{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:VY6OWB2RNEVGCAFZJAKS6MGCQ6","short_pith_number":"pith:VY6OWB2R","canonical_record":{"source":{"id":"1801.02883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-09T11:06:27Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"96c6327ed89b96ad2462307e2c147a7ff45108f2da75b009bb9d9c44e917822e","abstract_canon_sha256":"bb9f6542b982a5762a1db9e54dc4ee12970696fd80b7bf93eb6cdac298f334cc"},"schema_version":"1.0"},"canonical_sha256":"ae3ceb0751692a6100b948152f30c287ae8cb5d74a1205092b11ad66d9dfb98e","source":{"kind":"arxiv","id":"1801.02883","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02883","created_at":"2026-05-18T00:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02883v1","created_at":"2026-05-18T00:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02883","created_at":"2026-05-18T00:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"VY6OWB2RNEVG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VY6OWB2RNEVGCAFZ","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VY6OWB2R","created_at":"2026-05-18T12:32:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:VY6OWB2RNEVGCAFZJAKS6MGCQ6","target":"record","payload":{"canonical_record":{"source":{"id":"1801.02883","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-09T11:06:27Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"96c6327ed89b96ad2462307e2c147a7ff45108f2da75b009bb9d9c44e917822e","abstract_canon_sha256":"bb9f6542b982a5762a1db9e54dc4ee12970696fd80b7bf93eb6cdac298f334cc"},"schema_version":"1.0"},"canonical_sha256":"ae3ceb0751692a6100b948152f30c287ae8cb5d74a1205092b11ad66d9dfb98e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:22.171888Z","signature_b64":"wkisXliaMVfG+bPAI5FLDjkhognrMTN+vtttxEVAjZSVhSLkWs/THDC/ae/IJBy9GydZw13R5y9svWnaVeKOBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ae3ceb0751692a6100b948152f30c287ae8cb5d74a1205092b11ad66d9dfb98e","last_reissued_at":"2026-05-18T00:26:22.171018Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:22.171018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1801.02883","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":"2026-05-18T00:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MSONpaS0HfrYitfBhg/REODWRodKd2NlriqUaWmZx1HcmO8EZs/+t/vCtuIadJSiX3onbM+IXwJaCwS8HYBNBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:50:03.685332Z"},"content_sha256":"18e9f2530348ad86709162a3dfc0212a71d55c13ec489543bef9f0034b83d9d3","schema_version":"1.0","event_id":"sha256:18e9f2530348ad86709162a3dfc0212a71d55c13ec489543bef9f0034b83d9d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:VY6OWB2RNEVGCAFZJAKS6MGCQ6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean-field evolution of fermions with singular interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Chiara Saffirio","submitted_at":"2018-01-09T11:06:27Z","abstract_excerpt":"We consider a system of N fermions in the mean-field regime interacting though an inverse power law potential $V(x)=1/|x|^{\\alpha}$, for $\\alpha\\in(0,1]$. We prove the convergence of a solution of the many-body Schr\\\"{o}dinger equation to a solution of the time-dependent Hartree-Fock equation in the sense of reduced density matrices. We stress the dependence on the singularity of the potential in the regularity of the initial data. The proof is an adaptation of [22], where the case $\\alpha=1$ is treated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02883","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":"2026-05-18T00:26:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wz5y5FwXN0Sg6sdgMRH3UVxP1rrS2EmD8Ap96N5NcnuFoJs9JrsDZG9LSGAMNCimybhXGPufxbFI/m8BoS2KBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T16:50:03.685932Z"},"content_sha256":"1ff79913a25e2eec45c9cdd1b7512e26fa6874196749164d1de697d2de828ab4","schema_version":"1.0","event_id":"sha256:1ff79913a25e2eec45c9cdd1b7512e26fa6874196749164d1de697d2de828ab4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VY6OWB2RNEVGCAFZJAKS6MGCQ6/bundle.json","state_url":"https://pith.science/pith/VY6OWB2RNEVGCAFZJAKS6MGCQ6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VY6OWB2RNEVGCAFZJAKS6MGCQ6/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":"2026-06-07T16:50:03Z","links":{"resolver":"https://pith.science/pith/VY6OWB2RNEVGCAFZJAKS6MGCQ6","bundle":"https://pith.science/pith/VY6OWB2RNEVGCAFZJAKS6MGCQ6/bundle.json","state":"https://pith.science/pith/VY6OWB2RNEVGCAFZJAKS6MGCQ6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VY6OWB2RNEVGCAFZJAKS6MGCQ6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VY6OWB2RNEVGCAFZJAKS6MGCQ6","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":"bb9f6542b982a5762a1db9e54dc4ee12970696fd80b7bf93eb6cdac298f334cc","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-09T11:06:27Z","title_canon_sha256":"96c6327ed89b96ad2462307e2c147a7ff45108f2da75b009bb9d9c44e917822e"},"schema_version":"1.0","source":{"id":"1801.02883","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1801.02883","created_at":"2026-05-18T00:26:22Z"},{"alias_kind":"arxiv_version","alias_value":"1801.02883v1","created_at":"2026-05-18T00:26:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1801.02883","created_at":"2026-05-18T00:26:22Z"},{"alias_kind":"pith_short_12","alias_value":"VY6OWB2RNEVG","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VY6OWB2RNEVGCAFZ","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VY6OWB2R","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:1ff79913a25e2eec45c9cdd1b7512e26fa6874196749164d1de697d2de828ab4","target":"graph","created_at":"2026-05-18T00:26:22Z","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 a system of N fermions in the mean-field regime interacting though an inverse power law potential $V(x)=1/|x|^{\\alpha}$, for $\\alpha\\in(0,1]$. We prove the convergence of a solution of the many-body Schr\\\"{o}dinger equation to a solution of the time-dependent Hartree-Fock equation in the sense of reduced density matrices. We stress the dependence on the singularity of the potential in the regularity of the initial data. The proof is an adaptation of [22], where the case $\\alpha=1$ is treated.","authors_text":"Chiara Saffirio","cross_cats":["math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-09T11:06:27Z","title":"Mean-field evolution of fermions with singular interaction"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.02883","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":"sha256:18e9f2530348ad86709162a3dfc0212a71d55c13ec489543bef9f0034b83d9d3","target":"record","created_at":"2026-05-18T00:26:22Z","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":"bb9f6542b982a5762a1db9e54dc4ee12970696fd80b7bf93eb6cdac298f334cc","cross_cats_sorted":["math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2018-01-09T11:06:27Z","title_canon_sha256":"96c6327ed89b96ad2462307e2c147a7ff45108f2da75b009bb9d9c44e917822e"},"schema_version":"1.0","source":{"id":"1801.02883","kind":"arxiv","version":1}},"canonical_sha256":"ae3ceb0751692a6100b948152f30c287ae8cb5d74a1205092b11ad66d9dfb98e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ae3ceb0751692a6100b948152f30c287ae8cb5d74a1205092b11ad66d9dfb98e","first_computed_at":"2026-05-18T00:26:22.171018Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:26:22.171018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wkisXliaMVfG+bPAI5FLDjkhognrMTN+vtttxEVAjZSVhSLkWs/THDC/ae/IJBy9GydZw13R5y9svWnaVeKOBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:26:22.171888Z","signed_message":"canonical_sha256_bytes"},"source_id":"1801.02883","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:18e9f2530348ad86709162a3dfc0212a71d55c13ec489543bef9f0034b83d9d3","sha256:1ff79913a25e2eec45c9cdd1b7512e26fa6874196749164d1de697d2de828ab4"],"state_sha256":"abe69f1a14d08e902360a6be6915048974584d4494c352307fbbdbdffc30dc65"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Uwgnqk4zouxkSaYVqkbc2mgEEDn7OPi+c5tLQuISgLaRQU8iMzx+8TDaNB13YT2R0fS1Jlm9wHEyVccl1JhQDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T16:50:03.690183Z","bundle_sha256":"625f8ddb9edabed929987b58155178a5e521b4bb25b5780ddfcfea061e126e9b"}}