{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:ZAMM4AVNDLPVSD7M4KW472RRRY","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":"e8d464379d64e39d44438bebb8473226f949929396c76565135f22a81a1d7199","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2006-03-10T10:06:09Z","title_canon_sha256":"a91cb261baa52e928de2104c7051cf36382bccb5f73bb83edb758eb94293e4a9"},"schema_version":"1.0","source":{"id":"hep-ph/0603081","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-ph/0603081","created_at":"2026-07-04T17:01:41Z"},{"alias_kind":"arxiv_version","alias_value":"hep-ph/0603081v2","created_at":"2026-07-04T17:01:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-ph/0603081","created_at":"2026-07-04T17:01:41Z"},{"alias_kind":"pith_short_12","alias_value":"ZAMM4AVNDLPV","created_at":"2026-07-04T17:01:41Z"},{"alias_kind":"pith_short_16","alias_value":"ZAMM4AVNDLPVSD7M","created_at":"2026-07-04T17:01:41Z"},{"alias_kind":"pith_short_8","alias_value":"ZAMM4AVN","created_at":"2026-07-04T17:01:41Z"}],"graph_snapshots":[{"event_id":"sha256:dd446d848bfd07537c6f8166b48bb7bf46aa4512e9e005740e7d3a6b471be1ab","target":"graph","created_at":"2026-07-04T17:01:41Z","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/hep-ph/0603081/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present an algorithm to analyze numerically the bounce solution of first-order phase transitions. Our approach is well suited to treat phase transitions with several fields. The algorithm consists of two parts. In the first part the bounce solution without damping is determined, in which case energy is conserved. In the second part the continuation to the physically relevant case with damping is performed. The presented approach is numerically stable and easily implemented.","authors_text":"Stephan J. Huber, Thomas Konstandin","cross_cats":[],"headline":"","license":"","primary_cat":"hep-ph","submitted_at":"2006-03-10T10:06:09Z","title":"Numerical Approach to Multi Dimensional Phase Transitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-ph/0603081","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":"sha256:12031a087128af807ac3110b2b863f94a075e7b6a99a52b7469322d186bca88c","target":"record","created_at":"2026-07-04T17:01:41Z","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":"e8d464379d64e39d44438bebb8473226f949929396c76565135f22a81a1d7199","cross_cats_sorted":[],"license":"","primary_cat":"hep-ph","submitted_at":"2006-03-10T10:06:09Z","title_canon_sha256":"a91cb261baa52e928de2104c7051cf36382bccb5f73bb83edb758eb94293e4a9"},"schema_version":"1.0","source":{"id":"hep-ph/0603081","kind":"arxiv","version":2}},"canonical_sha256":"c818ce02ad1adf590fece2adcfea318e128a1d0e17aaacc553534e9fa77b386d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c818ce02ad1adf590fece2adcfea318e128a1d0e17aaacc553534e9fa77b386d","first_computed_at":"2026-07-04T17:01:41.590895Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:01:41.590895Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YGnVhDoe2F2UyMa5Bneuh9z1Kk5xT+QOaqzaH1mpoDaexN+EhbPPJYvxOWNSY6i48df2vMW/+xNUdDLpigwVCQ==","signature_status":"signed_v1","signed_at":"2026-07-04T17:01:41.591228Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-ph/0603081","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:12031a087128af807ac3110b2b863f94a075e7b6a99a52b7469322d186bca88c","sha256:dd446d848bfd07537c6f8166b48bb7bf46aa4512e9e005740e7d3a6b471be1ab"],"state_sha256":"f6fc20865bc80beb1924f9d5d841cea075088f292012cc9e94edf06fb51f0148"}