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Release 10.21 — FIN Laboratory Transfer Package

Krzysztof Żuchowski

Published Jul 27, 2026• 0 citations
Publisher

Abstract

# Release 10.21 — FIN Laboratory Transfer Package ## P240 Optimal Tomography + P241 Blind-Custody Validator + P242 One-Shot Pipeline ### A scientific transfer package and executable specification for theoretical and experimental physicists ## Record metadata - **Creator:** Żuchowski, Krzysztof- **Affiliation:** Independent Researcher — Fractal Information Theory Project- **ORCID:** 0009-0002-0909-3613- **Resource type:** Publication — Preprint and executable specification- **Version:** 1.0.0- **Publication date:** 2026-07-27- **Language:** English- **Publisher:** Zenodo- **Access:** Open access- **License:** Creative Commons Attribution 4.0 International (CC BY 4.0)- **Repository:** https://github.com/hyconiek/Fractal-Nadsoliton-Theory- **Related project DOI:** https://doi.org/10.5281/zenodo.21435332 --- ## Abstract This release transfers the experimentally actionable part of the FIN research programme to an independent team of theoretical and experimental physicists. It begins from the finite strict twelve-node kernel K_strict on C_12, not from cosmological or Theory-of-Everything claims. With W = K_strict, s ≈ 1.660307, and A = sI - W, the exact Dirichlet identity $$\langle f, Af \rangle = \frac{1}{2} \sum_{x,y} W_{xy} |f_x - f_y|^2 \geq 0$$ places the same self-adjoint generator under both the coherent group U_t = e^{-itA} and the reversible heat/Markov semigroup P_t = e^{-tA}. Program 240 delivers the optimal spectral tomography protocol. The inverse-log noise factor e^x/x yields the unique time minimizer at x = τ λ_max = 1. Equal allocation across all twelve basis preparations is proved minimax. Matrix-Bernstein spectral bounds supply a distribution-free concentration guarantee, accompanied by synthetic shot-plan analyses (50 000 shots per preparation). Program 241 supplies an executable blind-custody validator checking eleven mandatory measurement, data, calibration, control, chronology, hash, and role-separation fields. It enforces strict provider–registrar–analyst role separation with detached GPG signatures. Program 242 is a fail-closed one-shot analysis pipeline. It evaluates holdout prediction P_{2τ}^pred = P̂_τ^2 against the sealed P̂_{2τ} data and reports binary pass/fail without model repair. No external physical bundle is supplied in this release, keeping Program 242 locked until genuine laboratory data are admitted. --- ## Key Features & Main Results 1. Dual Semantics of One Generator: Proves that coherent quantum walk dynamics U_t = e^{-itA} and diffusive Markov heat flow P_t = e^{-tA} share the same spatial generator A = sI - W on C_12, while clarifying that temporal semantics require operational instrument definition.2. Exact Tomographic Time Minimizer (P240): Proves x = τ λ_max = 1 is the unique minimizer of local absolute-noise amplification e^x/x for matrix logarithm rate extraction.3. Minimax Equal Allocation (P240): Proves cyclic symmetrization makes equal shot allocation across all 12 basis preparations minimax within the declared convex design class.4. Production Custody Validator (P241): Provides an 11-field schema and hash validator (fin_lab_p241_validator.py) enforcing provider ≠ registrar ≠ analyst role separation.5. Fail-Closed One-Shot Pipeline (P242): Implements an atomic ledger-locked analysis pipeline (fin_lab_p242_pipeline.py) that evaluates time-homogeneity P_{2τ} = P_τ^2 and the 0.02 projective spectral fingerprint without post-hoc threshold adjustment or model repair.6. Fully Validated Test Suite: Includes an 18-test regression suite (test_fin_lab_p240_242.py), all passing cleanly. --- ## Included Files in FIN_Laboratory_Transfer_Package_P240_242.zip - FIN_Laboratory_Transfer_Package_P240_242.pdf — Archival English preprint and executable laboratory transfer specification.- fin_lab_p240_optimal_tomography.py — Target construction, time/allocation optimization, matrix Bernstein bounds, and synthetic shot planner.- FIN_Lab_P240_Design_Lock.json — Canonical registered design lock for Program 240.- FIN_Lab_P240_Optimal_Tomography_Results.json — Executed numerical results for P240.- fin_lab_p241_validator.py — Production 11-field schema, hash, chronology, and role-separation validator.- FIN_Lab_P241_Transfer_Template/ — Complete directory of raw data schemas, manifest templates, and calibration headers for laboratories.- fin_lab_p242_pipeline.py — Fail-closed one-run external analysis pipeline.- FIN_Lab_P242_Analysis_Lock.json — Canonical frozen analysis lock for Program 242.- test_fin_lab_p240_242.py — Complete test suite (18 unit/falsification tests).- FIN_Lab_P240_242_MANIFEST.sha256 — SHA-256 integrity manifest of all package files. --- ## Keywords quantum process tomography; Markov semigroups; continuous-time quantum walk; matrix logarithm; matrix Bernstein bounds; blind custody; preregistration; fail-closed pipeline; operational physics; spectral graph theory; experimental quantum optics; integrated photonics. --- ## Suggested Citation Żuchowski, K. (2026). FIN Laboratory Transfer Package — Release 10.21: P240 Optimal Tomography + P241 Blind-Custody Validator + P242 One-Shot Pipeline (FIN Research Monograph & Transfer Package; Version 1.0.0) [Preprint]. Zenodo. https://doi.org/10.5281/zenodo.21435332

DOI
10.5281/zenodo.21630878

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## Record metadata - **Title:** One FIN Operator, Two Temporal Dynamics: Unitary Propagation, Reversible Diffusion, a Finite Double-Slit Experiment, and Operational Completion- **Creator:** Żuchowski, Krzysztof- **Affiliation:** Independent Researcher — Fractal Information Theory Project- **ORCID:** 0009-0002-0909-3613- **Resource type:** Publication — Preprint - **Version:** 1.0.0- **Publication date:** 2026-07-19- **Language:** English- **Publisher:** Zenodo- **Access:** Open access, subject to the license confirmation below- **Reserved DOI:** [10.5281/zenodo.21435332](https://doi.org/10.5281/zenodo.21435332) ## Abstract This technical note studies a precisely defined twelve-site FIN matrix and the two canonical temporal calculi generated by its weighted graph Laplacian. Let (W) be the zero-diagonal real symmetric cyclic-distance matrix on (mathbb Z_{12}) sampled from \[K(d)=\frac{\cos(0.18575d+0.16250)}{1+d^{1.8}},\] using cyclic distances (d=1,ldots,6). Its common row sum is \[s=1.660307278766099\] to fifteen decimal places, and \[A=sI-W.\] All off-diagonal weights used at (N=12) are positive. Therefore (A) is a connected weighted graph Laplacian and \[\langle f,Af\rangle=\frac12\sum_{x,y}W_{xy}|f_x-f_y|^2\ge 0.\] The same positive self-adjoint operator generates the unitary group \[U_t=e^{-itA}\] and the irreducible, symmetric, uniform-reversible Markov semigroup \[P_t=e^{-tA}.\] Although the two evolutions share Fourier eigenvectors and eigenvalues, their operational predictions are inequivalent. Markov diffusion has linear short-time escape, exact Chapman–Kolmogorov composition and exponential relaxation to the uniform law. Unitary position probabilities have quadratic short-time escape, interference, failure of population-level Chapman–Kolmogorov composition and no pointwise equilibrium. The release includes a reproducible finite double-slit analogue. A coherent preparation at vertices (-2) and (+2) is compared with a perfectly distinguishing which-path record and with classical diffusion. The interference term is displayed across all twelve detectors and through time. At the first local maximum of total interference, (t_*=1.5525), the symmetry detector has unit ideal visibility; reducing the overlap of the two environment/apparatus records continuously suppresses the fringe. The note also identifies the missing structure needed to convert the operator into an experimental model. The smallest established-style candidate is a **calibrated process–tester model**: a causal process tensor (quantum comb), an admissible tester containing preparations and instruments with classical records, and a clock/reference calibration. This object carries state, multitime dynamics, preparation, instruments, environmental memory, apparatus and records up to operational equivalence. The operator alone does not select a physical clock, dimensional scale, environment, apparatus, Born rule, orientation or temporal semantics. No cosmological, Theory-of-Everything or continuum-physics claim is made. ## Plain-language significance One finite operator can generate both wave-like and diffusion-like mathematics. That fact does not mean an observer turns one physical law into another. It means the static operator underdetermines the experiment. State preparation, phase reference, clock, environment, measurement instrument and stored record must be supplied before either family becomes a testable physical model. The included double-slit analogue makes the distinction visible: coherent alternatives interfere; a which-path record removes the cross term; classical diffusion produces a different distribution. These are three operational protocols built around the same finite matrix. ## Main results and confidence labels ### Proven - (A=sI-W) is positive semidefinite with (ker A=\operatorname{span}\{\mathbf 1\}) under the declared cyclic-distance convention.- The spectral gap is (0.754121154207080) to displayed precision.- (U_t=e^{-itA}) is unitary.- (P_t=e^{-tA}) is an entrywise positive, symmetric, doubly stochastic Markov semigroup for (t>0).- The scalar shift (s) is the unique scalar shift of this regular (W) that makes (A\mathbf1=0).- Born-position matrices (|U_t|^{\circ2}) do not form a nontrivial differentiable Markov semigroup.- No nontrivial continuous finite evolution can be both unitary and entrywise nonnegative stochastic.- The two-slit probability law follows from the stated coherent preparation, record overlap and detector POVM.- A dimensionful time, energy, mass, length or action scale cannot be selected from the dimensionless matrix alone. ### Computed and independently checkable - All six weights, the complete spectrum, the spectral gap and the Dirichlet-form residual.- Markov mixing times and the nonuniform unitary Cesàro position law.- Unitarity, stochasticity and Chapman–Kolmogorov residuals.- The first two-slit interference maximum (t_*=1.5525) and total-variation interference (0.1232806696).- Ideal phase-fringe visibility (1) at detector (x=0) for record overlap (eta=1). ### Candidate / strong structural evidence - A calibrated process–tester model is the smallest standard mathematical structure found that simultaneously carries the requested operational roles. ### Not established - That the FIN matrix is a measured Hamiltonian or measured stochastic generator.- That unitary or diffusive time is selected by FIN itself.- That the displayed parameter (t) is measured in seconds.- That Shannon entropy in the plots is thermodynamic entropy.- That the (N=12) Markov interpretation survives a continuum limit.- That a microscopic apparatus, environment, selector, orientation or physical constants are derived from (A). ## Double-slit simulation The simulated slit modes are (a=10\equiv-2\pmod{12}) and (b=2). 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Zenodo. https://doi.org/10.5281/zenodo.21435332 ```bibtex@misc{zuchowski_fin_dual_dynamics_2026, author = {Krzysztof Żuchowski}, title = {One FIN Operator, Two Temporal Dynamics: Unitary Pro

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Release 10.21 — FIN Laboratory Transfer Package ## P240 Optimal Tomography + P241 Blind-Custody Validator + P242 One-Shot Pipeline ### A scientific transfer package and executable specification for theoretical and experimental physicists ## Record metadata - Creator: Żuchowski, Krzysztof- Affiliation: Independent Researcher — Fractal Information Theory Project- ORCID: 0009-0002-0909-3613- Resource type: Publication — Preprint and executable specification- Version: 1.0.0- Publication date: 2026-07-27- Language: English- Publisher: Zenodo- Access: Open access- License: Creative Commons Attribution 4.0 International (CC BY 4.0)- Repository: https://github.com/hyconiek/Fractal-Nadsoliton-Theory- Related project DOI: https://doi.org/10.5281/zenodo.21435332 --- ## Abstract This release transfers the experimentally actionable part of the FIN research programme to an independent team of theoretical and experimental physicists. It begins from the finite strict twelve-node kernel K_strict on C_12, not from cosmological or Theory-of-Everything claims. With W = K_strict, s ≈ 1.660307, and A = sI - W, the exact Dirichlet identity ⟨f,Af⟩=12∑x,yWxy∣fx−fy∣2≥0\langle f, Af \rangle = \frac{1}{2} \sum_{x,y} W_{xy} |f_x - f_y|^2 \geq 0⟨f,Af⟩=21​∑x,y​Wxy​∣fx​−fy​∣2≥0 places the same self-adjoint generator under both the coherent group U_t = e^{-itA} and the reversible heat/Markov semigroup P_t = e^{-tA}. Program 240 delivers the optimal spectral tomography protocol. The inverse-log noise factor e^x/x yields the unique time minimizer at x = τ λ_max = 1. Equal allocation across all twelve basis preparations is proved minimax. Matrix-Bernstein spectral bounds supply a distribution-free concentration guarantee, accompanied by synthetic shot-plan analyses (50 000 shots per preparation). Program 241 supplies an executable blind-custody validator checking eleven mandatory measurement, data, calibration, control, chronology, hash, and role-separation fields. It enforces strict provider–registrar–analyst role separation with detached GPG signatures. Program 242 is a fail-closed one-shot analysis pipeline. It evaluates holdout prediction P_{2τ}^pred = P̂_τ^2 against the sealed P̂_{2τ} data and reports binary pass/fail without model repair. No external physical bundle is supplied in this release, keeping Program 242 locked until genuine laboratory data are admitted. --- ## Key Features & Main Results 1. Dual Semantics of One Generator: Proves that coherent quantum walk dynamics U_t = e^{-itA} and diffusive Markov heat flow P_t = e^{-tA} share the same spatial generator A = sI - W on C_12, while clarifying that temporal semantics require operational instrument definition.2. Exact Tomographic Time Minimizer (P240): Proves x = τ λ_max = 1 is the unique minimizer of local absolute-noise amplification e^x/x for matrix logarithm rate extraction.3. Minimax Equal Allocation (P240): Proves cyclic symmetrization makes equal shot allocation across all 12 basis preparations minimax within the declared convex design class.4. Production Custody Validator (P241): Provides an 11-field schema and hash validator (fin_lab_p241_validator.py) enforcing provider ≠ registrar ≠ analyst role separation.5. Fail-Closed One-Shot Pipeline (P242): Implements an atomic ledger-locked analysis pipeline (fin_lab_p242_pipeline.py) that evaluates time-homogeneity P_{2τ} = P_τ^2 and the 0.02 projective spectral fingerprint without post-hoc threshold adjustment or model repair.6. Fully Validated Test Suite: Includes an 18-test regression suite (test_fin_lab_p240_242.py), all passing cleanly. --- ## Included Files in FIN_Laboratory_Transfer_Package_P240_242.zip - FIN_Laboratory_Transfer_Package_P240_242.pdf — Archival English preprint and executable laboratory transfer specification.- fin_lab_p240_optimal_tomography.py — Target construction, time/allocation optimization, matrix Bernstein bounds, and synthetic shot planner.- FIN_Lab_P240_Design_Lock.json — Canonical registered design lock for Program 240.- FIN_Lab_P240_Optimal_Tomography_Results.json — Executed numerical results for P240.- fin_lab_p241_validator.py — Production 11-field schema, hash, chronology, and role-separation validator.- FIN_Lab_P241_Transfer_Template/ — Complete directory of raw data schemas, manifest templates, and calibration headers for laboratories.- fin_lab_p242_pipeline.py — Fail-closed one-run external analysis pipeline.- FIN_Lab_P242_Analysis_Lock.json — Canonical frozen analysis lock for Program 242.- test_fin_lab_p240_242.py — Complete test suite (18 unit/falsification tests).- FIN_Lab_P240_242_MANIFEST.sha256 — SHA-256 integrity manifest of all package files. --- ## Keywords quantum process tomography; Markov semigroups; continuous-time quantum walk; matrix logarithm; matrix Bernstein bounds; blind custody; preregistration; fail-closed pipeline; operational physics; spectral graph theory; experimental quantum optics; integrated photonics. --- ## Suggested Citation Żuchowski, K. (2026). FIN Laboratory Transfer Package — Release 10.21: P240 Optimal Tomography + P241 Blind-Custody Validator + P242 One-Shot Pipeline (FIN Research Monograph & Transfer Package; Version 1.0.0) [Preprint]. Zenodo. https://doi.org/10.5281/zenodo.21435332

START HERE (read order / canonical artefacts): 1) Front Door notes (falsifiers & theorem/lemma map): DOI 10.5281/zenodo.18075645 2) Fork paper (Hard CNC + certified overlap + T=3 fork): DOI 10.5281/zenodo.18075546 3) Gravity paper (PAW / BR‑PAW + anomaly witness): DOI 10.5281/zenodo.18075607 4) Runner bundle (prereg mechanics + 30‑sec demo): DOI 10.5281/zenodo.18075677 Integrity rule (PAW/BR‑PAW): A null PAW result (no observed loop defect) does NOT, by itself, upper‑bound the worst‑case anomaly norm ||A||∞. PAW is soundness‑only in this direction; null‑result upper bounds require explicitly justified restricted norms (e.g., BR‑PAW with a physically motivated support/ensemble/code restriction) as stated in preregistered assumptions and budgets. Reference implementation for the CNC T=3 locked fork preregistration and the PAW/BR‑PAW inference pipeline. What it does: - Accepts preregistered inputs (including either externally supplied ε upper bound or tomography sufficient statistics + shot counts). - Produces preregistered bounds in two modes: (i) Bernstein/empirical‑Bernstein tightener; (ii) confidence‑region + SDP option (with preregistered solver tolerances and deterministic fallback). Included: - CNC_T3_Prereg_v7_bundle.zip - CNC_Release_Manifest_sha256_v2.txt Quick demo: - The bundle contains a one‑screen DEMO.md and a demo_simulation.py that generates synthetic data and runs the pipeline. Expected qualitative outcomes: signal run should be conclusive and reject Hard CNC; the two “bad” inputs should be inconclusive.
## Record metadata - **Title:** One FIN Operator, Two Temporal Dynamics: Unitary Propagation, Reversible Diffusion, a Finite Double-Slit Experiment, and Operational Completion- **Creator:** Żuchowski, Krzysztof- **Affiliation:** Independent Researcher — Fractal Information Theory Project- **ORCID:** 0009-0002-0909-3613- **Resource type:** Publication — Preprint - **Version:** 1.0.0- **Publication date:** 2026-07-19- **Language:** English- **Publisher:** Zenodo- **Access:** Open access, subject to the license confirmation below- **Reserved DOI:** [10.5281/zenodo.21435332](https://doi.org/10.5281/zenodo.21435332) ## Abstract This technical note studies a precisely defined twelve-site FIN matrix and the two canonical temporal calculi generated by its weighted graph Laplacian. Let (W) be the zero-diagonal real symmetric cyclic-distance matrix on (mathbb Z_{12}) sampled from K(d)=cos⁡(0.18575d+0.16250)1+d1.8,K(d)=\frac{\cos(0.18575d+0.16250)}{1+d^{1.8}},K(d)=1+d1.8cos(0.18575d+0.16250)​, using cyclic distances (d=1,ldots,6). Its common row sum is s=1.660307278766099s=1.660307278766099s=1.660307278766099 to fifteen decimal places, and A=sI−W.A=sI-W.A=sI−W. All off-diagonal weights used at (N=12) are positive. Therefore (A) is a connected weighted graph Laplacian and ⟨f,Af⟩=12∑x,yWxy∣fx−fy∣2≥0.\langle f,Af\rangle=\frac12\sum_{x,y}W_{xy}|f_x-f_y|^2\ge 0.⟨f,Af⟩=21​∑x,y​Wxy​∣fx​−fy​∣2≥0. The same positive self-adjoint operator generates the unitary group Ut=e−itAU_t=e^{-itA}Ut​=e−itA and the irreducible, symmetric, uniform-reversible Markov semigroup Pt=e−tA.P_t=e^{-tA}.Pt​=e−tA. Although the two evolutions share Fourier eigenvectors and eigenvalues, their operational predictions are inequivalent. Markov diffusion has linear short-time escape, exact Chapman–Kolmogorov composition and exponential relaxation to the uniform law. Unitary position probabilities have quadratic short-time escape, interference, failure of population-level Chapman–Kolmogorov composition and no pointwise equilibrium. The release includes a reproducible finite double-slit analogue. A coherent preparation at vertices (-2) and (+2) is compared with a perfectly distinguishing which-path record and with classical diffusion. The interference term is displayed across all twelve detectors and through time. At the first local maximum of total interference, (t_*=1.5525), the symmetry detector has unit ideal visibility; reducing the overlap of the two environment/apparatus records continuously suppresses the fringe. The note also identifies the missing structure needed to convert the operator into an experimental model. The smallest established-style candidate is a **calibrated process–tester model**: a causal process tensor (quantum comb), an admissible tester containing preparations and instruments with classical records, and a clock/reference calibration. This object carries state, multitime dynamics, preparation, instruments, environmental memory, apparatus and records up to operational equivalence. The operator alone does not select a physical clock, dimensional scale, environment, apparatus, Born rule, orientation or temporal semantics. No cosmological, Theory-of-Everything or continuum-physics claim is made. ## Plain-language significance One finite operator can generate both wave-like and diffusion-like mathematics. That fact does not mean an observer turns one physical law into another. It means the static operator underdetermines the experiment. State preparation, phase reference, clock, environment, measurement instrument and stored record must be supplied before either family becomes a testable physical model. The included double-slit analogue makes the distinction visible: coherent alternatives interfere; a which-path record removes the cross term; classical diffusion produces a different distribution. These are three operational protocols built around the same finite matrix. ## Main results and confidence labels ### Proven - (A=sI-W) is positive semidefinite with (ker A=\operatorname{span}\{\mathbf 1\}) under the declared cyclic-distance convention.- The spectral gap is (0.754121154207080) to displayed precision.- (U_t=e^{-itA}) is unitary.- (P_t=e^{-tA}) is an entrywise positive, symmetric, doubly stochastic Markov semigroup for (t>0).- The scalar shift (s) is the unique scalar shift of this regular (W) that makes (A\mathbf1=0).- Born-position matrices (|U_t|^{\circ2}) do not form a nontrivial differentiable Markov semigroup.- No nontrivial continuous finite evolution can be both unitary and entrywise nonnegative stochastic.- The two-slit probability law follows from the stated coherent preparation, record overlap and detector POVM.- A dimensionful time, energy, mass, length or action scale cannot be selected from the dimensionless matrix alone. ### Computed and independently checkable - All six weights, the complete spectrum, the spectral gap and the Dirichlet-form residual.- Markov mixing times and the nonuniform unitary Cesàro position law.- Unitarity, stochasticity and Chapman–Kolmogorov residuals.- The first two-slit interference maximum (t_*=1.5525) and total-variation interference (0.1232806696).- Ideal phase-fringe visibility (1) at detector (x=0) for record overlap (eta=1). ### Candidate / strong structural evidence - A calibrated process–tester model is the smallest standard mathematical structure found that simultaneously carries the requested operational roles. ### Not established - That the FIN matrix is a measured Hamiltonian or measured stochastic generator.- That unitary or diffusive time is selected by FIN itself.- That the displayed parameter (t) is measured in seconds.- That Shannon entropy in the plots is thermodynamic entropy.- That the (N=12) Markov interpretation survives a continuum limit.- That a microscopic apparatus, environment, selector, orientation or physical constants are derived from (A). ## Double-slit simulation The simulated slit modes are (a=10\equiv-2\pmod{12}) and (b=2). The coherent system–record state is ∣Ψϕ⟩=∣a⟩∣Ea⟩+eiϕ∣b⟩∣Eb⟩2,η=⟨Eb∣Ea⟩.|\Psi_\phi\rangle=\frac{|a\rangle|E_a\rangle+e^{i\phi}|b\rangle|E_b\rangle}{\sqrt2},\qquad \eta=\langle E_b|E_a\rangle.∣Ψϕ​⟩=2​∣a⟩∣Ea​⟩+eiϕ∣b⟩∣Eb​⟩​,η=⟨Eb​∣Ea​⟩. With (u_j(x,t)=\langle x|U_t|j\rangle), the detector law is pϕ,η(x,t)=∣ua∣2+∣ub∣22+Re⁡ ⁣(ηe−iϕuaub‾).p_{\phi,\eta}(x,t)=\frac{|u_a|^2+|u_b|^2}{2}+\operatorname{Re}\!\left(\eta e^{-i\phi}u_a\overline{u_b}\right).pϕ,η​(x,t)=2∣ua​∣2+∣ub​∣2​+Re(ηe−iϕua​ub​​). The figure compares: 1. coherent propagation, (eta=1);2. a which-path record / incoherent mixture, (eta=0);3. classical diffusion (P_t(\delta_a+\delta_b)/2). This is a finite two-path interferometer on (mathbb Z_{12}), not a continuum optical diffraction calculation. ## Important finite-size limitation The Markov conclusion uses positivity of all off-diagonal weights present at (N=12). The fixed profile becomes negative at distance (8): K(8)=−0.0017958784.K(8)=-0.0017958784.K(8)=−0.0017958784. A naive cyclic extension first includes that distance at (N=16), where the resulting off-diagonal matrix entry cannot be a Markov jump rate. Any truncation, rectification, absolute-value prescription or parameter running would be an additional axiom. The release therefore makes an exact (N=12) claim and no automatic continuum-limit claim. ## Files in this release | File | Purpose | SHA-256 ||---|---|---|| `FIN_Dual_Dynamics_Operational_Completion.pdf` | Archival English research note | `53bad7dfc10446211d9bc6bc28da53470ee3e46b4b4084d23f2301a439f2456c` || `FIN_Dual_Dynamics_Operational_Completion.tex` | LaTeX source | `be38e241f3b4b7ba73230845cc584806c1b5102c18de6dbcc1dde0818b614765` || `fin_dual_dynamics_release.py` | Deterministic numerical audit and figure generator | `671dca9f2ac0b40f17bad3cda8e253e934db825503f76e1efa787b47c262ad47` || `FIN_Dual_Dynamics_reference_results.json` | Machine-readable expected results | `3917ad393abe286d1f39caeac6596d218b56b369cffdfe405a3aa6f79156e5ab` || `FIN_One_Spectrum_Two_Dynamics.png` | Unitary/Markov comparison figure | `5e37f1ff1e49cce4855247c03f4bd298ade73e3da1ecd4136ad77875c43d2f42` || `FIN_Double_Slit_Operational_Simulation.png` | Four-panel double-slit simulation | `a6a1f59b9c6d5b4df17df6580679b18f9706421ca5a0aedeb916da84ac27488d` || `FIN_Dual_Dynamics_MANIFEST.sha256` | Checksums for the archival files | Generated after the final build | The Markdown release description is intentionally omitted from its own checksum table to avoid a self-referential digest. ## Reproducibility Reference environment used for this release: - Linux 7.0.0-28-generic, x86_64- Python 3.12.3- NumPy 1.26.4- Matplotlib 3.10.8- pdfTeX 3.141592653-2.6-1.40.25 / TeX Live 2023- Floating-point arithmetic: IEEE-754 binary64- Random seed used only for the Dirichlet identity spot-check: `20260719` Run: ```bashpython3 fin_dual_dynamics_release.pypdflatex -interaction=nonstopmode -halt-on-error FIN_Dual_Dynamics_Operational_Completion.texpdflatex -interaction=nonstopmode -halt-on-error FIN_Dual_Dynamics_Operational_Completion.tex``` The script reconstructs the operator from the displayed analytic parameters, generates both figures and writes the complete numerical audit to JSON. It tests symmetry, the constant mode, Dirichlet positivity, unitarity, stochasticity, minimum transition entries, Chapman–Kolmogorov composition, mixing, the raw-(W) heat failure, the first negative extended-profile weight and normalization of all double-slit distributions. ## Keywords FIN kernel; spectral operator; weighted graph Laplacian; unitary group; heat semigroup; reversible Markov chain; continuous-time quantum walk; double-slit interference; which-path information; decoherence; quantum instrument; process tensor; quantum comb; calibrated process–tester model; observer dependence; operational equivalence; finite operator theory; spectral dynamics. ## Suggested citation > Żuchowski, K. (2026). *One FIN Operator, Two Temporal Dynamics: Unitary Propagation, Reversible Diffusion, a Finite Double-Slit Experiment, and Operational Completion* (Version 1.0.0) [Technical note]. Zenodo. https://doi.org/10.5281/zenodo.21435332 ```bibtex@misc{zuchowski_fin_dual_dynamics_2026, author = {Krzysztof Żuchowski}, title = {One FIN Operator, Two Temporal Dynamics: Unitary Pro
A sealed laboratory fork for monitored quantum recurrence Can the location of a first-detection recurrence resonance distinguish two physically qualified time-reference classes after ordinary clock-transfer, Hamiltonian, waveform, detector, and environmental effects have been held fixed? This preregistration converts that question into a reciprocal two-device experiment with a machine-evaluable entrance gate and a finite outcome ledger. For device ddd and preregistered transition jjj, the laboratory reports one dimensionless root ratio, ydj=log⁡ ⁣(x^dLj∗x^dAj∗),Δ^=1TΣy−1y1TΣy−11,R^MRRS=eΔ^. y_{dj} = \log\!\left( \frac{\widehat x^{*}_{dLj}} {\widehat x^{*}_{dAj}} \right), \qquad \widehat\Delta = \frac{\mathbf 1^{\mathsf T}\Sigma_y^{-1}\mathbf y} {\mathbf 1^{\mathsf T}\Sigma_y^{-1}\mathbf 1}, \qquad \widehat R_{\rm MRRS}=e^{\widehat\Delta}. ydj​=log(xdAj∗​xdLj∗​​),Δ=1TΣy−1​11TΣy−1​y​,RMRRS​=eΔ. The two frozen point hypotheses are H0:Δ0=0,R0=1, H_0: \quad \Delta_0=0, \qquad R_0=1, H0​:Δ0​=0,R0​=1, HA1:ΔA1=log⁡ ⁣cos⁡ ⁣(π8)=−0.0791735919101875…,RA1=cos⁡ ⁣(π8)=0.9238795325112867…. H_{A1}: \quad \Delta_{A1}=\log\!\cos\!\left(\frac{\pi}{8}\right) =-0.0791735919101875\ldots, \qquad R_{A1}=\cos\!\left(\frac{\pi}{8}\right) =0.9238795325112867\ldots . HA1​:ΔA1​=logcos(8π​)=−0.0791735919101875…,RA1​=cos(8π​)=0.9238795325112867…. The A1 point is dormant unless the proposed physical terminal exists in the apparatus. Version 2.0 therefore places a fifteen-gate constructor ahead of all role-dependent recurrence output: GPT=∏i=115Pi. G_{\rm PT} = \prod_{i=1}^{15}P_i. GPT​=∏i=115​Pi​. The gate requires a completed source event, continuous physical source memory, no later laboratory write, a source intervention witness, a target-blind ordinary camera, a numerical rank-two terminal Jacobian, a complete clock graph, and an irreversible pre-data seal. A free-running oscillator alone is not a T⋆T^{\star}T⋆ terminal. If any gate fails, the registered result is GPT=0⟹TARGET_NOT_ACTIVATED. G_{\rm PT}=0 \quad\Longrightarrow\quad \texttt{TARGET\_NOT\_ACTIVATED}. GPT​=0⟹TARGET_NOT_ACTIVATED. The executable packet freezes two devices, two independent oscillator chains, four reciprocal role cells, four recurrence roots, eight supercycles, N=1024N=1024N=1024, an 81-point primary scan, and 16,384 trajectories per point, role, device, and transition. The estimator is the full finite-NNN multinomial likelihood, including the no-detection category; no manual fit window, pseudoinverse, post-unblinding regularization, or effect-directed exclusion is permitted. The two equivalence regions have fixed half-width 0.0250.0250.025 in log space, and the primary design gate is SE(Δ^)≤0.006. {\rm SE}(\widehat\Delta)\le 0.006. SE(Δ)≤0.006. A registered point must also exclude the other by at least five standard deviations. A fresh 400+400 finite-horizon synthetic campaign gives uΔsynth=0.0010808000,∣ΔA1−Δ0∣uΔsynth=73.25. u_{\Delta}^{\rm synth}=0.0010808000, \qquad \frac{|\Delta_{A1}-\Delta_0|}{u_{\Delta}^{\rm synth}} =73.25. uΔsynth​=0.0010808000,uΔsynth​∣ΔA1​−Δ0​∣​=73.25. Every synthetic campaign is classified correctly under the printed planning assumptions. This is a software and power receipt, not hardware activation or a laboratory observation. Release status: CLOSED: laboratory instruction layer and machine packet; CLOSED: synthetic activation, fail-closed, power, and outcome-classifier audits; PENDING: platform-specific hardware packet and physical-terminal activation; PENDING: qualified laboratory data and empirical A1 verdict. The reconstruction archive contains the LaTeX source, exact protocol JSON, activation templates and validator, raw-data dictionary, 31 exclusion codes, finite-NNN power program, six-outcome classifier, independent experimental review and response matrix, visual audit, a 60-check release receipt, and complete SHA-256 hashes. Stable concept DOI: 10.5281/zenodo.21703683 Physical Terminal constructor: 10.5281/zenodo.21739215 Main book: Quantum Traction Theory: Main Book v10.01 Website: quantumtraction.org