{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:LW56ORWCR3FW3XSBOTBN7WIVZP","short_pith_number":"pith:LW56ORWC","canonical_record":{"source":{"id":"2309.02589","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-05T21:25:50Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"abfd8cb78d9a4fda3455b8d1b2d3f12fcb70537b6d8fa5b92332c5ccf37af8e7","abstract_canon_sha256":"818b887f061d72fe0f2a9b8f9ab1a4bd245a4954571de0cce1c3370cf947d79d"},"schema_version":"1.0"},"canonical_sha256":"5dbbe746c28ecb6dde4174c2dfd915cbe08ba5c02da2b99250f2887f1f7d0528","source":{"kind":"arxiv","id":"2309.02589","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.02589","created_at":"2026-07-05T06:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"2309.02589v2","created_at":"2026-07-05T06:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.02589","created_at":"2026-07-05T06:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"LW56ORWCR3FW","created_at":"2026-07-05T06:48:24Z"},{"alias_kind":"pith_short_16","alias_value":"LW56ORWCR3FW3XSB","created_at":"2026-07-05T06:48:24Z"},{"alias_kind":"pith_short_8","alias_value":"LW56ORWC","created_at":"2026-07-05T06:48:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:LW56ORWCR3FW3XSBOTBN7WIVZP","target":"record","payload":{"canonical_record":{"source":{"id":"2309.02589","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-05T21:25:50Z","cross_cats_sorted":["cs.AI"],"title_canon_sha256":"abfd8cb78d9a4fda3455b8d1b2d3f12fcb70537b6d8fa5b92332c5ccf37af8e7","abstract_canon_sha256":"818b887f061d72fe0f2a9b8f9ab1a4bd245a4954571de0cce1c3370cf947d79d"},"schema_version":"1.0"},"canonical_sha256":"5dbbe746c28ecb6dde4174c2dfd915cbe08ba5c02da2b99250f2887f1f7d0528","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:48:24.356494Z","signature_b64":"dkZmSy+PiDTfK0MjMzIg/kKHkSRfnSJKW1gKGAaaDJjoDHkRjkEfS0eCKaNtqExA+w3Wa6gRrn48Jc/eofGSBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5dbbe746c28ecb6dde4174c2dfd915cbe08ba5c02da2b99250f2887f1f7d0528","last_reissued_at":"2026-07-05T06:48:24.356025Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:48:24.356025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2309.02589","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":"2026-07-05T06:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vJva3tgr9uaU/R/M3mwe2nc+sw+Bs0nEZkDImo1a6ZCicxQd22VCazMJfB5OQUSGpeGZyGsRm+NoBTkZ3l/gAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:35:28.122976Z"},"content_sha256":"a09d52a0b3383d9a45a98219e2347da804069d1019412bdd8cfa3f21bad8c0dc","schema_version":"1.0","event_id":"sha256:a09d52a0b3383d9a45a98219e2347da804069d1019412bdd8cfa3f21bad8c0dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:LW56ORWCR3FW3XSBOTBN7WIVZP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Approximating High-Dimensional Minimal Surfaces with Physics-Informed Neural Networks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.AI"],"primary_cat":"math.AP","authors_text":"Steven Zhou, Xiaojing Ye","submitted_at":"2023-09-05T21:25:50Z","abstract_excerpt":"In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot handle it in this case because of the Curse of Dimensionality, where the computational cost of these methods increases exponentially fast in response to higher problem dimensions, far beyond the computing capacity of any modern supercomputers. Only in the past few years have machine learning researchers been able to mitigate this problem. The solution method chosen here is a model known as a Physics-Informed Neural "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.02589","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/2309.02589/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":"2026-07-05T06:48:24Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MqZ4AK0L3e/w5S065NHlWjU1JTVo9s1WgBusgLPN+pJc+kAsqcs0LTLiLjxhi5lr9d3kTyf7gWPGi1fdohkGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T09:35:28.123614Z"},"content_sha256":"5aec76313102cdb158dce17b1768f780343e7852823a4c82f93f0a6beda34ba8","schema_version":"1.0","event_id":"sha256:5aec76313102cdb158dce17b1768f780343e7852823a4c82f93f0a6beda34ba8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LW56ORWCR3FW3XSBOTBN7WIVZP/bundle.json","state_url":"https://pith.science/pith/LW56ORWCR3FW3XSBOTBN7WIVZP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LW56ORWCR3FW3XSBOTBN7WIVZP/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":"2026-08-04T09:35:28Z","links":{"resolver":"https://pith.science/pith/LW56ORWCR3FW3XSBOTBN7WIVZP","bundle":"https://pith.science/pith/LW56ORWCR3FW3XSBOTBN7WIVZP/bundle.json","state":"https://pith.science/pith/LW56ORWCR3FW3XSBOTBN7WIVZP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LW56ORWCR3FW3XSBOTBN7WIVZP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:LW56ORWCR3FW3XSBOTBN7WIVZP","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":"818b887f061d72fe0f2a9b8f9ab1a4bd245a4954571de0cce1c3370cf947d79d","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-05T21:25:50Z","title_canon_sha256":"abfd8cb78d9a4fda3455b8d1b2d3f12fcb70537b6d8fa5b92332c5ccf37af8e7"},"schema_version":"1.0","source":{"id":"2309.02589","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2309.02589","created_at":"2026-07-05T06:48:24Z"},{"alias_kind":"arxiv_version","alias_value":"2309.02589v2","created_at":"2026-07-05T06:48:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2309.02589","created_at":"2026-07-05T06:48:24Z"},{"alias_kind":"pith_short_12","alias_value":"LW56ORWCR3FW","created_at":"2026-07-05T06:48:24Z"},{"alias_kind":"pith_short_16","alias_value":"LW56ORWCR3FW3XSB","created_at":"2026-07-05T06:48:24Z"},{"alias_kind":"pith_short_8","alias_value":"LW56ORWC","created_at":"2026-07-05T06:48:24Z"}],"graph_snapshots":[{"event_id":"sha256:5aec76313102cdb158dce17b1768f780343e7852823a4c82f93f0a6beda34ba8","target":"graph","created_at":"2026-07-05T06:48:24Z","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/2309.02589/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we compute numerical approximations of the minimal surfaces, an essential type of Partial Differential Equation (PDE), in higher dimensions. Classical methods cannot handle it in this case because of the Curse of Dimensionality, where the computational cost of these methods increases exponentially fast in response to higher problem dimensions, far beyond the computing capacity of any modern supercomputers. Only in the past few years have machine learning researchers been able to mitigate this problem. The solution method chosen here is a model known as a Physics-Informed Neural ","authors_text":"Steven Zhou, Xiaojing Ye","cross_cats":["cs.AI"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-05T21:25:50Z","title":"Approximating High-Dimensional Minimal Surfaces with Physics-Informed Neural Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.02589","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:a09d52a0b3383d9a45a98219e2347da804069d1019412bdd8cfa3f21bad8c0dc","target":"record","created_at":"2026-07-05T06:48:24Z","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":"818b887f061d72fe0f2a9b8f9ab1a4bd245a4954571de0cce1c3370cf947d79d","cross_cats_sorted":["cs.AI"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2023-09-05T21:25:50Z","title_canon_sha256":"abfd8cb78d9a4fda3455b8d1b2d3f12fcb70537b6d8fa5b92332c5ccf37af8e7"},"schema_version":"1.0","source":{"id":"2309.02589","kind":"arxiv","version":2}},"canonical_sha256":"5dbbe746c28ecb6dde4174c2dfd915cbe08ba5c02da2b99250f2887f1f7d0528","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5dbbe746c28ecb6dde4174c2dfd915cbe08ba5c02da2b99250f2887f1f7d0528","first_computed_at":"2026-07-05T06:48:24.356025Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:48:24.356025Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dkZmSy+PiDTfK0MjMzIg/kKHkSRfnSJKW1gKGAaaDJjoDHkRjkEfS0eCKaNtqExA+w3Wa6gRrn48Jc/eofGSBw==","signature_status":"signed_v1","signed_at":"2026-07-05T06:48:24.356494Z","signed_message":"canonical_sha256_bytes"},"source_id":"2309.02589","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a09d52a0b3383d9a45a98219e2347da804069d1019412bdd8cfa3f21bad8c0dc","sha256:5aec76313102cdb158dce17b1768f780343e7852823a4c82f93f0a6beda34ba8"],"state_sha256":"829e60d126f4193d2499a1662d531caa427805c0f7ea14141fe527c8f65e9cff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ssUP/BTg2g3rnxIyBHctm3GrKv2VW0+/Kfk9QLHp1NI9knNhw59mD76wzrS2fIFCAWr6lAElTq0X2o6YDbnZBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T09:35:28.130773Z","bundle_sha256":"456a2510487f49bc6dbc27c6d5c2c76ab9ed053798e3cca8789a20ac47bdfd5e"}}