A place for your next calculation
Turn a large theoretical question into a result another reader can examine: a proof, a counterexample, a model, an operational comparison or a careful philosophical analysis.
Find a challenge01 · Make the target precise
A large question becomes manageable when its central statement has a definite setting. Choose a source dynamics, a readout, an algebra, a class of physical protocols or an interpretive claim. Write down what is fixed and what you are allowed to vary. If you want to test a dimension argument, for example, say whether the allowed channels must come in opposite pairs and whether their coefficients can be negative.
The linked discussion supplies context, examples and references. Its challenge is a starting problem you can sharpen to match your expertise. A proof under a useful set of hypotheses, a small counterexample to an overly broad statement or an explicit physical dictionary can each be a substantial contribution.
Distinguish the desired result from the method you plan to use. “Select three dimensions” names an ambition; a classification of admissible readouts with a clearly stated selection criterion names work that another researcher can follow.
02 · Expose the reasoning
For a mathematical contribution, give definitions, the claim, a proof or counterexample, and enough intermediate steps to identify the decisive assumption. A small explicit matrix or finite state model often reveals a difficulty that a general description leaves hidden. Include limiting or degenerate cases when they test the scope of the argument.
For a physical model, specify preparation, controls, quantities read out, units and free parameters. A comparison is stronger when the same choices govern every observable. If a value is calibrated from a measurement, show which further observation or relation is used to assess the resulting model.
For philosophical work, identify the sense of the terms under discussion, the argument connecting them and a clear alternative interpretation. Cite the relevant passage or model rather than treating a shared word as evidence that two ideas have the same content.
03 · Open a collaboration
You can begin before a whole programme is complete. Describe the part you understand, the result you can establish, and the next calculation or conceptual question you would like to work on. A useful research note makes its relation to an existing article or paper explicit and tells a collaborator what can be checked immediately.
I welcome collaboration with experts in physics, mathematics and philosophy. Possible contributions include operator or representation theory, autonomous source models, quantum instruments, geometric readouts, spectral calculations, cosmological dynamics, philosophy of explanation and historical interpretation of time and creation.
Choose a challenge below and use Prepare a contribution to organize your note. Include a source link and a brief account of your relevant expertise, then share it through the contact page. You can also propose a new question when the existing directory does not capture the problem you want to examine.
Choose a problem to develop
Each discussion develops an argument, examines a worked example and ends with a concrete next step.
40 of 40 challenges
No matches for these filters. Try fewer words or choose another field.
Source, time & records
Does one source explain a world of many things?
Fix one preparation set, memory budget and test language; compare two autonomous updates with the same present labels.
A complete transition table, predictive equivalence classes and a shortest distinguishing intervention.
Space, locality & dimension
Does nested time select three spatial dimensions?
Use the same preparation, reversal and measurement tasks for both architectures, with a declared memory and runtime budget.
Operation counts, detector bounds and a proof identifying which physical premise excludes an alternative.
Space, locality & dimension
How could locality and relativity emerge from one source?
Specify all local registers, scheduling memory and read/write permissions; calibrate duration and compare two matter channels.
An exact support proof, a finite perturbation bound and a table of independently measured front and band velocities.
Source, time & records
Specify one autonomous finite update, retained registers and a completion flag; test removal or merger of each role.
A dependency table, transition diagram and six concrete interruption or simplification tests.
Source, time & records
Is outer time already a physical clock?
Fix one source law and vary branch and resolution activities independently while retaining the same clock couplings and calibration.
A response table, a protection proof or error bound, and every surviving counterexample to universality.
Source, time & records
Can renewed generation preserve the identity of an object?
Choose a finite transport law, an identity test and a bounded error model; include the memory and completion mechanism.
Conservation proofs, a retention or lifetime estimate, and outcomes for interrupted writes and corrupted records.
Source, time & records
Can a completed record support its own future predictions?
Fix a finite source, preparation family and control language; refine present-output classes until their transitions close.
The final partition, minimal required memory and a distinguishing test for every necessary split.
Meaning, observers & causation
Does an observer in SMM/DTT require consciousness?
Couple two finite detectors to one source with declared calibrations and error channels; include their completion flags.
A proof of agreement, a controlled disagreement example and an explicit account of what the model leaves about experience.
Meaning, observers & causation
What connects metaphysical unity to a physical theory?
Choose one claimed implication, define its source class and measurements, and compare at least two compatible-looking models.
A precise implication or counterexample with the indispensable bridge assumption identified.
Meaning, observers & causation
Does a common origin explain causal influence?
Construct two finite models with the same undisturbed record statistics and the same declared intervention vocabulary.
A protocol separating them, or a proof of operational indistinguishability within that vocabulary, with timing and control costs.
Space, locality & dimension
What makes a spatial readout physically meaningful?
Choose a finite source, detector map and raw comparison protocol; reconstruct a metric before fitting any propagation result.
The comparison table, metric proof, uncertainty bounds and an independent transport check.
Space, locality & dimension
Can a source dynamically select local structure?
Implement a finite graph-selection rule autonomously, account for its auxiliary memory, then restrict matter transport to retained edges.
A selection or stationary-law proof, convergence evidence with limits, and a perturbation audit of distances and support.
Space, locality & dimension
Are fractal dimension and spatial dimension the same?
Fix one source and refinement family; independently compute rank, neighborhood counts and a finite return observable with calibrated time.
A reproducible comparison across resolutions, with finite-size effects and every interpretation of dimension stated.
Space, locality & dimension
Can the clock–dimension relation be derived from one source?
Keep one source interaction, clock calibration and matter Hamiltonian fixed across several refinement settings; include an alternative clock coupling.
A proved endpoint or protection law, independently defined measurements and an error-controlled comparison of the joint relation.
Quantum theory & measurement
Which complex algebra belongs to which temporal role?
Give one finite source update and independent phase and delay–displacement instruments. Vary one source parameter without separately retuning either instrument.
Matrices, calibration rules and a proof or counterexample showing whether the two outputs remain linked.
Quantum theory & measurement
Does completion explain quantum measurement?
Specify a finite source–payload–apparatus Hamiltonian with a prepared initial state. Derive all outcomes, accepted work, false-positive rate and record lifetime from that same interaction.
The complete instrument, error bounds including entangled payloads, and a finite resource and timing table.
Quantum theory & measurement
Does completion derive the Born rule?
Give source-generated preparations and completion tests, including a coarse event and its physical refinement. Calculate their probabilities without assuming squared amplitudes.
A complete probability table, an explicit list of source assumptions and either a uniqueness proof or a surviving alternative law.
Quantum theory & measurement
Can rejected inner work be reversed?
Specify a finite source-controlled work sequence and all failure maps. Restrict the allowed inverse controls and the history registers that remain accessible.
A recovery construction or impossibility proof, including entangled inputs, total success probabilities and a complete time and preparation budget.
Quantum theory & measurement
Does entanglement through a common source allow signalling?
Specify a finite two-party source with local settings, outcomes, completion flags and clock readings. Include every rejected or delayed event in the joint distribution.
All setting-dependent tables, a correlation calculation and a proof or bound for remote marginal independence.
Quantum theory & measurement
What selects the composite system?
Specify local source preparations, joint updates and future tests for two and then three phase-bearing carriers. Define equivalence using those tests rather than assuming the complex tensor product.
The quotient state space, a distinguishing test basis, and proofs of operation compatibility and associativity.
Quantum theory & measurement
Does a four-pi rotation explain spin and statistics?
Give a finite retained carrier, its full rotation representation, a reference interferometer and a two-excitation exchange operation. Do not impose antisymmetry in the starting state space.
Explicit operators, an exchange-sign derivation under stated physical constraints, and a comparator showing which constraint is essential.
Constants & physical response
Does Schrödinger evolution fix Planck’s constant?
Specify one autonomous source, a clock, an interferometric phase readout and an independently defined energy transducer. Keep their free scales explicit.
A proof of a common energy-to-phase-rate ratio across a stated family, or an explicit rescaling counterexample identifying the surviving freedom.
Gauge structure & interactions
What is retained by a holonomy?
Give finite link transports, local frame changes, a prepared carrier and a complete readout experiment. Compare two transports that agree on one proposed observable.
Gauge-transformation calculations, all outcome probabilities and either a distinguishing second test or a proof of operational equivalence.
Gauge structure & interactions
Does winding fix electric charge?
Construct a phase-bearing source with explicit boundary conditions, admissible deformations, a field kinetic normalization and a calibrated transport probe.
An integer-classification proof, the stable-sector calculation and a statement of which coupling combinations are fixed or remain free.
Gauge structure & interactions
Can neutral completion select a gauge group?
Specify an operationally meaningful retained tensor family and its source-preservation law. Determine all transformations preserving those tensors, including the global group.
A complete stabilizer calculation, remove-one-tensor comparisons and an explicit account of representation and coupling freedom.
Gauge structure & interactions
Does a finite gap solve the Yang–Mills problem?
Take one explicit finite source gauge Hamiltonian, identify all physical sectors and define the refinement, volume and energy-calibration parameters.
A sector-complete spectrum or rigorous bound, its scaling law, and either a uniform positive estimate or a concrete collapsing-gap sequence.
Source, time & records
Is the vacuum the same as nothing?
Specify two source backgrounds with the same immediate spatial display, a common preparation class and a fixed family of future completion tests.
A distinguishing response or spectrum, or a proof of operational equivalence, with any gravitational coupling stated separately.
Source, time & records
Can loss of information create an arrow of time?
Specify a reversible finite source, prepared memory, completed-record map and a fixed future test family. Choose a directional statistic and a finite observation window.
A monotonicity or asymmetry proof with its preparation assumptions, validity bound, recurrence limit and memory/reset accounting.
Constants & physical response
What does the structural integer 137 establish?
Construct the legal-word table, completion tests and positive response matrix; vary every freedom left by the stated source law.
An exact rank calculation and either a unique normalized response or two admissible countermodels.
Proofs, comparisons & tests
What do the three published papers actually establish?
Specify one finite source, its symmetry, completion tests and projection; compute quotient dynamics, phase selection and reduced memory.
A reproducible model with an explicit hypothesis-to-result table and one counterexample for each indispensable interface.
Proofs, comparisons & tests
What would distinguish DTT from an effective one-time model?
Supply a finite source family, a resource-matched alternative, shared calibration and one held-out protocol with preparation-error bounds.
A table of admissible predictions, an exact separation or equivalence proof, and code or matrices reproducing it.
Constants & physical response
What connects the proposed vacuum counts 137 and 128?
Specify the two receiver tasks, an intertwining map if available, and their positive response operators under one calibration.
Exact ranks, a descent check, and either a protected response ratio or an explicit surviving normalization freedom.
Constants & physical response
Can a mode count fix a normalized physical coupling?
Give a finite positive source-response model with explicit current, inner product, calibration and all admissible deformations.
A proof that the dimensionless response is unique, a protected ratio, or a pair of calibrated models with different responses.
Constants & physical response
Does a hydrogen spectrum test the source or only its effective model?
Produce the source-to-Hamiltonian reduction with independently fixed response and mass inputs, then compute two linked atomic quantities.
A normalized bound state, a parameter ledger, a second preparation or observable, and an error estimate for the reduction.
Gravity & cosmology
Does a causal cone already give Einstein gravity?
Construct calibrated clock and matter observables from one finite source, then perturb its energy and derive the resulting geometric response.
A shared cone bound, a calibrated metric or weak-field readout, and a response law with explicit continuum errors.
Gravity & cosmology
What would derive the equivalence principle from one source?
Construct two source-generated excitation types, one bound state and two clock transitions under a shared weak-field perturbation.
Independently defined inertial and gravitational responses, a binding-energy audit, and a universality proof or explicit deformation.
Gravity & cosmology
Can vacuum response fix the cosmological constant?
Specify one finite source energy, current probe and geometric probe; calculate its vacuum offset, pressure and behavior under a controlled spectral change.
A derivation of the gravitational contribution, a list of allowed additive terms and a stability test with independently fixed scales.
Gravity & cosmology
Does one source ensure cosmic homogeneity?
Provide a finite local source, a spatial readout and a preparation class; compute invariant distributions, correlations and relaxation rates.
A measure-selection argument, an exact mixing or stability bound and independently calibrated completion durations.
Proofs, comparisons & tests
What makes a derivation non-circular?
Choose a source-to-observable claim, separate definitions from calibration, and enumerate the complete admissible parameter family.
A dependency table, a nonempty model, and either a uniqueness bound or an explicit countermodel preserving all premises.
Reading levels describe the mathematical background used in the discussion. The wider site search also connects articles, books, papers and other sections.
Physics · Mathematics · Philosophy
I welcome collaboration with experts in physics, mathematics and philosophy: a careful derivation, a useful counterexample, a sharper interpretation or a model we can develop together.
SMONAD
Share this page, or keep a clear reference to the work you are reading.
Use this reference for the explanation on this page. “n.d.” means its first publication date is not specified; the update date is recorded separately.
