{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:47HHYY7NFOLYTAQZSASX5D7BBC","short_pith_number":"pith:47HHYY7N","canonical_record":{"source":{"id":"1810.02078","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-04T07:27:04Z","cross_cats_sorted":["astro-ph.CO","math.MP"],"title_canon_sha256":"911fbb2d42028b6666a31b241377befc3fa15b20b0de4e3d556e507c03f6b319","abstract_canon_sha256":"a69c9b97fe852e2672f76822bff74b1d0738b4603b91e50df4726ce977d1fecc"},"schema_version":"1.0"},"canonical_sha256":"e7ce7c63ed2b9789821990257e8fe108b68da3c24201665136c074adf3d4a1d9","source":{"kind":"arxiv","id":"1810.02078","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02078","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02078v1","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02078","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"47HHYY7NFOLY","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"47HHYY7NFOLYTAQZ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"47HHYY7N","created_at":"2026-05-18T12:32:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:47HHYY7NFOLYTAQZSASX5D7BBC","target":"record","payload":{"canonical_record":{"source":{"id":"1810.02078","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-04T07:27:04Z","cross_cats_sorted":["astro-ph.CO","math.MP"],"title_canon_sha256":"911fbb2d42028b6666a31b241377befc3fa15b20b0de4e3d556e507c03f6b319","abstract_canon_sha256":"a69c9b97fe852e2672f76822bff74b1d0738b4603b91e50df4726ce977d1fecc"},"schema_version":"1.0"},"canonical_sha256":"e7ce7c63ed2b9789821990257e8fe108b68da3c24201665136c074adf3d4a1d9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:06.354928Z","signature_b64":"XFqpBOM1VMIBwjhM8TLBLEatUf3coRXTYh2v9kCeqf20Mm/MwOgkh+qsrjq1nMKsSlarR1NqUqqNij5CIepnCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7ce7c63ed2b9789821990257e8fe108b68da3c24201665136c074adf3d4a1d9","last_reissued_at":"2026-05-18T00:04:06.354100Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:06.354100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.02078","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":"2026-05-18T00:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C9OWFj5i2NZtkBT4IHd1kIWQ6T0mQPavsmIVUaGdxK8Va30ChIUXIiCjnCReUJT5Rmbfdv0jys6OwdY1fEbWCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:24:54.176723Z"},"content_sha256":"87f9dc044166388d8a164f28bea8564cac477726a00df2bd1e21991ee8ebd803","schema_version":"1.0","event_id":"sha256:87f9dc044166388d8a164f28bea8564cac477726a00df2bd1e21991ee8ebd803"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:47HHYY7NFOLYTAQZSASX5D7BBC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistics of Peaks in Chi-Squared Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Alan H. Guth, Jolyon K. Bloomfield, Saarik Kalia, Stephen H. P. Face, Zander Moss","submitted_at":"2018-10-04T07:27:04Z","abstract_excerpt":"Chi-squared random fields arise naturally from the study of fluctuations in field theories with SO(n) symmetry. The extrema of chi-squared fields are of particular physical interest. In this paper, we undertake a statistical analysis of the stationary points of chi-squared fields, with particular emphasis on extrema. We begin by describing the neighborhood of a stationary point in terms of a biased chi-squared random field, and then compute the expected profile of this field, as well as a variety of associated statistics. We are interested in understanding how spherically symmetric the neighbo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02078","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":"2026-05-18T00:04:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BE7tturEbSik0H1mW4RBZIJQFiAoaoMIq5QEx9iGnrk78PrBfJZ27K52HoaX/pCK2I8/cNPaGKXHmQE+5RRHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T18:24:54.177073Z"},"content_sha256":"5859605269f8dcbc78285332b0edc27b64eee5804541ca04962dab6b4074fc0d","schema_version":"1.0","event_id":"sha256:5859605269f8dcbc78285332b0edc27b64eee5804541ca04962dab6b4074fc0d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/47HHYY7NFOLYTAQZSASX5D7BBC/bundle.json","state_url":"https://pith.science/pith/47HHYY7NFOLYTAQZSASX5D7BBC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/47HHYY7NFOLYTAQZSASX5D7BBC/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":"2026-06-02T18:24:54Z","links":{"resolver":"https://pith.science/pith/47HHYY7NFOLYTAQZSASX5D7BBC","bundle":"https://pith.science/pith/47HHYY7NFOLYTAQZSASX5D7BBC/bundle.json","state":"https://pith.science/pith/47HHYY7NFOLYTAQZSASX5D7BBC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/47HHYY7NFOLYTAQZSASX5D7BBC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:47HHYY7NFOLYTAQZSASX5D7BBC","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":"a69c9b97fe852e2672f76822bff74b1d0738b4603b91e50df4726ce977d1fecc","cross_cats_sorted":["astro-ph.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-04T07:27:04Z","title_canon_sha256":"911fbb2d42028b6666a31b241377befc3fa15b20b0de4e3d556e507c03f6b319"},"schema_version":"1.0","source":{"id":"1810.02078","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.02078","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"arxiv_version","alias_value":"1810.02078v1","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.02078","created_at":"2026-05-18T00:04:06Z"},{"alias_kind":"pith_short_12","alias_value":"47HHYY7NFOLY","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_16","alias_value":"47HHYY7NFOLYTAQZ","created_at":"2026-05-18T12:32:05Z"},{"alias_kind":"pith_short_8","alias_value":"47HHYY7N","created_at":"2026-05-18T12:32:05Z"}],"graph_snapshots":[{"event_id":"sha256:5859605269f8dcbc78285332b0edc27b64eee5804541ca04962dab6b4074fc0d","target":"graph","created_at":"2026-05-18T00:04:06Z","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":"Chi-squared random fields arise naturally from the study of fluctuations in field theories with SO(n) symmetry. The extrema of chi-squared fields are of particular physical interest. In this paper, we undertake a statistical analysis of the stationary points of chi-squared fields, with particular emphasis on extrema. We begin by describing the neighborhood of a stationary point in terms of a biased chi-squared random field, and then compute the expected profile of this field, as well as a variety of associated statistics. We are interested in understanding how spherically symmetric the neighbo","authors_text":"Alan H. Guth, Jolyon K. Bloomfield, Saarik Kalia, Stephen H. P. Face, Zander Moss","cross_cats":["astro-ph.CO","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-04T07:27:04Z","title":"Statistics of Peaks in Chi-Squared Fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02078","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":"sha256:87f9dc044166388d8a164f28bea8564cac477726a00df2bd1e21991ee8ebd803","target":"record","created_at":"2026-05-18T00:04:06Z","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":"a69c9b97fe852e2672f76822bff74b1d0738b4603b91e50df4726ce977d1fecc","cross_cats_sorted":["astro-ph.CO","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-10-04T07:27:04Z","title_canon_sha256":"911fbb2d42028b6666a31b241377befc3fa15b20b0de4e3d556e507c03f6b319"},"schema_version":"1.0","source":{"id":"1810.02078","kind":"arxiv","version":1}},"canonical_sha256":"e7ce7c63ed2b9789821990257e8fe108b68da3c24201665136c074adf3d4a1d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7ce7c63ed2b9789821990257e8fe108b68da3c24201665136c074adf3d4a1d9","first_computed_at":"2026-05-18T00:04:06.354100Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:06.354100Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XFqpBOM1VMIBwjhM8TLBLEatUf3coRXTYh2v9kCeqf20Mm/MwOgkh+qsrjq1nMKsSlarR1NqUqqNij5CIepnCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:06.354928Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.02078","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87f9dc044166388d8a164f28bea8564cac477726a00df2bd1e21991ee8ebd803","sha256:5859605269f8dcbc78285332b0edc27b64eee5804541ca04962dab6b4074fc0d"],"state_sha256":"4cac5a367d8690d357e2b610f732fd499f44ecf8ca570afff89cac0458cc4598"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VxRa0WNcpXsr/OwpRub6vYlNWoe4W49kuRgt49z4wNBDlyl3MzGWa4GXgp77Twbj0PFjb8LKPU3zPuomiB9VAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T18:24:54.179056Z","bundle_sha256":"febeb8f019ed30f84129d9af738e3ae38a9f8fdb735f905698ad936958fda7d0"}}