{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:V5KIGX75N4F3BATJC2QCZAXTF6","short_pith_number":"pith:V5KIGX75","canonical_record":{"source":{"id":"2104.04750","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2021-04-10T12:22:41Z","cross_cats_sorted":[],"title_canon_sha256":"c32fd4a74b341b9ec1dad1566de0956330be8a3790cb379f07c716118d44fce8","abstract_canon_sha256":"98b5ac988e13def5697ce0bd32ee2076c65edf0f6080ed846ff8a10ea2727908"},"schema_version":"1.0"},"canonical_sha256":"af54835ffd6f0bb0826916a02c82f32f8f6fa33b8dc2152b753e5198afa8ca4d","source":{"kind":"arxiv","id":"2104.04750","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.04750","created_at":"2026-07-05T02:30:47Z"},{"alias_kind":"arxiv_version","alias_value":"2104.04750v1","created_at":"2026-07-05T02:30:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.04750","created_at":"2026-07-05T02:30:47Z"},{"alias_kind":"pith_short_12","alias_value":"V5KIGX75N4F3","created_at":"2026-07-05T02:30:47Z"},{"alias_kind":"pith_short_16","alias_value":"V5KIGX75N4F3BATJ","created_at":"2026-07-05T02:30:47Z"},{"alias_kind":"pith_short_8","alias_value":"V5KIGX75","created_at":"2026-07-05T02:30:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:V5KIGX75N4F3BATJC2QCZAXTF6","target":"record","payload":{"canonical_record":{"source":{"id":"2104.04750","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2021-04-10T12:22:41Z","cross_cats_sorted":[],"title_canon_sha256":"c32fd4a74b341b9ec1dad1566de0956330be8a3790cb379f07c716118d44fce8","abstract_canon_sha256":"98b5ac988e13def5697ce0bd32ee2076c65edf0f6080ed846ff8a10ea2727908"},"schema_version":"1.0"},"canonical_sha256":"af54835ffd6f0bb0826916a02c82f32f8f6fa33b8dc2152b753e5198afa8ca4d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:30:47.302248Z","signature_b64":"cRCdXt1+H6jOsSq7PJVswmZwKIVhCVEv0Ut4mHz77rwTjik6OdR4mc2s6fWITzJbTZYGnuFjPSpjHBidrXmlAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"af54835ffd6f0bb0826916a02c82f32f8f6fa33b8dc2152b753e5198afa8ca4d","last_reissued_at":"2026-07-05T02:30:47.301816Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:30:47.301816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2104.04750","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":"2026-07-05T02:30:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XScMZU+NZbT9sMnb2+QGNm+SmIDXd2norMzj26SOo7kJJ5ZqDPksaSb+IXJhn3g0Ht/UdN3T37vPVtE4aP2bCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:05:00.690160Z"},"content_sha256":"c0ebeedff294db7df28816bda98f2c0878481749be9cd4c290afc7d57e8cabff","schema_version":"1.0","event_id":"sha256:c0ebeedff294db7df28816bda98f2c0878481749be9cd4c290afc7d57e8cabff"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:V5KIGX75N4F3BATJC2QCZAXTF6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Application of Grey System Theory in Approximate Calculation of Wave Packet Evolution","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"physics.comp-ph","authors_text":"Dehong Gao, Jiayu Ni, Linfeng Ye, Xiangdong Feng","submitted_at":"2021-04-10T12:22:41Z","abstract_excerpt":"The study of wave packet is of great significance in quantum mechanics, optics and fluid mechanics. However, in order to solve the strict evolution behavior of wave packet, it is necessary not only to determine the parameters of various physical quantities such as mass, but also to carry out the complex integration process in configuration space and momentum space. In the final analysis, the evolution behavior of wave packet is the evolution behavior of distribution function parameters with time. Using the method of grey system theory, the time-varying parameters are replaced by time-varying r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.04750","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/2104.04750/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":"2026-07-05T02:30:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rp/G8vfhQrvXgzzBT1pjRWrGr5marrdZTMxkvn47f9V9JnqpDsCpaszKA1BGiS+qjRuV+AlLDSsPSglOytscDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T10:05:00.690555Z"},"content_sha256":"1b979059af7209b31f1e518c81e1d247f775e02b1d425bb7e02846ded54302e1","schema_version":"1.0","event_id":"sha256:1b979059af7209b31f1e518c81e1d247f775e02b1d425bb7e02846ded54302e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/V5KIGX75N4F3BATJC2QCZAXTF6/bundle.json","state_url":"https://pith.science/pith/V5KIGX75N4F3BATJC2QCZAXTF6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/V5KIGX75N4F3BATJC2QCZAXTF6/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":"2026-07-06T10:05:00Z","links":{"resolver":"https://pith.science/pith/V5KIGX75N4F3BATJC2QCZAXTF6","bundle":"https://pith.science/pith/V5KIGX75N4F3BATJC2QCZAXTF6/bundle.json","state":"https://pith.science/pith/V5KIGX75N4F3BATJC2QCZAXTF6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/V5KIGX75N4F3BATJC2QCZAXTF6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:V5KIGX75N4F3BATJC2QCZAXTF6","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":"98b5ac988e13def5697ce0bd32ee2076c65edf0f6080ed846ff8a10ea2727908","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2021-04-10T12:22:41Z","title_canon_sha256":"c32fd4a74b341b9ec1dad1566de0956330be8a3790cb379f07c716118d44fce8"},"schema_version":"1.0","source":{"id":"2104.04750","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2104.04750","created_at":"2026-07-05T02:30:47Z"},{"alias_kind":"arxiv_version","alias_value":"2104.04750v1","created_at":"2026-07-05T02:30:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2104.04750","created_at":"2026-07-05T02:30:47Z"},{"alias_kind":"pith_short_12","alias_value":"V5KIGX75N4F3","created_at":"2026-07-05T02:30:47Z"},{"alias_kind":"pith_short_16","alias_value":"V5KIGX75N4F3BATJ","created_at":"2026-07-05T02:30:47Z"},{"alias_kind":"pith_short_8","alias_value":"V5KIGX75","created_at":"2026-07-05T02:30:47Z"}],"graph_snapshots":[{"event_id":"sha256:1b979059af7209b31f1e518c81e1d247f775e02b1d425bb7e02846ded54302e1","target":"graph","created_at":"2026-07-05T02:30:47Z","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/2104.04750/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The study of wave packet is of great significance in quantum mechanics, optics and fluid mechanics. However, in order to solve the strict evolution behavior of wave packet, it is necessary not only to determine the parameters of various physical quantities such as mass, but also to carry out the complex integration process in configuration space and momentum space. In the final analysis, the evolution behavior of wave packet is the evolution behavior of distribution function parameters with time. Using the method of grey system theory, the time-varying parameters are replaced by time-varying r","authors_text":"Dehong Gao, Jiayu Ni, Linfeng Ye, Xiangdong Feng","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2021-04-10T12:22:41Z","title":"Application of Grey System Theory in Approximate Calculation of Wave Packet Evolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.04750","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:c0ebeedff294db7df28816bda98f2c0878481749be9cd4c290afc7d57e8cabff","target":"record","created_at":"2026-07-05T02:30:47Z","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":"98b5ac988e13def5697ce0bd32ee2076c65edf0f6080ed846ff8a10ea2727908","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","primary_cat":"physics.comp-ph","submitted_at":"2021-04-10T12:22:41Z","title_canon_sha256":"c32fd4a74b341b9ec1dad1566de0956330be8a3790cb379f07c716118d44fce8"},"schema_version":"1.0","source":{"id":"2104.04750","kind":"arxiv","version":1}},"canonical_sha256":"af54835ffd6f0bb0826916a02c82f32f8f6fa33b8dc2152b753e5198afa8ca4d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"af54835ffd6f0bb0826916a02c82f32f8f6fa33b8dc2152b753e5198afa8ca4d","first_computed_at":"2026-07-05T02:30:47.301816Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:30:47.301816Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cRCdXt1+H6jOsSq7PJVswmZwKIVhCVEv0Ut4mHz77rwTjik6OdR4mc2s6fWITzJbTZYGnuFjPSpjHBidrXmlAA==","signature_status":"signed_v1","signed_at":"2026-07-05T02:30:47.302248Z","signed_message":"canonical_sha256_bytes"},"source_id":"2104.04750","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c0ebeedff294db7df28816bda98f2c0878481749be9cd4c290afc7d57e8cabff","sha256:1b979059af7209b31f1e518c81e1d247f775e02b1d425bb7e02846ded54302e1"],"state_sha256":"0a5638dd485fa718882a28ca841df51352f53ab1ace08455f62e95060ea80008"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jge9HqZxst2c8ORJedKYj2LL+jn9ySwjYimoXBTFz2IDRsBEvOYICcCSvvAd9t/Rv7EpT//WIR/QqQQhnT3EAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T10:05:00.692495Z","bundle_sha256":"31a67feffb8022dc7b9eb0d02ee938558325b6c7d73282730e4821242416b7a7"}}