{"paper":{"title":"Gr\\\"unwald--Letnikov Memory Truncation in a Fractional Duffing Oscillator: Coherence Loss and Effective Delay Complexity","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"Truncating the Grünwald-Letnikov memory in a fractional Duffing oscillator produces effective delay dynamics whose spectral structure sets both coherence loss and delay complexity.","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Mattia Coccolo","submitted_at":"2026-05-05T10:01:37Z","abstract_excerpt":"We investigate the dynamical and analytical consequences of truncating the Gr\\\"unwald--Letnikov memory term in a fractional Duffing oscillator. The truncated memory is treated not merely as a computational approximation, but as a finite-memory modification of the underlying dynamical system. We define a coherence-loss time from direct comparisons between full-memory and truncated-memory trajectories, and use it to extract critical truncation thresholds in parameter planes involving the forcing amplitude and the fractional order. The results reveal strongly non-monotonic memory thresholds, show"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The truncated GL kernel emerges as an intermediate object between distributed fractional memory and delay-type dynamics, with a local spectral structure that controls both coherence loss and effective delay complexity.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That direct trajectory comparisons produce a robust coherence-loss time that reliably identifies critical truncation thresholds independent of numerical artifacts or initial conditions.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Truncating Grünwald-Letnikov memory in fractional Duffing oscillators yields non-monotonic coherence-loss thresholds and an effective delay-complexity measure r_min from positive-delay kernel approximations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Truncating the Grünwald-Letnikov memory in a fractional Duffing oscillator produces effective delay dynamics whose spectral structure sets both coherence loss and delay complexity.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4fb465d9cbfa8fade9a61cf17ab40ead1f8e8e094c2a000eab7d3aa3cb2fc88b"},"source":{"id":"2605.03587","kind":"arxiv","version":2},"verdict":{"id":"d3471767-2ee6-4647-8c06-8c87d1b9d18f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-09T15:39:56.477475Z","strongest_claim":"The truncated GL kernel emerges as an intermediate object between distributed fractional memory and delay-type dynamics, with a local spectral structure that controls both coherence loss and effective delay complexity.","one_line_summary":"Truncating Grünwald-Letnikov memory in fractional Duffing oscillators yields non-monotonic coherence-loss thresholds and an effective delay-complexity measure r_min from positive-delay kernel approximations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That direct trajectory comparisons produce a robust coherence-loss time that reliably identifies critical truncation thresholds independent of numerical artifacts or initial conditions.","pith_extraction_headline":"Truncating the Grünwald-Letnikov memory in a fractional Duffing oscillator produces effective delay dynamics whose spectral structure sets both coherence loss and delay complexity."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.03587/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T13:38:38.056279Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T01:01:21.112522Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T15:12:50.722593Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"0bbecea1eab734913c7595686958f6c3a3b883b23df9b2335a2f347a99eac1c7"},"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"}