{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:BKUGRBC5EYZBKZ7GX33BAMAPWD","short_pith_number":"pith:BKUGRBC5","canonical_record":{"source":{"id":"1303.4096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-17T20:03:21Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"4df6ebdcdef19d72b2e838ae3ce9645841e58bf59d9ddb36d49b875c977860d2","abstract_canon_sha256":"e8d082c068cdbc99907cb64191ffa9dd97d292d01b5d5893ea264c1562c27884"},"schema_version":"1.0"},"canonical_sha256":"0aa868845d26321567e6bef610300fb0c7b21070252fc3d0ddc3fc93ef863ba5","source":{"kind":"arxiv","id":"1303.4096","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4096","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4096v1","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4096","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"BKUGRBC5EYZB","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BKUGRBC5EYZBKZ7G","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BKUGRBC5","created_at":"2026-05-18T12:27:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:BKUGRBC5EYZBKZ7GX33BAMAPWD","target":"record","payload":{"canonical_record":{"source":{"id":"1303.4096","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-17T20:03:21Z","cross_cats_sorted":["math.CV"],"title_canon_sha256":"4df6ebdcdef19d72b2e838ae3ce9645841e58bf59d9ddb36d49b875c977860d2","abstract_canon_sha256":"e8d082c068cdbc99907cb64191ffa9dd97d292d01b5d5893ea264c1562c27884"},"schema_version":"1.0"},"canonical_sha256":"0aa868845d26321567e6bef610300fb0c7b21070252fc3d0ddc3fc93ef863ba5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:50:43.174496Z","signature_b64":"UMrGGDtSyeTOBQ06Z1T7aycQqAl0oQnMT2OPbyq385m5Ne8mBIeHWCi2YeTtxoTyrKmAdJ0Zbmmfmk3CAiXEBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0aa868845d26321567e6bef610300fb0c7b21070252fc3d0ddc3fc93ef863ba5","last_reissued_at":"2026-05-18T02:50:43.173723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:50:43.173723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1303.4096","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":"2026-05-18T02:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FAtY9FDGrMzuMtS0dtdyaMaACiA9/TiZTJ6fS0fFm3VS55nC/oJdE8wOqq9rDiuFS5edJH0sIUR2WtfL29wzAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:31:28.553340Z"},"content_sha256":"4595670ab53701df498cc20d8cac9307a085f5d254503771a6dccf847e5506f3","schema_version":"1.0","event_id":"sha256:4595670ab53701df498cc20d8cac9307a085f5d254503771a6dccf847e5506f3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:BKUGRBC5EYZBKZ7GX33BAMAPWD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Median and mean of the Supremum of $L^2$ normalized random holmorphic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.PR","authors_text":"Renjie Feng, Steve Zelditch","submitted_at":"2013-03-17T20:03:21Z","abstract_excerpt":"We prove that the expected value and median of the supremum of $L^2$ normalized random holomorphic fields of degree $n$ on $m$-dimensional K\\\"ahler manifolds are asymptotically of order $\\sqrt{m\\log n}$. This improves the prior result of Shiffman-Zelditch (arXiv:math/0303335) that the upper bound of the media is of order $\\sqrt{\\log n}$\n  The estimates are based on the entropy methods of Dudley and Sudakov combined with a precise analysis of the relevant pseudo-metric and its covering numbers, which can be precisely evaluated using off-diagonal asymptotics of Bergman kernels. Recent work of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4096","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":"2026-05-18T02:50:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6csQZOJ3pryMjnN4llQxtfBMZmbjzIjuR09rEKSDN8jKG10+8T0A4BBJZ0/Cv8+erdSLRlXVX3kY0g99WPy+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T02:31:28.553699Z"},"content_sha256":"fd524d2919c29b410eb0a4ef868cef436dc6c4bfeb6a009ee81c5a3c4f2fbb57","schema_version":"1.0","event_id":"sha256:fd524d2919c29b410eb0a4ef868cef436dc6c4bfeb6a009ee81c5a3c4f2fbb57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD/bundle.json","state_url":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD/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":"2026-06-03T02:31:28Z","links":{"resolver":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD","bundle":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD/bundle.json","state":"https://pith.science/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BKUGRBC5EYZBKZ7GX33BAMAPWD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:BKUGRBC5EYZBKZ7GX33BAMAPWD","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":"e8d082c068cdbc99907cb64191ffa9dd97d292d01b5d5893ea264c1562c27884","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-17T20:03:21Z","title_canon_sha256":"4df6ebdcdef19d72b2e838ae3ce9645841e58bf59d9ddb36d49b875c977860d2"},"schema_version":"1.0","source":{"id":"1303.4096","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1303.4096","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"arxiv_version","alias_value":"1303.4096v1","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.4096","created_at":"2026-05-18T02:50:43Z"},{"alias_kind":"pith_short_12","alias_value":"BKUGRBC5EYZB","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"BKUGRBC5EYZBKZ7G","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"BKUGRBC5","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:fd524d2919c29b410eb0a4ef868cef436dc6c4bfeb6a009ee81c5a3c4f2fbb57","target":"graph","created_at":"2026-05-18T02:50:43Z","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 prove that the expected value and median of the supremum of $L^2$ normalized random holomorphic fields of degree $n$ on $m$-dimensional K\\\"ahler manifolds are asymptotically of order $\\sqrt{m\\log n}$. This improves the prior result of Shiffman-Zelditch (arXiv:math/0303335) that the upper bound of the media is of order $\\sqrt{\\log n}$\n  The estimates are based on the entropy methods of Dudley and Sudakov combined with a precise analysis of the relevant pseudo-metric and its covering numbers, which can be precisely evaluated using off-diagonal asymptotics of Bergman kernels. Recent work of th","authors_text":"Renjie Feng, Steve Zelditch","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-17T20:03:21Z","title":"Median and mean of the Supremum of $L^2$ normalized random holmorphic fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.4096","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":"sha256:4595670ab53701df498cc20d8cac9307a085f5d254503771a6dccf847e5506f3","target":"record","created_at":"2026-05-18T02:50:43Z","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":"e8d082c068cdbc99907cb64191ffa9dd97d292d01b5d5893ea264c1562c27884","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-03-17T20:03:21Z","title_canon_sha256":"4df6ebdcdef19d72b2e838ae3ce9645841e58bf59d9ddb36d49b875c977860d2"},"schema_version":"1.0","source":{"id":"1303.4096","kind":"arxiv","version":1}},"canonical_sha256":"0aa868845d26321567e6bef610300fb0c7b21070252fc3d0ddc3fc93ef863ba5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0aa868845d26321567e6bef610300fb0c7b21070252fc3d0ddc3fc93ef863ba5","first_computed_at":"2026-05-18T02:50:43.173723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:50:43.173723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UMrGGDtSyeTOBQ06Z1T7aycQqAl0oQnMT2OPbyq385m5Ne8mBIeHWCi2YeTtxoTyrKmAdJ0Zbmmfmk3CAiXEBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:50:43.174496Z","signed_message":"canonical_sha256_bytes"},"source_id":"1303.4096","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4595670ab53701df498cc20d8cac9307a085f5d254503771a6dccf847e5506f3","sha256:fd524d2919c29b410eb0a4ef868cef436dc6c4bfeb6a009ee81c5a3c4f2fbb57"],"state_sha256":"c10f1906d8c3590e157660517913567ccbef555b3d2f4161fa067a303f335783"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hDIGZgtLZiLByFIWF5vRe20ZmPdfrKrFTJbQprq+sTbPqh8eB7yb6I5pafz0Q1n6S5qQJDF7CxDwmc2epAeuAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T02:31:28.555602Z","bundle_sha256":"94854af7244d148b4827b45573523c0ab6dc02eb5ba6683ca2678c27f8ca6790"}}