{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:HR4XMK6BR6Q75BUDU35ORTOGAY","short_pith_number":"pith:HR4XMK6B","canonical_record":{"source":{"id":"2606.23509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-06-22T15:57:01Z","cross_cats_sorted":["econ.EM","stat.ML"],"title_canon_sha256":"a6b95711499390ad89980e07f08183b6331b580dcb77afb755e996631cdf04c2","abstract_canon_sha256":"ab7506385ada7d277c9928145d6c180d9dd52527e29a5bcb1648f8f7a38e7c9b"},"schema_version":"1.0"},"canonical_sha256":"3c79762bc18fa1fe8683a6fae8cdc60638826a18f90bce803e8c4e710a5ba876","source":{"kind":"arxiv","id":"2606.23509","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23509","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23509v1","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23509","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"HR4XMK6BR6Q7","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"pith_short_16","alias_value":"HR4XMK6BR6Q75BUD","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"pith_short_8","alias_value":"HR4XMK6B","created_at":"2026-06-23T03:14:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:HR4XMK6BR6Q75BUDU35ORTOGAY","target":"record","payload":{"canonical_record":{"source":{"id":"2606.23509","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-06-22T15:57:01Z","cross_cats_sorted":["econ.EM","stat.ML"],"title_canon_sha256":"a6b95711499390ad89980e07f08183b6331b580dcb77afb755e996631cdf04c2","abstract_canon_sha256":"ab7506385ada7d277c9928145d6c180d9dd52527e29a5bcb1648f8f7a38e7c9b"},"schema_version":"1.0"},"canonical_sha256":"3c79762bc18fa1fe8683a6fae8cdc60638826a18f90bce803e8c4e710a5ba876","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T03:14:21.875854Z","signature_b64":"EHnHQGdrCuSafLc9IozvqfIAFMuna3J8lWLy8vVY5r6LqtZvUlqOCwCvL6Wtk+EL405Lq26FA+E9/wtlhGfZBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3c79762bc18fa1fe8683a6fae8cdc60638826a18f90bce803e8c4e710a5ba876","last_reissued_at":"2026-06-23T03:14:21.875455Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T03:14:21.875455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.23509","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":"2026-06-23T03:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5l9fXkSJ6329YSgLaJoLyrnfROtnMepSRnrYu7yeADRvVxIwhOrIhRUYn0Wy/ZIlc8lnGcsaD669vscwfYPcDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:51:04.022300Z"},"content_sha256":"9411573bfdc7eba5777688c4b3c9472b66b0206a05e8c5d0427d932fa831a93e","schema_version":"1.0","event_id":"sha256:9411573bfdc7eba5777688c4b3c9472b66b0206a05e8c5d0427d932fa831a93e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:HR4XMK6BR6Q75BUDU35ORTOGAY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variance or Standard Deviation? Shell Geometry and Global-Scale Priors in High-Dimensional Shrinkage","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["econ.EM","stat.ML"],"primary_cat":"stat.ME","authors_text":"Wayne Yuan Gao, Zhiheng You","submitted_at":"2026-06-22T15:57:01Z","abstract_excerpt":"We study how the choice of default prior for a common Gaussian scale affects high-dimensional shrinkage risk, highlighting the role played by high-dimensional geometry. Formally, we consider a high-dimensional setting in which the near-zero behavior of the common scale prior has first-order consequences for shrinkage risk, and show that priors that are flat on the variance and those flat on the standard deviation allocate markedly different mass near the zero-scale boundary, leading to distinct shrinkage behavior and informing principled default prior selection. Specifically, under a radial-po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23509","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.23509/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-06-23T03:14:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rxPfMHKFxY0shxPXxekb43vXSfCwImLXcIFySnFFTU0r2AyrXyBYGLSK2z7TfZueez53vkeY4hwvGC4lo8++AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T00:51:04.022679Z"},"content_sha256":"08ca35de8630445dc269e8ee26675250535a9e33ca9222beda5b48129b1a0ad8","schema_version":"1.0","event_id":"sha256:08ca35de8630445dc269e8ee26675250535a9e33ca9222beda5b48129b1a0ad8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY/bundle.json","state_url":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HR4XMK6BR6Q75BUDU35ORTOGAY/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":"2026-06-27T00:51:04Z","links":{"resolver":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY","bundle":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY/bundle.json","state":"https://pith.science/pith/HR4XMK6BR6Q75BUDU35ORTOGAY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HR4XMK6BR6Q75BUDU35ORTOGAY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:HR4XMK6BR6Q75BUDU35ORTOGAY","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":"ab7506385ada7d277c9928145d6c180d9dd52527e29a5bcb1648f8f7a38e7c9b","cross_cats_sorted":["econ.EM","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-06-22T15:57:01Z","title_canon_sha256":"a6b95711499390ad89980e07f08183b6331b580dcb77afb755e996631cdf04c2"},"schema_version":"1.0","source":{"id":"2606.23509","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.23509","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"arxiv_version","alias_value":"2606.23509v1","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.23509","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"pith_short_12","alias_value":"HR4XMK6BR6Q7","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"pith_short_16","alias_value":"HR4XMK6BR6Q75BUD","created_at":"2026-06-23T03:14:21Z"},{"alias_kind":"pith_short_8","alias_value":"HR4XMK6B","created_at":"2026-06-23T03:14:21Z"}],"graph_snapshots":[{"event_id":"sha256:08ca35de8630445dc269e8ee26675250535a9e33ca9222beda5b48129b1a0ad8","target":"graph","created_at":"2026-06-23T03:14:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.23509/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study how the choice of default prior for a common Gaussian scale affects high-dimensional shrinkage risk, highlighting the role played by high-dimensional geometry. Formally, we consider a high-dimensional setting in which the near-zero behavior of the common scale prior has first-order consequences for shrinkage risk, and show that priors that are flat on the variance and those flat on the standard deviation allocate markedly different mass near the zero-scale boundary, leading to distinct shrinkage behavior and informing principled default prior selection. Specifically, under a radial-po","authors_text":"Wayne Yuan Gao, Zhiheng You","cross_cats":["econ.EM","stat.ML"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-06-22T15:57:01Z","title":"Variance or Standard Deviation? Shell Geometry and Global-Scale Priors in High-Dimensional Shrinkage"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.23509","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":"sha256:9411573bfdc7eba5777688c4b3c9472b66b0206a05e8c5d0427d932fa831a93e","target":"record","created_at":"2026-06-23T03:14:21Z","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":"ab7506385ada7d277c9928145d6c180d9dd52527e29a5bcb1648f8f7a38e7c9b","cross_cats_sorted":["econ.EM","stat.ML"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"stat.ME","submitted_at":"2026-06-22T15:57:01Z","title_canon_sha256":"a6b95711499390ad89980e07f08183b6331b580dcb77afb755e996631cdf04c2"},"schema_version":"1.0","source":{"id":"2606.23509","kind":"arxiv","version":1}},"canonical_sha256":"3c79762bc18fa1fe8683a6fae8cdc60638826a18f90bce803e8c4e710a5ba876","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c79762bc18fa1fe8683a6fae8cdc60638826a18f90bce803e8c4e710a5ba876","first_computed_at":"2026-06-23T03:14:21.875455Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:14:21.875455Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EHnHQGdrCuSafLc9IozvqfIAFMuna3J8lWLy8vVY5r6LqtZvUlqOCwCvL6Wtk+EL405Lq26FA+E9/wtlhGfZBw==","signature_status":"signed_v1","signed_at":"2026-06-23T03:14:21.875854Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.23509","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9411573bfdc7eba5777688c4b3c9472b66b0206a05e8c5d0427d932fa831a93e","sha256:08ca35de8630445dc269e8ee26675250535a9e33ca9222beda5b48129b1a0ad8"],"state_sha256":"0f894fd950fa3e74c731ac5ae51dd526098cc4f89f11d3792aa101c40e0df0d4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NVa7kcq+trbTwm3B+vRbDWQwAdqW1EpDQxHRaiWY3SkQK8mXWwVgesX3u+GTPn4W7BPnGB2GTkUwd+qCcBSCBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T00:51:04.024527Z","bundle_sha256":"31d4392dd82608c2a6e0eef11cc952343903b5d61e52a21ef5ab5d302f28e81b"}}