| _version_ | 1866901068677382144 |
|---|---|
| author | Figurelli, Rogério |
| author_facet | Figurelli, Rogério |
| contents | <p>Math Machines established a seminal architectural separation between generative solvers and governed closure: generation explores, while machine-enforced contracts decide what may be promoted and what must remain held. Building on that foundation, this paper develops the Kernel–Solver Thesis as an operational and testable refinement and presents it in manifesto form: a two-agent loop in which a Solver proposes mathematical claims and proof attempts, while a governance Kernel enforces bounded promotability through explicit regimes, receipt requirements, monotonic promotion laws, and replayable verdicts. Rather than treating confidence as correctness, the Kernel formalizes a verdict algebra {HOLD, CONDITIONAL, PASS, INFEASIBLE} and prohibits upgrades under tightened admissibility or reduced verification budgets unless gaps are closed with admissible artifacts. We report adversarial refinement traces on linear-versus-cyclic threshold problems, where the Kernel detects regime slippage (interval reasoning incorrectly applied to ℤ_n), forces downgrades, and guides repair. The contribution is not the separation itself, but a concrete promotability protocol—regime ladder, receipt spine, a constitutional rule set for promotion, a proof promotability card schema, and convergence metrics—showing how verified mathematical claims can be produced as replayable state transitions under declared constraints.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18764454 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Kernel–Solver Thesis: Adversarial Learning Toward Verified Mathematical Claims Figurelli, Rogério Kernel–Solver Thesis bounded promotability adversarial proof refinement receipt-based verification monotonic promotion laws replayable verdicts autonomous mathematics governance computation manifesto <p>Math Machines established a seminal architectural separation between generative solvers and governed closure: generation explores, while machine-enforced contracts decide what may be promoted and what must remain held. Building on that foundation, this paper develops the Kernel–Solver Thesis as an operational and testable refinement and presents it in manifesto form: a two-agent loop in which a Solver proposes mathematical claims and proof attempts, while a governance Kernel enforces bounded promotability through explicit regimes, receipt requirements, monotonic promotion laws, and replayable verdicts. Rather than treating confidence as correctness, the Kernel formalizes a verdict algebra {HOLD, CONDITIONAL, PASS, INFEASIBLE} and prohibits upgrades under tightened admissibility or reduced verification budgets unless gaps are closed with admissible artifacts. We report adversarial refinement traces on linear-versus-cyclic threshold problems, where the Kernel detects regime slippage (interval reasoning incorrectly applied to ℤ_n), forces downgrades, and guides repair. The contribution is not the separation itself, but a concrete promotability protocol—regime ladder, receipt spine, a constitutional rule set for promotion, a proof promotability card schema, and convergence metrics—showing how verified mathematical claims can be produced as replayable state transitions under declared constraints.</p> |
| title | The Kernel–Solver Thesis: Adversarial Learning Toward Verified Mathematical Claims |
| topic | Kernel–Solver Thesis bounded promotability adversarial proof refinement receipt-based verification monotonic promotion laws replayable verdicts autonomous mathematics governance computation manifesto |
| url | https://doi.org/10.5281/zenodo.18764454 |