CP-H1-FORM-MOSCO-001: Source-Free Native-Graph Quadratic-Form Continuum Bridge — Pre-Execution Mathematical/Computational Protocol Freeze v0.1.0

Abstract

This record prospectively freezes the mathematical and computational protocol for CP-H1-FORM-MOSCO-001, the source-free native-graph quadratic-form continuum-bridge programme on a fixed three-dimensional domain. The protocol is subordinate to the controlling Analytical Architecture / Pre-Convergence Hypothesis Freeze v0.1.0: Krüger, M. (2026). CP-H1-FORM-MOSCO-001: Source-Free Native-Graph Quadratic-Form Continuum Bridge — Varying-Hilbert-Space Mosco Architecture on a Fixed 3D Domain — Analytical Architecture / Pre-Convergence Hypothesis Freeze v0.1.0. Zenodo. DOI: 10.5281/zenodo.22657352 The target question is whether the frozen source-free native scalar graph forms E_j, defined on the exact changing cut-and-project carriers and isometrically lifted into the fixed Hilbert space L²(Ω), converge in the sense of Mosco to the declared Neumann continuum form E_∞(f) = η ∫_Ω |∇f|² dx, with η = π(64 - 23√2)/48 ≈ 2.0599087969. The discrete baseline is fixed as E_j(u) = a_j Σ_{ {n,m} ∈ E_j^nat } |u_n - u_m|², with scale law a_j = 2^(-j/2), unit native-shell conductances, restricted-Voronoi cell measures, and no source term, potential, fitted diffusion coefficient, fitted exponent, Voronoi/Delaunay/DEC conductance, or other post-exposure correction. A theorem-level PASS is permitted only if the full declared sequence satisfies both Mosco obligations: M1 — liminf inequality; M2 — recovery-sequence condition; together with all load-bearing auxiliary obligations frozen in the controlling architecture, including: A1 — carrier resolution/density; A2 — connectivity / exclusion of persistent spurious zero modes; A3 — common-space projection approximation; A4 — native-shell bulk pair-frequency control; A5 — discrete compactness; A6 — liminf identification; A7 — recovery-sequence construction; A8 — Neumann boundary identification. Finite computation is explicitly secondary. It may verify implementation continuity, expose contradictions, test prospective finite diagnostics, and evaluate previously unexposed refinement levels under frozen rules, but no finite prefix can establish asymptotic Mosco convergence. The upstream source-sector conclusions remain unchanged: CP-H1-SRC-XSC-001: CPH1SRCXSC001_FAIL_FIXED15D_SOURCE_PROJECTOR_STABILITY DOI: 10.5281/zenodo.22349103 CP-H1-SRC-SYM-001: CPH1SRCSYM001_SYMMETRY_PRESENT_NOT_FORCING DOI: 10.5281/zenodo.22649127 No source rescue is permitted. The protocol forbids post-hoc exponent retuning, diffusion fitting, favorable-level selection, source or mass insertion, replacement of native-shell weights after exposure, and boundary-condition changes motivated by observed outputs. The allowed final classifications are restricted to theorem-level Mosco establishment, finite-support-only status, failure of the declared form/recovery obligations, or invalidation through provenance/form-contract violation. A positive result would establish only a mathematical scalar continuum bridge for the declared source-free form family. It would not establish a physical spacetime, quantum field theory, gauge theory, gravity model, cosmology, particle-physics model, or empirical validation. This record therefore freezes the pre-execution proof and computational contract before inspection of new target convergence outputs.