{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:YSZH3PX4DA4I2Q23UN7LF2BUBO","short_pith_number":"pith:YSZH3PX4","canonical_record":{"source":{"id":"1111.5286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2011-11-22T18:59:28Z","cross_cats_sorted":["nlin.CD","physics.data-an"],"title_canon_sha256":"01f00a241a9b7f08dfcb6918bd3f8af05c6ec2eaaf22d4bac8b9932257d85252","abstract_canon_sha256":"01f3b0536e46a91eac4e76695fb83a8283245fde2c12ecf3b1cb9dda7c718501"},"schema_version":"1.0"},"canonical_sha256":"c4b27dbefc18388d435ba37eb2e8340bbd99fa571712280a0b0dae9177ed8379","source":{"kind":"arxiv","id":"1111.5286","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5286","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5286v1","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5286","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"YSZH3PX4DA4I","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YSZH3PX4DA4I2Q23","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YSZH3PX4","created_at":"2026-05-18T12:26:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:YSZH3PX4DA4I2Q23UN7LF2BUBO","target":"record","payload":{"canonical_record":{"source":{"id":"1111.5286","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2011-11-22T18:59:28Z","cross_cats_sorted":["nlin.CD","physics.data-an"],"title_canon_sha256":"01f00a241a9b7f08dfcb6918bd3f8af05c6ec2eaaf22d4bac8b9932257d85252","abstract_canon_sha256":"01f3b0536e46a91eac4e76695fb83a8283245fde2c12ecf3b1cb9dda7c718501"},"schema_version":"1.0"},"canonical_sha256":"c4b27dbefc18388d435ba37eb2e8340bbd99fa571712280a0b0dae9177ed8379","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:44.563757Z","signature_b64":"LA9l0lj/NrGQttN3N8vk/4dF4lyBCKk8VYv7Ts8oSdcg8XKDoDquHacldcSwN9K2+V0PuYaozy+toBzck+SlCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4b27dbefc18388d435ba37eb2e8340bbd99fa571712280a0b0dae9177ed8379","last_reissued_at":"2026-05-18T04:06:44.563218Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:44.563218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.5286","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":"2026-05-18T04:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3OQfqrlsP5fc0Mpp3zVzOsHBDRrHFhHMv/jfM3suII8S0pje6vbdWuHNSTp2slGKaRydtmar8vV6kldWpT0qBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:16:03.973626Z"},"content_sha256":"d548c3c636395e97ea871b43e951f765d6e455a23670a3d84b61fcbefa280ac5","schema_version":"1.0","event_id":"sha256:d548c3c636395e97ea871b43e951f765d6e455a23670a3d84b61fcbefa280ac5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:YSZH3PX4DA4I2Q23UN7LF2BUBO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Critical point correlations in random gaussian fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["nlin.CD","physics.data-an"],"primary_cat":"cond-mat.dis-nn","authors_text":"Avraham Klein, Oded Agam","submitted_at":"2011-11-22T18:59:28Z","abstract_excerpt":"We consider fluctuations in the distribution of critical points - saddle points, minima and maxima - of random gaussian fields. We calculate the asymptotic limits of the two point correlation function for various critical point densities, for both long and short range. We perform the calculation for any dimension of the field, provide explicit formulae for two and three dimensions, and verify our results with numerical calculations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5286","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":"2026-05-18T04:06:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f/hPEw84T4E4nETQtniry6nCx/u62sfoU2NNcWM1/XSv+jNWBfj+kz08v9Gh9PX+SY8VxoUjb9R7zoMTByryBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T14:16:03.974093Z"},"content_sha256":"aac9f6286f0139388dc6cd4751867840d88edfcd159eb69aec4a4b054a4825d9","schema_version":"1.0","event_id":"sha256:aac9f6286f0139388dc6cd4751867840d88edfcd159eb69aec4a4b054a4825d9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YSZH3PX4DA4I2Q23UN7LF2BUBO/bundle.json","state_url":"https://pith.science/pith/YSZH3PX4DA4I2Q23UN7LF2BUBO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YSZH3PX4DA4I2Q23UN7LF2BUBO/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":"2026-05-27T14:16:03Z","links":{"resolver":"https://pith.science/pith/YSZH3PX4DA4I2Q23UN7LF2BUBO","bundle":"https://pith.science/pith/YSZH3PX4DA4I2Q23UN7LF2BUBO/bundle.json","state":"https://pith.science/pith/YSZH3PX4DA4I2Q23UN7LF2BUBO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YSZH3PX4DA4I2Q23UN7LF2BUBO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:YSZH3PX4DA4I2Q23UN7LF2BUBO","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":"01f3b0536e46a91eac4e76695fb83a8283245fde2c12ecf3b1cb9dda7c718501","cross_cats_sorted":["nlin.CD","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2011-11-22T18:59:28Z","title_canon_sha256":"01f00a241a9b7f08dfcb6918bd3f8af05c6ec2eaaf22d4bac8b9932257d85252"},"schema_version":"1.0","source":{"id":"1111.5286","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.5286","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"arxiv_version","alias_value":"1111.5286v1","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.5286","created_at":"2026-05-18T04:06:44Z"},{"alias_kind":"pith_short_12","alias_value":"YSZH3PX4DA4I","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_16","alias_value":"YSZH3PX4DA4I2Q23","created_at":"2026-05-18T12:26:47Z"},{"alias_kind":"pith_short_8","alias_value":"YSZH3PX4","created_at":"2026-05-18T12:26:47Z"}],"graph_snapshots":[{"event_id":"sha256:aac9f6286f0139388dc6cd4751867840d88edfcd159eb69aec4a4b054a4825d9","target":"graph","created_at":"2026-05-18T04:06:44Z","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 consider fluctuations in the distribution of critical points - saddle points, minima and maxima - of random gaussian fields. We calculate the asymptotic limits of the two point correlation function for various critical point densities, for both long and short range. We perform the calculation for any dimension of the field, provide explicit formulae for two and three dimensions, and verify our results with numerical calculations.","authors_text":"Avraham Klein, Oded Agam","cross_cats":["nlin.CD","physics.data-an"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2011-11-22T18:59:28Z","title":"Critical point correlations in random gaussian fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5286","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:d548c3c636395e97ea871b43e951f765d6e455a23670a3d84b61fcbefa280ac5","target":"record","created_at":"2026-05-18T04:06:44Z","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":"01f3b0536e46a91eac4e76695fb83a8283245fde2c12ecf3b1cb9dda7c718501","cross_cats_sorted":["nlin.CD","physics.data-an"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2011-11-22T18:59:28Z","title_canon_sha256":"01f00a241a9b7f08dfcb6918bd3f8af05c6ec2eaaf22d4bac8b9932257d85252"},"schema_version":"1.0","source":{"id":"1111.5286","kind":"arxiv","version":1}},"canonical_sha256":"c4b27dbefc18388d435ba37eb2e8340bbd99fa571712280a0b0dae9177ed8379","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4b27dbefc18388d435ba37eb2e8340bbd99fa571712280a0b0dae9177ed8379","first_computed_at":"2026-05-18T04:06:44.563218Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:44.563218Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LA9l0lj/NrGQttN3N8vk/4dF4lyBCKk8VYv7Ts8oSdcg8XKDoDquHacldcSwN9K2+V0PuYaozy+toBzck+SlCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:44.563757Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.5286","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d548c3c636395e97ea871b43e951f765d6e455a23670a3d84b61fcbefa280ac5","sha256:aac9f6286f0139388dc6cd4751867840d88edfcd159eb69aec4a4b054a4825d9"],"state_sha256":"0f272228bf52dbf4760e34f42306267a29b7c6f2f7b04094d99518d95af19562"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JiFgfM28uFwEtL2yHSOVVSHqJRtTKbvW7DDr5cH/I99t57Ja3HaXF4TvfuV4FvrCtaJhMwX5ctuOnVpLqUKcAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T14:16:03.976844Z","bundle_sha256":"de1dd317abf2ea6ecf524bd194b2553469f7106fadb191a7942bcb400e87acfd"}}