{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:GHY5II7IQKARNO72CIW5K52TFI","short_pith_number":"pith:GHY5II7I","canonical_record":{"source":{"id":"astro-ph/0012447","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2000-12-20T20:09:42Z","cross_cats_sorted":[],"title_canon_sha256":"15cbb4505e3f798289f357fbc71e1e223dd62635d66b1dd99f88b619332c3213","abstract_canon_sha256":"4e2f1f530be057e6644bf859db8b99906ffe0d021e307f153a153fe3d0af79b3"},"schema_version":"1.0"},"canonical_sha256":"31f1d423e8828116bbfa122dd577532a35730875100380f6a6f7559b828c056c","source":{"kind":"arxiv","id":"astro-ph/0012447","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0012447","created_at":"2026-07-04T16:17:50Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0012447v2","created_at":"2026-07-04T16:17:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0012447","created_at":"2026-07-04T16:17:50Z"},{"alias_kind":"pith_short_12","alias_value":"GHY5II7IQKAR","created_at":"2026-07-04T16:17:50Z"},{"alias_kind":"pith_short_16","alias_value":"GHY5II7IQKARNO72","created_at":"2026-07-04T16:17:50Z"},{"alias_kind":"pith_short_8","alias_value":"GHY5II7I","created_at":"2026-07-04T16:17:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:GHY5II7IQKARNO72CIW5K52TFI","target":"record","payload":{"canonical_record":{"source":{"id":"astro-ph/0012447","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"astro-ph","submitted_at":"2000-12-20T20:09:42Z","cross_cats_sorted":[],"title_canon_sha256":"15cbb4505e3f798289f357fbc71e1e223dd62635d66b1dd99f88b619332c3213","abstract_canon_sha256":"4e2f1f530be057e6644bf859db8b99906ffe0d021e307f153a153fe3d0af79b3"},"schema_version":"1.0"},"canonical_sha256":"31f1d423e8828116bbfa122dd577532a35730875100380f6a6f7559b828c056c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T16:17:50.178913Z","signature_b64":"Yl26RQ0wmodYQiwBG3WH3HHyrIHSj+sHuASDbFTWkmmnnQqHtTxyEg015ElvPzh6msJS0r2OIykeqdLyL3ioDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31f1d423e8828116bbfa122dd577532a35730875100380f6a6f7559b828c056c","last_reissued_at":"2026-07-04T16:17:50.178517Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T16:17:50.178517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"astro-ph/0012447","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":"2026-07-04T16:17:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nJgF/1NSwHT4FpE5VtCd892FvEXe1ZhlVl/pwl+IKfOe1mCHPQek4+yBJ4kMolKM/ipKBUe31sOHj9sFynMnBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:41:57.100685Z"},"content_sha256":"0f838a14ec460979c56e859b561fc7bcb4205dc952c8764ce3a1ab962f7d79e1","schema_version":"1.0","event_id":"sha256:0f838a14ec460979c56e859b561fc7bcb4205dc952c8764ce3a1ab962f7d79e1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:GHY5II7IQKARNO72CIW5K52TFI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Numerical Analysis of Magnetic Field Amplification by Turbulence","license":"","headline":"","cross_cats":[],"primary_cat":"astro-ph","authors_text":"Hongsong Chou","submitted_at":"2000-12-20T20:09:42Z","abstract_excerpt":"We apply a Fourier spectral numerical method to 3D incompressible MHD turbulence with a magnetic Prandtl number $Pr \\geq 1$. We examine the processes by which an initially weak, large-scale seed magnetic field and an initially weak, small-scale, impulse-like seed magnetic field are amplified. We find that in both cases the magnetic energy spectrum grows at all scales. The growth rates at different amplification stages are analyzed. For a large-scale seed magnetic field, the magnetic energy density grows as $\\sim t^2$ for the first few turbulence eddy turnover times, followed by a dynamic growt"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0012447","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/astro-ph/0012447/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T16:17:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ptBzoHqN66eH0XXYuqNGmpVWar48rEEJQJZBZv5326bDENo9ugY1ArTPkXzFPSCK5qqnrqbiu/1U8EF0RxWADw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T08:41:57.101054Z"},"content_sha256":"7cad0210ca3e427f570c29b850b506bef1bcdd4cd36972925e84b0273f3c31fc","schema_version":"1.0","event_id":"sha256:7cad0210ca3e427f570c29b850b506bef1bcdd4cd36972925e84b0273f3c31fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GHY5II7IQKARNO72CIW5K52TFI/bundle.json","state_url":"https://pith.science/pith/GHY5II7IQKARNO72CIW5K52TFI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GHY5II7IQKARNO72CIW5K52TFI/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":"2026-07-05T08:41:57Z","links":{"resolver":"https://pith.science/pith/GHY5II7IQKARNO72CIW5K52TFI","bundle":"https://pith.science/pith/GHY5II7IQKARNO72CIW5K52TFI/bundle.json","state":"https://pith.science/pith/GHY5II7IQKARNO72CIW5K52TFI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GHY5II7IQKARNO72CIW5K52TFI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:GHY5II7IQKARNO72CIW5K52TFI","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":"4e2f1f530be057e6644bf859db8b99906ffe0d021e307f153a153fe3d0af79b3","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2000-12-20T20:09:42Z","title_canon_sha256":"15cbb4505e3f798289f357fbc71e1e223dd62635d66b1dd99f88b619332c3213"},"schema_version":"1.0","source":{"id":"astro-ph/0012447","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"astro-ph/0012447","created_at":"2026-07-04T16:17:50Z"},{"alias_kind":"arxiv_version","alias_value":"astro-ph/0012447v2","created_at":"2026-07-04T16:17:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.astro-ph/0012447","created_at":"2026-07-04T16:17:50Z"},{"alias_kind":"pith_short_12","alias_value":"GHY5II7IQKAR","created_at":"2026-07-04T16:17:50Z"},{"alias_kind":"pith_short_16","alias_value":"GHY5II7IQKARNO72","created_at":"2026-07-04T16:17:50Z"},{"alias_kind":"pith_short_8","alias_value":"GHY5II7I","created_at":"2026-07-04T16:17:50Z"}],"graph_snapshots":[{"event_id":"sha256:7cad0210ca3e427f570c29b850b506bef1bcdd4cd36972925e84b0273f3c31fc","target":"graph","created_at":"2026-07-04T16:17:50Z","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/astro-ph/0012447/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We apply a Fourier spectral numerical method to 3D incompressible MHD turbulence with a magnetic Prandtl number $Pr \\geq 1$. We examine the processes by which an initially weak, large-scale seed magnetic field and an initially weak, small-scale, impulse-like seed magnetic field are amplified. We find that in both cases the magnetic energy spectrum grows at all scales. The growth rates at different amplification stages are analyzed. For a large-scale seed magnetic field, the magnetic energy density grows as $\\sim t^2$ for the first few turbulence eddy turnover times, followed by a dynamic growt","authors_text":"Hongsong Chou","cross_cats":[],"headline":"","license":"","primary_cat":"astro-ph","submitted_at":"2000-12-20T20:09:42Z","title":"Numerical Analysis of Magnetic Field Amplification by Turbulence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"astro-ph/0012447","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":"sha256:0f838a14ec460979c56e859b561fc7bcb4205dc952c8764ce3a1ab962f7d79e1","target":"record","created_at":"2026-07-04T16:17:50Z","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":"4e2f1f530be057e6644bf859db8b99906ffe0d021e307f153a153fe3d0af79b3","cross_cats_sorted":[],"license":"","primary_cat":"astro-ph","submitted_at":"2000-12-20T20:09:42Z","title_canon_sha256":"15cbb4505e3f798289f357fbc71e1e223dd62635d66b1dd99f88b619332c3213"},"schema_version":"1.0","source":{"id":"astro-ph/0012447","kind":"arxiv","version":2}},"canonical_sha256":"31f1d423e8828116bbfa122dd577532a35730875100380f6a6f7559b828c056c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"31f1d423e8828116bbfa122dd577532a35730875100380f6a6f7559b828c056c","first_computed_at":"2026-07-04T16:17:50.178517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T16:17:50.178517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yl26RQ0wmodYQiwBG3WH3HHyrIHSj+sHuASDbFTWkmmnnQqHtTxyEg015ElvPzh6msJS0r2OIykeqdLyL3ioDw==","signature_status":"signed_v1","signed_at":"2026-07-04T16:17:50.178913Z","signed_message":"canonical_sha256_bytes"},"source_id":"astro-ph/0012447","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0f838a14ec460979c56e859b561fc7bcb4205dc952c8764ce3a1ab962f7d79e1","sha256:7cad0210ca3e427f570c29b850b506bef1bcdd4cd36972925e84b0273f3c31fc"],"state_sha256":"95657903e4c8e6769a287f1ea7ecb33fcffc233af636917d8883dd66547a4e7a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JCE+wlPMrlQmqJkvK4hkaPvqJkJITsCJ4oCPQ+bYW9fT2tvJ7oeJuAbzGR54UMHm4CobhTBLbqIxdSLdRBNyCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T08:41:57.103200Z","bundle_sha256":"daa905e4ef5f53952d95875aedde48696ee15c231d83381a4f3c302d0da30b9d"}}