This technical report develops and tests TWMSE Candidate Equation 4A, a phenomenological, threshold-activated model of observer-induced quantum collapse formulated to preserve Born weights and operational no-signalling while producing experimentally distinguishable dynamics. Candidate Equation 4A introduces a branch-sensitive Lindblad term whose activation depends on whether an operationally defined observer record exceeds a specified threshold. The report evaluates the equation’s mathematical consistency, including trace preservation, positivity, Born-weight preservation and operational no-signalling. It also examines individual stochastic trajectories, ensemble behaviour, synthetic count-level parameter recovery, statistical power and the consequences of model misspecification. A retrospective analysis is performed using published fitted GHZ decoherence-rate summaries from two superconducting-qubit studies. This is not an analysis of original laboratory shot-level data. The combined profile analysis finds no robust positive signal for Candidate Equation 4A. Instead, it establishes provisional, threshold-dependent upper limits on the additional collapse rate. Across the report’s primary threshold range of R* = 1–9, the largest pointwise one-sided 95% upper limit is approximately 7.3 × 10³ s⁻¹, while the tightest limit is approximately 3.0 × 10³ s⁻¹ at R* = 8. These are pointwise limits and do not constitute a simultaneous confidence band. The retrospective results therefore constrain but do not favour Candidate Equation 4A. Standard quantum mechanics remains sufficient to describe the analysed GHZ summaries and does so with fewer parameters. Candidate Equation 4A survives this preliminary confrontation only in the limited scientific sense that portions of its parameter space remain unexcluded. This non-exclusion is not evidence that the candidate is correct. The report consequently specifies a dedicated amplify–hold–erase experiment using matched record-forming and coherent-control circuits. The proposed test varies observer-record size, conditional record strength and dwell time while collecting count-level measurement outcomes and contemporaneous calibrations of conventional noise. The protocol is designed to distinguish a threshold-activated observer-record contribution from smooth, conventional decoherence and other experimental effects. A preregistration template, empirical-data schema and data dictionary are supplied so that the proposed experiment can be performed and analysed as an independently reproducible and falsifiable test. The accompanying ZIP archive is the complete, self-contained reproducibility package for the results reported here. It contains the code, simulation data, published GHZ rate summaries used as inputs, derived numerical outputs, documentation, software requirements and integrity checks required to reproduce the reported computational analyses and verify the packaged results. The archive contains: • the complete report in PDF, DOCX and Markdown formats;• deterministic Python reproduction scripts;• results from 500 density-matrix consistency trials;• 250,000 simulated stochastic trajectories;• 14,336 synthetic count-level circuit rows;• synthetic parameter-recovery and statistical-power results;• model-misspecification tests;• the published fitted GHZ rate summaries used in the retrospective analysis;• individual and joint GHZ profile-likelihood results;• prediction grids and report figures;• an empty 37-column template for future empirical raw data;• a data dictionary and preregistration template;• software-environment requirements and citation metadata; and• a SHA-256 manifest for package-integrity verification. The simulated trajectories and synthetic circuit counts are computational data rather than laboratory observations. The included GHZ inputs are published fitted rate summaries and are not original experimental shot counts. No new laboratory data are included, and no empirical discovery claim is made. Successful reproduction verifies that the supplied code generates the reported mathematical checks, simulations and retrospective statistical results. It does not establish that nature follows Candidate Equation 4A, demonstrate observer-induced collapse, or show that TWMSE is empirically preferred over standard quantum mechanics. The physical ideas, TWMSE framework, research direction and scientific interpretation are those of the author. Computational assistance was used for mathematical checking, simulation, statistical analysis, document preparation and reproducibility auditing. The author directed the research and accepts responsibility for the methodology, scientific claims, interpretations and conclusions. Candidate Equation 4A should therefore be understood as an explicit, internally testable and falsifiable phenomenological candidate that has passed the reported mathematical and computational consistency checks, remains compatible with the limited published summaries examined, and now requires the proposed dedicated raw-data experiment for a meaningful empirical test.
This technical report develops and tests TWMSE Candidate Equation 4A, a phenomenological, threshold-activated model of observer-induced quantum collapse formulated to preserve Born weights and operational no-signalling while producing experimentally distinguishable dynamics. Candidate Equation 4A introduces a branch-sensitive Lindblad term whose activation depends on whether an operationally defined observer record exceeds a specified threshold. The report evaluates the equation’s mathematical consistency, including trace preservation, positivity, Born-weight preservation and operational no-signalling. It also examines individual stochastic trajectories, ensemble behaviour, synthetic count-level parameter recovery, statistical power and the consequences of model misspecification. A retrospective analysis is performed using published fitted GHZ decoherence-rate summaries from two superconducting-qubit studies. This is not an analysis of original laboratory shot-level data. The combined profile analysis finds no robust positive signal for Candidate Equation 4A. Instead, it establishes provisional, threshold-dependent upper limits on the additional collapse rate. Across the report’s primary threshold range of R* = 1–9, the largest pointwise one-sided 95% upper limit is approximately 7.3 × 10³ s⁻¹, while the tightest limit is approximately 3.0 × 10³ s⁻¹ at R* = 8. These are pointwise limits and do not constitute a simultaneous confidence band. The retrospective results therefore constrain but do not favour Candidate Equation 4A. Standard quantum mechanics remains sufficient to describe the analysed GHZ summaries and does so with fewer parameters. Candidate Equation 4A survives this preliminary confrontation only in the limited scientific sense that portions of its parameter space remain unexcluded. This non-exclusion is not evidence that the candidate is correct. The report consequently specifies a dedicated amplify–hold–erase experiment using matched record-forming and coherent-control circuits. The proposed test varies observer-record size, conditional record strength and dwell time while collecting count-level measurement outcomes and contemporaneous calibrations of conventional noise. The protocol is designed to distinguish a threshold-activated observer-record contribution from smooth, conventional decoherence and other experimental effects. A preregistration template, empirical-data schema and data dictionary are supplied so that the proposed experiment can be performed and analysed as an independently reproducible and falsifiable test. The accompanying ZIP archive is the complete, self-contained reproducibility package for the results reported here. It contains the code, simulation data, published GHZ rate summaries used as inputs, derived numerical outputs, documentation, software requirements and integrity checks required to reproduce the reported computational analyses and verify the packaged results. The archive contains: • the complete report in PDF, DOCX and Markdown formats;• deterministic Python reproduction scripts;• results from 500 density-matrix consistency trials;• 250,000 simulated stochastic trajectories;• 14,336 synthetic count-level circuit rows;• synthetic parameter-recovery and statistical-power results;• model-misspecification tests;• the published fitted GHZ rate summaries used in the retrospective analysis;• individual and joint GHZ profile-likelihood results;• prediction grids and report figures;• an empty 37-column template for future empirical raw data;• a data dictionary and preregistration template;• software-environment requirements and citation metadata; and• a SHA-256 manifest for package-integrity verification. The simulated trajectories and synthetic circuit counts are computational data rather than laboratory observations. The included GHZ inputs are published fitted rate summaries and are not original experimental shot counts. No new laboratory data are included, and no empirical discovery claim is made. Successful reproduction verifies that the supplied code generates the reported mathematical checks, simulations and retrospective statistical results. It does not establish that nature follows Candidate Equation 4A, demonstrate observer-induced collapse, or show that TWMSE is empirically preferred over standard quantum mechanics. The physical ideas, TWMSE framework, research direction and scientific interpretation are those of the author. Computational assistance was used for mathematical checking, simulation, statistical analysis, document preparation and reproducibility auditing. The author directed the research and accepts responsibility for the methodology, scientific claims, interpretations and conclusions. Candidate Equation 4A should therefore be understood as an explicit, internally testable and falsifiable phenomenological candidate that has passed the reported mathematical and computational consistency checks, remains compatible with the limited published summaries examined, and now requires the proposed dedicated raw-data experiment for a meaningful empirical test.
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 paper presents a revised unified account of the Total Wave Modified Schrödinger Equation (TWMSE), a proposed deterministic collapse framework in which quantum state reduction is investigated as a possible dynamical consequence of interaction between a system wavefunction and observer fields associated with physical interactions. The purpose of this revision is to distinguish clearly between mathematical structures that have been explicitly formulated, consequences that follow from the minimal written dynamics, and stronger experimental proposals that remain to be derived. A central result is that a spatially homogeneous scalar collapse term can modify the global amplitude of a quantum state but cannot, by itself, generate spatial localization or branch selection. After normalization, the common scalar factor cancels from the spatial probability distribution. Likewise, a spatially homogeneous multiplicative metric can restore a conserved physical norm but does not by itself produce a measurable spatial probability bias. The paper also corrects the treatment of the time dependent metric. Conservation of the physical norm requires the full time dependent metric condition, G˙+ℏi(H†G−GH)=0, rather than the time independent pseudo Hermitian relation alone. For the minimal scalar TWMSE model, the corresponding metric compensates exactly for the non Hermitian amplitude evolution, while also revealing a long time invertibility issue when the collapse functional possesses a nonzero mean. These results change the status of several experimental signatures proposed in the earlier unified TWMSE account. In particular, a nonzero Sorkin parameter, a second harmonic in Mach Zehnder interferometry, associated detection time estimates, and an already established branch dependent history bias are not treated in this revised paper as derived predictions of the minimal homogeneous TWMSE dynamics. They are retained instead as open derivation and experimental targets that require a genuinely spatially structured, operator level, or branch sensitive probability dynamics. The two system history experiment is consequently reformulated as a falsifiability target. A completed TWMSE model would need to demonstrate mathematically how different observer field histories could produce different normalized outcome statistics for systems having the same final standard quantum state, while remaining distinguishable from ordinary Hamiltonian evolution, decoherence, systematic effects, and competing collapse models. The paper further identifies the principal mathematical requirements for completing the framework, including branch sensitive collapse dynamics, existence and consistency of the time dependent metric, derivation of the physical probability law, strong coupling phase dynamics, accumulated interference and memory, multi particle consistency, no signalling, relativistic completion, conservation laws, parameter identification, and derivation or revision of the earlier interferometric proposals. This paper represents the author's current technical position on these questions and supersedes the experimental interpretation of the earlier technical unified account, Zenodo DOI 10.5281/zenodo.19537024, where those claims exceed what follows from the minimal written dynamics. The earlier technical paper remains part of the public development record. Its plain English companion, Zenodo DOI 10.5281/zenodo.19537305, likewise remains part of that record and should be read in light of the present revision. The objective of this revised account is therefore narrower but stronger: to state explicitly what TWMSE presently derives, what remains conditional, what remains open, and what must be demonstrated before the framework can yield a distinctive, normalized, causal, and experimentally testable prediction. Revision notice: This publication represents the author's current technical position on the experimental status of TWMSE. It supersedes the interpretation of experimental claims in Zenodo DOI 10.5281/zenodo.19537024 where those claims exceed what follows from the minimal homogeneous dynamics. The plain English companion to that earlier account, Zenodo DOI 10.5281/zenodo.19537305, should likewise be read in light of this revision. Both earlier records remain publicly available as part of the development history.
This record contains version 2 of the preprint “Identifiability Limits in Experimental Tests of Quantum Collapse.” It supersedes the conceptually broader first version deposited under DOI 10.5281/zenodo.19617199 and substantially revises the framing, formal results and experimental analysis. The paper formulates experimental tests of objective-collapse dynamics as an operational identifiability problem. It shows that finite accessible CPTP process statistics cannot uniformly distinguish fundamental nonunitarity from an unrestricted unitary-environment dilation. It then separates visibility loss, record formation and global measurement access, and derives a nuisance-profiled Fisher-information criterion for determining when complementary measurement channels jointly identify a shared collapse-parameter vector. A four-arm matched-control architecture is proposed that combines baseline stability, coherent reversibility, calibrated decoherence, durable-record formation and at least one independent side-effect channel. The result is a falsifiable experimental decision framework and a boundary on what accessible data can establish; it is not presented as an ontological solution of the quantum measurement problem. A major technical revision is available as version 3 under DOI 10.5281/zenodo.22072199. This record contains version 2 of the preprint “Identifiability Limits in Experimental Tests of Quantum Collapse.” It supersedes the conceptually broader first version deposited under DOI 10.5281/zenodo.19617199 and substantially revises the framing, formal results and experimental analysis. The paper formulates experimental tests of objective-collapse dynamics as an operational identifiability problem. It shows that finite accessible CPTP process statistics cannot uniformly distinguish fundamental nonunitarity from an unrestricted unitary-environment dilation. It then separates visibility loss, record formation and global measurement access, and derives a nuisance-profiled Fisher-information criterion for determining when complementary measurement channels jointly identify a shared collapse-parameter vector. A four-arm matched-control architecture is proposed that combines baseline stability, coherent reversibility, calibrated decoherence, durable-record formation and at least one independent side-effect channel. The result is a falsifiable experimental decision framework and a boundary on what accessible data can establish; it is not presented as an ontological solution of the quantum measurement problem. Files in this record:1. Main preprint PDF.2. Reproducibility package containing the journal-neutral source, editable manuscript, original figures, deterministic calculation and figure-generation code, machine-readable results, citation metadata and SHA-256 checksums. The included calculations are deterministic mathematical and synthetic checks; they are not experimental validation.
This paper presents a derivation-gated research programme for using the Nancy Grace Roman Space Telescope to test a possible cosmological consequence of the Total Wave Modified Schrödinger Equation (TWMSE). TWMSE is a proposed deterministic collapse framework in which system and observer fields interfere and collapse depends on a cumulative threshold condition. The revised unified TWMSE account establishes an important limitation: because the canonical scalar term C(t)I commutes with every Hamiltonian, it contributes only a common scalar factor and is empirically indistinguishable from standard quantum mechanics after physical normalisation. A cosmological bridge based solely on that scalar form therefore predicts α = 0. Any admissible cosmological completion must instead derive a branch-sensitive operator structure and map it quantitatively to a Roman observable before confirmatory data are examined. The programme is organised around one primary matched-history or path-degeneracy test. Populations would be balanced in present-state variables and in all conventionally relevant formation and line-of-sight histories, but separated by a pre-derived TWMSE coupling-history functional. Six supporting analyses—history-conditioned weak lensing, structure-growth residuals, accumulated environment, threshold behaviour, redshift scaling and cross-observable consistency—are treated as corroborating or falsifying views of the same mechanism rather than independent opportunities for anomaly discovery. The paper specifies the required derivation gate, standard-model controls, nuisance treatment, negative tests, blinding, preregistration, minimum detectable effect and interpretation rules. It does not claim that Roman has detected TWMSE or that a cosmological residual would establish a Theory of Everything. Without a dimensionally consistent bridge that fixes the predicted sign, magnitude, scaling and test domain in advance, Roman observations can motivate phenomenology but cannot test TWMSE specifically.
This theoretical and computational preprint integrates standard QND measurement and posterior-martingale results with finite-confidence decisions and physically retained observer records. Under a declared quantum instrument and its standard outcome probabilities, the posterior is a bounded martingale on an increasing observation filtration. A precise sufficient identification condition yields asymptotic terminal weights; a binary Gaussian benchmark gives exact mean stopping times, finite-threshold latch probabilities, and a controlled population-transfer bias bound. Version 2.3 is the first public release. It distinguishes accumulated observations from lossy current memory; assumed Born/instrument probabilities from derived consistency results; expected entropy from pathwise ambiguity; continuous confidence endpoints from discrete overshoot and unresolved runs; and Kramers first escape from endpoint readout error. It also clarifies the conditional D18/D19 persistence-selector interface and the separate D1092 finite-resource ledger, with direct attribution to established QND convergence and filtering literature. The companion archive includes the editable manuscript, PDF, equation sources, a fixed validation protocol, executable independent checks, numerical results, a revision ledger, and unchanged historical inputs. Historical simulation summaries are explicitly distinguished from new executions; some older executable sources were unavailable. The new audit includes exact finite-kernel and stopped-posterior checks, Gaussian likelihood-mixture calculations, five neutral and four population-transfer boundary-value cases, and retention/accounting controls. All examples are analytic or synthetic. No laboratory measurements, independent Born-rule derivation, measurement-problem solution, universal physical selector, or new empirical anchor are claimed.
Note added 10 August 2026: The experimental interpretation in this paper has been superseded. See the revised technical account, Zenodo DOI 10.5281/zenodo.21868322, which supersedes the Sorkin parameter, second harmonic, detection time estimates, and history bias claims where those exceed what follows from the minimal written dynamics. This record remains available as part of the development history. This paper presents the most complete account to date of the Total Wave Modified Schrödinger Equation (TWMSE), a deterministic framework in which quantum wavefunction collapse arises from interference between a system wavefunction and observer fields associated with the four fundamental interactions, rather than from a probabilistic postulate. The paper is organised in two parts with a formal bridge section. Part I constructs the minimal working model demonstrating well-posed pseudo-Hermitian evolution, collapse via interference thresholds, dynamical emergence of phase ergodicity via Weyl equidistribution and KAM theory, statistical recovery of the Born rule, and a quantified deviation ΔP(x) ~ δ²|Ψ|² bounded to δ ≲ 10⁻². The bridge section introduces the Two-System Falsifiability Argument: two identically prepared two-level systems with different environmental coupling histories must produce different collapse statistics under TWMSE and identical statistics under standard quantum mechanics — the conceptually minimal statement of the theory's falsifiability. Part II derives three concrete experimental signatures: the Sorkin parameter κ ~ δ²/3 from three-slit photon interference; a second harmonic fringe component at 2Δφ in Mach-Zehnder atom interferometry, strictly absent in all linear theories; and ILL-type neutron crystal interferometry. Detection of the second harmonic requires approximately 33 minutes at current cold-atom count rates. The architectural implications of TWMSE for quantum computing are developed in Appendix D of the forthcoming book Quantum Computing Is Stalling: A Way Forward (Larry Lim Kheng Cheong, forthcoming). Here is the link to the book -https://a.co/d/0hQ0I2i0 Note: A US non-provisional patent application (Application No. 19/645,198) covering collapse-based quantum computing architectures derived from this framework was filed on 12 April 2026 prior to this upload.