{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:Z6VR7SP5A3WPULPKV3I63OC7DQ","short_pith_number":"pith:Z6VR7SP5","canonical_record":{"source":{"id":"1312.6050","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-20T17:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"43e4e74f53439e244a307cad2a2e17835683e04b12e793fbb785b0ab4e3a047a","abstract_canon_sha256":"d8fd38295426b13c7744009344a4e78dd60b0a743b75ded9c8197d33ee2d0dbf"},"schema_version":"1.0"},"canonical_sha256":"cfab1fc9fd06ecfa2deaaed1edb85f1c1a846d891e2125446ebbf12a0db08c36","source":{"kind":"arxiv","id":"1312.6050","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6050","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6050v1","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6050","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"Z6VR7SP5A3WP","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z6VR7SP5A3WPULPK","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z6VR7SP5","created_at":"2026-05-18T12:28:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:Z6VR7SP5A3WPULPKV3I63OC7DQ","target":"record","payload":{"canonical_record":{"source":{"id":"1312.6050","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-20T17:16:52Z","cross_cats_sorted":[],"title_canon_sha256":"43e4e74f53439e244a307cad2a2e17835683e04b12e793fbb785b0ab4e3a047a","abstract_canon_sha256":"d8fd38295426b13c7744009344a4e78dd60b0a743b75ded9c8197d33ee2d0dbf"},"schema_version":"1.0"},"canonical_sha256":"cfab1fc9fd06ecfa2deaaed1edb85f1c1a846d891e2125446ebbf12a0db08c36","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:35.160661Z","signature_b64":"vlu+Vzmh/x246InXIRu986W8/TZQsxCkKmO66fQiTWoCYgy9jK6QoOyh5t0047enbDzpv/vpHMjM3A5CJ0PQDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfab1fc9fd06ecfa2deaaed1edb85f1c1a846d891e2125446ebbf12a0db08c36","last_reissued_at":"2026-05-17T23:53:35.159866Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:35.159866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.6050","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":"2026-05-17T23:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CX00hdlHZD+MnR9j2Bm8mxSwUKxfI3YjBZ4W1yK4Eml5sDneCy/RF5z6KhVNj3aFiY1m5CCpptcq8WX+sRe/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T11:44:57.180000Z"},"content_sha256":"a89554117c198c6b0cf1efc38cb24fd060f5a4dee6401a5590e839c8ac23ad2b","schema_version":"1.0","event_id":"sha256:a89554117c198c6b0cf1efc38cb24fd060f5a4dee6401a5590e839c8ac23ad2b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:Z6VR7SP5A3WPULPKV3I63OC7DQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Norming Sets and Related Remez-type Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"A. Brudnyi, Y. Yomdin","submitted_at":"2013-12-20T17:16:52Z","abstract_excerpt":"The classical Remez inequality bounds the maximum of the absolute value of a real polynomial $P$ of degree $d$ on $[-1,1]$ through the maximum of its absolute value on any subset $Z\\subset [-1,1]$ of positive Lebesgue measure. Extensions to several variables and to certain sets of Lebesgue measure zero, massive in a much weaker sense, are available.\n  Still, given a subset $Z\\subset [-1,1]^n\\subset {\\mathbb R}^n$ it is not easy to determine whether it is ${\\mathcal P}_d({\\mathbb R}^n)$-norming (here ${\\mathcal P}_d({\\mathbb R}^n)$ is the space of real polynomials of degree at most $d$ on ${\\ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6050","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":"2026-05-17T23:53:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BAP478jeqISSUk3liFFknRlZ8j24nOLWmq43jKXEr3gSTZnExKyhFVScgoJifz7CuL/t0ZexYVh4KEwLGskxAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T11:44:57.180360Z"},"content_sha256":"041aaba7a001d02e26abdbaef1be8ae42c2d5a8778a364aad3df2f3d61c23112","schema_version":"1.0","event_id":"sha256:041aaba7a001d02e26abdbaef1be8ae42c2d5a8778a364aad3df2f3d61c23112"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z6VR7SP5A3WPULPKV3I63OC7DQ/bundle.json","state_url":"https://pith.science/pith/Z6VR7SP5A3WPULPKV3I63OC7DQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z6VR7SP5A3WPULPKV3I63OC7DQ/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":"2026-07-02T11:44:57Z","links":{"resolver":"https://pith.science/pith/Z6VR7SP5A3WPULPKV3I63OC7DQ","bundle":"https://pith.science/pith/Z6VR7SP5A3WPULPKV3I63OC7DQ/bundle.json","state":"https://pith.science/pith/Z6VR7SP5A3WPULPKV3I63OC7DQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z6VR7SP5A3WPULPKV3I63OC7DQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:Z6VR7SP5A3WPULPKV3I63OC7DQ","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":"d8fd38295426b13c7744009344a4e78dd60b0a743b75ded9c8197d33ee2d0dbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-20T17:16:52Z","title_canon_sha256":"43e4e74f53439e244a307cad2a2e17835683e04b12e793fbb785b0ab4e3a047a"},"schema_version":"1.0","source":{"id":"1312.6050","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6050","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6050v1","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6050","created_at":"2026-05-17T23:53:35Z"},{"alias_kind":"pith_short_12","alias_value":"Z6VR7SP5A3WP","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"Z6VR7SP5A3WPULPK","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"Z6VR7SP5","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:041aaba7a001d02e26abdbaef1be8ae42c2d5a8778a364aad3df2f3d61c23112","target":"graph","created_at":"2026-05-17T23:53:35Z","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":"The classical Remez inequality bounds the maximum of the absolute value of a real polynomial $P$ of degree $d$ on $[-1,1]$ through the maximum of its absolute value on any subset $Z\\subset [-1,1]$ of positive Lebesgue measure. Extensions to several variables and to certain sets of Lebesgue measure zero, massive in a much weaker sense, are available.\n  Still, given a subset $Z\\subset [-1,1]^n\\subset {\\mathbb R}^n$ it is not easy to determine whether it is ${\\mathcal P}_d({\\mathbb R}^n)$-norming (here ${\\mathcal P}_d({\\mathbb R}^n)$ is the space of real polynomials of degree at most $d$ on ${\\ma","authors_text":"A. Brudnyi, Y. Yomdin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-20T17:16:52Z","title":"Norming Sets and Related Remez-type Inequalities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6050","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:a89554117c198c6b0cf1efc38cb24fd060f5a4dee6401a5590e839c8ac23ad2b","target":"record","created_at":"2026-05-17T23:53:35Z","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":"d8fd38295426b13c7744009344a4e78dd60b0a743b75ded9c8197d33ee2d0dbf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-12-20T17:16:52Z","title_canon_sha256":"43e4e74f53439e244a307cad2a2e17835683e04b12e793fbb785b0ab4e3a047a"},"schema_version":"1.0","source":{"id":"1312.6050","kind":"arxiv","version":1}},"canonical_sha256":"cfab1fc9fd06ecfa2deaaed1edb85f1c1a846d891e2125446ebbf12a0db08c36","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfab1fc9fd06ecfa2deaaed1edb85f1c1a846d891e2125446ebbf12a0db08c36","first_computed_at":"2026-05-17T23:53:35.159866Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:53:35.159866Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vlu+Vzmh/x246InXIRu986W8/TZQsxCkKmO66fQiTWoCYgy9jK6QoOyh5t0047enbDzpv/vpHMjM3A5CJ0PQDQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:53:35.160661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6050","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a89554117c198c6b0cf1efc38cb24fd060f5a4dee6401a5590e839c8ac23ad2b","sha256:041aaba7a001d02e26abdbaef1be8ae42c2d5a8778a364aad3df2f3d61c23112"],"state_sha256":"1392de04474cba9d0ea8a4bd73aa16fb5f91d7d557eb64770573cc6ef1cf326e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lgDuNVZCYzQnQshdqR3zIDNmuK6CkewLTOI7ULygx2bVlmhiAkAtMK0zzScXkPVdZ0uxb38wRtjTfT9vr2yKBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T11:44:57.182293Z","bundle_sha256":"062b16da67f56700c2b3fe84c30f59aab86ccc5127c09e13fbfc21af0d14e270"}}