4532e8ec2d4524aefdc067c207f9ffc639319e97"},"schema_version":"1.0","source":{"id":"0907.1158","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0907.1158","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"arxiv_version","alias_value":"0907.1158v2","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0907.1158","created_at":"2026-05-18T03:56:08Z"},{"alias_kind":"pith_short_12","alias_value":"QVSI4YIHGHX6","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"QVSI4YIHGHX6GDX7","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"QVSI4YIH","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:3fd44770d0ebff0efc049c2fd7f81bcb546cc4f902afe1999fffa002f2c89db4","target":"graph","created_at":"2026-05-18T03:56:08Z","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":"We give a variety of uniqueness results for minimal ellipsoids circumscribing and maximal ellipsoids inscribed into a convex body. Uniqueness follows from a convexity or concavity criterion on the function used to measure the size of the ellipsoid. Simple examples with non-unique minimal or maximal ellipsoids conclude this article.","authors_text":"Hans-Peter Schr\\\"ocker, Matthias J. Weber","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-07-07T07:48:18Z","title":"Davis' Convexity Theorem and Extremal Ellipsoids"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1158","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:ef49c10af81a3f6e0119252fa4a5adbd2871c92b12a1931c47cf1508ed877587","target":"record","created_at":"2026-05-18T03:56:08Z","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":"ddf5e01bf4dd7db717e3a6e43c361478e57f70181d40ced527a21243c70860a9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2009-07-07T07:48:18Z","title_canon_sha256":"652777f70ccae1b099acd87f4532e8ec2d4524aefdc067c207f9ffc639319e97"},"schema_version":"1.0","source":{"id":"0907.1158","kind":"arxiv","version":2}},"canonical_sha256":"85648e610731efe30eff8460de55653d8932d230cb7f6815d41fcd70c15e065c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"85648e610731efe30eff8460de55653d8932d230cb7f6815d41fcd70c15e065c","first_computed_at":"2026-05-18T03:56:08.814928Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:56:08.814928Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"boFXqQGAE4rj31InoTAbOrFJvoF4I+Y4pNYa6O+wca3Cx/8/5rk1hTGfwyhCTL6PrXAqEOOBYkp39m03ni00AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:56:08.815826Z","signed_message":"canonical_sha256_bytes"},"source_id":"0907.1158","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ef49c10af81a3f6e0119252fa4a5adbd2871c92b12a1931c47cf1508ed877587","sha256:3fd44770d0ebff0efc049c2fd7f81bcb546cc4f902afe1999fffa002f2c89db4"],"state_sha256":"8c9d3cd80f0becb2e348af118d4a35083cab1baaebc6b286ddd222bf8e590a98"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w3pInQpK6YhaU1gp9YI91QMGoLN/ZSWFVOVHcXR6IcICeIs+KoH2pKFtga9P10Uf8gvnK+rrgjtCICRYvskrBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T08:14:46.531450Z","bundle_sha256":"96eb288db012852149024f37cb04e92abea052e4a695ef219951d56ee5c1196e"}}