{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:NF3N6MRFIQHOL3XPSG6NQEXNMN","short_pith_number":"pith:NF3N6MRF","canonical_record":{"source":{"id":"quant-ph/0501137","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2005-01-24T20:07:32Z","cross_cats_sorted":[],"title_canon_sha256":"73297ca7a20b7166c281fc800170ca630d8bcb8da524bb32427df25c758df907","abstract_canon_sha256":"2427337c89115ae7d9187f3ad538156b63f35e84030a8bc3c91f93bc1d5fda51"},"schema_version":"1.0"},"canonical_sha256":"6976df3225440ee5eeef91bcd812ed6373fdcb666f32793306da8dd17c667ed4","source":{"kind":"arxiv","id":"quant-ph/0501137","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0501137","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0501137v2","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0501137","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"NF3N6MRFIQHO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NF3N6MRFIQHOL3XP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NF3N6MRF","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:NF3N6MRFIQHOL3XPSG6NQEXNMN","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/0501137","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"2005-01-24T20:07:32Z","cross_cats_sorted":[],"title_canon_sha256":"73297ca7a20b7166c281fc800170ca630d8bcb8da524bb32427df25c758df907","abstract_canon_sha256":"2427337c89115ae7d9187f3ad538156b63f35e84030a8bc3c91f93bc1d5fda51"},"schema_version":"1.0"},"canonical_sha256":"6976df3225440ee5eeef91bcd812ed6373fdcb666f32793306da8dd17c667ed4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:13:46.704502Z","signature_b64":"HfAs7x6/P2cQjqits4NN4BOBAUgltjuFJYcFMG5qidSfiAA2IcifPeWnMpcKwWwuScfPPb6TAZVyk0QTqtE5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6976df3225440ee5eeef91bcd812ed6373fdcb666f32793306da8dd17c667ed4","last_reissued_at":"2026-05-18T03:13:46.703678Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:13:46.703678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/0501137","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:13:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QcTo/LXy88Zwrq2qrgAFTK7W27UGv7snNR6kRPG6GVw7jHhpzQTIEMsO1r/Lsf4dI5oD0py/RuOcXqXT04YgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:27:05.514898Z"},"content_sha256":"f2475378dca2bb8096f0e40a2e319d428fd40ab33f4e6af7ec85a732a4fd230a","schema_version":"1.0","event_id":"sha256:f2475378dca2bb8096f0e40a2e319d428fd40ab33f4e6af7ec85a732a4fd230a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:NF3N6MRFIQHOL3XPSG6NQEXNMN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Jean Zinn-Justin, Ulrich D. Jentschura","submitted_at":"2005-01-24T20:07:32Z","abstract_excerpt":"In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton constributions to the partition function, using the formalism introduced in the first part of the treatise [J. Zinn-Justin and U. D. Jentschura, e-print quant-ph/0501136]. The following potentials are considered: (i) asymmetric potentials with degenerate minima, (ii) the periodic cosine potential, (iii) anharmonic oscillators with radial symmetry, and (iv) a specific p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0501137","kind":"arxiv","version":2},"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":"2026-05-18T03:13:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hq4FFq5xph9guj2aB2pb9wrUN0XHlkFggiTCnRrRj2eUyaXZ6yqI2Dk8vNdMKbmDI6ataTFQSH8M0kEAuMSTAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T08:27:05.515652Z"},"content_sha256":"80f25dd7bd974bcc2ec055ce4408f54d9a1a62d5988d56a158bda5f53fd1d3c9","schema_version":"1.0","event_id":"sha256:80f25dd7bd974bcc2ec055ce4408f54d9a1a62d5988d56a158bda5f53fd1d3c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NF3N6MRFIQHOL3XPSG6NQEXNMN/bundle.json","state_url":"https://pith.science/pith/NF3N6MRFIQHOL3XPSG6NQEXNMN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NF3N6MRFIQHOL3XPSG6NQEXNMN/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":"2026-06-10T08:27:05Z","links":{"resolver":"https://pith.science/pith/NF3N6MRFIQHOL3XPSG6NQEXNMN","bundle":"https://pith.science/pith/NF3N6MRFIQHOL3XPSG6NQEXNMN/bundle.json","state":"https://pith.science/pith/NF3N6MRFIQHOL3XPSG6NQEXNMN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NF3N6MRFIQHOL3XPSG6NQEXNMN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:NF3N6MRFIQHOL3XPSG6NQEXNMN","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":"2427337c89115ae7d9187f3ad538156b63f35e84030a8bc3c91f93bc1d5fda51","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2005-01-24T20:07:32Z","title_canon_sha256":"73297ca7a20b7166c281fc800170ca630d8bcb8da524bb32427df25c758df907"},"schema_version":"1.0","source":{"id":"quant-ph/0501137","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0501137","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0501137v2","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0501137","created_at":"2026-05-18T03:13:46Z"},{"alias_kind":"pith_short_12","alias_value":"NF3N6MRFIQHO","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"NF3N6MRFIQHOL3XP","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"NF3N6MRF","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:80f25dd7bd974bcc2ec055ce4408f54d9a1a62d5988d56a158bda5f53fd1d3c9","target":"graph","created_at":"2026-05-18T03:13:46Z","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":"In this second part of the treatment of instantons in quantum mechanics, the focus is on specific calculations related to a number of quantum mechanical potentials with degenerate minima. We calculate the leading multi-instanton constributions to the partition function, using the formalism introduced in the first part of the treatise [J. Zinn-Justin and U. D. Jentschura, e-print quant-ph/0501136]. The following potentials are considered: (i) asymmetric potentials with degenerate minima, (ii) the periodic cosine potential, (iii) anharmonic oscillators with radial symmetry, and (iv) a specific p","authors_text":"Jean Zinn-Justin, Ulrich D. Jentschura","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2005-01-24T20:07:32Z","title":"Multi-Instantons and Exact Results II: Specific Cases, Higher-Order Effects, and Numerical Calculations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0501137","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:f2475378dca2bb8096f0e40a2e319d428fd40ab33f4e6af7ec85a732a4fd230a","target":"record","created_at":"2026-05-18T03:13:46Z","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":"2427337c89115ae7d9187f3ad538156b63f35e84030a8bc3c91f93bc1d5fda51","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2005-01-24T20:07:32Z","title_canon_sha256":"73297ca7a20b7166c281fc800170ca630d8bcb8da524bb32427df25c758df907"},"schema_version":"1.0","source":{"id":"quant-ph/0501137","kind":"arxiv","version":2}},"canonical_sha256":"6976df3225440ee5eeef91bcd812ed6373fdcb666f32793306da8dd17c667ed4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6976df3225440ee5eeef91bcd812ed6373fdcb666f32793306da8dd17c667ed4","first_computed_at":"2026-05-18T03:13:46.703678Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:13:46.703678Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HfAs7x6/P2cQjqits4NN4BOBAUgltjuFJYcFMG5qidSfiAA2IcifPeWnMpcKwWwuScfPPb6TAZVyk0QTqtE5AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:13:46.704502Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0501137","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2475378dca2bb8096f0e40a2e319d428fd40ab33f4e6af7ec85a732a4fd230a","sha256:80f25dd7bd974bcc2ec055ce4408f54d9a1a62d5988d56a158bda5f53fd1d3c9"],"state_sha256":"ebf64681b54f01d0c6adf4e2846729714d36395d357ef49f01725a661cde754e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gw2irUv5gca+3pXEmZ2Zwc0jVCq5pTn5VrxYZC+rwsWiPkHRtwggE2+ANhzHmQS9emo8yHRfhBl+P1ync34KBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T08:27:05.519618Z","bundle_sha256":"8791290adce04dd1383b8821c27208d52f0aad96348a8c77a4c5e657ac54a24b"}}