A Closed Toy EFT for a Finite-Domain Zeno-Protected Dark Q-Ball Cavity

Status and scope.

This repository is a toy effective-field-theory and numerical-control model. It is not a real-world engineering feasibility claim, not an experimental claim, and not a Category A global Q-ball proof. The lead soliton branch is finite-domain certified to x=100. The final claim is internal consistency under exact toy-EFT assumptions:

Full toy EFT internally consistent under explicit one-way dark continuum sink; finite-domain x=100, not Category A; not real-world engineering feasibility.

Abstract

This repository develops and audits a closed toy effective field theory for a room-scale, Zeno-protected dark Q-ball cavity. The starting point is a complex scalar Q-ball sector with a finite-domain numerical radial profile. The final lead branch is the xi=0.5 balanced branch, with protected radius R_prot = 3.2011965876735604 m, room-boundary leakage leakage_R_room = 4.834303080161358e-09, and finite-domain certification to x=100. The numerical acceptance status is revised operational B++, with the original stricter gate retained transparently as B+.

The model couples the Q-ball profile to an encoded ordinary-sector code/leakage decomposition through an exact U(1)_G gauge/superselection syndrome. The monitor syndrome is S = Pbar, so the dark pointer bath sees leakage but annihilates the protected code subspace. At the exact-symmetry level this gives Gamma_code = 0, Gamma_leak = Gamma_dark, and the same finite-strength Zeno leakage formula used throughout the simulator. Ordinary portal heating is suppressed by an exact product-sector bridge and even-bridge rule: dangerous dimension-4 and dimension-5 ordinary portals are forbidden, while the leading residual ordinary portals begin at dimension 6 and are below the steel 1 nW proxy used in the audits.

The last conditional item, dark pointer-bath entropy export, is closed inside the toy EFT by an explicit one-way dark continuum sink with hybrid stiffness plus active high-pass filtering. The result is an internally consistent finite domain toy EFT, not a UV-complete microscopic theory, not a global soliton existence proof, and not a real-world engineering proposal.

Plain-language summary

This project asks a narrow theoretical question: can a simulated dark-sector Q-ball profile, a protected quantum subspace, a Zeno-style leakage monitor, and a set of exact toy symmetries be made mutually consistent on paper and in code? The answer reached by the repository is yes, inside a carefully scoped toy effective model.

That does not mean such an object can be built, exists in nature, or has a known microscopic origin. The result says only that the frozen equations, selection rules, numerical branch, leakage accounting, portal suppression, and sink/noise closure do not contradict each other within the assumptions encoded here.

Final result at a glance

Quantity	Frozen lead value
R_prot	3.2011965876735604 m
leakage_R_room	4.834303080161358e-09
x_cert	100
Gamma_dark	4.8e14 s^-1 = 3.159417e-01 eV
Delta_dark	3.291060e-08 eV
Gamma_ratio	240
Delta_ratio	50
E_total_J	1.103704e-02 J
Revised operational status	B++
Original strict status	B+
Global-tail status	finite-domain x=100, not Category A

Frozen lead branch:

Parameter	Value
xi	0.5
m_chi_eV	6.447791e-01
omega_eV_15sig	6.447790598202821e-01
Gamma_dark_s_inv	4.8e14
Gamma_dark_eV	3.159417e-01
a_threshold	0.02

What has been shown

• A closed toy EFT was constructed from the numerical Q-ball branch, exact syndrome algebra, dark pointer bath, product-sector bridge, and one-way dark continuum sink.
• The lead branch is finite-domain certified to x=100; the protected room lies well inside the certified interval.
• The model is revised operational B++ under the repaired numerical acceptance criteria.
• The original strict numerical gate is retained as B+ for transparency.
• The code/leakage algebra closes with S = Pbar.
• At exact symmetry, Gamma_code = 0 and Gamma_leak = Gamma_dark.
• Delta_dark acts only on Pbar.
• The dressed leakage operator is symmetry-compatible and monitorable.
• Dangerous dimension-4 and dimension-5 ordinary portals are forbidden by the exact even-bridge/product-sector rule.
• The leading residual ordinary portals are dimension 6 and have Gamma_portal/Gamma_dark = 1.728398e-49 at the 1 TeV reference scale, below the steel 1 nW proxy bound 6.381810e-38.
• Sink/noise closure passes under the explicit one-way dark continuum model: selected bandwidth 1.2e14 Hz, low-frequency fraction 3e-13, and omega RMS 1.2 Hz.

What has not been shown

• No global x -> infinity Category A Q-ball proof is claimed.
• No real microscopic realization of the exact symmetries is supplied.
• No real-world engineering feasibility is claimed.
• No experimental evidence is claimed.
• No complete nonlinear or environmental stability proof beyond the tested stress models is claimed.
• The Q-ball EFT counterterms are calibrated/frozen inputs, not derived from a UV-complete model.
• The entropy sink, source, bridge sector, and exact superselection rules remain toy EFT structures.

Model overview

Q-ball sector

The dark sector is a complex scalar chi with a Q-ball-style potential. The lead numerical branch is finite-domain certified to x=100 and is used only on that certified domain.

Code/leakage projectors

Ordinary-sector degrees of freedom are organized into a protected code subspace P and leakage complement Pbar = I - P. The model assumes a low-evolution encoded Hamiltonian inside P.

Syndrome operator

The exact gauge/superselection construction defines

S = Pbar = 1 - Pi(G=0).

The monitor sees leakage states but annihilates code states.

Dark pointer bath

The dark pointer bath supplies the Zeno dephasing channel through L_dark = sqrt(2 Gamma_dark) S. The bath is dark-sector only under the frozen architecture.

Product-sector bridge

The total toy Hilbert space factorizes into code, dark-pointer, sink, bridge, and ordinary sectors. The exact even-bridge rule forbids one-bridge ordinary-dark portals. This is the central portal-protection assumption.

Dressed leakage

Leakage is not a bare gauge-forbidden transition. It is dressed through X_leak/M:

V_leak = y_leak psi_leak^dagger X_leak psi_code M / Lambda_M^2 + h.c.

This keeps total U(1)_G charge neutral while giving [S, V_leak] != 0.

One-way dark continuum sink

The sink exports dark pointer-bath entropy through a dark-only one-way continuum. The selected closure uses the pointer-even reset current

J_B = sum_kl c_kl B_k C_l

and hybrid stiffness plus active high-pass filtering.

Residual portals

The first allowed ordinary portals are dimension 6 bridge-pair residuals, for example B_k^2 O_ord / Lambda^2 and M^dagger M O_ord / Lambda^2.

Consolidated equations

Q-ball potential and radial equation

$$U(|\chi|) = \frac{1}{2}m_\chi^2|\chi|^2 -\frac{1}{4}\lambda|\chi|^4 +\frac{1}{6}\kappa|\chi|^6 .$$

With

$$\chi(t,r)=\phi(r)e^{-i\omega t},$$

the radial equation is

$$\phi''+\frac{2}{r}\phi' = (m_\chi^2-\omega^2)\phi-\lambda\phi^3+\kappa\phi^5 .$$

Dimensionless numerical profile equation

Define

$$x=\mu_{\mathrm{wall}}r,\qquad y=\phi/\phi_0,\qquad \beta=\lambda\phi_0^2/\mu_{\mathrm{wall}}^2 .$$

The dimensionless equation is

$$y''+\frac{2}{x}y' = y-\beta y^3+(\beta-1)y^5 .$$

Frozen branch values:

m_chi = 0.6447790598204083 eV
omega = 6.447790598202821e-01 eV
R_prot = 3.2011965876735604 m
leakage_R_room = 4.834303080161358e-09
x_cert = 100

Projectors and syndrome

$$P=\Pi(G=0),\qquad \bar P=I-P,\qquad S=\bar P=1-\Pi(G=0).$$

The exact algebra used by the audits is

$$SP=0,\qquad S\bar P=\bar P,\qquad [S,PHP]=0 .$$

Dressed leakage operator

$$V_{\mathrm{leak}} = \frac{y_{\mathrm{leak}}}{\Lambda_M^2} \psi_{\mathrm{leak}}^\dagger X_{\mathrm{leak}}\psi_{\mathrm{code}}M + \mathrm{h.c.},$$

with

$$[S,V_{\mathrm{leak}}] \neq 0 .$$

Product-sector bridge and pointer current

$$\mathcal{H}_{\mathrm{total}} = \mathcal{H}_{\mathrm{code}} \otimes\mathcal{H}_{\mathrm{dark\ pointer}} \otimes\mathcal{H}_{\mathrm{sink}} \otimes\mathcal{H}_{\mathrm{bridge}} \otimes\mathcal{H}_{\mathrm{ord}}.$$

The pointer parity makes B_k and C_l odd, while

$$J_B=\sum_{kl}c_{kl}B_k C_l$$

is pointer-even and can drive the dark monitor.

Lindblad monitor

$$L_{\mathrm{dark}}=\sqrt{2\Gamma_{\mathrm{dark}}}\,S .$$

The open-system model is

$$\dot\rho = -i[H+\Delta_{\mathrm{dark}}S,\rho] +\mathcal{D}[L_{\mathrm{dark}}]\rho,$$

with

$$\mathcal{D}[L]\rho = L\rho L^\dagger-\frac{1}{2}\{L^\dagger L,\rho\}.$$

At exact symmetry:

$$\Gamma_{\mathrm{code}}=0,\qquad \Gamma_{\mathrm{leak}}=\Gamma_{\mathrm{dark}}.$$

Finite-strength Zeno leakage rate

For leakage coupling rate nu_pq and detuning delta_pq(r),

$$\gamma_{pq}(r) = \frac{2\Gamma(r)\nu_{pq}^2} {\Gamma(r)^2+\delta_{pq}(r)^2}.$$

In the strong-Zeno limit,

$$\gamma_{pq}(r)\simeq \frac{2\nu_{pq}^2}{\Gamma(r)} .$$

Residual portals

Forbidden exactly:

S O_ord
abs(chi)^2 O_ord
B_k C_l O_ord / Lambda
dimension-5 one-bridge ordinary portals

Leading allowed residuals:

B_k^2 O_ord / Lambda^2
S B_k^2 O_ord / Lambda^2
X_leak^dagger X_leak O_ord / Lambda^2
M^dagger M O_ord / Lambda^2

At Lambda = 1 TeV,

$$\Gamma_{\mathrm{portal}}/\Gamma_{\mathrm{dark}}=1.728398\times 10^{-49}.$$

Sink/noise constraints

Gamma_dark = 4.8e14 s^-1
Markovian bandwidth >= Gamma_dark/(2*pi) = 7.639437e13 Hz
selected one-way continuum bandwidth = 1.2e14 Hz
low-frequency fraction <= 9.355911e-13
selected low-frequency fraction = 3.0e-13
omega RMS <= 4.254944 Hz
selected omega RMS = 1.2 Hz

Numerical branch and certification

The accepted lead branch is not a logistic ansatz result. The project moved from analytic/logistic initialization to a numerical radial Q-ball profile, then to finite-domain certification. The final status is:

• Finite-domain certificate: x_cert = 100.
• Physical protected region lies far inside the certified domain.
• Global-tail status: finite-domain x=100, not Category A.
• Revised operational gate: B++.
• Original strict gate: B+, retained as a transparency label.
• Solver agreement: original relative E/Q and R_prot gates were stricter than operationally useful; the revised gate uses common-grid profile error, leakage agreement, absolute R_prot agreement, and E/Q uncertainty relative to the stability margin.
• Stability status: coupled-radial stability passed in the validated branch family.
• Stress status: bounded nonlinear rotating-frame stress models passed inside the tested regime.
• Precision limitation: one-shot global shooting is exponentially precision-limited beyond the certified interval.

Validation chain

Stage	What changed	Resulting status	Key output
Original astronomical toy candidate	Initial toy optimizer maximized protected volume	Rejected as physical target; objective changed	outputs/latest/
Room-scale physical ansatz	Targeted R_prot near room scale	Logistic ansatz became initializer only	outputs/room_physical/
Numerical Q-ball solve	Replaced ansatz ranking with radial numerical solve	Localized finite-domain candidate found	outputs/numerical_qball_room/report.md
Finite-domain certificate	Certified profile on finite domain	Category B+/finite-domain, not Category A	outputs/numerical_qball_finite_domain_certificate/report.md
Operational-B++ branch family	Repaired solver thresholds and scanned monitor caps	xi=0.5 selected as balanced lead	outputs/monitor_cap_branch_family_certificate/report.md
Detuning/control audit	Quantified near-threshold control burden	Detuning dominant but controllable in placeholder model	outputs/detuning_control_audit/report.md
QND monitor audit	Rejected absorptive monitoring	Dark pointer bath selected	outputs/qnd_monitor_mechanism_audit/report.md
Dark pointer bath	Parameterized QND-like dark monitor	Required exact selectivity and portal suppression	outputs/dark_pointer_bath_model_audit/report.md
Exact syndrome	Built exact S=Pbar model	Gauge/superselection preferred	outputs/exact_syndrome_pointer_bath_audit/report.md
Gauge/superselection Lagrangian	Made dressed leakage gauge-consistent	Needed portal protection	outputs/gauge_superselection_lagrangian_audit/report.md
Product-sector bridge	Forbade dimension-5 one-bridge portals	Technically natural under exact even-bridge rule	outputs/product_sector_bridge_model_audit/report.md
Full toy EFT certificate	Consolidated algebra, portals, branch, failures	Internally consistent except sink/noise conditional	outputs/full_toy_eft_consistency_certificate/report.md
Sink/noise closure	Added explicit one-way dark continuum sink	Full toy EFT internally consistent under sink model	outputs/sink_noise_closure_audit/report.md
Final closed toy EFT package	Wrote manuscript/reproducibility package	Final frozen public status	outputs/final_closed_toy_eft_package/report.md

Assumptions ledger

Assumption	Why needed	What breaks if it fails	Status in this toy model	Real-world status
Exact U(1)_G syndrome	Defines gauge/superselection leakage sectors	Gamma_code and unmonitored leakage can reappear	Closed by exact-syndrome and full-EFT algebra checks	Toy assumption
S=Pbar exact	Makes the bath see leakage but not code	Monitor can dephase code states or miss leakage	Algebra checks pass	Toy assumption
Exact Z2_pointer	Forbids odd bath/sink ordinary portals	B_k O_ord and C_l O_ord reappear	Portal and reset audits pass	Toy assumption
Exact even-bridge/product-sector rule	Forbids dimension-5 one-bridge ordinary portals	Portal heat bound fails badly	Product-sector no-go audit passes	Toy assumption
One-way dark continuum sink	Exports pointer entropy without ordinary heat branch	Reset can reopen ordinary portal or Gamma_code	Sink/noise closure passes	Toy assumption
Hybrid stiffness plus active high-pass filtering	Keeps detuning noise below tolerance	R_prot and leakage drift out of target	Closed-loop stress rows pass	Control placeholder
Dimension-6 residual portal scale	Keeps residual ordinary portal below steel 1 nW proxy	Portal ratio can exceed bound	1.728398e-49 at 1 TeV	Toy EFT input
Finite-domain x=100 certificate	Bounds profile on the physically relevant domain	No claim beyond certified interval	Numerical certificate	Numerical result with scope limit
Revised operational B++ gate	Defines practical numerical acceptance	Original strict label remains only B+	Solver-repair audit accepted revised gate	Numerical/operational criterion
Calibrated EFT counterterms	Absorbs loop shifts into frozen Q-ball inputs	Frozen branch may drift	Radiative closure treats as EFT input	Not UV-derived

Failure modes

Failure mode	Consequence	Current mitigation	Status
U(1)_G breaking	Gamma_code and unmonitored leakage can reappear	Exact gauge/superselection constraint	Closed by symmetry inside toy EFT
Bridge-even rule breaking	Dimension-5 ordinary portals fail heat bound	Exact even-bridge/product-sector rule	Closed by symmetry inside toy EFT
Pointer parity breaking	B_k O_ord or C_l O_ord reappears	Exact Z2_pointer	Closed by symmetry inside toy EFT
Product-sector locality breaking	S O_ord or abs(chi)^2 O_ord reappears	Product-sector factorization	Closed by symmetry inside toy EFT
Dimension-5 bridge accidentally allowed	Gamma_portal/Gamma_dark far above bound	Dimension-5 no-go catalog	Closed by symmetry inside toy EFT
Sink reset ordinary leakage	Ordinary heat branch or Gamma_code can reopen	Dark-only one-way sink through J_B	Closed by sink architecture
Low-frequency bath noise above tolerance	Detuning lock fails	Hybrid stiffness plus active high-pass filtering	Closed in toy stress model
Global tail failure beyond x=100	Not a Category A global soliton proof	Scope stated explicitly	Residual scope limit
Nonlinear instability outside tested regime	Operational B++ status could weaken	Bounded stress tests only	Residual scope limit
Microscopic source absent	No real-world realization follows	No feasibility claim	Outside toy EFT

Reproducibility

The commands below use repository-relative paths only. Run them from the root of a fresh clone.

Environment setup

cd <repo-root>
python3 -m venv .venv
source .venv/bin/activate
python -m pip install -U pip
python -m pip install -e .

Tests

python -m unittest discover -s tests

Expected result for the current package:

Ran 108 tests
OK

Q-ball finite-domain certificate

soliton-sim optimize \
  --config config/numerical_qball_finite_domain_certificate.yaml \
  --out outputs/numerical_qball_finite_domain_certificate

Expected key status: finite-domain certification reaches x>=100; global-tail status remains not Category A.

Operational-B++ branch family

soliton-sim monitor-cap-scan \
  --out outputs/monitor_cap_operational_Bpp_scan

soliton-sim branch-family-cert \
  --out outputs/monitor_cap_branch_family_certificate \
  --monitor-run outputs/monitor_cap_operational_Bpp_scan

Expected xi=0.5 key numbers:

R_prot = 3.2011965876735604
leakage_R_room = 4.834303080161358e-09
Gamma_ratio = 240
Delta_ratio = 50

Product-sector bridge no-go

soliton-sim product-sector-bridge-audit \
  --out outputs/product_sector_bridge_model_audit \
  --sequestered-run outputs/sequestered_sector_toy_model_audit

Expected key numbers:

dimension-6 residual ratio = 1.728398e-49
dimension-5 one-bridge ordinary portals = forbidden

Full toy EFT algebra check

soliton-sim full-eft-certificate \
  --out outputs/full_toy_eft_consistency_certificate \
  --product-run outputs/product_sector_bridge_model_audit

Expected key status:

internally consistent except sink/noise remains conditional

Sink/noise closure

soliton-sim sink-noise-closure-audit \
  --out outputs/sink_noise_closure_audit \
  --full-eft-run outputs/full_toy_eft_consistency_certificate

Expected key numbers:

one-way continuum bandwidth = 1.2e14 Hz
low-frequency fraction = 3e-13
omega RMS = 1.2 Hz

Final package generation

soliton-sim final-closed-package \
  --out outputs/final_closed_toy_eft_package \
  --sink-noise-run outputs/sink_noise_closure_audit

Expected final verdict:

Full toy EFT internally consistent under explicit one-way dark continuum sink;
finite-domain x=100, not Category A; not real-world engineering feasibility.

Regenerate a report from any output directory

soliton-sim report --run outputs/final_closed_toy_eft_package

Repository map

Important generated reports:

• outputs/final_closed_toy_eft_package/report.md
• outputs/final_closed_toy_eft_package/closed_toy_eft_equations.md
• outputs/final_closed_toy_eft_package/manuscript_final_status.md
• outputs/final_closed_toy_eft_package/reproducibility_readme.md
• outputs/sink_noise_closure_audit/report.md
• outputs/full_toy_eft_consistency_certificate/report.md
• outputs/product_sector_bridge_model_audit/report.md
• outputs/monitor_cap_branch_family_certificate/report.md

Main simulator package:

• soliton_sim/
• config/
• tests/

Diagrams

Sector architecture

flowchart LR
  Code["H_code: P=Pi(G=0)"] -->|dressed leakage V_leak| Bridge["H_bridge: X_leak, M"]
  Bridge --> Leak["Pbar leakage syndrome"]
  Dark["Q-ball chi, F(r)"] --> Syndrome["S=Pbar"]
  Syndrome --> Pointer["dark pointer B_k"]
  Pointer --> Current["J_B=sum c_kl B_k C_l"]
  Sink["one-way dark continuum C_l"] --> Current
  Current --> Lindblad["L_dark=sqrt(2 Gamma_dark) S"]
  Ordinary["H_ord"] -. "dimension-6 residual portals only" .- Bridge
  Ordinary -. "no S O_ord, no abs(chi)^2 O_ord" .- Dark

Loading

Information and entropy flow

flowchart TD
  Leakage["P-Pbar coherence"] --> Monitor["S=Pbar monitor"]
  Monitor --> PointerBath["dark pointer bath"]
  PointerBath --> Sink["one-way dark continuum sink"]
  Sink --> Export["dark entropy export"]
  Sink --> Filter["hybrid stiffness + active high-pass filter"]
  Filter --> Detuning["omega/mu_wall lock"]
  Detuning --> Protected["R_prot >= 3.0 m; leakage_R_room <= 1e-8"]
  PointerBath -. "no ordinary portal by bridge rule" .- Ordinary["ordinary sector"]

Loading

Manuscript-style final status

This repository constructs a closed toy effective field theory for a room-scale, Zeno-protected Q-ball cavity on a finite certified domain. The lead branch is the xi=0.5 balanced solution with R_prot = 3.2011965876735604 m, leakage_R_room = 4.834303080161358e-09, and finite-domain certification to x=100.

The model combines an exact U(1)_G gauge/superselection syndrome with S=Pbar, a dark pointer bath monitor, a product-sector bridge that forbids all one-bridge ordinary portals, dressed leakage through X_leak/M, and a one-way dark continuum sink. The Lindblad monitor gives Gamma_code=0, Gamma_leak=Gamma_dark, and finite-strength Zeno suppression in the leakage channel. The dangerous neutral portals are absent by exact symmetry, while the leading residual ordinary portals begin at dimension 6 and are below the steel 1 nW proxy at the reference scale.

What has been shown is internal consistency of the toy EFT under exact symmetry assumptions, finite-domain numerical certification, operational-B++ acceptance, and an explicit sink/noise closure model. What has not been shown is a global Category A Q-ball tail proof, nonlinear stability beyond the tested perturbative/stress regime, or any real-world microscopic realization of the exact symmetries, bridge rule, source, or dark entropy sink.

A future microscopic theory would need to supply the exact U(1)_G, the product-sector bridge as a real selection rule, a physical source for the Q-ball charge/frequency, a dark-only entropy sink with the specified low-frequency noise suppression, and a derivation of the residual portal scale. Until then, the result is a self-consistent toy EFT certificate, not an engineering feasibility claim.

License

This project is licensed under the MIT License.