{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:ORVA7NG3AZHC5SX3IJA2BEXAFL","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":"56d16c5304e4cfe7838394e409d417040d3bb4d2ddb3e2d943f0a1c123da8dac","cross_cats_sorted":["hep-lat","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-15T10:54:56Z","title_canon_sha256":"be167ee1b6ae4eab6542f70f65c7974ee596f95f5acff4654eb25d3b0de96fa5"},"schema_version":"1.0","source":{"id":"2605.15841","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.15841","created_at":"2026-05-20T00:01:21Z"},{"alias_kind":"arxiv_version","alias_value":"2605.15841v1","created_at":"2026-05-20T00:01:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.15841","created_at":"2026-05-20T00:01:21Z"},{"alias_kind":"pith_short_12","alias_value":"ORVA7NG3AZHC","created_at":"2026-05-20T00:01:21Z"},{"alias_kind":"pith_short_16","alias_value":"ORVA7NG3AZHC5SX3","created_at":"2026-05-20T00:01:21Z"},{"alias_kind":"pith_short_8","alias_value":"ORVA7NG3","created_at":"2026-05-20T00:01:21Z"}],"graph_snapshots":[{"event_id":"sha256:8d7a1c435ff04b342b289d28d25a15dec35448f3467ddde9df26a7901bbcd0fb","target":"graph","created_at":"2026-05-20T00:01:21Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"The critical non-equilibrium relaxation of the percolation order parameter is governed by a dynamical exponent z_p ≃ 2.6, consistent with that associated with the energy density, z_c. Importantly, the value of z_p is robust with respect to the initial quench condition and the choice of geometrical objects."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"That time-dependent finite-size scaling can be reliably applied to the percolation order parameter and geometric observables in this model, even in the absence of a local order parameter and without detailed knowledge of finite-size corrections or equilibration criteria."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Quench dynamics of the 3D Z2 gauge model yield a dynamical exponent z_p ≈ 2.6 for the percolation order parameter that matches the energy-density exponent and remains robust across initial conditions and geometric observables."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"In Wegner's Z2 gauge model the percolation order parameter relaxes at criticality with dynamical exponent z_p approximately 2.6, the same value found for the energy density."}],"snapshot_sha256":"ecb4415c9657b98d7ec1f374fba1c91c17330afa6911516f5601cb349d25bd6c"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"469057b3c5afdcc74e0c184a5e5be3a20151ceb8402b2e5e790f656f77af3586"},"integrity":{"available":true,"clean":true,"detectors_run":[{"findings_count":0,"name":"doi_title_agreement","ran_at":"2026-05-19T19:31:19.085813Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"doi_compliance","ran_at":"2026-05-19T19:31:11.914014Z","status":"completed","version":"1.0.0"},{"findings_count":0,"name":"ai_meta_artifact","ran_at":"2026-05-19T17:33:48.713680Z","status":"skipped","version":"1.0.0"},{"findings_count":0,"name":"claim_evidence","ran_at":"2026-05-19T17:21:55.843299Z","status":"completed","version":"1.0.0"}],"endpoint":"/pith/2605.15841/integrity.json","findings":[],"snapshot_sha256":"1aacb41fad030fda328d082b5543a574201dda024f638b0866c9b46c57c1460f","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Wegner's $\\mathbb{Z}_2$ gauge model is the earliest formulation of pure lattice gauge theory and predicts the topological nature of the confinement-deconfinement transition. In three dimensions ($D=3$), the equilibrium critical behavior of the model is understood in terms of geometrically defined objects, namely loop excitations and Fortuin-Kasteleyn (FK) clusters. This work investigates the critical quench dynamics of this model from a geometric perspective, following quenches from both a high-temperature percolation phase and the zero-temperature ground state. Using time-dependent finite-siz","authors_text":"Leticia F. Cugliandolo, Marco Picco, Ramgopal Agrawal","cross_cats":["hep-lat","hep-th"],"headline":"In Wegner's Z2 gauge model the percolation order parameter relaxes at criticality with dynamical exponent z_p approximately 2.6, the same value found for the energy density.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-15T10:54:56Z","title":"Critical quench dynamics of Wegner's $\\mathbb{Z}_2$ gauge model: a geometric perspective"},"references":{"count":65,"internal_anchors":1,"resolved_work":65,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"The critical relaxation of the percolation order parameter is governed by a dynamical exponentz p ≃2.6, consistent with the corresponding exponent for energy relaxation, zc","work_id":"2bf853d2-841b-4791-8136-c626eeb0a975","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"The value ofz p is robust, within error bars, with respect to both the quench protocol and the choice of geometrically defined objects","work_id":"ee05a01a-c2ea-4ff6-a29d-74196cac8724","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"The time evolution of the number statisticsN(s, t) of geometrical objects of sizes, following a quench from the percolation phase, supports a dynamic scaling framework governed by a time-dependent len","work_id":"2de2f7bb-ba1f-4432-83bd-770319f77033","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"We structure this paper as follows","work_id":"86df0935-f375-4613-9c30-b09a19274d91","year":null},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"At early times, large multiple-spanning objects shrink so that smaller ones can accom- modate","work_id":"c2759168-7166-4dc5-8ab0-43ac182cedcd","year":null}],"snapshot_sha256":"5db9fee82d4ff517432c2024cac7dbc0de29835c518f04754da4223a5d109197"},"source":{"id":"2605.15841","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T19:23:38.518554Z","id":"109c0d2a-aa57-4493-bd7c-44184cc2d9c4","model_set":{"reader":"grok-4.3"},"one_line_summary":"Quench dynamics of the 3D Z2 gauge model yield a dynamical exponent z_p ≈ 2.6 for the percolation order parameter that matches the energy-density exponent and remains robust across initial conditions and geometric observables.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"In Wegner's Z2 gauge model the percolation order parameter relaxes at criticality with dynamical exponent z_p approximately 2.6, the same value found for the energy density.","strongest_claim":"The critical non-equilibrium relaxation of the percolation order parameter is governed by a dynamical exponent z_p ≃ 2.6, consistent with that associated with the energy density, z_c. Importantly, the value of z_p is robust with respect to the initial quench condition and the choice of geometrical objects.","weakest_assumption":"That time-dependent finite-size scaling can be reliably applied to the percolation order parameter and geometric observables in this model, even in the absence of a local order parameter and without detailed knowledge of finite-size corrections or equilibration criteria."}},"verdict_id":"109c0d2a-aa57-4493-bd7c-44184cc2d9c4"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cb186bfb60ba934cc182eca4dbe574e00df702ba3ea20bd9b109739338ed41f5","target":"record","created_at":"2026-05-20T00:01:21Z","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":"56d16c5304e4cfe7838394e409d417040d3bb4d2ddb3e2d943f0a1c123da8dac","cross_cats_sorted":["hep-lat","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2026-05-15T10:54:56Z","title_canon_sha256":"be167ee1b6ae4eab6542f70f65c7974ee596f95f5acff4654eb25d3b0de96fa5"},"schema_version":"1.0","source":{"id":"2605.15841","kind":"arxiv","version":1}},"canonical_sha256":"746a0fb4db064e2ecafb4241a092e02ae0e904878408b331ad3831705061aa0f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"746a0fb4db064e2ecafb4241a092e02ae0e904878408b331ad3831705061aa0f","first_computed_at":"2026-05-20T00:01:21.214753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:21.214753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hCefHwykMsYac43mXIXYnKq54J4iUSyCgqExjxc6LF0S7EaE7u6Hmovap9mDdMcRlKGl9EoDjMSyyiHTWZw6Bw==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:21.215449Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.15841","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb186bfb60ba934cc182eca4dbe574e00df702ba3ea20bd9b109739338ed41f5","sha256:8d7a1c435ff04b342b289d28d25a15dec35448f3467ddde9df26a7901bbcd0fb"],"state_sha256":"2b91051cd112a998732452c2a506f579ec787c5308ec8fd7ac7b2cad02544354"}