{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:3WL6DNB6E6ELICNRFFYJOIYMSS","short_pith_number":"pith:3WL6DNB6","canonical_record":{"source":{"id":"cond-mat/0409439","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.soft","submitted_at":"2004-09-17T05:39:07Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"1b6be5500b39f2e96587e118455d70d3476e37f8315b83a7c72a5d85ed61ca89","abstract_canon_sha256":"464c2ef2675872f61d89c8a90e873592a7ef64bb7ee3c7ea2719c2e9914475e8"},"schema_version":"1.0"},"canonical_sha256":"dd97e1b43e2788b409b1297097230c94b5dedbd3e32f64f8f8c5e5f024062aa2","source":{"kind":"arxiv","id":"cond-mat/0409439","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0409439","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0409439v1","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0409439","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"pith_short_12","alias_value":"3WL6DNB6E6EL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"3WL6DNB6E6ELICNR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"3WL6DNB6","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:3WL6DNB6E6ELICNRFFYJOIYMSS","target":"record","payload":{"canonical_record":{"source":{"id":"cond-mat/0409439","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"cond-mat.soft","submitted_at":"2004-09-17T05:39:07Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"1b6be5500b39f2e96587e118455d70d3476e37f8315b83a7c72a5d85ed61ca89","abstract_canon_sha256":"464c2ef2675872f61d89c8a90e873592a7ef64bb7ee3c7ea2719c2e9914475e8"},"schema_version":"1.0"},"canonical_sha256":"dd97e1b43e2788b409b1297097230c94b5dedbd3e32f64f8f8c5e5f024062aa2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:39:57.718133Z","signature_b64":"HH4zDNDq5U4kXbnXXLLJ8NWH2qcrZ/hkshQSpJ2r2krmVEkHNwdKaOg84UMlRtcSWFkeuQyDAn7fLJCCbsc1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dd97e1b43e2788b409b1297097230c94b5dedbd3e32f64f8f8c5e5f024062aa2","last_reissued_at":"2026-05-18T01:39:57.717682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:39:57.717682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"cond-mat/0409439","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":"2026-05-18T01:39:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tE5NKLZwG94T/LX3ob7mnkmRu7k1AntGHVvBLFquH5e1nPraLbfxtT3mm76BCmf7dfOkbYdqEMD/GwRCC3WrAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:20:50.405618Z"},"content_sha256":"29e9d26f3e283498bac09b796b0bd0b1b636428164c8d60f814ed66eff57929c","schema_version":"1.0","event_id":"sha256:29e9d26f3e283498bac09b796b0bd0b1b636428164c8d60f814ed66eff57929c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:3WL6DNB6E6ELICNRFFYJOIYMSS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Conformal mapping methods for interfacial dynamics","license":"","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.soft","authors_text":"Darren Crowdy (Mathematics, Imperial College, London), Martin Z. Bazant (Mathematics, MIT)","submitted_at":"2004-09-17T05:39:07Z","abstract_excerpt":"The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the article begins with an overview of continuous conformal-map dynamics. This includes problems of interfacial motion driven by harmonic fields (such as viscous fingering and void electromigration), bi-harmonic fields (such as viscous sintering and elastic pore evolution), and non-harmonic, conformally invariant fields (such as growth by advection-diffusion and e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0409439","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":"2026-05-18T01:39:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LjVsY+5ETwUUifTmJYjxV7fSW9fqNHpuGvfMVNkOApqGNIOr/f3oMj6PP1ME4W0hi1Qsa3Y0ovVCuNUvKdPICA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T09:20:50.406039Z"},"content_sha256":"9275c66fb33b68b045c1a54987ad84e34a54db37ef62ddfa7bc340b16076d5e7","schema_version":"1.0","event_id":"sha256:9275c66fb33b68b045c1a54987ad84e34a54db37ef62ddfa7bc340b16076d5e7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3WL6DNB6E6ELICNRFFYJOIYMSS/bundle.json","state_url":"https://pith.science/pith/3WL6DNB6E6ELICNRFFYJOIYMSS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3WL6DNB6E6ELICNRFFYJOIYMSS/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":"2026-06-11T09:20:50Z","links":{"resolver":"https://pith.science/pith/3WL6DNB6E6ELICNRFFYJOIYMSS","bundle":"https://pith.science/pith/3WL6DNB6E6ELICNRFFYJOIYMSS/bundle.json","state":"https://pith.science/pith/3WL6DNB6E6ELICNRFFYJOIYMSS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3WL6DNB6E6ELICNRFFYJOIYMSS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:3WL6DNB6E6ELICNRFFYJOIYMSS","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":"464c2ef2675872f61d89c8a90e873592a7ef64bb7ee3c7ea2719c2e9914475e8","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.soft","submitted_at":"2004-09-17T05:39:07Z","title_canon_sha256":"1b6be5500b39f2e96587e118455d70d3476e37f8315b83a7c72a5d85ed61ca89"},"schema_version":"1.0","source":{"id":"cond-mat/0409439","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cond-mat/0409439","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"arxiv_version","alias_value":"cond-mat/0409439v1","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cond-mat/0409439","created_at":"2026-05-18T01:39:57Z"},{"alias_kind":"pith_short_12","alias_value":"3WL6DNB6E6EL","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"3WL6DNB6E6ELICNR","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"3WL6DNB6","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:9275c66fb33b68b045c1a54987ad84e34a54db37ef62ddfa7bc340b16076d5e7","target":"graph","created_at":"2026-05-18T01:39:57Z","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":"The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the article begins with an overview of continuous conformal-map dynamics. This includes problems of interfacial motion driven by harmonic fields (such as viscous fingering and void electromigration), bi-harmonic fields (such as viscous sintering and elastic pore evolution), and non-harmonic, conformally invariant fields (such as growth by advection-diffusion and e","authors_text":"Darren Crowdy (Mathematics, Imperial College, London), Martin Z. Bazant (Mathematics, MIT)","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"","primary_cat":"cond-mat.soft","submitted_at":"2004-09-17T05:39:07Z","title":"Conformal mapping methods for interfacial dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cond-mat/0409439","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":"sha256:29e9d26f3e283498bac09b796b0bd0b1b636428164c8d60f814ed66eff57929c","target":"record","created_at":"2026-05-18T01:39:57Z","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":"464c2ef2675872f61d89c8a90e873592a7ef64bb7ee3c7ea2719c2e9914475e8","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"cond-mat.soft","submitted_at":"2004-09-17T05:39:07Z","title_canon_sha256":"1b6be5500b39f2e96587e118455d70d3476e37f8315b83a7c72a5d85ed61ca89"},"schema_version":"1.0","source":{"id":"cond-mat/0409439","kind":"arxiv","version":1}},"canonical_sha256":"dd97e1b43e2788b409b1297097230c94b5dedbd3e32f64f8f8c5e5f024062aa2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dd97e1b43e2788b409b1297097230c94b5dedbd3e32f64f8f8c5e5f024062aa2","first_computed_at":"2026-05-18T01:39:57.717682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:39:57.717682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HH4zDNDq5U4kXbnXXLLJ8NWH2qcrZ/hkshQSpJ2r2krmVEkHNwdKaOg84UMlRtcSWFkeuQyDAn7fLJCCbsc1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T01:39:57.718133Z","signed_message":"canonical_sha256_bytes"},"source_id":"cond-mat/0409439","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:29e9d26f3e283498bac09b796b0bd0b1b636428164c8d60f814ed66eff57929c","sha256:9275c66fb33b68b045c1a54987ad84e34a54db37ef62ddfa7bc340b16076d5e7"],"state_sha256":"a6cc969afc7a293b0327f042bb5ddafa8812b4fb13d5c3798d80b8ac3438425b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ckeaGsaVW7xE6XBfuL6CwQtevMSA8ehZxpzmgjR7gx/I23aMWF1dE49Vf6V1zxAix974C7zyZCtrwnRhg8fVBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T09:20:50.408173Z","bundle_sha256":"7c9a5576beabae6d23491bc0ac9577b5b29b9e2cdd07da9e8af36957fa7d3ac5"}}