{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:Z67ILZIGKWAQ5MOYOZUV3O5OP3","short_pith_number":"pith:Z67ILZIG","canonical_record":{"source":{"id":"1112.6151","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-28T17:13:01Z","cross_cats_sorted":["math.ST","stat.AP","stat.TH"],"title_canon_sha256":"713c4dbec40464266eb2e41ef74a768bcd5046c75157f6e29d1eb976835e111b","abstract_canon_sha256":"91c5cebe360732cc4383be80851c3f4d684192d8c0c7c51a9cb58f6cc8e86a67"},"schema_version":"1.0"},"canonical_sha256":"cfbe85e50655810eb1d876695dbbae7eea48d8b9e4bf3022a5abd0454fa45809","source":{"kind":"arxiv","id":"1112.6151","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.6151","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"arxiv_version","alias_value":"1112.6151v2","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6151","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"pith_short_12","alias_value":"Z67ILZIGKWAQ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z67ILZIGKWAQ5MOY","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z67ILZIG","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:Z67ILZIGKWAQ5MOYOZUV3O5OP3","target":"record","payload":{"canonical_record":{"source":{"id":"1112.6151","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-28T17:13:01Z","cross_cats_sorted":["math.ST","stat.AP","stat.TH"],"title_canon_sha256":"713c4dbec40464266eb2e41ef74a768bcd5046c75157f6e29d1eb976835e111b","abstract_canon_sha256":"91c5cebe360732cc4383be80851c3f4d684192d8c0c7c51a9cb58f6cc8e86a67"},"schema_version":"1.0"},"canonical_sha256":"cfbe85e50655810eb1d876695dbbae7eea48d8b9e4bf3022a5abd0454fa45809","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:33:14.280097Z","signature_b64":"Ls9eG1m/W/ytmsopo2Pg5Do+XsmHJszIeTSH0K2cpCq4RxNmjAjKPfsEiwd0iZtd0nR+qr0mZViNVjQcw1evAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfbe85e50655810eb1d876695dbbae7eea48d8b9e4bf3022a5abd0454fa45809","last_reissued_at":"2026-05-18T03:33:14.279399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:33:14.279399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.6151","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:33:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lH5IsICW1DAKVweYsPQBNuJ8oY+nBVzme2335865+0uTBOSV8LEF3fXhe0//lgUmJxQ2EDajzUxUYQ3WJdIyAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:19:30.812310Z"},"content_sha256":"30303f13c3e22dc1a7aedbf1e71a56cdcf5840968d09cb821b65b3d219e19eb6","schema_version":"1.0","event_id":"sha256:30303f13c3e22dc1a7aedbf1e71a56cdcf5840968d09cb821b65b3d219e19eb6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:Z67ILZIGKWAQ5MOYOZUV3O5OP3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Rotation and scale space random fields and the Gaussian kinematic formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.AP","stat.TH"],"primary_cat":"math.PR","authors_text":"Eliran Subag, Jonathan E. Taylor, Robert J. Adler","submitted_at":"2011-12-28T17:13:01Z","abstract_excerpt":"We provide a new approach, along with extensions, to results in two important papers of Worsley, Siegmund and coworkers closely tied to the statistical analysis of fMRI (functional magnetic resonance imaging) brain data. These papers studied approximations for the exceedence probabilities of scale and rotation space random fields, the latter playing an important role in the statistical analysis of fMRI data. The techniques used there came either from the Euler characteristic heuristic or via tube formulae, and to a large extent were carefully attuned to the specific examples of the paper. This"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6151","kind":"arxiv","version":2},"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":"2026-05-18T03:33:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pqTPlNk44fac0n12htIFIDprMEwHPVU3rXa3u57tUDfb0shHDJZSqvlm3gsGHVf+FCDJ7Ke9NgwKPbvlrS7CCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T10:19:30.812671Z"},"content_sha256":"800dfa4de7c8250a60afbefedabb27857237476bb765c8867d47c22c40beb23d","schema_version":"1.0","event_id":"sha256:800dfa4de7c8250a60afbefedabb27857237476bb765c8867d47c22c40beb23d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z67ILZIGKWAQ5MOYOZUV3O5OP3/bundle.json","state_url":"https://pith.science/pith/Z67ILZIGKWAQ5MOYOZUV3O5OP3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z67ILZIGKWAQ5MOYOZUV3O5OP3/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":"2026-06-04T10:19:30Z","links":{"resolver":"https://pith.science/pith/Z67ILZIGKWAQ5MOYOZUV3O5OP3","bundle":"https://pith.science/pith/Z67ILZIGKWAQ5MOYOZUV3O5OP3/bundle.json","state":"https://pith.science/pith/Z67ILZIGKWAQ5MOYOZUV3O5OP3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z67ILZIGKWAQ5MOYOZUV3O5OP3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:Z67ILZIGKWAQ5MOYOZUV3O5OP3","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":"91c5cebe360732cc4383be80851c3f4d684192d8c0c7c51a9cb58f6cc8e86a67","cross_cats_sorted":["math.ST","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-28T17:13:01Z","title_canon_sha256":"713c4dbec40464266eb2e41ef74a768bcd5046c75157f6e29d1eb976835e111b"},"schema_version":"1.0","source":{"id":"1112.6151","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.6151","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"arxiv_version","alias_value":"1112.6151v2","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.6151","created_at":"2026-05-18T03:33:14Z"},{"alias_kind":"pith_short_12","alias_value":"Z67ILZIGKWAQ","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"Z67ILZIGKWAQ5MOY","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"Z67ILZIG","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:800dfa4de7c8250a60afbefedabb27857237476bb765c8867d47c22c40beb23d","target":"graph","created_at":"2026-05-18T03:33:14Z","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 provide a new approach, along with extensions, to results in two important papers of Worsley, Siegmund and coworkers closely tied to the statistical analysis of fMRI (functional magnetic resonance imaging) brain data. These papers studied approximations for the exceedence probabilities of scale and rotation space random fields, the latter playing an important role in the statistical analysis of fMRI data. The techniques used there came either from the Euler characteristic heuristic or via tube formulae, and to a large extent were carefully attuned to the specific examples of the paper. This","authors_text":"Eliran Subag, Jonathan E. Taylor, Robert J. Adler","cross_cats":["math.ST","stat.AP","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-28T17:13:01Z","title":"Rotation and scale space random fields and the Gaussian kinematic formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.6151","kind":"arxiv","version":2},"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":"sha256:30303f13c3e22dc1a7aedbf1e71a56cdcf5840968d09cb821b65b3d219e19eb6","target":"record","created_at":"2026-05-18T03:33:14Z","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":"91c5cebe360732cc4383be80851c3f4d684192d8c0c7c51a9cb58f6cc8e86a67","cross_cats_sorted":["math.ST","stat.AP","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-28T17:13:01Z","title_canon_sha256":"713c4dbec40464266eb2e41ef74a768bcd5046c75157f6e29d1eb976835e111b"},"schema_version":"1.0","source":{"id":"1112.6151","kind":"arxiv","version":2}},"canonical_sha256":"cfbe85e50655810eb1d876695dbbae7eea48d8b9e4bf3022a5abd0454fa45809","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfbe85e50655810eb1d876695dbbae7eea48d8b9e4bf3022a5abd0454fa45809","first_computed_at":"2026-05-18T03:33:14.279399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:33:14.279399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ls9eG1m/W/ytmsopo2Pg5Do+XsmHJszIeTSH0K2cpCq4RxNmjAjKPfsEiwd0iZtd0nR+qr0mZViNVjQcw1evAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:33:14.280097Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.6151","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30303f13c3e22dc1a7aedbf1e71a56cdcf5840968d09cb821b65b3d219e19eb6","sha256:800dfa4de7c8250a60afbefedabb27857237476bb765c8867d47c22c40beb23d"],"state_sha256":"7fc29745af81e6b30bc39f55800b778a31a9351fee5426f0a340e5a934e98595"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HwgbxTibB4ucULK2o9tY4ssKqGYiju8JyfBgRVnaj9QSWsvi9ggv8jmjwRgevGalBUod+Quyx2HK1h7vruG0BA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T10:19:30.814640Z","bundle_sha256":"e0ab1fb8cf16b202a073d0695db96fa6d413cb8f44316ccd2e6cb460ce54ead3"}}