Addendum I to the Berg Theory

Addendum I extends the Berg Theory and is aligned with the Core Article, “The Berg Theory: A scalar–tensor energy web as a common foundation of space–time, gravitation, quantum phenomena, and entropy” (Collection DOI: 10.5281/zenodo.17937466). Version 8 develops the vacuum and prestress sector as a bounded classical/effective field construction with explicit reproducibility, falsification, and interface rules. The physical vacuum is treated as the first realized nonzero state of the same three-dimensional energy web that also carries excitations and bound structures. The formal zero-field limit represents absence of the realized web and is not part of the admitted internal physical state space. The physical vacuum floor is therefore neither empty space nor a material wall. It is a lower admissible state of the same field, while microscopic phase, stress, and energy-flow organization may remain dynamical. A central distinction of the addendum is the separation of three quantities that can otherwise be conflated in vacuum language: the vacuum floor, the calibrated energy height, and the local restoring stiffness. The floor fixes the lower admissible state, the energy height controls the background normalization, and the restoring stiffness characterizes the local response to disturbances. This permits a low calibrated vacuum-energy height to coexist with a strong restoring response without identifying the two quantities. Version 8 implements the floor as a one-sided constrained field problem and provides both a positive-floor construction and an on-shell compact same-field branch above that floor. The algebraic benchmark family is retained as a diagnostic and support-classification layer rather than being promoted to a physical background by itself. Positive radial support, monotone prestress behavior, a positive gravitational prefactor margin, weak-field availability, dynamical prefactor stability, and radiative-height admissibility are kept as separate gates that must survive before calibration is interpreted. A major Version-8 addition is NSM-01, the first local non-spherical polar contact-spectrum calculation on the frozen compact positive-floor branch. The calculation identifies one damped quadrupolar contact mode in the declared local, stationary, strict-active regime. A structured finite-annulus exterior completion then tests the same mode over a predeclared matching interval with independent holdout points and closed-return checks. The damped root is preserved throughout that local window, with a projected shift negligible relative to the damping margin. The present structured-local result does not depend on the older unknown remainder coefficient; the older unstructured norm alarm is retained transparently as a negative control rather than removed. The NSM-01 result is deliberately limited. It is not a theorem of global cosmological stability, moving-contact dynamics, nonlinear or all-orders stability, and it does not establish contact energy, capture, absorption, transport efficiency, matter retention, or shortening of the surrounding network. Those remain separate physical calculations. Version 8 also introduces CWS-01, a candidate-specific cross-scale collapse-work sign witness. A macroscopic moving-worldtube transport calculation and an independently predicted microscopic no-reset compression-work calculation locate the same change in energy-exchange behavior to approximately 0.109 percent in the declared Lagrangian scale coordinate, while the microscopic holdout remains within its conservative bound-state gates. This result is intentionally narrower than a completed release, matter-destruction, free-field, angular-momentum, or primary-ring calculation. The empirical interface is kept separate from the internal construction. For EXP-01, the DESI DR2 data object is recorded as data-valid. A qualitative prediction published before the present comparison — that late-time acceleration is dynamical rather than an eternal fixed point — is qualitatively aligned with the DESI DR2 preference for evolving late-time dark energy. Independently, the Version-8 epoch-map audit recovers all 13 declared DESI rows inside the already-proved active-floor domain, and a Pantheon+ full-covariance distance comparison provides a non-adverse cross-check. The numerical present-epoch normalization remains a calibration quantity rather than a pre-specified quantitative forecast. The local-gravity and gravitational-wave routes remain more restricted. LOC-01 retains an analytic bound and constraint-screening result, but observational support is not assigned because the realized source/environment response map is still open. GW-01 gives exact analytic compatibility on the proved active segment under the constant-prefactor condition, but this is not promoted to a gravitational-wave population or standard-siren likelihood result. Accordingly, the combined label vacuum-sector conditional support remains reserved and is not assigned in Version 8. The appendices separate derivation, evidence, protocol, and notation. Appendix A contains the action-checked conventions, background recovery, radial-support and monotonicity derivations, non-spherical contact calculation, benchmark and scan structure, regularization and persistence interfaces, CWS-01 derivation layer, calibration bridge, and comparison with established scalar–tensor, modified-gravity, quintessence, and QFT-vacuum language. Appendix B provides the release-facing reproducibility, benchmark, prediction-lock, evidence, bound, and public-anchor registry. Appendix C fixes executable protocol, control, downgrade, and decision logic for NSM-01 and CWS-01. Appendix X is the synchronized local symbol reference for the public Addendum-I documents and remains subordinate to the series-wide Core symbol authority. The public supplement preserves the frozen Version-7 provenance files while adding explicit Version-8 current-status ledgers that take precedence for Version-8 interpretation. It contains the public source-policy layer, derived route outputs, benchmark and support-scan material, prediction and status registries, NSM-01 machine evidence and reproduction scripts, the structured local-completion evidence, CWS-01 preregistration and reproduction material, the explicit Floor-constraint/KKT formalism, the Jordan-frame sign-convention audit, a synchronized local symbol list, complete manifests, and SHA-256 verification records. The neutral NSM reproduction archive contains 17 executable stages and records 207 of 207 numerical gates as passed. The result is a constrained and auditable vacuum-sector module rather than a generic vacuum metaphor: a nonzero physical floor, a separated energy-height and restoring-stiffness structure, explicit lower-condition and failure logic, a local non-spherical stability witness, a cross-scale collapse-work witness, frozen empirical interfaces, and a reproducible public evidence package. The scope remains intentionally below series-wide empirical validation and preserves the open interfaces required for later quantum, matter, cosmological, local-gravity, and combined-series closure. Addendum I cite-all-versions DOI: 10.5281/zenodo.18009770Version 8 DOI: 10.5281/zenodo.21995291 Public data and route references recorded for Version 8 CobayaSampler. BAO data repository, including DESI DR2 BAO likelihood files. GitHub repository: CobayaSampler/bao_data. Accessed 21 June 2026. DESI Collaboration. DESI DR2 Results II: Measurements of Baryon Acoustic Oscillations and Cosmological Constraints. arXiv:2503.14738, 2025. Brout et al. The Pantheon+ Analysis: Cosmological Constraints. Astrophysical Journal 938, 110, 2022. arXiv:2202.04077. Scolnic et al. The Pantheon+ Analysis: The Full Data Set and Light-curve Release. Astrophysical Journal 938, 113, 2022. arXiv:2112.03863. LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. GWTC-5.0: Observations from the Second Part of the Fourth LIGO-Virgo-KAGRA Observing Run. arXiv:2605.27225, 2026. LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration. GWTC-5.0: Constraints on the Cosmic Expansion Rate and Modified Gravitational-wave Propagation. arXiv:2605.27227, 2026.