{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:QIHHOT4D463YRAP36HVDIWG2C4","short_pith_number":"pith:QIHHOT4D","canonical_record":{"source":{"id":"2405.03378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-06T11:32:39Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ca801fa57fc37c15f693f3362504e4e29fdf65583ac43e28ff40b22bfbf3808c","abstract_canon_sha256":"bc8299eab964a49e5e26ec2ca42afe9b0aa8e202aa7a44293a807aeac5532385"},"schema_version":"1.0"},"canonical_sha256":"820e774f83e7b78881fbf1ea3458da171934dee94bd9835c9b793ecb291effbe","source":{"kind":"arxiv","id":"2405.03378","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.03378","created_at":"2026-07-05T08:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"2405.03378v1","created_at":"2026-07-05T08:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.03378","created_at":"2026-07-05T08:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"QIHHOT4D463Y","created_at":"2026-07-05T08:16:02Z"},{"alias_kind":"pith_short_16","alias_value":"QIHHOT4D463YRAP3","created_at":"2026-07-05T08:16:02Z"},{"alias_kind":"pith_short_8","alias_value":"QIHHOT4D","created_at":"2026-07-05T08:16:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:QIHHOT4D463YRAP36HVDIWG2C4","target":"record","payload":{"canonical_record":{"source":{"id":"2405.03378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-06T11:32:39Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ca801fa57fc37c15f693f3362504e4e29fdf65583ac43e28ff40b22bfbf3808c","abstract_canon_sha256":"bc8299eab964a49e5e26ec2ca42afe9b0aa8e202aa7a44293a807aeac5532385"},"schema_version":"1.0"},"canonical_sha256":"820e774f83e7b78881fbf1ea3458da171934dee94bd9835c9b793ecb291effbe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:16:02.221843Z","signature_b64":"tTxGQjsPEFryD8uLhgHrIuhWqr1owW9pgGq1EypDE9ru6KyaTh3plFKhPCNAd2edCgabXHwsVsRfB5SAFTPxBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"820e774f83e7b78881fbf1ea3458da171934dee94bd9835c9b793ecb291effbe","last_reissued_at":"2026-07-05T08:16:02.221377Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:16:02.221377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.03378","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":"2026-07-05T08:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8v9gs4x1yjnUVeNxLO2noUT2a/8qM2Rei+GZEjDjjjlraurT1OwIoss+m14FITnOAHtJQqB797ATnzqiaHkcBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:33:40.282439Z"},"content_sha256":"cbceb55f7a17de067f17083c4715206ebb6a1710c8f49abc2430288d65f54b1a","schema_version":"1.0","event_id":"sha256:cbceb55f7a17de067f17083c4715206ebb6a1710c8f49abc2430288d65f54b1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:QIHHOT4D463YRAP36HVDIWG2C4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Upper Bound for the Free Energy of Dilute Bose Gases at Low Temperature","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Arnaud Triay, Benjamin Schlein, Christian Hainzl, Florian Haberberger","submitted_at":"2024-05-06T11:32:39Z","abstract_excerpt":"We consider a Bose gas at density $\\rho > 0$, interacting through a repulsive potential $V \\in L^2 (\\mathbb{R}^3)$ with scattering length $\\mathfrak{a} > 0$. We prove an upper bound for the free energy of the system, valid at low temperature $T \\lesssim \\rho \\mathfrak{a}$. Combined with the recent lower bound obtained in \\cite{HabHaiNamSeiTri-23}, our estimate resolves the free energy per unit volume up to and including the Lee--Huang--Yang order $\\mathfrak{a} \\rho^2 (\\rho \\mathfrak{a}^3)^{1/2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03378","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.03378/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:16:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OgjYUNnBTk7KCgxYI8JPxkAJ27KACJ0aiJlQzI1b+Gdsh9vvDCn3g5XhYi5m68Vx+9I0jajI6zj5K28rqFczDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T21:33:40.282825Z"},"content_sha256":"d1cc9c43ce5529838722b761c3db7a6e9a10fa9ce710c14edce9428918ebebd8","schema_version":"1.0","event_id":"sha256:d1cc9c43ce5529838722b761c3db7a6e9a10fa9ce710c14edce9428918ebebd8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QIHHOT4D463YRAP36HVDIWG2C4/bundle.json","state_url":"https://pith.science/pith/QIHHOT4D463YRAP36HVDIWG2C4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QIHHOT4D463YRAP36HVDIWG2C4/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":"2026-08-03T21:33:40Z","links":{"resolver":"https://pith.science/pith/QIHHOT4D463YRAP36HVDIWG2C4","bundle":"https://pith.science/pith/QIHHOT4D463YRAP36HVDIWG2C4/bundle.json","state":"https://pith.science/pith/QIHHOT4D463YRAP36HVDIWG2C4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QIHHOT4D463YRAP36HVDIWG2C4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:QIHHOT4D463YRAP36HVDIWG2C4","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":"bc8299eab964a49e5e26ec2ca42afe9b0aa8e202aa7a44293a807aeac5532385","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-06T11:32:39Z","title_canon_sha256":"ca801fa57fc37c15f693f3362504e4e29fdf65583ac43e28ff40b22bfbf3808c"},"schema_version":"1.0","source":{"id":"2405.03378","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.03378","created_at":"2026-07-05T08:16:02Z"},{"alias_kind":"arxiv_version","alias_value":"2405.03378v1","created_at":"2026-07-05T08:16:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.03378","created_at":"2026-07-05T08:16:02Z"},{"alias_kind":"pith_short_12","alias_value":"QIHHOT4D463Y","created_at":"2026-07-05T08:16:02Z"},{"alias_kind":"pith_short_16","alias_value":"QIHHOT4D463YRAP3","created_at":"2026-07-05T08:16:02Z"},{"alias_kind":"pith_short_8","alias_value":"QIHHOT4D","created_at":"2026-07-05T08:16:02Z"}],"graph_snapshots":[{"event_id":"sha256:d1cc9c43ce5529838722b761c3db7a6e9a10fa9ce710c14edce9428918ebebd8","target":"graph","created_at":"2026-07-05T08:16:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2405.03378/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a Bose gas at density $\\rho > 0$, interacting through a repulsive potential $V \\in L^2 (\\mathbb{R}^3)$ with scattering length $\\mathfrak{a} > 0$. We prove an upper bound for the free energy of the system, valid at low temperature $T \\lesssim \\rho \\mathfrak{a}$. Combined with the recent lower bound obtained in \\cite{HabHaiNamSeiTri-23}, our estimate resolves the free energy per unit volume up to and including the Lee--Huang--Yang order $\\mathfrak{a} \\rho^2 (\\rho \\mathfrak{a}^3)^{1/2}$.","authors_text":"Arnaud Triay, Benjamin Schlein, Christian Hainzl, Florian Haberberger","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-06T11:32:39Z","title":"Upper Bound for the Free Energy of Dilute Bose Gases at Low Temperature"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.03378","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:cbceb55f7a17de067f17083c4715206ebb6a1710c8f49abc2430288d65f54b1a","target":"record","created_at":"2026-07-05T08:16:02Z","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":"bc8299eab964a49e5e26ec2ca42afe9b0aa8e202aa7a44293a807aeac5532385","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2024-05-06T11:32:39Z","title_canon_sha256":"ca801fa57fc37c15f693f3362504e4e29fdf65583ac43e28ff40b22bfbf3808c"},"schema_version":"1.0","source":{"id":"2405.03378","kind":"arxiv","version":1}},"canonical_sha256":"820e774f83e7b78881fbf1ea3458da171934dee94bd9835c9b793ecb291effbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"820e774f83e7b78881fbf1ea3458da171934dee94bd9835c9b793ecb291effbe","first_computed_at":"2026-07-05T08:16:02.221377Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:16:02.221377Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tTxGQjsPEFryD8uLhgHrIuhWqr1owW9pgGq1EypDE9ru6KyaTh3plFKhPCNAd2edCgabXHwsVsRfB5SAFTPxBw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:16:02.221843Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.03378","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cbceb55f7a17de067f17083c4715206ebb6a1710c8f49abc2430288d65f54b1a","sha256:d1cc9c43ce5529838722b761c3db7a6e9a10fa9ce710c14edce9428918ebebd8"],"state_sha256":"16cf80a74e4aa3be192480676cecaeaa7ae6a98d9c20371e6f2d6abbf058b804"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PS40KPu7Eg3SjrTdRfVRkP55WZGG4ELZixIy/IkFgR+ZAakWwDoiskHDLAbyOV8g1dmEyOqUVxjdRj0MqCJRBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T21:33:40.285783Z","bundle_sha256":"38ab83a7494a13ede5cec5076adcf7564f6bdff061bb5cce0d1bcc39ead4bdab"}}