{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:NWCWL5IKHXO6VP6O6ALCCPAUKS","short_pith_number":"pith:NWCWL5IK","canonical_record":{"source":{"id":"2501.01381","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-02T17:52:06Z","cross_cats_sorted":["math.AP","math.MP","math.SP","quant-ph"],"title_canon_sha256":"9cdc79833e6f26734abc21ca68f755caeeac8b17464b106bb48252a831a78efd","abstract_canon_sha256":"9a0b3fb42215f2f6995bdc67a89cfdf716853778e0181c3be9b2a5b2d2cb21bf"},"schema_version":"1.0"},"canonical_sha256":"6d8565f50a3dddeabfcef016213c1454887694f53ace67ac47f7bf935f3a10db","source":{"kind":"arxiv","id":"2501.01381","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.01381","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"arxiv_version","alias_value":"2501.01381v2","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01381","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_12","alias_value":"NWCWL5IKHXO6","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_16","alias_value":"NWCWL5IKHXO6VP6O","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_8","alias_value":"NWCWL5IK","created_at":"2026-07-05T10:18:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:NWCWL5IKHXO6VP6O6ALCCPAUKS","target":"record","payload":{"canonical_record":{"source":{"id":"2501.01381","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-02T17:52:06Z","cross_cats_sorted":["math.AP","math.MP","math.SP","quant-ph"],"title_canon_sha256":"9cdc79833e6f26734abc21ca68f755caeeac8b17464b106bb48252a831a78efd","abstract_canon_sha256":"9a0b3fb42215f2f6995bdc67a89cfdf716853778e0181c3be9b2a5b2d2cb21bf"},"schema_version":"1.0"},"canonical_sha256":"6d8565f50a3dddeabfcef016213c1454887694f53ace67ac47f7bf935f3a10db","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:18:12.044743Z","signature_b64":"gpKGQyer+ulVjIp3MA5YwN9k4lQE8qO0F5yqhjoCgIPgSybUgPzVBzYozq7VTZEr62iOGBrNYxOAF1yrK4fyBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6d8565f50a3dddeabfcef016213c1454887694f53ace67ac47f7bf935f3a10db","last_reissued_at":"2026-07-05T10:18:12.044250Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:18:12.044250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.01381","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:18:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROZ8Jxou90VfXCq2lDX7QzmVITe43V9bnR+Vf6Ky9QGp3/Ap7mdjGC5MNPl78bMPj0d184XjaopyKPYAxJkTDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:35:32.055484Z"},"content_sha256":"49cc9166f5ccfd71538c97ed3f44f4bd4e0b91f90c2fcbb9bf93fca029939497","schema_version":"1.0","event_id":"sha256:49cc9166f5ccfd71538c97ed3f44f4bd4e0b91f90c2fcbb9bf93fca029939497"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:NWCWL5IKHXO6VP6O6ALCCPAUKS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Commutator Estimates and Quantitative Local Weyl's Law for Schr\\\"odinger Operators with Non-Smooth Potentials","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"Esteban C\\'ardenas, Laurent Lafleche","submitted_at":"2025-01-02T17:52:06Z","abstract_excerpt":"We analyze semi-classical Schr\\\"odinger operators with potentials of class $C^{1,1/2}$ and establish commutator estimates for the associated projection operators in Schatten norms. These are then applied to prove quantitative versions of the local and phase space Weyl laws in $L^p$ spaces. We study both non-interacting, and interacting particle systems. In particular, we are able to treat the case of the minimizers of the Hartree energy in the case of repulsive singular pair interactions such as the Coulomb potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01381","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/2501.01381/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":"2026-07-05T10:18:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kUP+eEOmME3UasBklpLe8WDF3v/id2oIA+Zv0l3SiXLTHWVgDoa5m9Ef9IfJaP97B6XPWc7HQBxSSIAEu6tdDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T14:35:32.055998Z"},"content_sha256":"ea9e34526104917a67671db36b2498dd0869e9dcb27edd8d96d0f721574085b0","schema_version":"1.0","event_id":"sha256:ea9e34526104917a67671db36b2498dd0869e9dcb27edd8d96d0f721574085b0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NWCWL5IKHXO6VP6O6ALCCPAUKS/bundle.json","state_url":"https://pith.science/pith/NWCWL5IKHXO6VP6O6ALCCPAUKS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NWCWL5IKHXO6VP6O6ALCCPAUKS/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":"2026-08-09T14:35:32Z","links":{"resolver":"https://pith.science/pith/NWCWL5IKHXO6VP6O6ALCCPAUKS","bundle":"https://pith.science/pith/NWCWL5IKHXO6VP6O6ALCCPAUKS/bundle.json","state":"https://pith.science/pith/NWCWL5IKHXO6VP6O6ALCCPAUKS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NWCWL5IKHXO6VP6O6ALCCPAUKS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NWCWL5IKHXO6VP6O6ALCCPAUKS","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":"9a0b3fb42215f2f6995bdc67a89cfdf716853778e0181c3be9b2a5b2d2cb21bf","cross_cats_sorted":["math.AP","math.MP","math.SP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-02T17:52:06Z","title_canon_sha256":"9cdc79833e6f26734abc21ca68f755caeeac8b17464b106bb48252a831a78efd"},"schema_version":"1.0","source":{"id":"2501.01381","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.01381","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"arxiv_version","alias_value":"2501.01381v2","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.01381","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_12","alias_value":"NWCWL5IKHXO6","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_16","alias_value":"NWCWL5IKHXO6VP6O","created_at":"2026-07-05T10:18:12Z"},{"alias_kind":"pith_short_8","alias_value":"NWCWL5IK","created_at":"2026-07-05T10:18:12Z"}],"graph_snapshots":[{"event_id":"sha256:ea9e34526104917a67671db36b2498dd0869e9dcb27edd8d96d0f721574085b0","target":"graph","created_at":"2026-07-05T10:18:12Z","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/2501.01381/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We analyze semi-classical Schr\\\"odinger operators with potentials of class $C^{1,1/2}$ and establish commutator estimates for the associated projection operators in Schatten norms. These are then applied to prove quantitative versions of the local and phase space Weyl laws in $L^p$ spaces. We study both non-interacting, and interacting particle systems. In particular, we are able to treat the case of the minimizers of the Hartree energy in the case of repulsive singular pair interactions such as the Coulomb potential.","authors_text":"Esteban C\\'ardenas, Laurent Lafleche","cross_cats":["math.AP","math.MP","math.SP","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-02T17:52:06Z","title":"Commutator Estimates and Quantitative Local Weyl's Law for Schr\\\"odinger Operators with Non-Smooth Potentials"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.01381","kind":"arxiv","version":2},"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":"sha256:49cc9166f5ccfd71538c97ed3f44f4bd4e0b91f90c2fcbb9bf93fca029939497","target":"record","created_at":"2026-07-05T10:18:12Z","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":"9a0b3fb42215f2f6995bdc67a89cfdf716853778e0181c3be9b2a5b2d2cb21bf","cross_cats_sorted":["math.AP","math.MP","math.SP","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2025-01-02T17:52:06Z","title_canon_sha256":"9cdc79833e6f26734abc21ca68f755caeeac8b17464b106bb48252a831a78efd"},"schema_version":"1.0","source":{"id":"2501.01381","kind":"arxiv","version":2}},"canonical_sha256":"6d8565f50a3dddeabfcef016213c1454887694f53ace67ac47f7bf935f3a10db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6d8565f50a3dddeabfcef016213c1454887694f53ace67ac47f7bf935f3a10db","first_computed_at":"2026-07-05T10:18:12.044250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:18:12.044250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gpKGQyer+ulVjIp3MA5YwN9k4lQE8qO0F5yqhjoCgIPgSybUgPzVBzYozq7VTZEr62iOGBrNYxOAF1yrK4fyBA==","signature_status":"signed_v1","signed_at":"2026-07-05T10:18:12.044743Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.01381","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49cc9166f5ccfd71538c97ed3f44f4bd4e0b91f90c2fcbb9bf93fca029939497","sha256:ea9e34526104917a67671db36b2498dd0869e9dcb27edd8d96d0f721574085b0"],"state_sha256":"d73af0e7c6bad8f152803b8b3fa15201529e9239709445b3325d69a025881c9e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BS63SR+QSV29ZRRkET8IFWHxI09fT3uh3c+XVk9AxOufcGKeeE/2OlRQhkKLk4w6+Uidq7Z1VUpzSdHUWix5DA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T14:35:32.060196Z","bundle_sha256":"3f00a3bfc23f83fcc233a62ad55c9ba699b956ee1f8e3bec71853a964b29ecf4"}}