The Dynamic Planck Network is the proposed microscopic source of causal memory; continuum geometry and retarded-kernel selection remain conditional long-wavelength constructions. The CMG XIII birth selector fixes graph-history weights only up to an open coefficient law and clock anchor.

ConceptDefinitionEquationStatusSource
DPN graph dataDirected graph with causal edges, plaquettes, coarse cells, memory fields, transfer matrix, and stochastic novelty sources.$\displaystyle \mathcal R=(V,E,F,\partial F,C),$ $\displaystyle \mu_e(t+1)=\sum_k T_{ek}\mu_k(t)+\sigma_e(t)$Derived / definedCMG III, Microscopic Foundations, Handbook
Transfer stabilitySubcritical transfer, $\rho(T)<1$, is the condition under which memory decays instead of accumulating without bound.$\displaystyle \rho(T)<1$ConditionalCMG III, Handbook
Spectral-gap memory scaleThe action-level memory rate is conditionally matched to the slow elastic DPN mode in the dimensionally closed one-pole closure; the physical derivation of the coarse-volume factor $C_V$ remains open.$\displaystyle \beta_{\rm rate}^2=C_V(K_\theta/I_\theta)\lambda_2(L_{\rm el}),$ $\displaystyle C_V=V_{\rm graph}^{-1}$ConditionalCMG III, Microscopic Foundations
Controlled-shear coefficientThe static proxy is separated from the dynamic reduced-DPN derivative; halo/N-body embedding remains open.$\displaystyle \xi_{\rm red}=0.292\pm0.041,$ $\displaystyle \xi_{\rm dyn}^{(D)}=0.297\pm0.010_{\rm ens}$Benchmark / numericMicroscopic Foundations
Conditional birth selector (XIII Part II)Seven of eight operational inputs of the DPN birth selector have explicit constructions; within a positive measurable pointwise single-score class, universal common-score-shift invariance gives exponential weights. The provider of effective degree and cycle coefficients (row 5) is the open input, so the result is a parameterised graph-history law inside a specified model.$\displaystyle w(s)=C\exp(-\beta_{\rm sel}s),$ $\displaystyle {\rm ledger}\ 7/8,$ $\displaystyle {\rm row\ 5\ open}$ConditionalXIII
Measure law and event clockA factorised graph–carrier measure cancels the row-5 coefficients from the normalised fixed-geometry response; specified couplings restore sensitivity only after geometry is marginalised. A fixed three-volume alone supplies neither a time dimension nor a physical event tick. The return-history route for the frozen corpus was closed on 16 September 2026 (OD0); reopening requires a registered new theoretical input or an external units bridge.$\displaystyle V_3\ {\rm fixed}\;\not\Rightarrow\;{\rm physical\ event\ tick}$OpenXIII

The action sector uses a retarded curvature-memory term with $\eta_{\rm act}=-\tilde\alpha$; the fixed-background closure uses the distinct amplitude $\eta_{\rm cl}$ until a matched perturbation derivation exists.

ConceptDefinitionEquationStatusSource
CMG effective actionRetarded nonlocal scalar-curvature memory correction to Einstein gravity.$\displaystyle S\supset-\frac{\tilde\alpha}{2}\int d^4x\sqrt{-g}\;R(\Box+\beta_{\rm rate}^2)^{-1}_{\rm ret}R$Derived / definedCMG I, Microscopic Foundations
Auxiliary fieldLocalized representation with the retarded boundary condition imposed on the auxiliary solution.$\displaystyle (\Box+\beta_{\rm rate}^2)U=-R$Derived / definedCMG I, Microscopic Foundations
Linearized stability windowThe linearized effective-scalar truncation is stable at tree level for negative alpha-tilde; this is not full nonlinear, retarded, or UV stability.$\displaystyle -1<\tilde\alpha<0,$ $\displaystyle \eta_{\rm act}\equiv-\tilde\alpha\in(0,1)$Derived / definedCMG I, Microscopic Foundations
Beta hierarchyThe action rate, dimensional inverse length, operational closure scale, local dissipation, screened Poisson scale, and GKSL kernel scale are distinct. The relation $\beta_{\rm IR}=\beta_{\rm rate}/c$ fixes units but not the missing amplitude matching.$\displaystyle \beta_{\rm IR}=\beta_{\rm rate}/c,$ $\displaystyle \Gamma_{\rm eff}(x)\neq\beta_\mu(x)$Derived / definedMicroscopic Foundations, Handbook, Synthesis
GR recovery limitsAction-level and perturbation-level GR limits are not the same; local screening uses beta_mu, not large homogeneous beta_IR.$\displaystyle \tilde\alpha\to0\;(\eta_{\rm act}\to0)\;{\rm or}\;\beta_{\rm rate}\to\infty;$ $\displaystyle \eta_{\rm cl}\to0\;{\rm or}\;\beta_{\rm IR}\to0$Derived / definedMicroscopic Foundations, Handbook
Action-level scalar system (C2)The general-scalar-gauge SymPy route and radiation cross-check pass at prototype level. Direct oscillator integration replaces the rejected averaged-fluid route; start-time insensitivity fails, the Lambda root is branch-nonunique, and the production and likelihood gates remain closed.$\displaystyle \gamma_{\rm action}^{\rm QS}=\frac{\bar F+2\eta_{\rm act}s}{\bar F+4\eta_{\rm act}s}$ConditionalActive C2 addendum, C2e, C2 Phase 1--4 note

The supported cosmological result is a near-GR fixed-background linear benchmark in $(\eta_{\rm cl},\beta_{\rm IR})$, not a unique non-GR detection and not a nonlinear $S_8$ solution.

ConceptDefinitionEquationStatusSource
Poisson modifierScale-dependent weakening of the density-growth source; short wavelengths recover GR.$\displaystyle \mu(k,a)=1-\frac{\eta_{\rm cl}a^2\beta_{\rm IR}^2}{k^2+a^2\beta_{\rm IR}^2}$Derived / definedCMG I, CMG VII
No slipThe minimal no-slip closure sets the two metric potentials equal; it is a closure assumption, not a theorem of every CMG completion.$\displaystyle \gamma(k,a)=1$ConditionalCMG I, CMG VII
DESI compressed amplitudeFull 6x6 DESI DR1 ShapeFit covariance and exact flat-LambdaCDM growth equation give a GR-centered amplitude.$\displaystyle A_g=0.9962\pm0.0437,$ $\displaystyle 1-A_g=0.0038\pm0.0437$Benchmark / numericCMG VII, I
Goodness of fitCMG is allowed but not preferred after the extra growth parameter is penalized.$\displaystyle \chi^2_{\rm CMG}=5.480,$ $\displaystyle \chi^2_{\Lambda{\rm CDM}}=5.487,$ $\displaystyle \Delta{\rm AIC}=+1.99,$ $\displaystyle \Delta{\rm BIC}=+1.78$Benchmark / numericCMG VII
Degeneracy productDESI constrains eta_cl times the DESI response functional, not a unique eta_cl-beta_IR point.$\displaystyle A_g=1-\eta_{\rm cl}S_{\rm DESI}(\beta_{\rm IR}),$ $\displaystyle \eta_{\rm cl}(\beta_{\rm IR})=\frac{1-A_g}{S_{\rm DESI}(\beta_{\rm IR})}$Benchmark / numericCMG VII, Synthesis
Full-shape profiled limitsAt fixed beta_ratio, the unified-prior joint ShapeFit-vector and full-shape nuisance-profile analyses give one-sided 95% limits on the closure amplitude.$\displaystyle \begin{aligned}\eta_{{\rm cl},95}^{\rm joint}=&(0.2269,0.05764,\\&0.02860,0.02006,0.01483)\end{aligned}$ $\displaystyle \begin{aligned}\eta_{{\rm cl},95}^{\rm FS}=&(0.2544,0.0680,\\&0.0316,0.0212,0.0153)\end{aligned}$Benchmark / numericCMG VII
Separate DR2 BAO background interfaceThe action-derived FLRW background was passed to the DESI DR2 BAO operator at fixed standard parameters. The sampled grid difference is an interface test, not a profiled constraint or evidence measure.$\displaystyle \eta_{\rm act}=0.1,$ $\displaystyle \beta_{\rm rate}/H_0=10^5,$ $\displaystyle \Delta\chi^2_{\rm BAO}=-5.415287$Benchmark / numericCMG VII
S8 boundaryThe linear sector is near-GR; substantial S8 suppression requires calibrated nonlinear screening.$\displaystyle \begin{gathered}A_g\simeq1\Rightarrow\text{no linear }S_8\text{ solution}\\\text{in the locked closure}\end{gathered}$OpenCMG VII, Handbook

Dense and tidally distorted environments increase memory dissipation; the direct Poisson memory scale then decreases and GR is locally recovered.

ConceptDefinitionEquationStatusSource
Effective dissipationChannel saturation and tidal degradation define the local memory-dissipation rate.$\displaystyle \Gamma_{\rm eff}(x)=\Gamma_0\frac{N(x)}{N_0}\left(1+\xi\ell_0^2\sqrt{s_{ij}s^{ij}}\right)$ConditionalMicroscopic Foundations, I, Handbook
Screened Poisson scaleThe scale entering the local Poisson modifier is beta_mu; it decreases as dissipation increases.$\displaystyle \ell_0=c/\beta_{0,\rm rate},$ $\displaystyle \beta_\mu(x)=\beta_{0,\rm IR}\frac{\Gamma_0}{\Gamma_{\rm eff}(x)}$ConditionalMicroscopic Foundations, Synthesis
Screened modifierThe same perturbation-level GR logic beta to zero is applied locally through beta_mu(x).$\displaystyle \mu(k,a,x)=1-\eta_{{\rm cl},{\rm eff}}(x)\frac{a^2\beta_\mu^2(x)}{k^2+a^2\beta_\mu^2(x)},$ $\displaystyle \gamma(k,a,x)=1$ConditionalMicroscopic Foundations, Synthesis
Local GR chainWithin the screening ansatz, increasing dissipation reduces the local Poisson inverse-length scale and restores the locked GR limit.$\displaystyle \Gamma_{\rm eff}\to\infty\Rightarrow\beta_\mu\to0\Rightarrow\mu(k,a,x)\to1$ConditionalMicroscopic Foundations, Handbook, Synthesis
Spherical screening precursor (C3)1D NFW single-halo solver for $\beta_\mu(r)$ with a Yukawa boundary-value problem; validates the screened force solver and the sign of the response ahead of any PM/N-body calibration.$\displaystyle \beta_\mu(r)\Rightarrow\mu_{\rm eff}(r)$Benchmark / numericC3 Addendum
Conditional LLR interface (SREQ v2)Action-level Lunar Laser Ranging interface; its suppression sequence is conditional, preserves $\eta_{\rm act}\neq\eta_{\rm cl}$, and is an interface statement, not a screening derivation.$\displaystyle G_{\rm eff}/G=(1-\eta_{\rm act}U)^{-1}$ConditionalSREQ v2 Final Addendum
Nonlinear validation statusEFT/PM-N-body form is specified, but production N-body and halo embedding are still required.$\displaystyle \xi_{\rm dyn}^{(D)}\;{\rm reduced\ DPN};$ $\displaystyle S_8^{\rm nonlinear}\;{\rm not\ derived}$OpenMicroscopic Foundations, Handbook

The current galactic sector is a separate DPN-saturated SEM--RAR halo response, not a direct reuse of the homogeneous linear cosmology kernel.

ConceptDefinitionEquationStatusSource
DPN saturation factorThe factor $x/(e^x-1)$ is the proposed DPN occupancy interpretation of the SEM response; it remains an ansatz.$\displaystyle x=\sqrt{g_b/g_\dagger},$ $\displaystyle {\cal S}_{\rm DPN}(x)=\frac{x}{e^x-1}$Proxy / ansatzCMG II, Handbook
SEM--RAR lawPreferred Paper II closure; analytically identical to the exponential RAR law.$\displaystyle g_{\rm obs}=g_b+\sqrt{g_\dagger g_b}\,{\cal S}_{\rm DPN}(x)=\frac{g_b}{1-e^{-\sqrt{g_b/g_\dagger}}}$Benchmark / numericCMG II, Synthesis
SPARC calibrationProfiled fit over 175 galaxies and 3391 rotation-curve points.$\displaystyle g_\dagger=1.1735\times10^{-10}{\rm m\,s^{-2}},$ $\displaystyle \sigma_{\rm int}=5.83{\rm km\,s^{-1}}$Benchmark / numericCMG II
Numerical identity checkThe SEM--RAR implementation matches exponential RAR to floating-point precision.$\displaystyle \max|V_{\rm SEMRAR}-V_{\rm RAR}|=6.37\times10^{-12}{\rm km\,s^{-1}}$Benchmark / numericCMG II
Reduced dynamic bridge (C4)Dynamic-DPN shear estimator suggests a reduced galactic bridge with $\beta_{\rm rate}\simeq H_0$; the ratio $\mathcal{B}_{\rm gal}(H_0)\simeq0.178$ is a dimensional diagnostic. The elastic continuum diagnostic reaches only 0.64--0.72 of $(2\pi)^2$ at $N=8192$, with a persistent knn/annulus offset.$\displaystyle g_\dagger\simeq\frac{\xi_\infty}{e-1}c\,\beta_{\rm rate},\ \xi_\infty\simeq0.297$Benchmark / numericCMG II, C4 spectral appendix
Dark-matter boundaryCMG II gives a viable galactic halo-response channel; it is not a completed replacement for cluster mass, CMB matter density, or nonlinear structure formation.$\displaystyle g_\dagger\;{\rm calibrated};$ $\displaystyle g_\dagger\leftrightarrow\beta_{\rm IR}\;{\rm open}$OpenCMG II, Handbook
Cluster/web residual pilotReal-$\kappa$ CLASH lensing layer is usable at pilot level, but the matched lensing-clean and valid-web sample fails the count gate, so no cluster residual coefficient is estimated.$\displaystyle N_{\rm clean+web}=4<8\Rightarrow b_C\ {\rm not\ estimated}$OpenCluster/web pilot closeout, CMG II

The recovered complex supports incidence/Hodge and finite-volume control calculations. A physical DPN gauge provider, a two-species common cone and the several distinct gap notions remain open. CMG XIII adds a conditional gauge construction on fixed complexes and audits the recovered generator, which does not supply the provider.

ConceptDefinitionEquationStatusSource
Hodge decompositionEdge 1-forms decompose into exact, coexact, and harmonic components; curvature is carried by the coexact sector on the exported sample.$\displaystyle \omega=d\alpha+\delta\beta_H+\gamma,$ $\displaystyle \Theta_p=(B_2^{\top}\phi)_p$Derived / definedCMG V, V Addendum
Recovered-export Maxwell checkIncidence and Hodge identities are verified on the recovered static complex. Its faces are a post-hoc export structure, not an independently derived microscopic gauge-provider receipt.$\displaystyle |V|=2000,$ $\displaystyle |E|=9203,$ $\displaystyle |F|=4326,$ $\displaystyle B_1B_2=0$Benchmark / numericCMG V Addendum
Zero-flux harmonic baselineStatic zero-momentum Maxwell proxy with plaquette tensions from the zero-flux harmonic fit; it is not a measured propagation speed or a ratio to a physical DPN cone.$\displaystyle \tau_p=\prod_{e\in\partial p}t_e,$ $\displaystyle (\chi_0,\kappa_0)=(0.247072914977,0.134566980860),$ $\displaystyle c_\gamma=0.7380\;{\rm(static\ proxy)}$Benchmark / numericCMG XII, CMG V Addendum, C5 closeout
Lorentz-deficit decomposition (C5)Exact factorization of the photon-speed deficit: dominated by the spacelike/timelike face count-area structure of the exported complex ($N_s/N_t=631/3695$); generator geometry vs sampling imbalance vs physical stiffness is undecidable without the raw export and causal rule.$\displaystyle \begin{aligned}\ln(\kappa_0/\chi_0)&=-1.7674_{\rm cnt}\\&+1.1254_{\rm area}+0.0344_{\rm ten}\\&=-0.6076\end{aligned}$Benchmark / numericC5 closeout (2026-07-18)
Villain sign and harmonic marginalityThe electric Villain channel has $\Delta\chi\ge0$ (sum of squares), so with $\kappa<\chi$ it alone cannot close the Lorentz gap; the measured quadratic flow of $\rho_L=\ln(\kappa/\chi)$ is exactly marginal, so any Lorentz-surface attractor must come from the unmeasured defect/nonlinear dynamics.$\displaystyle \Delta\chi\ge0,$ $\displaystyle d\rho_L/d\ln b=0\ ({\rm quadratic\ level})$Derived / definedCMG XII, C5 closeout
Photon-speed identifiability boundaryThe static coefficient is c_gamma=0.7380, while c_DPN is not physically identified. The preregistered D2 reference-family verdict is D2_CONTRACT_FAILED; FINITE_TIME_TRANSIENT_SUPPORTED is a later depth diagnostic, not a replacement verdict.$\displaystyle c_\gamma/c_{\rm DPN}\;{\rm not\ identified}$OpenC5 closeout and D2 result notes
Fine-structure statusThe physical electromagnetic coupling remains a proxy-level calibration; the inverse roots $(p_E,p_B)=(0.005917234656,\,0.006117050451)$ are inverse-calibration comparison targets and are never used as inputs.$\displaystyle \alpha_{\rm em}^{\rm phys}=1/137.036$ $\displaystyle {\rm target};$ $\displaystyle \alpha_{\rm DPN}\;{\rm open}$OpenCMG V Addendum, C5 closeout
D2 reference-family verdictThe preregistered multi-size and multi-seed contract fails. The later temporal-depth ladder supports a finite-time-transient diagnosis without identifying a physical photon cone.$\displaystyle \texttt{D2\_CONTRACT\_FAILED}$Benchmark / numericC5/D2 result notes
Regular SU(2) V4 controlA reproducible finite-volume positive-kernel control is closed. The simplest correlation plateau is not common to both couplings, and the result is not a physical DPN port.$\displaystyle \lambda_2(L_{\rm el})\neq\Delta_{\rm transfer}\neq m_{\rm corr}\neq\Delta_{\rm YM}$Benchmark / numericCMG--Yang--Mills V4 closeout, XIII
Conditional DPN gauge construction (XIII Part I)An explicit construction emits oriented 3+1 cell complexes with exact chain identities; on fixed complexes the declared Hamiltonian preserves gauge invariance and the Gauss constraint, and the construction transfers to a second generator family without retuning. It is conditional on the supplied complex, not a derivation from a DPN microlaw.$\displaystyle B_1B_2=B_2B_3=B_3B_4=0,$ $\displaystyle b_0=1,$ $\displaystyle b_1=b_2=b_3=b_4=0$ConditionalXIII
Microscopic gauge provider (XIII audit)The recovered historical generator supplies three of fourteen required provider fields, derives none, leaves ten underdetermined and contradicts native face emission. The conditional SU(2) decay estimates fail the predeclared scale-admission criteria and the transfer-operator gate stays closed; no confinement or continuum Yang–Mills gap is claimed.$\displaystyle 3/14\ {\rm present},$ $\displaystyle 0\ {\rm derivable},$ $\displaystyle 10\ {\rm underdetermined},$ $\displaystyle 1\ {\rm contradicted}$OpenXIII

The matter sector uses relational GKSL dynamics, conditional chirality, charge superselection, and local loss of criticality as a measurement mechanism.

ConceptDefinitionEquationStatusSource
GKSL matter closureRelational open-system dynamics with exact fermion-number conservation in the baseline sector.$\displaystyle \partial_t\rho=-i[H,\rho]+\sum_e\left(A_e\rho A_e^\dagger-\frac12\{A_e^\dagger A_e,\rho\}\right)$Derived / definedCMG VIII, X
Charge superselectionThe lightest Q=1 excitation is stable by charge conservation and spectral ordering.$\displaystyle [Q,H]=0,$ $\displaystyle [Q,A_e]=0$Derived / definedCMG VIII, XII
Composite Q=3 necessary conditionThe positive binding combination is necessary within the stated closure. Physical stability additionally requires rho above the three-body threshold with mass gaps and memory density extracted consistently; no proton identification follows.$\displaystyle u_3-3u_1=6\chi>0$ $\displaystyle {\rm necessary},$ $\displaystyle \rho>\rho_{3,*}$ $\displaystyle {\rm still\ required}$ConditionalCMG XII
Chiral projectorsDirected ladder-ring transfer gives chiral projectors under spectral isolation, weak directed scaling, and doublet factorization.$\displaystyle P_L=\frac{1-\gamma^5}{2},$ $\displaystyle P_R=\frac{1+\gamma^5}{2}$ConditionalCMG XI
Measurement thresholdWithin the local feedback model, loss of criticality occurs at the threshold $J=J_{c,q}$; a complete measurement theory remains open.$\displaystyle J=J_{c,q}$ConditionalCMG XII

The published minimal-truncation exponents are retained as a historical sign-branch benchmark. The corrected positive-mass flow and its stability matrix remain open.

ConceptDefinitionEquationStatusSource
Wetterich flowThe auxiliary memory formulation is embedded in the effective average action flow.$\displaystyle \partial_t\Gamma_k=\frac12{\rm STr}\left[(\Gamma_k^{(2)}+R_k)^{-1}\partial_tR_k\right]$Derived / definedCMG IX
Historical minimal-truncation exponentsThese exponents belong to the superseded-sign benchmark and are not the current positive-mass fixed-point result.$\displaystyle \theta_{b^2}=4,$ $\displaystyle \theta_{\alpha}=-2$Benchmark / numericCMG IX
Open FRG extensionMatter backreaction, larger nonlocal truncations, and regulator dependence remain to be tested.$\displaystyle \Gamma_k^{\rm full}=\Gamma_k^{\rm grav}+\Gamma_k^{\rm matter}+\Gamma_k^{\rm nonlocal}$OpenCMG IX, Handbook
Corrected positive-mass flowThe Euclidean positive-mass branch must be recomputed and its fixed point and stability matrix audited before an ultraviolet completion claim is promoted.$\displaystyle +\beta_{\rm rate}^{2}\;{\rm branch:~open}$OpenCMG IX correction/status layer

Claim Lock Table

These are the currently locked public-facing statements and boundaries.

ClaimStatusEquationBoundary note
Core action conventionLocked$\displaystyle S\supset-\frac{\tilde\alpha}{2}R(\Box+\beta_{\rm rate}^2)^{-1}_{\rm ret}R,$ $\displaystyle \eta_{\rm act}=-\tilde\alpha\in(0,1)$The fixed-background closure uses the distinct amplitude eta_cl.
GR limitsLocked$\displaystyle \tilde\alpha\to0\;(\eta_{\rm act}\to0)\;{\rm or}\;\beta_{\rm rate}\to\infty;$ $\displaystyle \eta_{\rm cl}\to0\;{\rm or}\;\beta_{\rm IR}\to0$Do not state beta_IR -> infinity as the perturbation-sector GR limit.
Local screening signLocked$\displaystyle \Gamma_{\rm eff}\to\infty\Rightarrow\beta_\mu\to0\Rightarrow\mu\to1$Dense environments reduce the local Poisson inverse-length scale in the screening ansatz.
DESI compressed benchmarkNumerically supported$\displaystyle A_g=0.9962\pm0.0437,$ $\displaystyle \Delta\chi^2=-0.0075,$ $\displaystyle \Delta{\rm AIC}=+1.99,$ $\displaystyle \Delta{\rm BIC}=+1.78$Allowed, near-GR, not preferred over LambdaCDM.
DESI degeneracyLocked$\displaystyle A_g=1-\eta_{\rm cl}S_{\rm DESI}(\beta_{\rm IR})$This is a degeneracy product, not a unique measurement of eta_cl or beta_IR.
Full-shape nuisance profilingNumerically supported$\displaystyle \begin{array}{c|c}\beta_{\rm ratio}&\eta_{{\rm cl},95}^{\rm FS}\\100&0.2544\\300&0.0680\\1000&0.0316\\3000&0.0212\\10^4&0.0153\end{array}$At beta_ratio=30 the physical interval 0<=eta_cl<=1 is unconstrained. The profile reference is chi2_GR,prof=339.560305 and the maximum shallow improvement is 0.0501.
DESI DR2 BAO background interfaceBenchmark$\displaystyle \eta_{\rm act}=0.1,$ $\displaystyle \beta_{\rm rate}/H_0=10^5,$ $\displaystyle \Delta\chi^2_{\rm BAO}=-5.415287$Fixed-standard-parameter sparse-grid interface test; do not combine it with the DR1 eta_cl limits.
S8 boundaryOpen$\displaystyle A_g\simeq1\Rightarrow{\rm no\ linear\ }S_8{\rm\ solution\ in\ the\ locked\ closure}$Any substantial suppression requires nonlinear PM/N-body validation.
C2 action-level scalar closureConditional$\displaystyle \gamma_{\rm action}^{\rm QS}=\frac{\bar F+2\eta_{\rm act}s}{\bar F+4\eta_{\rm act}s}\neq1$General-gauge SymPy route and radiation cross-check passed. Direct integration replaces the rejected averaged-fluid route; start-time insensitivity fails and the Lambda branch is non-unique. Prototype provider passed, production pending; independent tensor-tool confirmation and every likelihood-facing gate remain open. Do not combine (eta_act,beta_rate) with CMG VII (eta_cl,beta_IR).
SEM--RAR boundaryNumerically supported$\displaystyle g_{\rm obs}=g_b/(1-e^{-\sqrt{g_b/g_\dagger}})$Equivalent to exponential RAR; not a completed dark-matter replacement for clusters/CMB/nonlinear structure.
C4 reduced dynamic bridgeBenchmark$\displaystyle g_\dagger\simeq\frac{\xi_\infty}{e-1}c\,\beta_{\rm rate},$ $\displaystyle \xi_\infty\simeq0.297,$ $\displaystyle \beta_{\rm rate}\simeq H_0$Reduced dynamic benchmark, not a microscopic g_dagger derivation: xi_infty is not xi_phys, and the elastic diagnostic reaches only 0.64--0.72 of (2 pi)^2 at N=8192 with a persistent knn/annulus topology offset.
C3 screening precursorBenchmark$\displaystyle \beta_\mu(r)\Rightarrow\mu_{\rm eff}(r)$ (1D NFW, Yukawa BVP)Validates the spherical screened force solver and the sign of the response; microscopic calibration and PM/N-body embedding remain open.
Cluster/web residual pilotOpen$\displaystyle N_{\rm clean+web}=4<8$Below the minimum cluster-count gate; no b_C is estimated and no physical interpretation is allowed.
Maxwell sectorMixed$\displaystyle B_1B_2=0,$ $\displaystyle c_\gamma=0.7380\;{\rm(static\ proxy)}$Incidence/Hodge structure is supported on the recovered post-hoc face complex. The static coefficient has no physically identified c_DPN denominator; a native edge carrier/provider, alpha_em calibration and a two-species common cone remain open.
C5 photon-speed identifiabilityOpen$\displaystyle c_\gamma/c_{\rm DPN}\;{\rm not\ identifiable\ from\ the\ static\ export}$The static ratio remains unidentifiable. The D2 reference-family execution returned D2_CONTRACT_FAILED; the temporal-depth audit returned FINITE_TIME_TRANSIENT_SUPPORTED as a diagnostic only. Raw-export dispersion, a physical DPN provider and a common-cone test remain open.
Chirality sectorConditional$\displaystyle P_L=(1-\gamma^5)/2,$ $\displaystyle P_R=(1+\gamma^5)/2$Conditional theorem plus exact ladder-ring realization; generic irregular DPN proof open.
FRG sectorOpen$\displaystyle \theta_{b^2}=4,$ $\displaystyle \theta_{\alpha}=-2$The displayed exponents are a historical superseded-sign benchmark. The corrected positive-mass flow, fixed point and stability matrix remain open.
Yang--Mills control boundaryBenchmark$\displaystyle \lambda_2(L_{\rm el})\neq\Delta_{\rm transfer}\neq m_{\rm corr}\neq\Delta_{\rm YM}$Regular-lattice and conditional-provider controls do not establish a physical DPN derivation, confinement or a continuum Yang--Mills gap.
CMG XIII conditional provider and birth selectorConditional$\displaystyle w(s)=C\exp(-\beta_{\rm sel}s),$ $\displaystyle {\rm ledger}\ 7/8$Conditional constructions with bounded negative results: the historical generator derives no gauge provider, scale admission was not achieved, the effective-coefficient law (row 5) is open and a fixed three-volume is not a clock. The frozen corpus was closed on 16 September 2026 (OD0); no confinement, continuum Yang--Mills gap or Clay result is claimed.

Theory Maturity Dashboard

Concept count per layer: derived/defined, benchmark/numeric, open, conditional, proxy/ansatz.

Exact concept counts
Counts describe the status of listed concepts, not probabilities or validation scores.
LayerDerived / definedBenchmark / numericOpenConditionalProxy / ansatz
DPN microstructure and continuum bridge11130
Nonlocal gravitational action and parameter lock50010
Linear cosmology and DESI DR1 constraints15110
Nonlinear screening interface01150
Galactic SEM--RAR response04201
Gauge sector and emergent electromagnetism25310
Fermions, chirality, and measurement20030
UV completion and FRG boundary11200

Master Symbol Table

The beta hierarchy and the distinction between cosmological, screened, galactic, and GKSL kernels are explicit.

SymbolDefinitionUnitsSource
$\displaystyle \tilde\alpha$Dimensionless nonlocal coupling at the action level; stable window is negative.1CMG I, Microscopic Foundations
$\displaystyle \eta_{\rm act}=-\tilde\alpha$Positive action-level coupling in the linearized effective-scalar window.1CMG I, Microscopic Foundations
$\displaystyle \eta_{\rm cl}$Fixed-background Poisson-closure amplitude; not globally identified with $\eta_{\rm act}$.1CMG VII, Handbook, Synthesis
$\displaystyle U$Auxiliary scalar satisfying $(\Box+\beta_{\rm rate}^2)U=-R$.1CMG I
$\displaystyle \beta_{\rm rate}$Action-level memory relaxation rate.$s^{-1}$CMG I, III
$\displaystyle \beta_{\rm IR}=\beta_{\rm rate}/c$Dimensional inverse-length bridge used operationally in the fixed-background closure; full action-to-perturbation matching remains open.$L^{-1}$CMG VII
$\displaystyle \Gamma_{\rm eff}(x)$Environment-dependent dissipation rate from channel saturation and tidal degradation.$s^{-1}$Microscopic Foundations
$\displaystyle \beta_\mu(x)$Local Poisson inverse-length scale used in screened environments.$L^{-1}$Microscopic Foundations
$\displaystyle \mu(k,a)$Modified density-growth coupling.1CMG VII
$\displaystyle A_g$DESI compressed growth amplitude, $A_g=0.9962\pm0.0437$.1CMG VII
$\displaystyle S_{\rm DESI}(\beta_{\rm IR})$DESI response functional in $A_g=1-\eta_{\rm cl}S_{\rm DESI}$.1CMG VII
$\displaystyle g_\dagger$SEM--RAR acceleration scale, calibrated from SPARC; distinct from beta_IR.$m\,s^{-2}$CMG II
$\displaystyle K_\theta$DPN torsional stiffness controlling spectral-gap memory scale.model-dependent before SI calibrationCMG III, VI
$\displaystyle B_1,B_2$Chain-complex incidence operators; Maxwell check uses $B_1B_2=0$.matrixCMG V Addendum
$\displaystyle Q$Fermion-number/charge superselection operator.1CMG VIII, XII
$\displaystyle P_L,P_R$Chiral projectors from directed memory flow under CMG XI hypotheses.operatorCMG XI
$\displaystyle J_{c,q}$Local critical-load threshold in the measurement mechanism.model-dependentCMG XII
$\displaystyle \Gamma_k$FRG effective average action.actionCMG IX
$\displaystyle c_{\rm DPN}$Physical causal-cone speed required in r_gamma=c_gamma/c_DPN. The D2 reference-family contract was executed and failed; a physical DPN value remains unidentified.$L\,s^{-1}$C5/D2 closeout
$\displaystyle \tau_p^{(0)},\;\tau_p^{\rm loc},\;\tau_p^{\rm dyn}$Plaquette-tension hierarchy: zero-flux harmonic fit $\tau_p^{(0)}=T_p$, local curvature $\tau_p^{\rm loc}=T_p\cos\Theta_p^{(0)}$, and the unmeasured dynamic response $\tau_p^{\rm dyn}$; the uniform placeholder $\tau_p=1$ is historical.1CMG XII, C5 closeout
$\displaystyle \beta_{\rm sel}$Birth-selector weight parameter in $w(s)=C\exp(-\beta_{\rm sel}s)$; $\beta_{\rm sel}>0$ for strict preference of lower action and $\beta_{\rm sel}=0$ for the uniform control. Its value is not selected because row 5 is open.1CMG XIII

Publication Library

Full titles and DOI record metadata; research summaries retain the public edition’s claim boundaries.

Titles and dates from public DOI metadata, checked . Version numbers are not supplied in these metadata; the linked Zenodo records contain the available versions and files. Research summaries reflect the 1 October 2026 edition.

15 publications

CMG V

Causal Memory Gravity V: Continuum Limit and Emergent Quantum Dynamics from Discrete Planck Networks

DOI record date: · Version: see Zenodo record

Conditional continuum and emergent quantum/gauge constructions; the same Zenodo record includes the SU(2) frame-gap supplement and Maxwell/Plaquette addendum.

$\displaystyle \hbar_{\rm eff}=K_\theta\Delta t$
DOI: 10.5281/zenodo.18636726 ↗
CMG VI

Causal Memory Gravity VI: Microscopic Origin of Inertia and Dark Energy — Controlled Mean-Field Baseline with Reduced-DPN Fluctuation Validation

DOI record date: · Version: see Zenodo record

Mean-field and reduced-DPN fluctuation validation for inertia and dark-energy-like behavior; includes the Thermal Criticality / Spectral Matching / RG Closure addendum.

$\displaystyle \sigma_{\bar\rho}\propto N^{-0.516}$
DOI: 10.5281/zenodo.18652123 ↗
CMG XIII

Causal Memory Gravity XIII: Conditional Microscopic Gauge Dynamics and the Conditional Birth Selector (Parts I and II)

DOI record date: · Version: see Zenodo record

Conditional constructions and bounded negative results for the microscopic gauge provider, scale admission, coefficient-selection law and physical event clock. The frozen corpus is closed; the 7/8 selector ledger and open row 5 are retained.

$\displaystyle \lambda_2(L_{\rm el})\neq\Delta_{\rm transfer}\neq m_{\rm corr}\neq\Delta_{\rm YM}$
DOI: 10.5281/zenodo.23076279 ↗