{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FDR2VX2MGCQTN4ASOEOPQAKGAJ","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":"9ef06b806ce3c5cbb7b2bdba98eb0847cb17b6cb8fb7f28f1fdff826a83fb61d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-06-25T16:46:55Z","title_canon_sha256":"a377df99490d8ba93e86685447e3d4af2adf1cc78b77c4473cf7b6cee1213177"},"schema_version":"1.0","source":{"id":"2606.27263","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.27263","created_at":"2026-06-26T01:16:16Z"},{"alias_kind":"arxiv_version","alias_value":"2606.27263v1","created_at":"2026-06-26T01:16:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.27263","created_at":"2026-06-26T01:16:16Z"},{"alias_kind":"pith_short_12","alias_value":"FDR2VX2MGCQT","created_at":"2026-06-26T01:16:16Z"},{"alias_kind":"pith_short_16","alias_value":"FDR2VX2MGCQTN4AS","created_at":"2026-06-26T01:16:16Z"},{"alias_kind":"pith_short_8","alias_value":"FDR2VX2M","created_at":"2026-06-26T01:16:16Z"}],"graph_snapshots":[{"event_id":"sha256:e5da84994b5f9c1fbcb881fa532193cc8b617faba8b2de61b0d8e58ced96ec41","target":"graph","created_at":"2026-06-26T01:16:16Z","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/2606.27263/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Loop-erased random walks (LERW), the $O(n)$-model at ${n=-2}$ and Laplacian random walks (LRW) are three realizations of the same random process. While this equivalence holds on any graph, renormalization is possible only via the $O(-2)$-model. To generalize LRWs to $b$-LRWs or to Diffusion Limited Aggregation (DLA), a field theory directly on the Laplacian growth process is necessary. Here we construct an exact lattice action for LRWs and show that its perturbative expansion equals that of LERWs. We then generalize this approach to $b$-LRWs and DLA.","authors_text":"Assaf Shapira, Kay Joerg Wiese, Paolo Pisapia","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-06-25T16:46:55Z","title":"Field theories for Laplacian Growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.27263","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":"sha256:0157b50d8a32c029fcb77186830b6690d7fdfa6cf6804b42bf2e9b19b230cf13","target":"record","created_at":"2026-06-26T01:16:16Z","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":"9ef06b806ce3c5cbb7b2bdba98eb0847cb17b6cb8fb7f28f1fdff826a83fb61d","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-06-25T16:46:55Z","title_canon_sha256":"a377df99490d8ba93e86685447e3d4af2adf1cc78b77c4473cf7b6cee1213177"},"schema_version":"1.0","source":{"id":"2606.27263","kind":"arxiv","version":1}},"canonical_sha256":"28e3aadf4c30a136f012711cf801460278e34e503524e60b27b738bf93742f59","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28e3aadf4c30a136f012711cf801460278e34e503524e60b27b738bf93742f59","first_computed_at":"2026-06-26T01:16:16.802853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-26T01:16:16.802853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jnB8WSNuOgUz0YyAcT4OWl9DX+F+Cg+xDa8SNRzWFlnijW/AeMdc6iOerUeJfBF8RDPHJnLSiaqK+4LrSXRFCg==","signature_status":"signed_v1","signed_at":"2026-06-26T01:16:16.803221Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.27263","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0157b50d8a32c029fcb77186830b6690d7fdfa6cf6804b42bf2e9b19b230cf13","sha256:e5da84994b5f9c1fbcb881fa532193cc8b617faba8b2de61b0d8e58ced96ec41"],"state_sha256":"4568f00f05cec0e65161fea8d27bb441877c6ca82df31fe37f7b7a4ee0012cc0"}