{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ZIZ623YTNFEA4OTVSIY6OD3GFY","short_pith_number":"pith:ZIZ623YT","canonical_record":{"source":{"id":"1607.07283","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-25T14:14:49Z","cross_cats_sorted":[],"title_canon_sha256":"c043dc916e3b8a48bc938c1308b7d63c0281fee00ff17e414e88c1f8501c16e3","abstract_canon_sha256":"ded14991202018eed12664e2b6e5848e50e2d56f3b7e11813dac29f673b8e2b5"},"schema_version":"1.0"},"canonical_sha256":"ca33ed6f1369480e3a759231e70f662e02bb12d6b9601a1480ea904e3b10c46a","source":{"kind":"arxiv","id":"1607.07283","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07283","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07283v1","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07283","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZIZ623YTNFEA","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZIZ623YTNFEA4OTV","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZIZ623YT","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ZIZ623YTNFEA4OTVSIY6OD3GFY","target":"record","payload":{"canonical_record":{"source":{"id":"1607.07283","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-25T14:14:49Z","cross_cats_sorted":[],"title_canon_sha256":"c043dc916e3b8a48bc938c1308b7d63c0281fee00ff17e414e88c1f8501c16e3","abstract_canon_sha256":"ded14991202018eed12664e2b6e5848e50e2d56f3b7e11813dac29f673b8e2b5"},"schema_version":"1.0"},"canonical_sha256":"ca33ed6f1369480e3a759231e70f662e02bb12d6b9601a1480ea904e3b10c46a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:34.309446Z","signature_b64":"JpJoppmVIlIBGFhFs4NFYNZSSFwMqL9emMh9800qzEzmsF4CYmWfIq+0aQhbO0W+Ss8PCWg62Xx70xaAW7m/Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca33ed6f1369480e3a759231e70f662e02bb12d6b9601a1480ea904e3b10c46a","last_reissued_at":"2026-05-18T01:10:34.308867Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:34.308867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1607.07283","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":"2026-05-18T01:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nv77ZNzA1rqR4J5OVHBzMIimBGjWGHamwCxXVv0qSsParFRjr68kmVevZf2VLoGyyTY6HuMAsKJz1q4z1LKsBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:30:24.306909Z"},"content_sha256":"b0f017d83ffbc8bffc30121bd10e77693d0cce847b0d1d2419c525893df330e1","schema_version":"1.0","event_id":"sha256:b0f017d83ffbc8bffc30121bd10e77693d0cce847b0d1d2419c525893df330e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ZIZ623YTNFEA4OTVSIY6OD3GFY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A minimum principle for potentials with application to Chebyshev constants","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"A. Reznikov, E. B. Saff, O. V. Vlasiuk","submitted_at":"2016-07-25T14:14:49Z","abstract_excerpt":"For \"Riesz-like\" kernels $K(x,y)=f(|x-y|)$ on $A\\times A$, where $A$ is a compact $d$-regular set $A\\subset \\mathbb{R}^p$, we prove a minimum principle for potentials $U_K^\\mu=\\int K(x,y)d\\mu(x)$, where $\\mu$ is a Borel measure supported on $A$. Setting $P_K(\\mu)=\\inf_{y\\in A}U^\\mu(y)$, the $K$-polarization of $\\mu$, the principle is used to show that if $\\{\\nu_N\\}$ is a sequence of measures on $A$ that converges in the weak-star sense to the measure $\\nu$, then $P_K(\\nu_N)\\to P_K(\\nu)$ as $N\\to \\infty$. The continuous Chebyshev (polarization) problem concerns maximizing $P_K(\\mu)$ over all pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07283","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":"2026-05-18T01:10:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"na1dAiC1Lp0JBnoFlmRBRderXDlDOeQrzOC9JjbZXGAJVy4iuapScwMytImMHUIVApipZk4yuNXQw6l9g3CqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T22:30:24.307502Z"},"content_sha256":"e45609f04c2443e5a43ba2278f8eb4eaa0022255eaf4fd724f16d7af01285bbe","schema_version":"1.0","event_id":"sha256:e45609f04c2443e5a43ba2278f8eb4eaa0022255eaf4fd724f16d7af01285bbe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZIZ623YTNFEA4OTVSIY6OD3GFY/bundle.json","state_url":"https://pith.science/pith/ZIZ623YTNFEA4OTVSIY6OD3GFY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZIZ623YTNFEA4OTVSIY6OD3GFY/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":"2026-05-28T22:30:24Z","links":{"resolver":"https://pith.science/pith/ZIZ623YTNFEA4OTVSIY6OD3GFY","bundle":"https://pith.science/pith/ZIZ623YTNFEA4OTVSIY6OD3GFY/bundle.json","state":"https://pith.science/pith/ZIZ623YTNFEA4OTVSIY6OD3GFY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZIZ623YTNFEA4OTVSIY6OD3GFY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ZIZ623YTNFEA4OTVSIY6OD3GFY","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":"ded14991202018eed12664e2b6e5848e50e2d56f3b7e11813dac29f673b8e2b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-25T14:14:49Z","title_canon_sha256":"c043dc916e3b8a48bc938c1308b7d63c0281fee00ff17e414e88c1f8501c16e3"},"schema_version":"1.0","source":{"id":"1607.07283","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1607.07283","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"arxiv_version","alias_value":"1607.07283v1","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1607.07283","created_at":"2026-05-18T01:10:34Z"},{"alias_kind":"pith_short_12","alias_value":"ZIZ623YTNFEA","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"ZIZ623YTNFEA4OTV","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"ZIZ623YT","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:e45609f04c2443e5a43ba2278f8eb4eaa0022255eaf4fd724f16d7af01285bbe","target":"graph","created_at":"2026-05-18T01:10:34Z","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 \"Riesz-like\" kernels $K(x,y)=f(|x-y|)$ on $A\\times A$, where $A$ is a compact $d$-regular set $A\\subset \\mathbb{R}^p$, we prove a minimum principle for potentials $U_K^\\mu=\\int K(x,y)d\\mu(x)$, where $\\mu$ is a Borel measure supported on $A$. Setting $P_K(\\mu)=\\inf_{y\\in A}U^\\mu(y)$, the $K$-polarization of $\\mu$, the principle is used to show that if $\\{\\nu_N\\}$ is a sequence of measures on $A$ that converges in the weak-star sense to the measure $\\nu$, then $P_K(\\nu_N)\\to P_K(\\nu)$ as $N\\to \\infty$. The continuous Chebyshev (polarization) problem concerns maximizing $P_K(\\mu)$ over all pr","authors_text":"A. Reznikov, E. B. Saff, O. V. Vlasiuk","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-25T14:14:49Z","title":"A minimum principle for potentials with application to Chebyshev constants"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.07283","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:b0f017d83ffbc8bffc30121bd10e77693d0cce847b0d1d2419c525893df330e1","target":"record","created_at":"2026-05-18T01:10:34Z","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":"ded14991202018eed12664e2b6e5848e50e2d56f3b7e11813dac29f673b8e2b5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2016-07-25T14:14:49Z","title_canon_sha256":"c043dc916e3b8a48bc938c1308b7d63c0281fee00ff17e414e88c1f8501c16e3"},"schema_version":"1.0","source":{"id":"1607.07283","kind":"arxiv","version":1}},"canonical_sha256":"ca33ed6f1369480e3a759231e70f662e02bb12d6b9601a1480ea904e3b10c46a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca33ed6f1369480e3a759231e70f662e02bb12d6b9601a1480ea904e3b10c46a","first_computed_at":"2026-05-18T01:10:34.308867Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:34.308867Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JpJoppmVIlIBGFhFs4NFYNZSSFwMqL9emMh9800qzEzmsF4CYmWfIq+0aQhbO0W+Ss8PCWg62Xx70xaAW7m/Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:34.309446Z","signed_message":"canonical_sha256_bytes"},"source_id":"1607.07283","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0f017d83ffbc8bffc30121bd10e77693d0cce847b0d1d2419c525893df330e1","sha256:e45609f04c2443e5a43ba2278f8eb4eaa0022255eaf4fd724f16d7af01285bbe"],"state_sha256":"0dff8b6e454488d231bb48a46dbf0b92d084c30d7a7d9d974782ebc9c48eab1d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dkEbRW3Bwtnm//L6nUDMu30RH4thdWdjAPAw0IbPI2O3y5utqPkFBOl9QeFHDxYWu5ea4i2/bSP8LpdOvMaJBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T22:30:24.310287Z","bundle_sha256":"856415d5af8192ee6adfc05bfbd39daa8175acbcb1e0cbecbe8122ea1bf2ce45"}}