{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:SQLVLGRJ53LMECDIY6WCU52XHT","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":"15bc1d3ea9f2c25e8fa24074a7b712cad519e57d3dc7b80100695a195611fa06","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-09-22T18:03:06Z","title_canon_sha256":"9684f3c4a5628dc812bf9359c68fad8c9303c789febaf1db71ce094811ceb704"},"schema_version":"1.0","source":{"id":"2209.11256","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.11256","created_at":"2026-07-05T05:55:41Z"},{"alias_kind":"arxiv_version","alias_value":"2209.11256v1","created_at":"2026-07-05T05:55:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.11256","created_at":"2026-07-05T05:55:41Z"},{"alias_kind":"pith_short_12","alias_value":"SQLVLGRJ53LM","created_at":"2026-07-05T05:55:41Z"},{"alias_kind":"pith_short_16","alias_value":"SQLVLGRJ53LMECDI","created_at":"2026-07-05T05:55:41Z"},{"alias_kind":"pith_short_8","alias_value":"SQLVLGRJ","created_at":"2026-07-05T05:55:41Z"}],"graph_snapshots":[{"event_id":"sha256:c486866d11c51a2181fa398ba8bb2e3270087fa9985165033fe782fc1746b6d9","target":"graph","created_at":"2026-07-05T05:55:41Z","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/2209.11256/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In a quantum system, different energy eigenstates have different properties or features, allowing us define a classifier to divide them into different groups. We find that the ratio of each type of energy eigenstates in an energy shell $[E_{c}-\\Delta E/2,E_{c}+\\Delta E/2]$ is invariant with changing width $\\Delta E$ or Planck constant $\\hbar$ as long as the number of eigenstates in the shell is statistically large enough. We give an argument that such self-similarity in energy eigenstates is a general feature for all quantum systems, which is further illustrated numerically with various quantu","authors_text":"Biao Wu, Zhelun Zhang, Zhenduo Wang","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-09-22T18:03:06Z","title":"Self-Similarity Among Energy Eigenstates"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.11256","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:b0954195d6e5b494891ffad56a71566de607285149ee3b5c53a7b035e0e0ad01","target":"record","created_at":"2026-07-05T05:55:41Z","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":"15bc1d3ea9f2c25e8fa24074a7b712cad519e57d3dc7b80100695a195611fa06","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2022-09-22T18:03:06Z","title_canon_sha256":"9684f3c4a5628dc812bf9359c68fad8c9303c789febaf1db71ce094811ceb704"},"schema_version":"1.0","source":{"id":"2209.11256","kind":"arxiv","version":1}},"canonical_sha256":"9417559a29eed6c20868c7ac2a77573cfe6795811757ad75529eae839b4a62c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9417559a29eed6c20868c7ac2a77573cfe6795811757ad75529eae839b4a62c2","first_computed_at":"2026-07-05T05:55:41.440508Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:55:41.440508Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oSq14GELs9r2ACht1UzP+aXTtG/BIfNSzUCJ0CX0VLpmxX+48bUCvPf0PMla1z2oXOI+2D7yq4kT+bO+o7drCg==","signature_status":"signed_v1","signed_at":"2026-07-05T05:55:41.440923Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.11256","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b0954195d6e5b494891ffad56a71566de607285149ee3b5c53a7b035e0e0ad01","sha256:c486866d11c51a2181fa398ba8bb2e3270087fa9985165033fe782fc1746b6d9"],"state_sha256":"7e457f872d99b23996c4bfd6e56ebd2026d4ca40f1d7485458e22e58905d3514"}