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We define an energy-weighted correlation length that remains finite at the classical site occupation threshold (p_c(ε=0)) and shrinks with increasing ε, capturing the energetic suppression of large-scale connectivity.","weakest_assumption":"The real-space RG with Kadanoff block recursions accurately tracks the continuous evolution of the correlation-length exponent ν from 1/2 to 4/3 to 1 and matches Coulomb-gas predictions for loop models without requiring additional parameters or post-hoc adjustments specific to the energy term."}},"verdict_id":"305f7100-a8fd-44ed-aef5-218f825a5f58"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ce145787168dedffd63fb732b772b1dc865592755a73c430a52441f5ac22773e","target":"record","created_at":"2026-05-20T00:05:54Z","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":"3d76627c954c44d41b7599c00c4468051ed2233d1fa58956eaf174378b51363a","cross_cats_sorted":["cond-mat.dis-nn"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-18T12:30:51Z","title_canon_sha256":"66d0abc3c176b044f2e36524e9b7c2c2f6ce18e154a1b23fba504e3324012bac"},"schema_version":"1.0","source":{"id":"2605.18312","kind":"arxiv","version":1}},"canonical_sha256":"1702ba31e77b6257e545e1d4906747008034e37ba8889b25e4ca19c90df36536","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1702ba31e77b6257e545e1d4906747008034e37ba8889b25e4ca19c90df36536","first_computed_at":"2026-05-20T00:05:54.552113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:05:54.552113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YXU+KnZttznx5lkb+hvnk85B4YYvghZLDLx63YpzObdt6KxOD7eLC7eaGimFViq6xqYr2bmZrj+0OXubqJ2MAw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:05:54.552808Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.18312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce145787168dedffd63fb732b772b1dc865592755a73c430a52441f5ac22773e","sha256:6c26138135b81d09aef88a9bf3ecb3f3636f2453e234f79ce8ecfb46d3522388"],"state_sha256":"de2098fb47606a99393b3e3fba403de4c38cab042d05eab5d429af3f808d5d47"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VMb1BxdoWUY3Eyt5CJD/qnfLdd3Na3d2t7MmIvl52/dPRkvHUoIFwtMWF50nyoX+TeJQHD7Jfa0uVu/m+As+DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T19:26:18.862812Z","bundle_sha256":"4b5559d8032d00ecdd89fe7c5818dc7446531d2ac14e27751a653200270b31ba"}}