{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:VACVS2YLBB5HCJNRINYGIHFONS","short_pith_number":"pith:VACVS2YL","canonical_record":{"source":{"id":"1301.1095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-01-07T02:08:47Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"0c29064ce858ef0547f83973d5f548e7dbd0ce22375c40a4348356b5170f4db5","abstract_canon_sha256":"aa7fe58cec70ed34ff33125f2f0424fb6f72d049c9d4d7145bfb7dba23ab5e36"},"schema_version":"1.0"},"canonical_sha256":"a805596b0b087a7125b14370641cae6c9662295f3cd102db430bff1e21ab5f6c","source":{"kind":"arxiv","id":"1301.1095","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1095","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1095v1","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1095","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"VACVS2YLBB5H","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VACVS2YLBB5HCJNR","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VACVS2YL","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:VACVS2YLBB5HCJNRINYGIHFONS","target":"record","payload":{"canonical_record":{"source":{"id":"1301.1095","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-01-07T02:08:47Z","cross_cats_sorted":["math.CA","math.PR"],"title_canon_sha256":"0c29064ce858ef0547f83973d5f548e7dbd0ce22375c40a4348356b5170f4db5","abstract_canon_sha256":"aa7fe58cec70ed34ff33125f2f0424fb6f72d049c9d4d7145bfb7dba23ab5e36"},"schema_version":"1.0"},"canonical_sha256":"a805596b0b087a7125b14370641cae6c9662295f3cd102db430bff1e21ab5f6c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:06.846406Z","signature_b64":"V2tCJJlKw5d+3nXzGSZBeyCwiclvQ8sglU84hN1O+c7skb4WmqMNvtCto3CpWNIDlwNanMB3tgosS3K62dQJBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a805596b0b087a7125b14370641cae6c9662295f3cd102db430bff1e21ab5f6c","last_reissued_at":"2026-05-18T03:37:06.845687Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:06.845687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1301.1095","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":"2026-05-18T03:37:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"d8KOHIewdouxfQm9Qkg5WhXADNWhniR1+j3ggYi0du8jJIOakGNhAmHl6xm3kk9cQy8Hb7i0U90sBgdN+sWeAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:34:59.284351Z"},"content_sha256":"9eef569adb4d92ae11d59149e3824c48338f102f937a38f49a1bb2588a444077","schema_version":"1.0","event_id":"sha256:9eef569adb4d92ae11d59149e3824c48338f102f937a38f49a1bb2588a444077"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:VACVS2YLBB5HCJNRINYGIHFONS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vector Energy and Large Deviation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.CV","authors_text":"F. Wielonsky, N. Levenberg, T. Bloom","submitted_at":"2013-01-07T02:08:47Z","abstract_excerpt":"For d nonpolar compact sets K_1,...,K_d in the complex plane, d admissible weights Q_1,...,Q_d, and a positive semidefinite d x d interaction matrix C with no zero column, we define natural discretizations of the associated weighted vector energy of a d-tuple of positive measures \\mu=(\\mu_1,...,\\mu_d) where \\mu_j is supported in K_j and has mass r_j. We have an L^{\\infty}-type discretization W(\\mu) and an L^2-type discretization J(\\mu) defined using a fixed measure \\nu=(\\nu_1,...,\\nu_d). This leads to a large deviation principle for a canonical sequence of probability measures on this space of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1095","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":"2026-05-18T03:37:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aXVwJ2rVYSV6iw2zBw2PVFzj/A+pdqoqErqpDIGMrlfMiwtOstOklhMHnKAANkD8RnsPxKOuh+wj3SZerVfhAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T16:34:59.285129Z"},"content_sha256":"caca5ee67c47d1bf55db5af15c574079a822d5017eed983526a1d06d4446ae6b","schema_version":"1.0","event_id":"sha256:caca5ee67c47d1bf55db5af15c574079a822d5017eed983526a1d06d4446ae6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VACVS2YLBB5HCJNRINYGIHFONS/bundle.json","state_url":"https://pith.science/pith/VACVS2YLBB5HCJNRINYGIHFONS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VACVS2YLBB5HCJNRINYGIHFONS/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":"2026-05-31T16:34:59Z","links":{"resolver":"https://pith.science/pith/VACVS2YLBB5HCJNRINYGIHFONS","bundle":"https://pith.science/pith/VACVS2YLBB5HCJNRINYGIHFONS/bundle.json","state":"https://pith.science/pith/VACVS2YLBB5HCJNRINYGIHFONS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VACVS2YLBB5HCJNRINYGIHFONS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VACVS2YLBB5HCJNRINYGIHFONS","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":"aa7fe58cec70ed34ff33125f2f0424fb6f72d049c9d4d7145bfb7dba23ab5e36","cross_cats_sorted":["math.CA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-01-07T02:08:47Z","title_canon_sha256":"0c29064ce858ef0547f83973d5f548e7dbd0ce22375c40a4348356b5170f4db5"},"schema_version":"1.0","source":{"id":"1301.1095","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.1095","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"arxiv_version","alias_value":"1301.1095v1","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.1095","created_at":"2026-05-18T03:37:06Z"},{"alias_kind":"pith_short_12","alias_value":"VACVS2YLBB5H","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VACVS2YLBB5HCJNR","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VACVS2YL","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:caca5ee67c47d1bf55db5af15c574079a822d5017eed983526a1d06d4446ae6b","target":"graph","created_at":"2026-05-18T03:37:06Z","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":"For d nonpolar compact sets K_1,...,K_d in the complex plane, d admissible weights Q_1,...,Q_d, and a positive semidefinite d x d interaction matrix C with no zero column, we define natural discretizations of the associated weighted vector energy of a d-tuple of positive measures \\mu=(\\mu_1,...,\\mu_d) where \\mu_j is supported in K_j and has mass r_j. We have an L^{\\infty}-type discretization W(\\mu) and an L^2-type discretization J(\\mu) defined using a fixed measure \\nu=(\\nu_1,...,\\nu_d). This leads to a large deviation principle for a canonical sequence of probability measures on this space of","authors_text":"F. Wielonsky, N. Levenberg, T. Bloom","cross_cats":["math.CA","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-01-07T02:08:47Z","title":"Vector Energy and Large Deviation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1095","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":"sha256:9eef569adb4d92ae11d59149e3824c48338f102f937a38f49a1bb2588a444077","target":"record","created_at":"2026-05-18T03:37:06Z","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":"aa7fe58cec70ed34ff33125f2f0424fb6f72d049c9d4d7145bfb7dba23ab5e36","cross_cats_sorted":["math.CA","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2013-01-07T02:08:47Z","title_canon_sha256":"0c29064ce858ef0547f83973d5f548e7dbd0ce22375c40a4348356b5170f4db5"},"schema_version":"1.0","source":{"id":"1301.1095","kind":"arxiv","version":1}},"canonical_sha256":"a805596b0b087a7125b14370641cae6c9662295f3cd102db430bff1e21ab5f6c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a805596b0b087a7125b14370641cae6c9662295f3cd102db430bff1e21ab5f6c","first_computed_at":"2026-05-18T03:37:06.845687Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:37:06.845687Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V2tCJJlKw5d+3nXzGSZBeyCwiclvQ8sglU84hN1O+c7skb4WmqMNvtCto3CpWNIDlwNanMB3tgosS3K62dQJBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:37:06.846406Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.1095","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9eef569adb4d92ae11d59149e3824c48338f102f937a38f49a1bb2588a444077","sha256:caca5ee67c47d1bf55db5af15c574079a822d5017eed983526a1d06d4446ae6b"],"state_sha256":"6f640b29f9f51bdd51fcaef56577867e6f4bc433420742e82e9c74f6f3f14a40"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iYVfZ25PCbqf8UtHP3c4Ti4ibbWjH1skfDaFY4bZ6FZbBJqcd7jWbA5b0rehgzX5k0dLEE40AqaniKPaM+cmDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T16:34:59.291391Z","bundle_sha256":"afbcdd09510ba3d5cc85f4b3d6bccf9c2847fc5d87499f2fcd6a8c9e29b5e788"}}