{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T18:12:26Z","timestamp":1788459146852,"version":"build-2803163510"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T00:00:00Z","timestamp":1788393600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Natural-language documents contain many causal claims, but those claims are unstable under paraphrase, granularity shifts, and contextual drift. A collection may express one mechanism in many surface forms, while neighboring studies may agree locally yet fail to glue globally because relation families, polarities, temporal scopes, or regimes differ. This paper studies that post-extraction problem through Democritus, an implemented system for extracting, normalizing, localizing, and diagnosing causal discourse. We do not claim to identify ground-truth causal structure from text alone. Instead, we formulate the post-extraction layer as a homotopical repair problem for a non-compositional causal-discourse sketch. A normalization functor induces a class of weak equivalences on textual mentions; we prove that these data form a relative category with two-out-of-three and that normalization factors through its localization. Strict repair requires a corpus diagram to satisfy the sketch exactly, whereas homotopy repair asks for a weakly equivalent diagram that factors coherently after localization. We also define the conditions under which grounded discourse localization maps functorially into the observational-equivalence spaces of causal models studied by higher algebraic K-theory. The implementation approximates these formal constructions through normalized claim classes, an observed compatibility complex, regime-sensitive gluing, and provenance-preserving database artifacts. On a frozen 404-passage AltLex\/UniCausal comparison, a restricted verbatim-span Democritus extractor attains 57.1% causal-classification F1 and 39.1% macro span F1, compared with 59.2% and 43.6% for the public UniCausal baseline. This similar classification F1 reflects a clear precision\u2013recall tradeoff: Democritus achieves higher recall (80.9% versus 68.7%) but lower precision (44.1% versus 52.0%). Case studies on Emperor-penguin climate discourse, Mediterranean-diet studies, red-wine cardiovascular studies, and rising-ocean-temperature corpora expose both stable repeated mechanisms and cases where local causal claims cannot be assembled into one coherent corpus-level account.<\/jats:p>","DOI":"10.3390\/e28090986","type":"journal-article","created":{"date-parts":[[2026,9,3]],"date-time":"2026-09-03T17:13:25Z","timestamp":1788455605000},"page":"986","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Democritus: Homotopy-Localized Causal Discourse Extraction from Language"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6507-9109","authenticated-orcid":false,"given":"Sridhar","family":"Mahadevan","sequence":"first","affiliation":[{"name":"Adobe Research, 345 Park Avenue, San Jose, CA 95110, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,3]]},"reference":[{"key":"ref_1","unstructured":"Mahadevan, S. 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