{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:LYPIK3GBFQASYTNAMX4BABGE2I","short_pith_number":"pith:LYPIK3GB","canonical_record":{"source":{"id":"2109.03134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2021-09-07T14:59:29Z","cross_cats_sorted":[],"title_canon_sha256":"b03db012f90b6f6f0a0a9518fc85efe50b3257155420c8511b3b5e777afab8fe","abstract_canon_sha256":"6159049e106f0df5a36849537d0a77954fea01d52407269b2f5ca082bc4cf414"},"schema_version":"1.0"},"canonical_sha256":"5e1e856cc12c012c4da065f81004c4d22bcbbb71076ce0f5e55e29e5664656f9","source":{"kind":"arxiv","id":"2109.03134","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.03134","created_at":"2026-07-05T08:33:22Z"},{"alias_kind":"arxiv_version","alias_value":"2109.03134v1","created_at":"2026-07-05T08:33:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.03134","created_at":"2026-07-05T08:33:22Z"},{"alias_kind":"pith_short_12","alias_value":"LYPIK3GBFQAS","created_at":"2026-07-05T08:33:22Z"},{"alias_kind":"pith_short_16","alias_value":"LYPIK3GBFQASYTNA","created_at":"2026-07-05T08:33:22Z"},{"alias_kind":"pith_short_8","alias_value":"LYPIK3GB","created_at":"2026-07-05T08:33:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:LYPIK3GBFQASYTNAMX4BABGE2I","target":"record","payload":{"canonical_record":{"source":{"id":"2109.03134","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2021-09-07T14:59:29Z","cross_cats_sorted":[],"title_canon_sha256":"b03db012f90b6f6f0a0a9518fc85efe50b3257155420c8511b3b5e777afab8fe","abstract_canon_sha256":"6159049e106f0df5a36849537d0a77954fea01d52407269b2f5ca082bc4cf414"},"schema_version":"1.0"},"canonical_sha256":"5e1e856cc12c012c4da065f81004c4d22bcbbb71076ce0f5e55e29e5664656f9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:33:22.832260Z","signature_b64":"He4IMM1m/6/K2Fg0fuWonKTqVGYQNkMQpVlpATb7EJBjYDUFTd4eGWePo/uJ9ZMFXo/sTUwgqz+QFhhQ0Y7hCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5e1e856cc12c012c4da065f81004c4d22bcbbb71076ce0f5e55e29e5664656f9","last_reissued_at":"2026-07-05T08:33:22.831751Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:33:22.831751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2109.03134","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":"2026-07-05T08:33:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ThLEoNm2umLhSuHKGhxJe/o6dSTNIx3RfBKBluxq9Iy7mqjwW7uPhSKz6ZLLFKj5MgMTJadAd0fPUjLDcQ+iAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:38:59.958152Z"},"content_sha256":"d5885dfcfab64d199bbd0dee854e18cc35f0417cd49d1af662b0fdc2f2fb1c06","schema_version":"1.0","event_id":"sha256:d5885dfcfab64d199bbd0dee854e18cc35f0417cd49d1af662b0fdc2f2fb1c06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:LYPIK3GBFQASYTNAMX4BABGE2I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Time Evolution of ML-MCTDH Wavefunctions II: Application of the Projector Splitting Integrator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"physics.chem-ph","authors_text":"Benedikt Kloss, David R. Reichman, Lachlan P. Lindoy","submitted_at":"2021-09-07T14:59:29Z","abstract_excerpt":"The multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) approach suffers from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of a regularization parameter. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.03134","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/2109.03134/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":"2026-07-05T08:33:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ECq/3OdTEqmDS5BaK74AuvqNounpdrmeKXVFRFnZvpri84eOA9vc3Ok1zgeiuqHB9brxa8pdtUhaxDCDKxzbCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T18:38:59.958531Z"},"content_sha256":"929992936d5c181cf79e5d930ef4b90c4a275374a0809e87f38690be67fc75bb","schema_version":"1.0","event_id":"sha256:929992936d5c181cf79e5d930ef4b90c4a275374a0809e87f38690be67fc75bb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LYPIK3GBFQASYTNAMX4BABGE2I/bundle.json","state_url":"https://pith.science/pith/LYPIK3GBFQASYTNAMX4BABGE2I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LYPIK3GBFQASYTNAMX4BABGE2I/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":"2026-07-06T18:38:59Z","links":{"resolver":"https://pith.science/pith/LYPIK3GBFQASYTNAMX4BABGE2I","bundle":"https://pith.science/pith/LYPIK3GBFQASYTNAMX4BABGE2I/bundle.json","state":"https://pith.science/pith/LYPIK3GBFQASYTNAMX4BABGE2I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LYPIK3GBFQASYTNAMX4BABGE2I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:LYPIK3GBFQASYTNAMX4BABGE2I","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":"6159049e106f0df5a36849537d0a77954fea01d52407269b2f5ca082bc4cf414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2021-09-07T14:59:29Z","title_canon_sha256":"b03db012f90b6f6f0a0a9518fc85efe50b3257155420c8511b3b5e777afab8fe"},"schema_version":"1.0","source":{"id":"2109.03134","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2109.03134","created_at":"2026-07-05T08:33:22Z"},{"alias_kind":"arxiv_version","alias_value":"2109.03134v1","created_at":"2026-07-05T08:33:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2109.03134","created_at":"2026-07-05T08:33:22Z"},{"alias_kind":"pith_short_12","alias_value":"LYPIK3GBFQAS","created_at":"2026-07-05T08:33:22Z"},{"alias_kind":"pith_short_16","alias_value":"LYPIK3GBFQASYTNA","created_at":"2026-07-05T08:33:22Z"},{"alias_kind":"pith_short_8","alias_value":"LYPIK3GB","created_at":"2026-07-05T08:33:22Z"}],"graph_snapshots":[{"event_id":"sha256:929992936d5c181cf79e5d930ef4b90c4a275374a0809e87f38690be67fc75bb","target":"graph","created_at":"2026-07-05T08:33:22Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2109.03134/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) approach suffers from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of a regularization parameter. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement ","authors_text":"Benedikt Kloss, David R. Reichman, Lachlan P. Lindoy","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2021-09-07T14:59:29Z","title":"Time Evolution of ML-MCTDH Wavefunctions II: Application of the Projector Splitting Integrator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2109.03134","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:d5885dfcfab64d199bbd0dee854e18cc35f0417cd49d1af662b0fdc2f2fb1c06","target":"record","created_at":"2026-07-05T08:33:22Z","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":"6159049e106f0df5a36849537d0a77954fea01d52407269b2f5ca082bc4cf414","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.chem-ph","submitted_at":"2021-09-07T14:59:29Z","title_canon_sha256":"b03db012f90b6f6f0a0a9518fc85efe50b3257155420c8511b3b5e777afab8fe"},"schema_version":"1.0","source":{"id":"2109.03134","kind":"arxiv","version":1}},"canonical_sha256":"5e1e856cc12c012c4da065f81004c4d22bcbbb71076ce0f5e55e29e5664656f9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5e1e856cc12c012c4da065f81004c4d22bcbbb71076ce0f5e55e29e5664656f9","first_computed_at":"2026-07-05T08:33:22.831751Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:33:22.831751Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"He4IMM1m/6/K2Fg0fuWonKTqVGYQNkMQpVlpATb7EJBjYDUFTd4eGWePo/uJ9ZMFXo/sTUwgqz+QFhhQ0Y7hCA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:33:22.832260Z","signed_message":"canonical_sha256_bytes"},"source_id":"2109.03134","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5885dfcfab64d199bbd0dee854e18cc35f0417cd49d1af662b0fdc2f2fb1c06","sha256:929992936d5c181cf79e5d930ef4b90c4a275374a0809e87f38690be67fc75bb"],"state_sha256":"f5bee8006f5d87374ca4d4bc6730a631a15603f6139fa5932c57e42cf7e41b74"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Rh0FkF3tIVAiWr4M0sh4Cm4pO25Qf7x3ubFB3bo18Vt0mDW0qZci2iveVBFpBUp2BBLwzDyIZrm5LONn0S8ADw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T18:38:59.960377Z","bundle_sha256":"700da30118e82d173ea43124f6f22980aab9415486ad37a24113f92c1a8d0a4e"}}