{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:IBYFTLVKSUIEGEP5G2COLFNZE2","short_pith_number":"pith:IBYFTLVK","canonical_record":{"source":{"id":"1109.2192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-10T04:43:59Z","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"title_canon_sha256":"188e39b399a076459e5c4075b3820b7a4aaf86125d209f9116abb820f5006025","abstract_canon_sha256":"c47502f45c5828d6578533be283912cf0b5225ea788940bc9883304128ab32fb"},"schema_version":"1.0"},"canonical_sha256":"407059aeaa95104311fd3684e595b9269a830548d4a3062647a3efc096a2c929","source":{"kind":"arxiv","id":"1109.2192","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2192","created_at":"2026-05-18T03:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2192v1","created_at":"2026-05-18T03:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2192","created_at":"2026-05-18T03:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"IBYFTLVKSUIE","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IBYFTLVKSUIEGEP5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IBYFTLVK","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:IBYFTLVKSUIEGEP5G2COLFNZE2","target":"record","payload":{"canonical_record":{"source":{"id":"1109.2192","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-10T04:43:59Z","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"title_canon_sha256":"188e39b399a076459e5c4075b3820b7a4aaf86125d209f9116abb820f5006025","abstract_canon_sha256":"c47502f45c5828d6578533be283912cf0b5225ea788940bc9883304128ab32fb"},"schema_version":"1.0"},"canonical_sha256":"407059aeaa95104311fd3684e595b9269a830548d4a3062647a3efc096a2c929","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:56.051093Z","signature_b64":"wpmJRXWTBOlKvtf4tzQN3G9/kZ8OyKo2vXLFXEoSvwVZLLByYgiywxNR9nDeCpIO9oVxs0ZmWZk4GPTzB5MoDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"407059aeaa95104311fd3684e595b9269a830548d4a3062647a3efc096a2c929","last_reissued_at":"2026-05-18T03:10:56.050333Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:56.050333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.2192","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":"2026-05-18T03:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kO+KJZZCfUPAipcCqJBXkEjMpFMU0RI2s/v1aXlz+dnwt4egvoJX5+huZNbMOb9dUAyBc7oEnqGT/v88UHP3CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:26:42.377896Z"},"content_sha256":"59163d54029b2925df31b6ad42a9f2bcb961172e045a81f9b6226fd1eed15057","schema_version":"1.0","event_id":"sha256:59163d54029b2925df31b6ad42a9f2bcb961172e045a81f9b6226fd1eed15057"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:IBYFTLVKSUIEGEP5G2COLFNZE2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On an isoperimetric problem with a competing non-local term. I. The planar case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.PS"],"primary_cat":"math.AP","authors_text":"Cyrill B. Muratov, Hans Knuepfer","submitted_at":"2011-09-10T04:43:59Z","abstract_excerpt":"This paper is concerned with a study of the classical isoperimetric problem modified by an addition of a non-local repulsive term. We characterize existence, non-existence and radial symmetry of the minimizers as a function of mass in the situation where the non-local term is generated by a kernel given by an inverse power of the distance. We prove that minimizers of this problem exist for sufficiently small masses and are given by disks with prescribed mass below a certain threshold, when the interfacial term in the energy is dominant. At the same time, we prove that minimizers fail to exist "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2192","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":"2026-05-18T03:10:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"26jVmRO0jtWGVgDaJbwijKz3wcLL3X3+cqGElIUZ4v3GuSe6AB5BRcgMnAOULx4l4OGR8esNUUiMSNGuiLStAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T02:26:42.378240Z"},"content_sha256":"5a8cde8362fc5b1e8b2de066c19bd69e2eed750f9be26d1cf8f00268aa42b854","schema_version":"1.0","event_id":"sha256:5a8cde8362fc5b1e8b2de066c19bd69e2eed750f9be26d1cf8f00268aa42b854"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IBYFTLVKSUIEGEP5G2COLFNZE2/bundle.json","state_url":"https://pith.science/pith/IBYFTLVKSUIEGEP5G2COLFNZE2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IBYFTLVKSUIEGEP5G2COLFNZE2/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":"2026-06-02T02:26:42Z","links":{"resolver":"https://pith.science/pith/IBYFTLVKSUIEGEP5G2COLFNZE2","bundle":"https://pith.science/pith/IBYFTLVKSUIEGEP5G2COLFNZE2/bundle.json","state":"https://pith.science/pith/IBYFTLVKSUIEGEP5G2COLFNZE2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IBYFTLVKSUIEGEP5G2COLFNZE2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:IBYFTLVKSUIEGEP5G2COLFNZE2","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":"c47502f45c5828d6578533be283912cf0b5225ea788940bc9883304128ab32fb","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-10T04:43:59Z","title_canon_sha256":"188e39b399a076459e5c4075b3820b7a4aaf86125d209f9116abb820f5006025"},"schema_version":"1.0","source":{"id":"1109.2192","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.2192","created_at":"2026-05-18T03:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"1109.2192v1","created_at":"2026-05-18T03:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2192","created_at":"2026-05-18T03:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"IBYFTLVKSUIE","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"IBYFTLVKSUIEGEP5","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"IBYFTLVK","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:5a8cde8362fc5b1e8b2de066c19bd69e2eed750f9be26d1cf8f00268aa42b854","target":"graph","created_at":"2026-05-18T03:10:56Z","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":"This paper is concerned with a study of the classical isoperimetric problem modified by an addition of a non-local repulsive term. We characterize existence, non-existence and radial symmetry of the minimizers as a function of mass in the situation where the non-local term is generated by a kernel given by an inverse power of the distance. We prove that minimizers of this problem exist for sufficiently small masses and are given by disks with prescribed mass below a certain threshold, when the interfacial term in the energy is dominant. At the same time, we prove that minimizers fail to exist ","authors_text":"Cyrill B. Muratov, Hans Knuepfer","cross_cats":["math-ph","math.MP","nlin.PS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-10T04:43:59Z","title":"On an isoperimetric problem with a competing non-local term. I. The planar case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2192","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":"sha256:59163d54029b2925df31b6ad42a9f2bcb961172e045a81f9b6226fd1eed15057","target":"record","created_at":"2026-05-18T03:10:56Z","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":"c47502f45c5828d6578533be283912cf0b5225ea788940bc9883304128ab32fb","cross_cats_sorted":["math-ph","math.MP","nlin.PS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2011-09-10T04:43:59Z","title_canon_sha256":"188e39b399a076459e5c4075b3820b7a4aaf86125d209f9116abb820f5006025"},"schema_version":"1.0","source":{"id":"1109.2192","kind":"arxiv","version":1}},"canonical_sha256":"407059aeaa95104311fd3684e595b9269a830548d4a3062647a3efc096a2c929","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"407059aeaa95104311fd3684e595b9269a830548d4a3062647a3efc096a2c929","first_computed_at":"2026-05-18T03:10:56.050333Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:56.050333Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wpmJRXWTBOlKvtf4tzQN3G9/kZ8OyKo2vXLFXEoSvwVZLLByYgiywxNR9nDeCpIO9oVxs0ZmWZk4GPTzB5MoDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:56.051093Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.2192","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:59163d54029b2925df31b6ad42a9f2bcb961172e045a81f9b6226fd1eed15057","sha256:5a8cde8362fc5b1e8b2de066c19bd69e2eed750f9be26d1cf8f00268aa42b854"],"state_sha256":"a0aa1b87846e8bf0f5439c8be2058ff9f2c7641d8c8455be45f70765d85b529f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0u4kQXPD5NVnBMxI5Y5S7z2SRa53j+Zu+9UEa3C4bxT+rACaXkXQClCqsktsM6RTqCxJ+C1CR+8b1POHgqVzBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T02:26:42.380264Z","bundle_sha256":"66354de8d341d511d017948f0472c238e9b793f5048556f2d9b6162cb2c05404"}}