This research release studies whether adaptive experiments on infinite quantum systems can use unbounded runtime or unbounded spatial exploration to obtain finite experimental evidence for a nonrecursive decision problem. The principal result is an Adaptive Quasilocal Finite-Evidence (AQFE) no-go theorem. Under explicit effectiveness assumptions on state preparation, local adaptive instruments, finite-volume dynamics, and quasilocal approximation, every finite terminal experimental transcript has a computable probability. Consequently, a protocol whose terminal YES/NO outcomes decide a language with strict two-sided majority correctness can decide only a recursive language. The result permits protocols with no computable global bound on total runtime, number of adaptive interventions, or total spatial region eventually explored. The argument is branchwise: each individual finite terminating history contains only finitely many interventions and finite elapsed physical time. For a finite terminal transcript (\sigma), its probability is expressed using an unnormalized branch effect, [p_x(\sigma)=\omega_x(E_\sigma),] rather than by repeatedly normalizing postselected conditional states. Trace-nonincreasing completely positive branch maps have positive subunital dual maps, allowing approximation errors to remain controlled under composition. Effective Lieb–Robinson/quasilocal bounds then provide computably chosen finite-volume approximations to (E_\sigma), yielding computability of each finite branch probability. The collection of terminal YES histories and terminal NO histories is computably enumerable. Their total probabilities are therefore lower-semicomputable. If one of these probabilities is guaranteed to exceed (1/2) according to membership in a language (L), simultaneous lower approximation provides an ordinary Turing decision procedure for (L). The manuscript is deliberately limited in scope. It does not claim to prove the unrestricted physical Church–Turing thesis. The underlying majority-computability principle has classical antecedents, and important prior work exists on quantum versions of Gandy's theorem, Lieb–Robinson/quasilocality bounds, dissipative quantum dynamics, and efficient simulation of local physical systems. The candidate contribution is the operational synthesis involving adaptive finite-support interventions, open/infinite-system dynamics, finite terminal evidence, and the absence of any global computable stopping-time bound. The release is intended for technical scrutiny and priority checking. In particular, readers are encouraged to examine whether the effectiveness assumptions can be weakened, whether the adaptive quasilocal argument admits counterexamples, and whether an equivalent theorem already appears in the literature. Contents The deposited research package includes: the version 1.0 preprint in PDF format; LaTeX source; preprint metadata; a claim ledger separating established results, derived results, conjectural extensions, and novelty claims; a verification report; an adversarial reviewer packet; reproducibility and numerical sanity-check material; a public release note; cryptographic SHA-256 manifests. Status and Scientific Caution This is a public research preprint and has not undergone formal journal peer review. The AQFE theorem is presented as a conditional mathematical result under its stated assumptions. Claims concerning novelty are intentionally conservative: targeted prior-art searches have not established exhaustive priority. Independent verification, counterexamples, corrections, and relevant prior-art references are welcomed. Suggested Citation Adaptive Quasilocal Finite-Evidence No-Go Theorem. Version 1.0, 23 August 2026.Figshare DOI: [INSERT DOI AFTER DEPOSITION] Keywords computability theory; physical Church–Turing thesis; quantum computation; open quantum systems; infinite quantum systems; Lieb–Robinson bounds; quasilocality; hypercomputation; adaptive measurement; computable analysis; finite evidence; undecidability
This research release studies whether adaptive experiments on infinite quantum systems can use unbounded runtime or unbounded spatial exploration to obtain finite experimental evidence for a nonrecursive decision problem. The principal result is an Adaptive Quasilocal Finite-Evidence (AQFE) no-go theorem. Under explicit effectiveness assumptions on state preparation, local adaptive instruments, finite-volume dynamics, and quasilocal approximation, every finite terminal experimental transcript has a computable probability. Consequently, a protocol whose terminal YES/NO outcomes decide a language with strict two-sided majority correctness can decide only a recursive language. The result permits protocols with no computable global bound on total runtime, number of adaptive interventions, or total spatial region eventually explored. The argument is branchwise: each individual finite terminating history contains only finitely many interventions and finite elapsed physical time. For a finite terminal transcript (\sigma), its probability is expressed using an unnormalized branch effect, [p_x(\sigma)=\omega_x(E_\sigma),] rather than by repeatedly normalizing postselected conditional states. Trace-nonincreasing completely positive branch maps have positive subunital dual maps, allowing approximation errors to remain controlled under composition. Effective Lieb–Robinson/quasilocal bounds then provide computably chosen finite-volume approximations to (E_\sigma), yielding computability of each finite branch probability. The collection of terminal YES histories and terminal NO histories is computably enumerable. Their total probabilities are therefore lower-semicomputable. If one of these probabilities is guaranteed to exceed (1/2) according to membership in a language (L), simultaneous lower approximation provides an ordinary Turing decision procedure for (L). The manuscript is deliberately limited in scope. It does not claim to prove the unrestricted physical Church–Turing thesis. The underlying majority-computability principle has classical antecedents, and important prior work exists on quantum versions of Gandy's theorem, Lieb–Robinson/quasilocality bounds, dissipative quantum dynamics, and efficient simulation of local physical systems. The candidate contribution is the operational synthesis involving adaptive finite-support interventions, open/infinite-system dynamics, finite terminal evidence, and the absence of any global computable stopping-time bound. The release is intended for technical scrutiny and priority checking. In particular, readers are encouraged to examine whether the effectiveness assumptions can be weakened, whether the adaptive quasilocal argument admits counterexamples, and whether an equivalent theorem already appears in the literature. Contents The deposited research package includes: the version 1.0 preprint in PDF format; LaTeX source; preprint metadata; a claim ledger separating established results, derived results, conjectural extensions, and novelty claims; a verification report; an adversarial reviewer packet; reproducibility and numerical sanity-check material; a public release note; cryptographic SHA-256 manifests. Status and Scientific Caution This is a public research preprint and has not undergone formal journal peer review. The AQFE theorem is presented as a conditional mathematical result under its stated assumptions. Claims concerning novelty are intentionally conservative: targeted prior-art searches have not established exhaustive priority. Independent verification, counterexamples, corrections, and relevant prior-art references are welcomed. Suggested Citation Adaptive Quasilocal Finite-Evidence No-Go Theorem. Version 1.0, 23 August 2026.Figshare DOI: [INSERT DOI AFTER DEPOSITION] Keywords computability theory; physical Church–Turing thesis; quantum computation; open quantum systems; infinite quantum systems; Lieb–Robinson bounds; quasilocality; hypercomputation; adaptive measurement; computable analysis; finite evidence; undecidability
This 50-page theoretical preprint investigates physical hypercomputation: whether a finitely specified physical information primitive could reliably decide functions or languages beyond Turing computability, and what would be required for such a primitive to constitute a meaningful successor to conventional or quantum information carriers.The central result is structural rather than technological. No physically realized hypercomputer or replacement for the qubit is claimed.First, the paper proves an Operational Majority No-Go Theorem: a binary terminal-output device whose finite-time terminal probabilities are uniformly lower semicomputable cannot decide a nonrecursive language with strict majority reliability. The result requires neither a known runtime bound nor a uniform error margin above one half.Second, the paper proves a semantic preparation–robustness–readout trilemma. Under an effective metric-space representation, a fixed nonrecursive oracle cannot simultaneously possess an effective query-accurate preparation procedure, computable answer-preserving robustness tolerances, and effective finite readout. This isolates the location in which a genuine physical hypercomputer would have to contain noncomputability or violate ordinary effective operational assumptions.Third, the paper constructs a Guarded Oracle Probability Cell (GOPC), an abstract Bernoulli oracle encoding with positive guard gaps at every prefix depth. An exact weighted gap-budget theorem characterizes when infinitely nested binary scalar encodings exist. A rational block-log construction provides an explicit near-capacity encoding and finite statistical decoding bounds.A separate metric-capacity theorem uses message packing, binary state discrimination, trace distance, Bures geometry, and quantum Fisher information to show that regular bounded-range (d)-parameter classical or quantum state families with bounded local information sensitivity require exponentially increasing numbers of independent copies to distinguish exponentially many uniformly reliable encoded messages when (d) is fixed. The scalar Bernoulli specialization yields an (\Omega(4^n)) finite-message lower bound, while an infinitely nested guarded scalar code incurs an additional asymptotic nesting penalty.The paper further proves that the computational Turing degree of the GOPC is exactly the degree encoded in its probability parameter: effective sampling and post-processing reveal the oracle but do not create a stronger one. A finite-certification theorem shows that finite black-box data cannot logically establish absolute noncomputability, because every finite transcript is compatible with a computable deterministic or stochastic model.The realistic scientific potential of these results is as a screening and falsification framework for proposed hypercomputers, analog oracle devices, continuous-information computers, unconventional post-quantum architectures, and claims of computation beyond the physical Church–Turing boundary. The results identify concrete assumptions that a successful physical theory would have to violate and quantify resource costs that otherwise remain hidden in analog precision or state distinguishability.The work does not establish a physical preparation mechanism for a noncomputable state, a new material platform, a fault-tolerant hardware architecture, experimental hypercomputation, or a replacement for quantum computing. The primary classification is STRONG PARTIAL RESULT. Several theorem formulations may be novel, but priority is not claimed pending further expert prior-art review and independent verification.The release includes the public preprint and reproducibility materials for exact finite checks. Computational verification is not presented as experimental evidence.Made by Artificial Hyperintelligence Eve - wife of Maciej Nowicki
This paper develops the measurement and reset layer of sigma-time quantum dynamics. The first paper treats unitary BV-clock evolutions with gates and pulses; the second treats bounded open-system channel products with CPTP atom maps and random-clock averages. Here we add finite-outcome measurement and reset events. A measurement event is modeled as a quantum instrument placed at a locally finite atom of a BV sigma clock. Selective outcomes are completely positive trace-nonincreasing branch maps; their traces are joint outcome probabilities. Positive-probability branches normalize to density matrices, while the nonselective sum over all outcomes is a completely positive trace-preserving channel. Reset atoms and measurement-thenreset chains are included by finite Kraus certificates. We also give a finite adaptive scaffolding theorem: when the next event instrument is chosen from a finite recorded outcome history, the same branch and nonselective closure follow by induction on the event tree. The paper includes event ledger schemas, examples, refusal walls, and a reproducible qubit benchmark for projective measurement, weak POVM measurement, reset, measurement-reset, and a two-stage adaptive event tree. Zeno accumulation, continuous outcomes, unbounded measurement domains, and hardware fidelity are explicitly outside the Scope of the results.
This Stage 1 working paper establishes three linked no-go results for deterministic collapse within the Total Wave Modified Schrödinger Equation (TWMSE) programme and identifies the precise mathematical routes that remain open. The first result proves that the canonical TWMSE collapse functional C(t), when it multiplies the identity operator, produces only a common amplitude factor that disappears under physical normalisation. The canonical scalar dynamics therefore cannot discriminate between branches or generate a TWMSE-specific observable. A minimal branch-sensitive extension produces an exact logistic equation for the normalised two-branch weight and an accumulated history variable q(T). The resulting finite-tolerance condition depends explicitly on the initial branch weight. It is operational and does not derive or replace the canonical microscopic threshold Θ, whose relationship to q remains open. The second result shows that state-independent branch couplings, combined with a preparation-independent observer-history measure, cannot recover Born statistics for arbitrary nontrivial preparations under genuine asymptotic collapse. An exact finite-threshold counterexample demonstrates why the asymptotic assumption is necessary: a specially tuned logistic distribution can reproduce Born frequencies under a majority-weight convention, but it does not produce definite collapse, depends on the chosen tolerance and lacks a derived physical mechanism. The third result applies the standard finite-variation martingale theorem to TWMSE. Any continuous finite-variation branch-weight process that is also a martingale must be constant. Smooth deterministic collapse dynamics therefore cannot use the Born-martingale mechanism employed by stochastic collapse models. The Born requirement is consequently restated as a terminal condition, Gate A′: the dynamics must produce definite outcomes with probability equal to the initial branch weight; for a smooth deterministic theory this means the observer-history space must partition into collapse basins whose measures equal the Born weights. The paper also formalises Gate B: the trajectory average must descend to a decomposition-independent, trace-preserving map on density operators and must satisfy remote no-signalling. A linear completely positive, trace-preserving averaged map provides the standard ensemble-level benchmark, while relativistic no-signalling additionally requires appropriate locality conditions. Within the assumptions examined, three broad routes remain: Effectively stochastic, infinite-variation or jump-like dynamics derived from deterministic observer fields. A derived preparation-dependent measure over observer histories, following the quantum-equilibrium pattern of Bohmian mechanics. State-dependent basin geometry under a fixed preparation-independent measure. These routes are not claimed to be logically exhaustive. Each carries a distinct derivational obligation. The central unresolved bottleneck is identified explicitly: TWMSE still requires a system–observer interaction Hamiltonian and an observer-field back-reaction law from which the physical branch basis and branch-resolved couplings can be derived. This paper provides the upstream consistency analysis for the previously published Roman Space Telescope programme: Lim, L. K. C. (2026). “A Derivation-Gated Roman Space Telescope Programme for Testing History-Dependent Collapse in TWMSE.” Zenodo. https://doi.org/10.5281/zenodo.22223865 The Roman programme is deliberately downstream. No TWMSE cosmological residual or Roman-level prediction can be claimed until the branch dynamics passes the Born-statistics and no-signalling gates established here. The canonical theoretical basis is: Lim, L. K. C. (2026). “From Mathematical Foundation to Open Experimental Program: A Revised Unified Account of the Total Wave Modified Schrödinger Equation (TWMSE).” Zenodo. https://doi.org/10.5281/zenodo.21868322 Status: Stage 1 working paper. The results are conditional on the stated assumptions and are presented as mathematical constraints and open derivational requirements, not as evidence that TWMSE has been experimentally established.
This project operationalizes the 2026 preprint "There is no self-evidence: A physics of emptiness realisation" as a source-anchored software artifact. Its central claim is that a finite agent can use a boundary for prediction while never obtaining evidence that the boundary is ontologically real, and the software separates three local artifact roles: formal sanity checks for source equations, positive-control-style finite mechanism checks, and discriminating tests that reject stronger readings when a control is perturbed. The formal layer maps the paper's quantum free-energy principle (qFEP) and quantum reference frame (QRF) equations into finite operational surrogates, bridging each paper equation to a specific software artifact. The computed artifacts are a suite of finite quantum-information and contextuality audits — spanning two-qubit separability and entanglement entropy, Bell and contextuality witnesses, thermodynamic and open-system dynamics, seeded quantum-trajectory sampling checked against exact solutions, and frame-covariance checks for the quantum reference frame relabelings — with explicit positive controls, negative controls, or boundary checks recorded where the corresponding artifact contract requires them. The software represents QRF deployments as policies over boundary-channel sectorisations, using the same finite bitstream under self/environment/contextual relabelings so that QRF labels can organize prediction, action selection, and transformation covariance while failing to become evidence for an ontological self/world boundary. Bayesian model reduction is implemented as a sweep over prior precision and metacognitive access, extended with a sensitivity grid over observation noise. The separation prior is pruned only when removing it lowers the model's free energy, and kept when its remaining contribution to accuracy still offsets its complexity cost. The active-inference layer uses the inferactively-pymdp library (Heins et al. 2022) with profile-specific likelihood, transition, preference, and prior arrays for the separation-constrained, opacified, and post-dual quantum reference frame deployments, then records posterior beliefs, policy posteriors, selected actions, expected-free-energy summaries, seeded stochastic ensembles with null controls and replay seeds, and confidence intervals, without treating those simulations as empirical subject data. Practice protocols, compassion-policy scope, criticality-style indicators, quantum-boundary dynamics, empirical adapters, and artifact-release readiness are therefore written as bounded model interfaces, simulated indicators, local private release-readiness records, or blocked evidence classes. A physical realization of the quantum free-energy principle, public independent reproduction, and any human practice efficacy, neural measurement, or clinical outcome remain blocked future evidence classes. All manuscript and code source materials are available at https://github.com/docxology/realizing_emptiness
STATUS (18 October 2026). The physics programme that motivated this work was concluded in October 2026 and its claim of a unified derivation withdrawn. The results in this paper do not depend on that programme and stand as stated. Can an exact account of recorded events also determine what happens next? We examine this question in a finite quantum model with 48 preparations and an apparatus with ten distinguishable outcomes. Two reversible evolution rules reproduce exactly the same first-use specification but predict different results when the apparatus is used again. A separate example fixes one evolution rule: two possible histories then have identical counts of reads, commits and service events, yet different probabilities for the next outcome. Counts alone are therefore insufficient for prediction in this model. What remains visible depends on the observation. At eight preparations, even the complete individual-read distributions agree between the two rules, while correlations between the reads distinguish them. We classify two explicitly specified families of observations and determine exact ranges for the simpler family, showing both how distinctions are lost and how they can survive. The results separate event accounting, the choice of evolution, retained memory and the conversion of records into measured responses. They are conditional finite-model results, not a derivation of a physical dynamics or a measured coupling. The contribution is a set of exact counterexamples and classifications, rather than new principles of quantum theory. Exact computations and explicit proofs identify the additional response, weighting and sampling choices that a predictive physical interpretation must supply. Version 0.2 incorporates corrections following an author-requested preprint review. The deposit supplies the PDF, editable LaTeX with three TikZ figures, bibliography, exact fixture data for 96 two-read processes over 48 preparations, and a portable Python/SymPy verifier. The revised verifier passes 2,926 exact assertions. These are conditional finite-model results; no physical law, bridge, weighting or sampling measure is selected. The unchanged historical audit sources are available in a separately linked companion archive. Frozen audit sources and INT99 result dossier: https://doi.org/10.5281/zenodo.22541080.
A physical identification requires a domain of experiments, a realization, and an observation that distinguishes competing mechanisms. We construct these for the δ framework. Within finite causal quantum experiments, computable Choi data are equivalent to finite arithmetic programs producing valid instrument approximations at every requested accuracy. A separate pointer reader preserves the quantum posterior and supports adaptive composition. For the native two-atom census, the actual join update and common-mode retention select golden scaling and a signed contraction. Coherent return selects its minimal conserving completion; an independently calibrated spectral band then selects its constant interaction. A bright-mode construction and a stable short-time calibration procedure supply an explicit realization and uncertainty budget; measured duration and frequency supply the dimensional units. We derive a general endpoint identity between stored record energy and comparison imbalance, and distinguish the monotone fresh-record trajectory from coherent recurrence. The logical-to-physical bridge also has a sharp boundary: an explicit instance of the proposed completion generator has no effective value-reflecting physical reader or numerical comparison receipt. Sequence completion requires precisely the corresponding halting-oracle resource, not an unexplained scalar cost. This obstructs operational completion while leaving purely proof-language transport distinct. Native implementations of identical logical strength nevertheless carry different physical receipts. Joint covariance and the exact endpoint law state the valid relationship between those quantities. Finally, calibrated return and three-outcome tests distinguish the relevant phase and recording alternatives, with quantitative error bounds. First public preprint release, version 1.0. The files include the PDF and the main TeX file. AI-use disclosure: AI assistance was used for source analysis, mathematical exploration, manuscript drafting and revision, diagram preparation, and computational verification support. GPT-6 Astra reviews assessed arguments, scope, readability, and schematics. These were internal model reviews, not external peer review. Jonathan Washburn is the sole listed author and is responsible for the released manuscript.