#TW-Sunflower-318 (1 article)

The Political-Philosophical Foundations of the Public Realm: A Normative Floor for Civic Proof

The nineteenth and final article of the civic-proof series (A2). This article provides an affirmative account of the political-philosophical foundations implicitly relied upon across the preceding eighteen articles. Taking Arendt's plurality, Habermas's Öffentlichkeit, Pettit's contestation, and Mouffe's agonism as its four anchors, the article defines the Public Realm Floor (PRF) (a composite term proposed by the present author, synthesising Arendt's notion of the public realm with the normative 'floor' metaphor from political philosophy) as PRF ≜ ⟨plurality, validity, contestation, agonism⟩, and articulates the conditional implication PRF_violated(d) ⇒ LegitimacyDegrade(d) ≥ θ_dem ≈ 0.5 via a LegitimacyDegrade function. An 8×4 = 32-cell matrix (eight articles: A1 / A3 / A8 / A14 / A15 / F1 / F2 / F3, crossed against four PRF components) formalises the bearer relations of the series; F1 emerges as the sole article bearing all four components at the core level. Four formal theorems T_PRF1–T_PRF4 establish the conjunctive floor structure in which each component is necessary within the PRF framework and cannot be fully substituted by the remaining three; theorem T_PRF5 extends the Z₃-intrinsic boundaries of F1's RT-ℬ ✗ and AA-ℬ ✗ into an engineering unreachability lemma for the existing engineering design layer (stated explicitly as a formal theorem at the engineering rather than the normative layer). The θ_dem ≈ 0.5 threshold in the LegitimacyDegrade function is an analytic suggestion only, not an empirically calibrated value; this article records it as a strict position awaiting calibration via regression across at least five cases. Counter-argument stress tests address five categories—Coeckelbergh's relational personhood, Floridi's infosphere monism, posthumanism (Braidotti / Hayles), digital-democracy optimism (Benkler), and the meta-objection (why these four thinkers)—and show, under a likelihood × impact matrix, that each weakens but does not overturn PRF's four-component conjunctive floor. The indigenisation of the framework to Chinese intellectual traditions proceeds along four lines: structural homology tests between Zhu Yunhan's 'qun' (群), Wang Hui's 'gong' (公), the Confucian 'jianyi' (諫議) tradition, and the Confucian 'zheng-you' (諍友) tradition and the four anchor thinkers; disparities in historical bearer conditions are stated at the honesty boundary. A special section for Taiwanese readers addresses the concrete impact of TW DIW's entry into the LLM-agent phase on PRF, and its engineering correspondence with F3's supporter UI three-layer separation. The honesty boundary comprises seven conditional implications; open questions comprise 27 items classified under four successor pathways (F4+ follow-on work, expanded academic-community examination, policy implementation empirical research, and technology–philosophy intersection). The series concludes with this article; the extension of the PRF framework to further applications, reinforcement from other political-philosophical approaches, posthumanist re-elaboration of PRF, and cross-national calibration of θ_dem for democratic legitimacy are all left as open space.