{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CADDEAHLGVE7QOAKYVHSARHYHU","short_pith_number":"pith:CADDEAHL","canonical_record":{"source":{"id":"1509.06200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-21T12:24:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"dfd1e4d0582d9237a19f02a790640e2f1395f3ed574604e8c43e8253cc58b9b7","abstract_canon_sha256":"7e2e01044a548ff390079e4bff459e230f38e404cdd05f9d656b812b0b9d243f"},"schema_version":"1.0"},"canonical_sha256":"10063200eb3549f8380ac54f2044f83d274760e18af230098d0ee330c9a24631","source":{"kind":"arxiv","id":"1509.06200","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06200","created_at":"2026-05-18T01:27:31Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06200v2","created_at":"2026-05-18T01:27:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06200","created_at":"2026-05-18T01:27:31Z"},{"alias_kind":"pith_short_12","alias_value":"CADDEAHLGVE7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CADDEAHLGVE7QOAK","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CADDEAHL","created_at":"2026-05-18T12:29:14Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CADDEAHLGVE7QOAKYVHSARHYHU","target":"record","payload":{"canonical_record":{"source":{"id":"1509.06200","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-21T12:24:25Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"dfd1e4d0582d9237a19f02a790640e2f1395f3ed574604e8c43e8253cc58b9b7","abstract_canon_sha256":"7e2e01044a548ff390079e4bff459e230f38e404cdd05f9d656b812b0b9d243f"},"schema_version":"1.0"},"canonical_sha256":"10063200eb3549f8380ac54f2044f83d274760e18af230098d0ee330c9a24631","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:31.201768Z","signature_b64":"+cSCHDVbs9fG3ri3LdeYt8LfV2gzb8gTy0eX6Yy1YkLTiqFmVqDJ0RS0OTtt4eKtav1jNEmrUsEBX5hzoLGpAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10063200eb3549f8380ac54f2044f83d274760e18af230098d0ee330c9a24631","last_reissued_at":"2026-05-18T01:27:31.201290Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:31.201290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.06200","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":"2026-05-18T01:27:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O2PxPe9VbvJEUW2gkpIRvkaggAeyIPxbZdFC3Qv5976UrSH8VcgV1zVGUE3odi9OV62r3GWJhr5IfI4yXCZHCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:45:53.123678Z"},"content_sha256":"75b01e963f7893af6fb8f76d9a28f7db64422ee0007bb783c34d6545d378dac8","schema_version":"1.0","event_id":"sha256:75b01e963f7893af6fb8f76d9a28f7db64422ee0007bb783c34d6545d378dac8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CADDEAHLGVE7QOAKYVHSARHYHU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A CLT concerning critical points of random functions on a Euclidean space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Liviu I. Nicolaescu","submitted_at":"2015-09-21T12:24:25Z","abstract_excerpt":"We prove a central limit theorem concerning the number of critical points in large cubes of an isotropic Gaussian random function on a Euclidean space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06200","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":"2026-05-18T01:27:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kt8IYF+q5tfztIIJhRY87lqTyeMXjkY7UdDmGFzUA4/Ix9tlEHh8cyehfvhrDmOYjeLG5ZxWxtyfoIcQpJJFAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T17:45:53.124022Z"},"content_sha256":"8e61b6a9f4470e68813e4d5062f4ba87ff7e67bbf1793c935da073845347e48a","schema_version":"1.0","event_id":"sha256:8e61b6a9f4470e68813e4d5062f4ba87ff7e67bbf1793c935da073845347e48a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CADDEAHLGVE7QOAKYVHSARHYHU/bundle.json","state_url":"https://pith.science/pith/CADDEAHLGVE7QOAKYVHSARHYHU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CADDEAHLGVE7QOAKYVHSARHYHU/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":"2026-06-23T17:45:53Z","links":{"resolver":"https://pith.science/pith/CADDEAHLGVE7QOAKYVHSARHYHU","bundle":"https://pith.science/pith/CADDEAHLGVE7QOAKYVHSARHYHU/bundle.json","state":"https://pith.science/pith/CADDEAHLGVE7QOAKYVHSARHYHU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CADDEAHLGVE7QOAKYVHSARHYHU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CADDEAHLGVE7QOAKYVHSARHYHU","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":"7e2e01044a548ff390079e4bff459e230f38e404cdd05f9d656b812b0b9d243f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-21T12:24:25Z","title_canon_sha256":"dfd1e4d0582d9237a19f02a790640e2f1395f3ed574604e8c43e8253cc58b9b7"},"schema_version":"1.0","source":{"id":"1509.06200","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.06200","created_at":"2026-05-18T01:27:31Z"},{"alias_kind":"arxiv_version","alias_value":"1509.06200v2","created_at":"2026-05-18T01:27:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06200","created_at":"2026-05-18T01:27:31Z"},{"alias_kind":"pith_short_12","alias_value":"CADDEAHLGVE7","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_16","alias_value":"CADDEAHLGVE7QOAK","created_at":"2026-05-18T12:29:14Z"},{"alias_kind":"pith_short_8","alias_value":"CADDEAHL","created_at":"2026-05-18T12:29:14Z"}],"graph_snapshots":[{"event_id":"sha256:8e61b6a9f4470e68813e4d5062f4ba87ff7e67bbf1793c935da073845347e48a","target":"graph","created_at":"2026-05-18T01:27:31Z","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 a central limit theorem concerning the number of critical points in large cubes of an isotropic Gaussian random function on a Euclidean space.","authors_text":"Liviu I. Nicolaescu","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-21T12:24:25Z","title":"A CLT concerning critical points of random functions on a Euclidean space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06200","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":"sha256:75b01e963f7893af6fb8f76d9a28f7db64422ee0007bb783c34d6545d378dac8","target":"record","created_at":"2026-05-18T01:27:31Z","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":"7e2e01044a548ff390079e4bff459e230f38e404cdd05f9d656b812b0b9d243f","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-21T12:24:25Z","title_canon_sha256":"dfd1e4d0582d9237a19f02a790640e2f1395f3ed574604e8c43e8253cc58b9b7"},"schema_version":"1.0","source":{"id":"1509.06200","kind":"arxiv","version":2}},"canonical_sha256":"10063200eb3549f8380ac54f2044f83d274760e18af230098d0ee330c9a24631","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10063200eb3549f8380ac54f2044f83d274760e18af230098d0ee330c9a24631","first_computed_at":"2026-05-18T01:27:31.201290Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:31.201290Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+cSCHDVbs9fG3ri3LdeYt8LfV2gzb8gTy0eX6Yy1YkLTiqFmVqDJ0RS0OTtt4eKtav1jNEmrUsEBX5hzoLGpAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:31.201768Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.06200","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75b01e963f7893af6fb8f76d9a28f7db64422ee0007bb783c34d6545d378dac8","sha256:8e61b6a9f4470e68813e4d5062f4ba87ff7e67bbf1793c935da073845347e48a"],"state_sha256":"330ac3ef704a3285f2282faf164fd41a53206a620a37d682c3e3aed4c1094fca"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a5FhyLd+AhAA0lj7cvH7joB71pGaeLk0bW3hqHMhjOlwwi6+D04YQ+EyVQdhiuw8t6fHEhhOkjYWtmjZrT5TDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T17:45:53.125975Z","bundle_sha256":"a5bd5106c0554208887a0b8caf328b02d27dec74651e8e78bb96f658fd44083d"}}