{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ASBKNQPZGVLNQNLGLOFDIMOS4G","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":"b9a0769267df203f36b787ff5d647ecfc01d9d03a28134648e200278499aa3ba","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-18T16:56:46Z","title_canon_sha256":"36f942b14074fd11fcc8f5bc4230eeaa1e63518303c63720a87edcec03e30d96"},"schema_version":"1.0","source":{"id":"1604.05240","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1604.05240","created_at":"2026-05-18T00:58:33Z"},{"alias_kind":"arxiv_version","alias_value":"1604.05240v3","created_at":"2026-05-18T00:58:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.05240","created_at":"2026-05-18T00:58:33Z"},{"alias_kind":"pith_short_12","alias_value":"ASBKNQPZGVLN","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"ASBKNQPZGVLNQNLG","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"ASBKNQPZ","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:02ef641398dc68171ade74d07c3b62251a449be0db5c42103641de34174fd911","target":"graph","created_at":"2026-05-18T00:58:33Z","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 study the norm approximation to the Schr\\\"odinger dynamics of $N$ bosons in $\\mathbb{R}^3$ with an interaction potential of the form $N^{3\\beta-1}w(N^{\\beta}(x-y))$. Assuming that in the initial state the particles outside of the condensate form a quasi-free state with finite kinetic energy, we show that in the large $N$ limit, the fluctuations around the condensate can be effectively described using Bogoliubov approximation for all $0\\le \\beta<1/2$. The range of $\\beta$ is expected to be optimal for this large class of initial states.","authors_text":"Marcin Napi\\'orkowski, Phan Th\\`anh Nam","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-18T16:56:46Z","title":"A note on the validity of Bogoliubov correction to mean-field dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.05240","kind":"arxiv","version":3},"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":"sha256:8a012b549c1966009a27f5805a10399dd2a5bd45425cb98d802a32d0c47bf7c9","target":"record","created_at":"2026-05-18T00:58:33Z","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":"b9a0769267df203f36b787ff5d647ecfc01d9d03a28134648e200278499aa3ba","cross_cats_sorted":["math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2016-04-18T16:56:46Z","title_canon_sha256":"36f942b14074fd11fcc8f5bc4230eeaa1e63518303c63720a87edcec03e30d96"},"schema_version":"1.0","source":{"id":"1604.05240","kind":"arxiv","version":3}},"canonical_sha256":"0482a6c1f93556d835665b8a3431d2e1b72c5cabc1adad2abf48e4e96a2cd281","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0482a6c1f93556d835665b8a3431d2e1b72c5cabc1adad2abf48e4e96a2cd281","first_computed_at":"2026-05-18T00:58:33.686976Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:33.686976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7R98vHawaE1DHMBw19s90VJI6wa2bOc00w5tyRiTh5Rrkb4k3fed8BhPjynrPm8rjz4ZZjODkuGEgzsP185yCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:33.687669Z","signed_message":"canonical_sha256_bytes"},"source_id":"1604.05240","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a012b549c1966009a27f5805a10399dd2a5bd45425cb98d802a32d0c47bf7c9","sha256:02ef641398dc68171ade74d07c3b62251a449be0db5c42103641de34174fd911"],"state_sha256":"cf2e14c456b346cdaef378977866a7d6d5c532da53fa067570c0deb05bc98586"}