Iterative Epistemic Repair in a Brain-Inspired Artificial Reasoning System: A Case Study in Mathematical Claim Correction
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2026
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| _version_ | 1866901455906013184 |
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| author | Skye, Laflamme |
| author_facet | Skye, Laflamme |
| contents | <p>This publication documents a case study of iterative epistemic repair in Lilith, a brain-inspired artificial reasoning system developed at RavenNest Scientific. The study analyzes a five-round mathematical correction session in which Lilith initially generated an overstrong conjectural route from Pell-type trace data on <span class="katex"><span class="katex-mathml">Γ0(2)\H</span><span class="katex-html"><span class="base"><span class="mord">Γ<span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span><span class="mord">\</span><span class="mord mathbb">H</span></span></span></span> toward the Riemann Hypothesis, then revised the work under targeted critique.</p> <p>Across the session, the system corrected concrete arithmetic errors, repaired malformed LaTeX, refined the distinction between primitive and non-primitive geodesics, clarified the role of the compactified modular curve <span class="katex"><span class="katex-mathml">X0(2)</span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">X</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span></span></span></span>, and ultimately contracted the claim to a defensible diagnostic note. The final mathematical substrate shows that Pell-type trace data yield candidate geodesic lengths, but do not by themselves enumerate primitive <span class="katex"><span class="katex-mathml">Γ0(2)</span><span class="katex-html"><span class="base"><span class="mord">Γ<span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span></span></span></span>-geodesics, and that term-wise positivity of a Selberg-type geometric sum does not imply Weil positivity for the Riemann zeta function.</p> <p>The paper argues that the transcript provides behavioral evidence of iterative epistemic repair: the capacity of an artificial system to accept falsification, revise claims downward, correct formal errors, and preserve a coherent mathematical through-line. The authors explicitly separate this behavioral claim from stronger architectural or consciousness claims, which require independent evidence.</p> <p>Keywords</p> <p>artificial reasoning, epistemic repair, mathematical verification, brain-inspired AI, Riemann Hypothesis, Selberg trace formula, <span class="katex"><span class="katex-mathml">Γ0(2)</span><span class="katex-html"><span class="base"><span class="mord">Γ<span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span></span></span></span>, Pell equations, AI evaluation, claim correction</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19929774 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Iterative Epistemic Repair in a Brain-Inspired Artificial Reasoning System: A Case Study in Mathematical Claim Correction Skye, Laflamme <p>This publication documents a case study of iterative epistemic repair in Lilith, a brain-inspired artificial reasoning system developed at RavenNest Scientific. The study analyzes a five-round mathematical correction session in which Lilith initially generated an overstrong conjectural route from Pell-type trace data on <span class="katex"><span class="katex-mathml">Γ0(2)\H</span><span class="katex-html"><span class="base"><span class="mord">Γ<span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span><span class="mord">\</span><span class="mord mathbb">H</span></span></span></span> toward the Riemann Hypothesis, then revised the work under targeted critique.</p> <p>Across the session, the system corrected concrete arithmetic errors, repaired malformed LaTeX, refined the distinction between primitive and non-primitive geodesics, clarified the role of the compactified modular curve <span class="katex"><span class="katex-mathml">X0(2)</span><span class="katex-html"><span class="base"><span class="mord"><span class="mord mathnormal">X</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span></span></span></span>, and ultimately contracted the claim to a defensible diagnostic note. The final mathematical substrate shows that Pell-type trace data yield candidate geodesic lengths, but do not by themselves enumerate primitive <span class="katex"><span class="katex-mathml">Γ0(2)</span><span class="katex-html"><span class="base"><span class="mord">Γ<span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span></span></span></span>-geodesics, and that term-wise positivity of a Selberg-type geometric sum does not imply Weil positivity for the Riemann zeta function.</p> <p>The paper argues that the transcript provides behavioral evidence of iterative epistemic repair: the capacity of an artificial system to accept falsification, revise claims downward, correct formal errors, and preserve a coherent mathematical through-line. The authors explicitly separate this behavioral claim from stronger architectural or consciousness claims, which require independent evidence.</p> <p>Keywords</p> <p>artificial reasoning, epistemic repair, mathematical verification, brain-inspired AI, Riemann Hypothesis, Selberg trace formula, <span class="katex"><span class="katex-mathml">Γ0(2)</span><span class="katex-html"><span class="base"><span class="mord">Γ<span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span class="vlist-s"></span></span></span></span></span><span class="mopen">(</span><span class="mord">2</span><span class="mclose">)</span></span></span></span>, Pell equations, AI evaluation, claim correction</p> |
| title | Iterative Epistemic Repair in a Brain-Inspired Artificial Reasoning System: A Case Study in Mathematical Claim Correction |
| url | https://doi.org/10.5281/zenodo.19929774 |