{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AV4QMZESYOKG2HGC5U5LK6TBHO","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":"5ac75b900e071f68348862242a27f79cb226d6c37a3d5be971af24ecc1d787c8","cross_cats_sorted":["cond-mat.other","hep-ph","hep-th","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-10T10:54:50Z","title_canon_sha256":"67437c6123aa35505cd613b864502215045a9dbd0e0da32343672146824822ea"},"schema_version":"1.0","source":{"id":"1408.2211","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.2211","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"arxiv_version","alias_value":"1408.2211v1","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.2211","created_at":"2026-05-18T02:43:08Z"},{"alias_kind":"pith_short_12","alias_value":"AV4QMZESYOKG","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AV4QMZESYOKG2HGC","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AV4QMZES","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:d6361722bc4e37b789197e1d85c1d5c5e5a3adc2da128fc9176d1abb68bbbbaf","target":"graph","created_at":"2026-05-18T02:43:08Z","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":"Effective Hamiltonians governing the time evolution in a subspace of unstable states can be found using more or less accurate approximations. A convenient tool for deriving them is the evolution equation for a subspace of state space sometime called the Krolikowski-Rzewuski (KR) equation. KR equation results from the Schr\\\"{o}dinger equation for the total system under considerations. We will discuss properties of approximate effective Hamiltonians derived using KR equation for $n$--particle, two particle and for one particle subspaces. In a general case these affective Hamiltonians depend on t","authors_text":"K. Urbanowski","cross_cats":["cond-mat.other","hep-ph","hep-th","nucl-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-10T10:54:50Z","title":"Effective Hamiltonians for Complexes of Unstable Particles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.2211","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:ac1cf5eb67ff9a116154c5fe849170f35a4a29a0e0ce8a90b97069d1010ea7c5","target":"record","created_at":"2026-05-18T02:43:08Z","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":"5ac75b900e071f68348862242a27f79cb226d6c37a3d5be971af24ecc1d787c8","cross_cats_sorted":["cond-mat.other","hep-ph","hep-th","nucl-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2014-08-10T10:54:50Z","title_canon_sha256":"67437c6123aa35505cd613b864502215045a9dbd0e0da32343672146824822ea"},"schema_version":"1.0","source":{"id":"1408.2211","kind":"arxiv","version":1}},"canonical_sha256":"0579066492c3946d1cc2ed3ab57a613bac7215a718e7beee146dfa426df8ab7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0579066492c3946d1cc2ed3ab57a613bac7215a718e7beee146dfa426df8ab7a","first_computed_at":"2026-05-18T02:43:08.927480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:08.927480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lay39gAf5S2FU2Ie4+rMz701rw7s1dZMLV6vYKXYiaiiJdD6wv+PBWQrUqSs3UCcQjhhE84uT4uJbkn6c5OwCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:08.927870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.2211","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac1cf5eb67ff9a116154c5fe849170f35a4a29a0e0ce8a90b97069d1010ea7c5","sha256:d6361722bc4e37b789197e1d85c1d5c5e5a3adc2da128fc9176d1abb68bbbbaf"],"state_sha256":"a381927bea2118975910b85bcd3f949e227efe0fe96cb88f13ff51c9cae2bf70"}