{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GGBIHRJD7NX5WSY5XR4C7QW4FO","short_pith_number":"pith:GGBIHRJD","canonical_record":{"source":{"id":"1602.03581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-11T00:22:42Z","cross_cats_sorted":[],"title_canon_sha256":"4e7db47802f9a86f532a1436ef07de09685194a3d8bfef2704f905984dbb8b7c","abstract_canon_sha256":"6695693e792313284e02e42e59ca41fcb11c8609c9dffaadd15ecd92374c306c"},"schema_version":"1.0"},"canonical_sha256":"318283c523fb6fdb4b1dbc782fc2dc2ba6c15d93d53b1f6b460f3dbf93070962","source":{"kind":"arxiv","id":"1602.03581","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03581","created_at":"2026-05-18T01:20:58Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03581v1","created_at":"2026-05-18T01:20:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03581","created_at":"2026-05-18T01:20:58Z"},{"alias_kind":"pith_short_12","alias_value":"GGBIHRJD7NX5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GGBIHRJD7NX5WSY5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GGBIHRJD","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GGBIHRJD7NX5WSY5XR4C7QW4FO","target":"record","payload":{"canonical_record":{"source":{"id":"1602.03581","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-11T00:22:42Z","cross_cats_sorted":[],"title_canon_sha256":"4e7db47802f9a86f532a1436ef07de09685194a3d8bfef2704f905984dbb8b7c","abstract_canon_sha256":"6695693e792313284e02e42e59ca41fcb11c8609c9dffaadd15ecd92374c306c"},"schema_version":"1.0"},"canonical_sha256":"318283c523fb6fdb4b1dbc782fc2dc2ba6c15d93d53b1f6b460f3dbf93070962","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:58.454014Z","signature_b64":"reoWyyZrawrERUAAJ9+m/IaneUv7A5X4QaA9octL++2IBwgRto0jy1evtIrxY518bDPFBicvWLqSoylBwnDACA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"318283c523fb6fdb4b1dbc782fc2dc2ba6c15d93d53b1f6b460f3dbf93070962","last_reissued_at":"2026-05-18T01:20:58.453607Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:58.453607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.03581","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":"2026-05-18T01:20:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6JqlWFJMougoPv3UDzmpkDAsfEkr0UOZFKyCifuiDSvtZGp6j1Gc4tTKUCNpyoDTf2xIpDnryAfxiVAq0LpwAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:07:30.065963Z"},"content_sha256":"16a8cb7fe1ffbe15ffa522f268af63026aea5eb600898c2c6064e64cf27d8130","schema_version":"1.0","event_id":"sha256:16a8cb7fe1ffbe15ffa522f268af63026aea5eb600898c2c6064e64cf27d8130"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GGBIHRJD7NX5WSY5XR4C7QW4FO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Efficient methods for time-dependence in semiclassical Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Arieh Iserles, Karolina Kropielnicka, Philipp Bader, Pranav Singh","submitted_at":"2016-02-11T00:22:42Z","abstract_excerpt":"We build an efficient and unitary (hence stable) method for the solution of the semi-classical Schr\\\"odinger equation subject with explicitly time-dependent potentials. The method is based on a combination of the Zassenhaus decomposition (Bader, Iserles, Kropielnicka & Singh 2014) with the Magnus expansion of the time-dependent Hamiltonian. We conclude with numerical experiments."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03581","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":"2026-05-18T01:20:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wZMfv89wylNCHZVdAJlfF9TZ3sT7JN5RpZdmfUKSfKTAgT4K/CUlk0CrtYA49bWWZkGaAN/j9eatICc06IhOBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T15:07:30.066335Z"},"content_sha256":"d0e208f51f6a8d146eed9b35b975f94e528db5341ede11f3d7b93f0b0c591116","schema_version":"1.0","event_id":"sha256:d0e208f51f6a8d146eed9b35b975f94e528db5341ede11f3d7b93f0b0c591116"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GGBIHRJD7NX5WSY5XR4C7QW4FO/bundle.json","state_url":"https://pith.science/pith/GGBIHRJD7NX5WSY5XR4C7QW4FO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GGBIHRJD7NX5WSY5XR4C7QW4FO/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":"2026-06-02T15:07:30Z","links":{"resolver":"https://pith.science/pith/GGBIHRJD7NX5WSY5XR4C7QW4FO","bundle":"https://pith.science/pith/GGBIHRJD7NX5WSY5XR4C7QW4FO/bundle.json","state":"https://pith.science/pith/GGBIHRJD7NX5WSY5XR4C7QW4FO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GGBIHRJD7NX5WSY5XR4C7QW4FO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GGBIHRJD7NX5WSY5XR4C7QW4FO","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":"6695693e792313284e02e42e59ca41fcb11c8609c9dffaadd15ecd92374c306c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-11T00:22:42Z","title_canon_sha256":"4e7db47802f9a86f532a1436ef07de09685194a3d8bfef2704f905984dbb8b7c"},"schema_version":"1.0","source":{"id":"1602.03581","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.03581","created_at":"2026-05-18T01:20:58Z"},{"alias_kind":"arxiv_version","alias_value":"1602.03581v1","created_at":"2026-05-18T01:20:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.03581","created_at":"2026-05-18T01:20:58Z"},{"alias_kind":"pith_short_12","alias_value":"GGBIHRJD7NX5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GGBIHRJD7NX5WSY5","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GGBIHRJD","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:d0e208f51f6a8d146eed9b35b975f94e528db5341ede11f3d7b93f0b0c591116","target":"graph","created_at":"2026-05-18T01:20:58Z","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 build an efficient and unitary (hence stable) method for the solution of the semi-classical Schr\\\"odinger equation subject with explicitly time-dependent potentials. The method is based on a combination of the Zassenhaus decomposition (Bader, Iserles, Kropielnicka & Singh 2014) with the Magnus expansion of the time-dependent Hamiltonian. We conclude with numerical experiments.","authors_text":"Arieh Iserles, Karolina Kropielnicka, Philipp Bader, Pranav Singh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-11T00:22:42Z","title":"Efficient methods for time-dependence in semiclassical Schr\\\"odinger equations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03581","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":"sha256:16a8cb7fe1ffbe15ffa522f268af63026aea5eb600898c2c6064e64cf27d8130","target":"record","created_at":"2026-05-18T01:20:58Z","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":"6695693e792313284e02e42e59ca41fcb11c8609c9dffaadd15ecd92374c306c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-02-11T00:22:42Z","title_canon_sha256":"4e7db47802f9a86f532a1436ef07de09685194a3d8bfef2704f905984dbb8b7c"},"schema_version":"1.0","source":{"id":"1602.03581","kind":"arxiv","version":1}},"canonical_sha256":"318283c523fb6fdb4b1dbc782fc2dc2ba6c15d93d53b1f6b460f3dbf93070962","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"318283c523fb6fdb4b1dbc782fc2dc2ba6c15d93d53b1f6b460f3dbf93070962","first_computed_at":"2026-05-18T01:20:58.453607Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:58.453607Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"reoWyyZrawrERUAAJ9+m/IaneUv7A5X4QaA9octL++2IBwgRto0jy1evtIrxY518bDPFBicvWLqSoylBwnDACA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:58.454014Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.03581","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16a8cb7fe1ffbe15ffa522f268af63026aea5eb600898c2c6064e64cf27d8130","sha256:d0e208f51f6a8d146eed9b35b975f94e528db5341ede11f3d7b93f0b0c591116"],"state_sha256":"6d7ee263d31bd8c6d6d9c2f4c78e2027bd6663b2208bad9652b38705689a904e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kS9/KCFsA/3JS6t73FPgDt37GStxzrOdUemspAAM8aNOfBGrIsfTCB+1EkukRRT0YcqrTbX6+pgNTX7QyYgqAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T15:07:30.068488Z","bundle_sha256":"e06820dc06c1a861433132d739dc4e760320964a37c6481e7fb81e1b76687e21"}}