{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:P44AIBZS7IOGIAO6DH6OCDDPU7","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":"b559e2e8d3ae8ba42f974a4670ffe48e86ea4bf988636d639b1ac946f1206da9","cross_cats_sorted":["gr-qc","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-02-02T15:51:20Z","title_canon_sha256":"32b59033cd6a4d5ae21c1c5f988f27bbd82cb80acbb8213eb7636657a34f6f06"},"schema_version":"1.0","source":{"id":"1802.01441","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.01441","created_at":"2026-05-18T00:00:57Z"},{"alias_kind":"arxiv_version","alias_value":"1802.01441v2","created_at":"2026-05-18T00:00:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.01441","created_at":"2026-05-18T00:00:57Z"},{"alias_kind":"pith_short_12","alias_value":"P44AIBZS7IOG","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"P44AIBZS7IOGIAO6","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"P44AIBZS","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:8e9970c64142764b13b5e01c7aacd64e7510e6795448262b64e8aa200d49ae99","target":"graph","created_at":"2026-05-18T00:00:57Z","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 consider a model of a unstable state defined by the truncated Breit-Wigner energy density distribution function. An analytical form of the survival amplitude $a(t)$ of the state considered is found. Our attention is focused on the late time properties of $a(t)$ and on effects generated by the non--exponential behavior of this amplitude in the late time region: In 1957 Khalfin proved that this amplitude tends to zero as $t$ goes to the infinity more slowly than any exponential function of $t$. This effect can be described using a time-dependent decay rate $\\gamma(t)$ and then the Khalfin res","authors_text":"K. Raczynska, K. Urbanowski","cross_cats":["gr-qc","hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-02-02T15:51:20Z","title":"Survival amplitude, instantaneous energy and decay rate of an unstable system: Analytical results"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.01441","kind":"arxiv","version":2},"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":"sha256:9f43ebaf852047228cc0b17432dc168469c253a2830320302e0629cc7612148d","target":"record","created_at":"2026-05-18T00:00:57Z","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":"b559e2e8d3ae8ba42f974a4670ffe48e86ea4bf988636d639b1ac946f1206da9","cross_cats_sorted":["gr-qc","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-02-02T15:51:20Z","title_canon_sha256":"32b59033cd6a4d5ae21c1c5f988f27bbd82cb80acbb8213eb7636657a34f6f06"},"schema_version":"1.0","source":{"id":"1802.01441","kind":"arxiv","version":2}},"canonical_sha256":"7f38040732fa1c6401de19fce10c6fa7e9ef8e253bfd5c5bec1e78d0676e24b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f38040732fa1c6401de19fce10c6fa7e9ef8e253bfd5c5bec1e78d0676e24b8","first_computed_at":"2026-05-18T00:00:57.521451Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:57.521451Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NXZfMaZV5dy5C37DbO2D2cgEG/7yMHW59nSzUXh8iYyHYtFnFBO4NAftkh/tj00fiBU7FzHHdBGzs4ZcadqmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:57.521900Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.01441","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9f43ebaf852047228cc0b17432dc168469c253a2830320302e0629cc7612148d","sha256:8e9970c64142764b13b5e01c7aacd64e7510e6795448262b64e8aa200d49ae99"],"state_sha256":"d9fb5a0aa29ab8686cd5f16bcf5286611b72bd1b2b993005b52814c198098b92"}