{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:ZGA4AWST5YSAPCJVKJSQN2J45F","short_pith_number":"pith:ZGA4AWST","schema_version":"1.0","canonical_sha256":"c981c05a53ee24078935526506e93ce96db04dc8ba82486ca0798f6ea45d887f","source":{"kind":"arxiv","id":"2006.10399","version":2},"attestation_state":"computed","paper":{"title":"The anisotropy of the power spectrum in periodic cosmological simulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"G\\'abor R\\'acz, Istv\\'an Csabai, Istv\\'an Szapudi, L\\'aszl\\'o Dobos","submitted_at":"2020-06-18T10:01:19Z","abstract_excerpt":"The classical gravitational force on a torus is anisotropic and always lower than Newton's $1/r^2$ law. We demonstrate the effects of periodicity in dark matter only $N$-body simulations of spherical collapse and standard $\\Lambda$CDM initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations are a consequence of the missing large scale modes and the equally important smaller periodic forces. The effect is most significant when the l"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2006.10399","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2020-06-18T10:01:19Z","cross_cats_sorted":[],"title_canon_sha256":"ae9c2ac9f1b63b808015ab49b29417d303ed3082dc921bec6675025fe45c21c9","abstract_canon_sha256":"07a6f73dd1b5a0ad5d8e8002de3adaf6f57b2c8db14e14c4eda220dd61586d36"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:29:27.773529Z","signature_b64":"fLmWLT4WZAm2B3kMUECBcI1baDRDBWyJvefblzzyJY6+tiq4YOVq7rDRcJyZfSxwuAxXiGlSzQtIozRu0M59AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c981c05a53ee24078935526506e93ce96db04dc8ba82486ca0798f6ea45d887f","last_reissued_at":"2026-07-05T02:29:27.773047Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:29:27.773047Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The anisotropy of the power spectrum in periodic cosmological simulations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"G\\'abor R\\'acz, Istv\\'an Csabai, Istv\\'an Szapudi, L\\'aszl\\'o Dobos","submitted_at":"2020-06-18T10:01:19Z","abstract_excerpt":"The classical gravitational force on a torus is anisotropic and always lower than Newton's $1/r^2$ law. We demonstrate the effects of periodicity in dark matter only $N$-body simulations of spherical collapse and standard $\\Lambda$CDM initial conditions. Periodic boundary conditions cause an overall negative and anisotropic bias in cosmological simulations of cosmic structure formation. The lower amplitude of power spectra of small periodic simulations are a consequence of the missing large scale modes and the equally important smaller periodic forces. The effect is most significant when the l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2006.10399","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2006.10399/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2006.10399","created_at":"2026-07-05T02:29:27.773103+00:00"},{"alias_kind":"arxiv_version","alias_value":"2006.10399v2","created_at":"2026-07-05T02:29:27.773103+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2006.10399","created_at":"2026-07-05T02:29:27.773103+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZGA4AWST5YSA","created_at":"2026-07-05T02:29:27.773103+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZGA4AWST5YSAPCJV","created_at":"2026-07-05T02:29:27.773103+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZGA4AWST","created_at":"2026-07-05T02:29:27.773103+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZGA4AWST5YSAPCJVKJSQN2J45F","json":"https://pith.science/pith/ZGA4AWST5YSAPCJVKJSQN2J45F.json","graph_json":"https://pith.science/api/pith-number/ZGA4AWST5YSAPCJVKJSQN2J45F/graph.json","events_json":"https://pith.science/api/pith-number/ZGA4AWST5YSAPCJVKJSQN2J45F/events.json","paper":"https://pith.science/paper/ZGA4AWST"},"agent_actions":{"view_html":"https://pith.science/pith/ZGA4AWST5YSAPCJVKJSQN2J45F","download_json":"https://pith.science/pith/ZGA4AWST5YSAPCJVKJSQN2J45F.json","view_paper":"https://pith.science/paper/ZGA4AWST","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2006.10399&json=true","fetch_graph":"https://pith.science/api/pith-number/ZGA4AWST5YSAPCJVKJSQN2J45F/graph.json","fetch_events":"https://pith.science/api/pith-number/ZGA4AWST5YSAPCJVKJSQN2J45F/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZGA4AWST5YSAPCJVKJSQN2J45F/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZGA4AWST5YSAPCJVKJSQN2J45F/action/storage_attestation","attest_author":"https://pith.science/pith/ZGA4AWST5YSAPCJVKJSQN2J45F/action/author_attestation","sign_citation":"https://pith.science/pith/ZGA4AWST5YSAPCJVKJSQN2J45F/action/citation_signature","submit_replication":"https://pith.science/pith/ZGA4AWST5YSAPCJVKJSQN2J45F/action/replication_record"}},"created_at":"2026-07-05T02:29:27.773103+00:00","updated_at":"2026-07-05T02:29:27.773103+00:00"}