{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QUX6IRGE236L3M7WAHP37TSLZS","short_pith_number":"pith:QUX6IRGE","canonical_record":{"source":{"id":"1507.01440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-06T13:24:51Z","cross_cats_sorted":["math.AP","math.FA","math.MP"],"title_canon_sha256":"bde58bd30186cb06cbc337c20c2f9547bc41f60ed35566a5a8efb82eb960fff4","abstract_canon_sha256":"7d36510c53f6679ffcf4c1b85cfc21adb7ef5a603f49bc4554c25f27ded274a6"},"schema_version":"1.0"},"canonical_sha256":"852fe444c4d6fcbdb3f601dfbfce4bcc9d70aeac904e7f006e53ec0087449e81","source":{"kind":"arxiv","id":"1507.01440","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01440","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01440v1","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01440","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"pith_short_12","alias_value":"QUX6IRGE236L","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QUX6IRGE236L3M7W","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QUX6IRGE","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QUX6IRGE236L3M7WAHP37TSLZS","target":"record","payload":{"canonical_record":{"source":{"id":"1507.01440","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-06T13:24:51Z","cross_cats_sorted":["math.AP","math.FA","math.MP"],"title_canon_sha256":"bde58bd30186cb06cbc337c20c2f9547bc41f60ed35566a5a8efb82eb960fff4","abstract_canon_sha256":"7d36510c53f6679ffcf4c1b85cfc21adb7ef5a603f49bc4554c25f27ded274a6"},"schema_version":"1.0"},"canonical_sha256":"852fe444c4d6fcbdb3f601dfbfce4bcc9d70aeac904e7f006e53ec0087449e81","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:49.497538Z","signature_b64":"9ZTrU1KZRhU1D/ItoVfxfIEQ8IHst9uMOyaWXqmONkn6hPZiFyG5Uyj1/ngxmrFP0FdqFQ0DpXPfcGvooYXSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"852fe444c4d6fcbdb3f601dfbfce4bcc9d70aeac904e7f006e53ec0087449e81","last_reissued_at":"2026-05-18T01:36:49.496950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:49.496950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.01440","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":"2026-05-18T01:36:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"EJNDZScHLHmgaW7I/pmfwXVs1viKqM93AnWyOR/Sj5BQW+/Egf8uecLEf03rgblzbg+i6opWywbNgPo7HuxMBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T20:39:14.454632Z"},"content_sha256":"1a2b4cc4a84b4e5051fe9e28502686231e22881b6c08f93dacae67b7aefb8496","schema_version":"1.0","event_id":"sha256:1a2b4cc4a84b4e5051fe9e28502686231e22881b6c08f93dacae67b7aefb8496"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QUX6IRGE236L3M7WAHP37TSLZS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"From Bosonic Grand-Canonical Ensembles to Nonlinear Gibbs Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.FA","math.MP"],"primary_cat":"math-ph","authors_text":"Nicolas Rougerie (LPMMC)","submitted_at":"2015-07-06T13:24:51Z","abstract_excerpt":"In a recent paper, in collaboration with Mathieu Lewin and Phan Th{\\`a}nh Nam, we showed that nonlinear Gibbs measures based on Gross-Pitaevskii like functionals could be derived from many-body quantum mechanics, in a mean-field limit. This text summarizes these findings. It focuses on the simplest, but most physically relevant, case we could treat so far, namely that of the defocusing cubic NLS functional on a 1D interval. The measure obtained in the limit, which (almost) lives over H^{1/2} , has been previously shown to be invariant under the NLS flow by Bourgain."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01440","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":"2026-05-18T01:36:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kU4tgtrQzTgZCCQvnoyNZlw4v3r4u1ZfpXbMrS4aNptHrKPhsUFZ4AhLsLv+3pMMypAe54CE+mtQ11q2KtXBAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T20:39:14.454969Z"},"content_sha256":"061beb5802d68fe20ae2164d5f0087f290193521df30c799fabb38e911b3fb9c","schema_version":"1.0","event_id":"sha256:061beb5802d68fe20ae2164d5f0087f290193521df30c799fabb38e911b3fb9c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QUX6IRGE236L3M7WAHP37TSLZS/bundle.json","state_url":"https://pith.science/pith/QUX6IRGE236L3M7WAHP37TSLZS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QUX6IRGE236L3M7WAHP37TSLZS/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":"2026-06-28T20:39:14Z","links":{"resolver":"https://pith.science/pith/QUX6IRGE236L3M7WAHP37TSLZS","bundle":"https://pith.science/pith/QUX6IRGE236L3M7WAHP37TSLZS/bundle.json","state":"https://pith.science/pith/QUX6IRGE236L3M7WAHP37TSLZS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QUX6IRGE236L3M7WAHP37TSLZS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QUX6IRGE236L3M7WAHP37TSLZS","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":"7d36510c53f6679ffcf4c1b85cfc21adb7ef5a603f49bc4554c25f27ded274a6","cross_cats_sorted":["math.AP","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-06T13:24:51Z","title_canon_sha256":"bde58bd30186cb06cbc337c20c2f9547bc41f60ed35566a5a8efb82eb960fff4"},"schema_version":"1.0","source":{"id":"1507.01440","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01440","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01440v1","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01440","created_at":"2026-05-18T01:36:49Z"},{"alias_kind":"pith_short_12","alias_value":"QUX6IRGE236L","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QUX6IRGE236L3M7W","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QUX6IRGE","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:061beb5802d68fe20ae2164d5f0087f290193521df30c799fabb38e911b3fb9c","target":"graph","created_at":"2026-05-18T01:36:49Z","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":"In a recent paper, in collaboration with Mathieu Lewin and Phan Th{\\`a}nh Nam, we showed that nonlinear Gibbs measures based on Gross-Pitaevskii like functionals could be derived from many-body quantum mechanics, in a mean-field limit. This text summarizes these findings. It focuses on the simplest, but most physically relevant, case we could treat so far, namely that of the defocusing cubic NLS functional on a 1D interval. The measure obtained in the limit, which (almost) lives over H^{1/2} , has been previously shown to be invariant under the NLS flow by Bourgain.","authors_text":"Nicolas Rougerie (LPMMC)","cross_cats":["math.AP","math.FA","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-06T13:24:51Z","title":"From Bosonic Grand-Canonical Ensembles to Nonlinear Gibbs Measures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01440","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":"sha256:1a2b4cc4a84b4e5051fe9e28502686231e22881b6c08f93dacae67b7aefb8496","target":"record","created_at":"2026-05-18T01:36:49Z","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":"7d36510c53f6679ffcf4c1b85cfc21adb7ef5a603f49bc4554c25f27ded274a6","cross_cats_sorted":["math.AP","math.FA","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-07-06T13:24:51Z","title_canon_sha256":"bde58bd30186cb06cbc337c20c2f9547bc41f60ed35566a5a8efb82eb960fff4"},"schema_version":"1.0","source":{"id":"1507.01440","kind":"arxiv","version":1}},"canonical_sha256":"852fe444c4d6fcbdb3f601dfbfce4bcc9d70aeac904e7f006e53ec0087449e81","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"852fe444c4d6fcbdb3f601dfbfce4bcc9d70aeac904e7f006e53ec0087449e81","first_computed_at":"2026-05-18T01:36:49.496950Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:36:49.496950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9ZTrU1KZRhU1D/ItoVfxfIEQ8IHst9uMOyaWXqmONkn6hPZiFyG5Uyj1/ngxmrFP0FdqFQ0DpXPfcGvooYXSBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:36:49.497538Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01440","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1a2b4cc4a84b4e5051fe9e28502686231e22881b6c08f93dacae67b7aefb8496","sha256:061beb5802d68fe20ae2164d5f0087f290193521df30c799fabb38e911b3fb9c"],"state_sha256":"1973a6319479e2103b3044f6a964feff98ec23994c4a5aae8f5c8683ea023ed9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VSlpKc7gnOyyRxS+Ezys/B6MdmgxkWOdLPN0eKIC2VVaBMJacjvTTfF9GjyOv9soFHgCQLT2LG127QBlifVRBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T20:39:14.456831Z","bundle_sha256":"48ccd9926e82dbf66547438de10804f0847dd67cc2914b4f0d936a08b8ce5a8f"}}