Low-energy testability of source-only emergent gravity: a laboratory lock-in protocol - Reference release (prior to journal submission)

Pedagogical Guide, Foundations Audit, Uniqueness & Substitutability Analysis, Literature Comparison, and Reading Guidance : A Pedagogical Guide to Understanding the OT–GKSL Architecture This work proposes a low-energy laboratory test of a possible source-side state dependence in gravity using lock-in atom-interferometric gravimetry at fixed source geometry. The experimental concept combines a Bose--Einstein-condensate atom gravimeter, a kilogram- to multi-kilogram superfluid 4He^{4} source operated in the He-II regime, a second-sound channel used as an independently monitored source-state proxy, and phase-coherent demodulation referenced to a common master clock. The central question is whether, at fixed mass distribution and fixed geometry, a controlled modulation of the prepared internal state of a source can generate a synchronous narrow-band anomaly in the engineered-source gravitational readout. The framework does not modify the Einstein--Hilbert kinetic sector and does not introduce any state-dependent prefactor in front of R[g]. Any admissible effect is treated instead as a source-side constitutive response, parameterized locally by a susceptibility relating the driven source-state proxy to a lock-in gravimetric signal. For realistic source configurations, the calibrated Newtonian field of the engineered source lies naturally in the 20–300 nm s−2 range, which maps the targeted phenomenological interval onto a signal window extending from the 10−3 nm s−2 scale up to a few 10 nm s−2 nms−2. The protocol is intrinsically veto-rich and includes phase reversals, proxy-suppressed controls, detector-only tests, geometry checks, multi-pattern source drives, and monitor-based regression against motion, redistribution, thermal, electromagnetic, and vibrational artifacts. A null result would set a direct laboratory bound on a weakly constrained source-side response channel at fixed geometry. A positive result would establish a controlled source-state-correlated anomaly in the engineered-source gravitational readout and open a new narrow-band experimental regime at the interface between quantum matter preparation and classical gravitational measurement. Einstein-Locked OT/GKSL Corpus: This corpus should not be read as a single paper claiming a complete microscopic theory of spacetime, nor as a modified-gravity program, nor as a loose stack of phenomenological add-ons. It should be read as a layered certified architecture with explicitly different logical statuses at different levels: native OT/GKSL dynamics → certified readout → exact reduced sector → nonlinear Einstein-locked readout closure → controlled recoveries → branch-resolved physical outputs → operational observables and protocols. The corpus is already explicit that these layers must not be conflated. Native objects are not readout objects. Readout objects are not recoveries. Recoveries are not definitions of the framework. Numerical atlases and protocols are not ontology. 1. First rule: always ask what level an object belongs to The most common misreading is to take a readout-level object as if it were native, or to take a controlled recovery as if it defined the whole theory. The corpus is explicit that the native level is OT/GKSL dynamics on finite effective state-space support, not primitive spacetime; classical spacetime geometry appears only later as a certified readout. Likewise, controlled recoveries are local, windowed, and hypothesis-dependent, and must not be read as global equivalences between the full OT/GKSL framework and the recovered low-energy theory. 2. The certified windows are not weaknesses; they are part of the theory’s positive content The certified window Wₐcc is not an external restriction added because the theory “only works in a small region.” It is the internal domain on which a classical readout claim is physically licensed at all: stable records, readable coframe directions, controlled bridge transfer, visible-branch auditability, and sufficient finite spectral, entropic, and inferential headroom must coexist there. Outside Wₐcc, the native OT/GKSL dynamics may remain meaningful; what weakens first is the certified status of the classical readout claim, not the native theory itself. The certified boundary is therefore a theorem-level statement of bounded classical readability, not an embarrassment or a loophole. 3. Certification is a positive licitness condition, not a post hoc caveat Certification in this corpus does not mean a semantic disclaimer added after the fact. It means the operational conditions under which a readout statement becomes physically assertable. This is why the corpus treats certification as part of the architecture itself: the cutoff fixes the effective support and finite effective dimension, the finite support bounds the readout burden, and certification identifies the corridor where classical geometry, classical time, and eventually full spacetime semantics are jointly maintainable. The theory is stronger because it states where classical readability is licensed, rather than silently assuming it everywhere. 4. The reduced layer is a genuine dynamical layer, not a disposable intermediate trick The reduced sector is not a weak-field shortcut, an infrared ansatz, or a convenient approximation that can be ignored once familiar equations are recovered. On the certified reduced domain, the corpus treats the reduced equations as exact reduced exactness: once the collective projection is fixed and the analysis is restricted to the certified reduced window, the resulting reduced nonlinear system has its own stationary branches, barriers, bifurcations, stability structure, and branch-resolved observables. This layer is architecturally prior to standard classical recoveries and must be read on its own terms. 5. The Einstein lock is a structural prohibition, not a phenomenological taste A reader must keep one non-negotiable rule in mind throughout: no readable state dependence is allowed in front of the Einstein–Hilbert kinetic term. The kinetic gravitational block remains universal. Readable state dependence is confined to the source/response side together with the response/exchange completion required by covariant closure. If this rule is forgotten, the whole corpus will be misread as a modified-gravity program, which it explicitly says it is not. 6. The nonlinear Einstein-readout paper is the missing readout core, not a UV derivation of gravity The nonlinear Einstein-readout manuscript should be read as the structural bridge between the exact reduced OT/GKSL dynamics and their controlled weak-field recoveries. Its claim is not that OT dynamics alone uniquely derive the full Einstein equations at microscopic level. Its claim is more precise: once the certified OT-to-readout bridge, the Einstein lock, source-only constitutive placement, and covariant closure are accepted, the readout sector admits a genuine nonlinear Einstein-locked closure, with controlled interface defects, while the Newtonian limit appears only later as a corollary. 7. The physical core of the corpus sits in the reduced constitutive–holonomic branch problem The central reduced object is the constitutive–holonomic effective potential U_eff(r) = U_src(r) + U_hol(r; J). This is not an optional toy. It is the source-side branch-selection engine of the framework. From this same reduced branch structure, the corpus derives a positive effective mass scale, a vacuum-like residual energy, and later an intermediate CDM-like regime. The deep point is that visible, vacuum-like, and dark-matter-like outputs are not three unrelated add-ons: they are three physically distinct readings of the same reduced constitutive–holonomic architecture. 8. Read mass generation and vacuum-like lifting before reading the visible/vacuum/dark triplet The logical order matters. First, the reduced constitutive–holonomic branch analysis establishes that a stable nontrivial branch carries both a positive effective mass scale and a nonzero vacuum-like residual energy, and that the residual lifts consistently into the Einstein-locked source/response closure without introducing a new primitive fluid or modifying the Einstein kinetic block. Only after these two outputs are in place does the triplet analysis ask whether the same branch architecture also supports an intermediate materially active but weakly visible regime. 9. The visible/vacuum/dark triplet is branch-resolved, not ontology-resolved The corpus does not append a primitive dark sector, a primitive vacuum sector, and a primitive visible sector as separate ontologies. It shows instead that stable reduced branches can carry three distinct source-side readings: a visible mass-bearing branch, a vacuum-like residual branch, and an intermediate CDM-like branch. Darkness is a readout statement, not a sourcing statement; vacuum-likeness is a branch-dominance statement after closure, not a second ontology; and visible mass, vacuum-like lifting, and CDM-like behavior all arise from the same reduced constitutive–holonomic carrier set. 10. The vacuum-like papers must be read in two steps, not collapsed into one The first vacuum-like result is local and reduced: a stable reduced branch carries a residual energy E_vac. The second step is a controlled lifting logic: this residual populates a vacuum-like source-side slot through a matching relation, and only after source/response closure does it become physically meaningful as an effective vacuum-like density in the homogeneous readout sector. The homogeneous closed model is therefore a controlled specialization of the Einstein-locked readout architecture under finite spacetime-readout budget; it is not a new native cosmology, and it does not claim that the budget itself generates ρ_Λ. 11. Time, spacetime, causality, locality, and relativity are certified readout achievements A major source of confusion is to assume that relativity and causality are n