{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1996:3NCSGQDWVK4SUZEUMC2F2VOZS3","short_pith_number":"pith:3NCSGQDW","canonical_record":{"source":{"id":"quant-ph/9609027","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1996-09-28T22:57:51Z","cross_cats_sorted":[],"title_canon_sha256":"54bcff0139b01ba1c814c7b690046bdbdff8e0f7a4b2da375d527d76f9b01383","abstract_canon_sha256":"06ad0ea22d832dd295e7716e1d922ca9996830a2ba8ecaa93128c915fb85ec48"},"schema_version":"1.0"},"canonical_sha256":"db45234076aab92a649460b45d55d996d821067fb0d8ede457eb1fa14b7bbb0f","source":{"kind":"arxiv","id":"quant-ph/9609027","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9609027","created_at":"2026-05-18T01:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9609027v1","created_at":"2026-05-18T01:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9609027","created_at":"2026-05-18T01:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"3NCSGQDWVK4S","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"3NCSGQDWVK4SUZEU","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"3NCSGQDW","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1996:3NCSGQDWVK4SUZEUMC2F2VOZS3","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/9609027","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1996-09-28T22:57:51Z","cross_cats_sorted":[],"title_canon_sha256":"54bcff0139b01ba1c814c7b690046bdbdff8e0f7a4b2da375d527d76f9b01383","abstract_canon_sha256":"06ad0ea22d832dd295e7716e1d922ca9996830a2ba8ecaa93128c915fb85ec48"},"schema_version":"1.0"},"canonical_sha256":"db45234076aab92a649460b45d55d996d821067fb0d8ede457eb1fa14b7bbb0f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:02.041972Z","signature_b64":"L4KCtUFUYSr6Wdmf8Its289XkK2UkBYmFxVf4oBssOo9i5AsL2Dp26DdhI7mPepUzInt6Xjjjg1QXSLrqOoLDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"db45234076aab92a649460b45d55d996d821067fb0d8ede457eb1fa14b7bbb0f","last_reissued_at":"2026-05-18T01:05:02.041294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:02.041294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/9609027","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":"2026-05-18T01:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"V2lYoxSzjq+Eblm7WqKJldJd4iBCqfbTIrf3kFnv2l7ykUfhcbx6J2C2Zv6z2CUO5ImGN12aLNgkdQYlMpsABw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:26:11.613111Z"},"content_sha256":"6241edde1144a11d7a0263b87974f5f8560423a2ad7f3c63317744f68d162173","schema_version":"1.0","event_id":"sha256:6241edde1144a11d7a0263b87974f5f8560423a2ad7f3c63317744f68d162173"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1996:3NCSGQDWVK4SUZEUMC2F2VOZS3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence Behavior of Variational Perturbation Expansions","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"FU Berlin), Hagen Kleinert (JGU Mainz, Wolfhard Janke","submitted_at":"1996-09-28T22:57:51Z","abstract_excerpt":"Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we explain the physical origin of the empirically observed convergence behavior which is exponentially fast with superimposed oscillations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9609027","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":"2026-05-18T01:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JDPf7dMu3vHovclSo+u24Ouj8ECNia4vgnGeVcrLbwI4bOI0eQ+iCJBTzjben+ULyA69K63ZgVSURZjU4bwnDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T05:26:11.613463Z"},"content_sha256":"7474cedeab454cc570d6bf4dd26336995de13336ce387a1caff74ba1ed76fffa","schema_version":"1.0","event_id":"sha256:7474cedeab454cc570d6bf4dd26336995de13336ce387a1caff74ba1ed76fffa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3NCSGQDWVK4SUZEUMC2F2VOZS3/bundle.json","state_url":"https://pith.science/pith/3NCSGQDWVK4SUZEUMC2F2VOZS3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3NCSGQDWVK4SUZEUMC2F2VOZS3/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":"2026-06-27T05:26:11Z","links":{"resolver":"https://pith.science/pith/3NCSGQDWVK4SUZEUMC2F2VOZS3","bundle":"https://pith.science/pith/3NCSGQDWVK4SUZEUMC2F2VOZS3/bundle.json","state":"https://pith.science/pith/3NCSGQDWVK4SUZEUMC2F2VOZS3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3NCSGQDWVK4SUZEUMC2F2VOZS3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1996:3NCSGQDWVK4SUZEUMC2F2VOZS3","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":"06ad0ea22d832dd295e7716e1d922ca9996830a2ba8ecaa93128c915fb85ec48","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1996-09-28T22:57:51Z","title_canon_sha256":"54bcff0139b01ba1c814c7b690046bdbdff8e0f7a4b2da375d527d76f9b01383"},"schema_version":"1.0","source":{"id":"quant-ph/9609027","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9609027","created_at":"2026-05-18T01:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9609027v1","created_at":"2026-05-18T01:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9609027","created_at":"2026-05-18T01:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"3NCSGQDWVK4S","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"3NCSGQDWVK4SUZEU","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"3NCSGQDW","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:7474cedeab454cc570d6bf4dd26336995de13336ce387a1caff74ba1ed76fffa","target":"graph","created_at":"2026-05-18T01:05:02Z","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":"Variational weak-coupling perturbation theory yields converging approximations, uniformly in the coupling strength. This allows us to calculate directly the coefficients of `strong-coupling' expansions. For the anharmonic oscillator we explain the physical origin of the empirically observed convergence behavior which is exponentially fast with superimposed oscillations.","authors_text":"FU Berlin), Hagen Kleinert (JGU Mainz, Wolfhard Janke","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"1996-09-28T22:57:51Z","title":"Convergence Behavior of Variational Perturbation Expansions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/9609027","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":"sha256:6241edde1144a11d7a0263b87974f5f8560423a2ad7f3c63317744f68d162173","target":"record","created_at":"2026-05-18T01:05:02Z","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":"06ad0ea22d832dd295e7716e1d922ca9996830a2ba8ecaa93128c915fb85ec48","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1996-09-28T22:57:51Z","title_canon_sha256":"54bcff0139b01ba1c814c7b690046bdbdff8e0f7a4b2da375d527d76f9b01383"},"schema_version":"1.0","source":{"id":"quant-ph/9609027","kind":"arxiv","version":1}},"canonical_sha256":"db45234076aab92a649460b45d55d996d821067fb0d8ede457eb1fa14b7bbb0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"db45234076aab92a649460b45d55d996d821067fb0d8ede457eb1fa14b7bbb0f","first_computed_at":"2026-05-18T01:05:02.041294Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:02.041294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"L4KCtUFUYSr6Wdmf8Its289XkK2UkBYmFxVf4oBssOo9i5AsL2Dp26DdhI7mPepUzInt6Xjjjg1QXSLrqOoLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:02.041972Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9609027","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6241edde1144a11d7a0263b87974f5f8560423a2ad7f3c63317744f68d162173","sha256:7474cedeab454cc570d6bf4dd26336995de13336ce387a1caff74ba1ed76fffa"],"state_sha256":"22d42ae6be142ccabab66809275100e4342db03073b48fa158e50c1609aabbf6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CuQcJp9+JTgXwy8+LLGHJaoUR02Lyt+zccq6rNzR70hocR2ZqgBWN4pp4Q9Ao20lFBhQO/0SlfOgIQssNys9CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T05:26:11.615217Z","bundle_sha256":"d891947df6947a878bb469cf785e334c347ef9bad33e1250557f93e3ac01f0fa"}}