{ "schema": "smonad-problems-v1", "modified": "2026-11-09", "categories": { "time": "Time, quantum physics & information", "space": "Space, relativity & gravity", "matter": "Matter, constants & interactions", "cosmos": "Cosmology & the vacuum" }, "statuses": { "example": "Worked example", "conditional": "Conditional result", "target": "Open research target" }, "apps": { "timing": { "title": "Ultra-Fine Timing", "url": "timing/index.html" }, "constants": { "title": "DTT Constants Explorer", "url": "dtt-constants/index.html" }, "hydrogen": { "title": "Hydrogen & Spectroscopy", "url": "applications/hydrogen.html" }, "quantum": { "title": "Quantum Interference", "url": "applications/quantum.html" }, "gauge": { "title": "Gauge & Quantum Simulation", "url": "applications/gauge.html" }, "geometry": { "title": "Emergent Space & Geometry", "url": "applications/geometry.html" }, "memory": { "title": "Memory & Information", "url": "applications/memory.html" }, "comparison": { "title": "Experimental Comparison", "url": "applications/comparison.html" } }, "topics": [ { "slug": "arrow-of-time", "title": "The arrow of time: generation, memory and irreversibility", "order": 1, "original_minutes": 6, "description": "Develop the DTT account of temporal direction through nested generation, completed records, an exact relaxation example and an explicit entropy-production target.", "summary": "The central idea The proposed chronological order supplies a direction for construction. Entropy production becomes a physical consequence when the completion dynamics, retained memory and environment obey a demonstrable balance law.", "category": "time", "apps": [ "memory", "timing" ], "status": "example", "inner": "Inner generation carries the source state and the correlations needed for its next operation. Reversibility of this full description can coexist with information inaccessible in a reduced record.", "outer": "Outer completion leaves a retained event whose order can be compared with later records and with a physical clock.", "potential": "This distinction could connect microscopic evolution, memory and macroscopic direction through one account of how records are produced.", "result": "The article calculates finite relaxation and an exact memory term obtained by eliminating a hidden variable.", "gap": "Chronological construction alone does not imply positive thermodynamic entropy production or select the initial conditions.", "next_step": "Specify the source, record and environment dynamics; derive their entropy and energy balance including reset and rejected events.", "exercise": "Change a memory transition table and compare states that look identical now but predict different future records.", "targets": [ "universal-clock-law", "joint-source-dynamics" ], "kind": "foundation", "level": "introductory", "url": "problems/arrow-of-time.html", "modified": "2026-11-09" }, { "slug": "causality", "title": "Causality: from sequential creation to physical influence", "order": 2, "original_minutes": 6, "description": "Develop causality as a consequence of SMM/DTT source dependencies, with a finite propagation example, a distinction between correlation and intervention, and a concrete locality target.", "summary": "The central idea Sequential generation becomes an explanation of causality when the update law determines dependency, preserves records and bounds controllable influence in the geometry read by observers.", "category": "time", "apps": [ "geometry", "memory" ], "status": "conditional", "inner": "Inner operations depend on retained outputs of preceding operations. Those actual dependencies define which changes can influence other changes.", "outer": "Completion exposes a spatial arrangement and a sequence of records in which an intervention has a measurable effect.", "potential": "A common source could generate both the causal ordering and the geometry used to measure propagation.", "result": "A finite update example gives an exact support-propagation bound under a specified neighbourhood rule.", "gap": "The rule and its correspondence to physical distance must be selected and remain stable under perturbations.", "next_step": "Derive a persistent neighbourhood and a uniform influence bound from the same autonomous update.", "exercise": "Compare spatial readout with the clock workbench; keep the readout definition and clock calibration independent.", "targets": [ "stable-locality", "joint-source-dynamics" ], "kind": "foundation", "level": "introductory", "url": "problems/causality.html", "modified": "2026-11-09" }, { "slug": "quantum-interpretation", "title": "A temporal interpretation of quantum mechanics", "order": 3, "original_minutes": 6, "description": "Develop the SMM/DTT interpretation of waves, particles and observation through coherent inner generation, an explicit interference calculation and physical detector records.", "summary": "The central idea The temporal interpretation becomes concrete when inner operations retain relative phase, the detector interaction creates a stable record, and the completed statistics follow the measured interference and probability laws.", "category": "time", "apps": [ "quantum", "memory" ], "status": "example", "inner": "Alternative inner generative routes retain relative phase and can contribute coherently to the same final record.", "outer": "A detector interaction produces a localized outward event; many events reveal the distribution set by those coherent routes.", "potential": "Wave-like formation and particle-like detection could be two temporal roles of a single process, giving complementarity a concrete physical interpretation.", "result": "The two-path calculation reproduces interference and the loss of visibility when distinguishable path records are retained.", "gap": "Coherent amplitude composition and the outcome rule are supplied in this realization, not derived solely from sequential generation.", "next_step": "Derive the admitted phase operations and completion instrument together, then test a shared relation among visibility, memory and completion delay.", "exercise": "Vary phase, coherence and unequal path populations; export the resulting detection probabilities.", "targets": [ "phase-and-composition", "joint-source-dynamics" ], "kind": "foundation", "level": "introductory", "url": "problems/quantum-interpretation.html", "modified": "2026-11-09" }, { "slug": "physical-information", "title": "Physical information: what recreation preserves", "order": 4, "original_minutes": 7, "description": "Expand the SMM/DTT information problem through retained memory, unitary correlations, finite-capacity reset costs and a precise black-hole information target.", "summary": "The central idea Recreation becomes dynamically meaningful when it specifies what information survives. Total-state preservation, accessible records and thermodynamic reset are different questions that can be measured within one model.", "category": "time", "apps": [ "memory", "quantum" ], "status": "example", "inner": "The source retains distinctions between possible continuations, including correlations absent from an observer’s current record.", "outer": "Completion makes selected distinctions accessible and stores a record that can be used again.", "potential": "The same temporal architecture could explain how information is preserved globally, hidden locally and consumed as a physical memory resource.", "result": "Entangled-state and finite-memory examples separate inaccessible information from actual erasure.", "gap": "The minimal retained state, its physical implementation and its preparation/reset cost require one resource account.", "next_step": "Construct a source memory sufficient for all admitted future operations and calculate the energetic cost of maintaining it.", "exercise": "Supply a deterministic state table and inspect the smallest partition preserving every future output sequence.", "targets": [ "joint-source-dynamics", "phase-and-composition" ], "kind": "foundation", "level": "introductory", "url": "problems/physical-information.html", "modified": "2026-11-09" }, { "slug": "nonlocality", "title": "EPR and nonlocality: a joint source with local observations", "order": 5, "original_minutes": 6, "description": "Develop the SMM/DTT common-source account of entanglement through singlet correlations, an exact no-signalling calculation and an explicit Bell-test target.", "summary": "The central idea A common generative source must reproduce the quantum joint distribution while preserving local control of observable signals. The decisive calculation combines Bell correlations, no-signalling and physically defined completion times.", "category": "time", "apps": [ "quantum" ], "status": "example", "inner": "A joint inner state can encode relations between parts that appear far apart only in the completed spatial readout.", "outer": "Separated apparatuses register local outcomes whose joint statistics reflect the preparation, while local control must preserve no-signalling.", "potential": "Shared generation offers a way to interpret entanglement without treating observed distance as a measure of independent origin.", "result": "The article presents singlet correlations and a no-signalling calculation within ordinary quantum instruments.", "gap": "A common classical cause alone cannot reproduce Bell correlations under the usual Bell assumptions; the source must justify its quantum composition rule.", "next_step": "Calculate a complete joint preparation and all local outcomes, and identify the precise assumptions the proposed source satisfies.", "exercise": "Use the interference lab to examine coherent versus distinguishable records. It is a phase benchmark, not a Bell-test simulator.", "targets": [ "phase-and-composition", "stable-locality" ], "kind": "foundation", "level": "technical", "url": "problems/nonlocality.html", "modified": "2026-11-09" }, { "slug": "planck-scale", "title": "The Planck scale: granularity, refinement and physical resolution", "order": 6, "original_minutes": 6, "description": "Develop the DTT proposal of scale-relative granularity through Planck units, a refinement example, operational dimension and the resource cost of increasingly fine records.", "summary": "The central idea The Planck scale combines gravity, quantum action and light propagation. A temporal-generation model must explain its relation to the smallest resolvable record, the refinement law and the physical cost of probing finer structure.", "category": "space", "apps": [ "geometry", "constants" ], "status": "example", "inner": "Nested generation permits a family of resolutions rather than identifying every construction stage with one universal smallest cell.", "outer": "A completed apparatus resolves distances and durations only through its calibrated records and available resources.", "potential": "The proposal could explain a scale-dependent relation between geometric resolution, clock response and accessible energy.", "result": "The guide distinguishes Planck units from a demonstrated minimum length and works through a refinement example.", "gap": "A physical resolution bound and any dispersion correction need a source-derived scale and measurement protocol.", "next_step": "Calculate the cost and accuracy of a refinement family while measuring length and duration independently.", "exercise": "Vary refinement parameters and compare geometric dimension, record counts and separately defined clock readings.", "targets": [ "stable-locality", "gravitational-limit" ], "kind": "foundation", "level": "introductory", "url": "problems/planck-scale.html", "modified": "2026-11-09" }, { "slug": "quantum-gravity", "title": "Quantum gravity: generating the geometry that matter reads", "order": 7, "original_minutes": 6, "description": "Develop SMM/DTT quantum gravity through generated relations, discrete curvature, an effective gravitational action and common clock–matter response.", "summary": "The central idea The constructive target is one source dynamics that produces a quantum state space, a stable geometric readout and the same effective metric for matter propagation and physical clocks.", "category": "space", "apps": [ "geometry", "gauge" ], "status": "example", "inner": "The source generates quantum relations, adjacency and transport before a smooth background geometry is assumed.", "outer": "Completed rods, clocks and matter records define the effective geometry seen by observers.", "potential": "Generating geometry and matter together could reconcile their descriptions and make gravitational response part of the same dynamics.", "result": "Discrete-curvature and effective-action examples identify quantities a successful reconstruction must calculate.", "gap": "The effective equations, universal matter coupling and controlled continuum limit remain to be derived.", "next_step": "Use one finite source model to compute a geometric response and several independent matter/clock responses.", "exercise": "Explore geometric readout and local gauge transport as separate finite benchmarks; compare their declared assumptions.", "targets": [ "gravitational-limit", "joint-source-dynamics" ], "kind": "foundation", "level": "technical", "url": "problems/quantum-gravity.html", "modified": "2026-11-09" }, { "slug": "hierarchy-problem", "title": "The hierarchy problem", "order": 8, "original_minutes": 6, "description": "A source-sector approach to the separation of gravitational and electroweak scales, with an explicit calculation of protected weak coupling.", "summary": "The central idea Complementary temporal sectors suggest a mechanism for suppressed visible coupling. A successful realization must derive that suppression and show that heavy-sector fluctuations do not destabilize the electroweak scale.", "category": "matter", "apps": [ "gauge", "constants" ], "status": "example", "inner": "A shared source may contain sectors with different overlaps, symmetry constraints and responses to its internal operations.", "outer": "Outward instruments access particular channels, so an effective visible coupling may be suppressed relative to internal scales.", "potential": "Temporal organization could provide a dynamical reason for weak visible interactions if the suppression is selected and protected.", "result": "A small-overlap model illustrates suppressed coupling and the associated heavy-sector correction estimate.", "gap": "The overlap cannot simply be chosen small; its stability and physical sector identification require a mechanism.", "next_step": "Derive the mixing from source symmetries and bound radiative or effective corrections under allowed perturbations.", "exercise": "Inspect retained symmetries and projection responses, then track which coupling normalizations remain independent.", "targets": [ "normalized-coupling", "matter-spectrum" ], "kind": "foundation", "level": "introductory", "url": "problems/hierarchy-problem.html", "modified": "2026-11-09" }, { "slug": "unification", "title": "Unification of the fundamental interactions", "order": 9, "original_minutes": 6, "description": "How one source can generate several interaction channels, and how a local transport calculation gives that proposal a precise gauge-theory form.", "summary": "The central idea Interaction channels can be organized as symmetries of local comparison and completion. Their shared origin becomes physically explanatory when it selects the gauge structure, matter representations and normalized couplings together.", "category": "matter", "apps": [ "gauge", "constants" ], "status": "conditional", "inner": "The same generative history supplies internal comparison states and the operations relating neighbouring records.", "outer": "Completion retains gauge-invariant relations; different interaction channels would appear as distinct responses of the same source.", "potential": "This could explain why several forces share geometric structures and could eventually constrain their groups, representations and strengths together.", "result": "Local frame changes and loop transport provide exact gauge-covariant examples for a declared group.", "gap": "The physical gauge content, matter representations and normalized couplings are not selected by covariance alone.", "next_step": "Find one operation algebra that fixes a carrier, its allowed transport and a cross-channel coupling relation.", "exercise": "Change local frames and verify that the loop observable is unchanged while intermediate link descriptions change.", "targets": [ "joint-source-dynamics", "normalized-coupling" ], "kind": "foundation", "level": "introductory", "url": "problems/unification.html", "modified": "2026-11-09" }, { "slug": "magnetic-monopoles", "title": "Magnetic monopoles: source topology and observable charge", "order": 10, "original_minutes": 6, "description": "Developing the SMM/DTT proposal that magnetic structure originates in temporal generation, with charge quantization, flux tests, and a precise distinction between source structure and a detectable monopole.", "summary": "The central idea The physical question is whether temporal topology produces a nonzero magnetic flux through an observable closed surface. This turns the original proposal into a constructive programme: derive the electromagnetic connection, its charge lattice, and the rule that permits or forbids isolated magnetic excitations.", "category": "matter", "apps": [ "gauge" ], "status": "example", "inner": "Inner phase and transport relations can support nontrivial winding or topological sectors.", "outer": "An observable monopole requires a completed flux measurement on a surrounding surface and a physical magnetic coupling.", "potential": "A source-topology account could explain which magnetic sectors exist and why isolated magnetic charge is accessible or excluded.", "result": "The guide states an integer flux calculation for a specified connection and closed surface.", "gap": "Internal winding does not by itself identify an electromagnetic monopole or fix its energy and detectability.", "next_step": "Construct the physical connection and admissible sectors, then compute flux, energy and a detection channel.", "exercise": "Study loop transport as a finite connection benchmark. This laboratory does not simulate a monopole search.", "targets": [ "matter-spectrum", "normalized-coupling" ], "kind": "foundation", "level": "introductory", "url": "problems/magnetic-monopoles.html", "modified": "2026-11-09" }, { "slug": "mass-generation", "title": "Mass generation: inertia from sequential coupling", "order": 11, "original_minutes": 6, "description": "An expanded SMM/DTT account of mass as a response of coherently generated structures, with an explicit two-channel dispersion model and connections to Higgs physics and composite mass.", "summary": "The central idea The strongest formulation treats mass as a calculated response coefficient of the source dynamics. It must connect internal coupling, physical clock readings, and the observed energy–momentum relation, while reproducing the successful Higgs and strong-interaction descriptions in their tested regimes.", "category": "matter", "apps": [ "hydrogen", "gauge" ], "status": "example", "inner": "Coordinated internal formation can create persistent modes whose phases and couplings carry an energy scale.", "outer": "Outer clocks and momentum measurements reveal a mode’s dispersion, inertia and transition energies.", "potential": "Mass could become a calculable cost of maintaining a coherent generative structure and its response to motion.", "result": "A two-channel Hamiltonian gives an exact relativistic-form dispersion after its coupling and clock scale are supplied.", "gap": "The source must select those parameters and reproduce the relevant Higgs and composite-mass regimes.", "next_step": "Track one stable mode through formation, dispersion and an independently calculated acceleration response.", "exercise": "Compare linked atomic scales and spectral transitions while identifying which masses and constants are inputs.", "targets": [ "matter-spectrum", "universal-clock-law" ], "kind": "foundation", "level": "introductory", "url": "problems/mass-generation.html", "modified": "2026-11-09" }, { "slug": "neutrino-masses", "title": "Neutrino masses: open chains and coherent flavour change", "order": 12, "original_minutes": 6, "description": "Developing the original SMM/DTT open-chain proposal into a spectral model of neutrino masses, mixing and coherence, with an explicit path-graph example and experimental targets.", "summary": "The central idea An open chain has a calculable spectrum, but its lengths, couplings and boundary conditions matter. A useful temporal model must derive the observed mass-squared hierarchy and mixing from one formation law, while retaining the coherence required for neutrino interference.", "category": "matter", "apps": [ "gauge", "comparison" ], "status": "example", "inner": "An open generative chain suggests coherent collective modes with different eigenvalues and boundary responses.", "outer": "Flavor preparation and detection sample superpositions of those modes after propagation.", "potential": "One formation rule could potentially connect mass splittings, mixing and coherence instead of assigning them independently.", "result": "A finite path-graph spectrum and the standard oscillation amplitude illustrate the calculation to be performed.", "gap": "Graph length, couplings, flavor map and absolute mass remain physical inputs unless a source law selects them.", "next_step": "Derive one spectrum and mixing matrix, calibrate a declared subset and reserve independent observables for testing.", "exercise": "Use finite spectral examples for intuition. The generic comparison tool is not a neutrino likelihood or oscillation fitter.", "targets": [ "matter-spectrum", "phase-and-composition" ], "kind": "foundation", "level": "technical", "url": "problems/neutrino-masses.html", "modified": "2026-11-09" }, { "slug": "color-confinement", "title": "Color confinement: from inner constituents to completed singlets", "order": 13, "original_minutes": 6, "description": "The SMM/DTT account of confined lower-dimensional constituents, developed through gauge-neutral completion, flux energy and Wilson-loop tests.", "summary": "The central idea A completion rule can explain why observable records are gauge invariant. Confinement additionally requires an energetic result: separating color sources must create a costly field configuration. Deriving both from one source update would connect the temporal proposal to quantitative strong-interaction physics.", "category": "matter", "apps": [ "gauge" ], "status": "conditional", "inner": "Internal color labels belong to coherently generated constituents and the transport connecting them.", "outer": "A neutral-completion rule can restrict outward records to gauge singlets.", "potential": "Combining neutral completion with a growing separation cost could explain both observable color neutrality and energetic confinement.", "result": "Singlet projection and a specified flux-energy model give exact finite checks of neutrality and separation cost.", "gap": "Gauge neutrality alone does not prove confinement in the physical theory or in a continuum limit.", "next_step": "Derive the completion projector and source-separation energy from the same interacting model.", "exercise": "Calculate singlet-loop energies and compare exact results with the approximation while keeping the finite-model scope visible.", "targets": [ "matter-spectrum", "stable-locality" ], "kind": "foundation", "level": "technical", "url": "problems/color-confinement.html", "modified": "2026-11-09" }, { "slug": "yang-mills", "title": "Yang–Mills theory: from discrete formation to a physical mass gap", "order": 14, "original_minutes": 6, "description": "How the SMM/DTT intuition of minimum coupled formation can be developed into a gauge-invariant spectral problem, with finite-size tests and a clear continuum construction target.", "summary": "The central idea Discreteness can make a regulated model calculable, but a field-theoretic mass gap must survive increasing volume and removing the regulator. The temporal programme becomes concrete when one source update yields gauge transport, a physical vacuum, positive dynamics and a uniform spectral bound.", "category": "matter", "apps": [ "gauge" ], "status": "target", "inner": "A continuously generated vacuum must support interacting gauge transport and a well-defined physical constraint space.", "outer": "Completed gauge-invariant correlations reveal the energies of physical excitations above that vacuum.", "potential": "The temporal picture could turn minimum formation requirements into a spectral theorem if the same dynamics controls large scales.", "result": "Finite gap and correlation examples show what to compute; a finite chain also demonstrates how a positive gap can vanish with size.", "gap": "A four-dimensional interacting continuum construction with the required positive gap is not established here.", "next_step": "First prove Gauss-law preservation and a size-uniform bound in a precisely specified regime, then investigate regulator removal.", "exercise": "Use the singlet-loop calculator as a finite benchmark; its spectral gap does not settle the Yang–Mills mass-gap problem.", "targets": [ "matter-spectrum", "stable-locality" ], "kind": "foundation", "level": "technical", "url": "problems/yang-mills.html", "modified": "2026-11-09" }, { "slug": "baryon-asymmetry", "title": "Baryon asymmetry: temporal orientation and sector balance", "order": 15, "original_minutes": 6, "description": "A quantitative development of the SMM/DTT dual-sector interpretation of matter and antimatter, with visible baryon number, coherent selection, production and washout.", "summary": "The central idea A balanced source can contain unequal sector populations, but symmetry alone does not choose their sign or size. A predictive theory must derive which states populate the observed sector, how a baryon asymmetry is generated or transferred, and why subsequent reactions do not erase it.", "category": "matter", "apps": [ "memory", "comparison" ], "status": "example", "inner": "Complementary source sectors can carry opposite charges while an oriented interaction transfers population between them.", "outer": "Visible records sample one physically specified sector and its abundance after production and washout.", "potential": "A globally balanced source could still produce a visible excess if its dynamics selects the sector, sign and surviving amount.", "result": "The article gives a balanced two-sector state and a production–washout equation with explicit source terms.", "gap": "Sector balance alone selects neither the observed asymmetry nor the required interaction history.", "next_step": "Derive the charges, transfer rates and cosmological evolution, then calculate the surviving abundance with fixed parameters.", "exercise": "Explore record selection with the memory lab. Its state counts are not a calculation of cosmological baryon abundance.", "targets": [ "joint-source-dynamics", "matter-spectrum" ], "kind": "foundation", "level": "introductory", "url": "problems/baryon-asymmetry.html", "modified": "2026-11-09" }, { "slug": "supersymmetry", "title": "Supersymmetry: temporal sectors and graded dynamics", "order": 16, "original_minutes": 6, "description": "Developing the SMM/DTT proposal of complementary bosonic and fermionic sectors through a precise graded Hamiltonian, physical spin requirements and observable partner couplings.", "summary": "The central idea A dual-sector picture motivates a symmetry, but a calculable graded algebra establishes its content. The key questions are which source states are paired, how outward completion exposes or hides those pairs, and which interaction or spectral relation could distinguish the proposal experimentally.", "category": "matter", "apps": [ "gauge" ], "status": "example", "inner": "Complementary inner sectors motivate paired states and transformations that exchange them.", "outer": "Outward completion determines which states and couplings can be prepared or observed.", "potential": "If a physical graded symmetry follows from the source, it could relate apparently different particle sectors and their spectra.", "result": "A graded Hamiltonian supplies an exact algebraic pairing example under its declared construction.", "gap": "Paired sectors do not establish spacetime supersymmetry, physical spins, partner masses or a breaking mechanism.", "next_step": "Identify admissible supercharges and physical representations, then derive an observable relation surviving symmetry breaking.", "exercise": "Use the symmetry laboratory to distinguish a selected algebra from its physical identification; no superpartner prediction is implied.", "targets": [ "phase-and-composition", "matter-spectrum" ], "kind": "foundation", "level": "introductory", "url": "problems/supersymmetry.html", "modified": "2026-11-09" }, { "slug": "horizon-problem", "title": "Homogeneity and the horizon problem", "order": 17, "original_minutes": 6, "description": "How common inner generation can coordinate an outward universe, and how to calculate the resulting cosmic correlations.", "summary": "The central idea A shared source can explain why separated regions inherit related conditions. Its symmetry and fluctuation law must then produce the measured sky, including the small departures from uniformity.", "category": "cosmos", "apps": [ "geometry", "memory" ], "status": "example", "inner": "Regions may share generative preparation before their separation is defined by the outward spatial readout.", "outer": "Completed observations compare temperatures and correlations across the resulting sky.", "potential": "A common origin could supply correlated initial conditions while subsequent observable propagation remains local.", "result": "A shared-variable covariance model illustrates inherited correlations and the guide identifies the required angular-spectrum calculation.", "gap": "A common source does not select the observed homogeneity, fluctuation spectrum or acoustic structure without further dynamics.", "next_step": "Calculate primordial correlations from one preparation law and propagate them through a specified cosmological model.", "exercise": "Explore generated addresses and shared memory as conceptual ingredients; these tools do not compute a CMB spectrum.", "targets": [ "stable-locality", "gravitational-limit" ], "kind": "foundation", "level": "introductory", "url": "problems/horizon-problem.html", "modified": "2026-11-09" }, { "slug": "cosmic-inflation", "title": "Cosmic inflation and perpetual generation", "order": 18, "original_minutes": 6, "description": "Connecting repeated inner formation with a measurable expansion history, primordial fluctuations and the end of an early accelerated phase.", "summary": "The central idea Rapid generation gives physical inflation when completed distances expand fast enough relative to outward clocks. The same source law should also determine the initial fluctuations and a transition into the hot expanding universe.", "category": "cosmos", "apps": [ "geometry" ], "status": "example", "inner": "Repeated inner generation changes record number and physical scale through a specified refinement or growth law.", "outer": "Outer clocks measure whether the completed physical distances accelerate and for how long.", "potential": "Generation could supply an origin for early expansion if the same source also accounts for perturbations and the transition to ordinary evolution.", "result": "The article expresses expansion using generated volume, cell scale and an independently defined completion interval.", "gap": "Increasing record count alone is insufficient: cell size, clock calibration, fluctuations and exit dynamics must be determined.", "next_step": "Derive a calibrated expansion history, its perturbations and its exit from one model.", "exercise": "Vary record growth and scale contraction independently to see why more records need not mean a larger physical volume.", "targets": [ "gravitational-limit", "joint-source-dynamics" ], "kind": "foundation", "level": "introductory", "url": "problems/cosmic-inflation.html", "modified": "2026-11-09" }, { "slug": "dark-matter", "title": "Dark matter and the persistent source ground state", "order": 19, "original_minutes": 6, "description": "The original (c,0) proposal developed through a concrete collective-mode example that can cluster and carry nearly pressureless energy.", "summary": "The central idea The original (c,0) label specifies a proposed temporal structure. A pressureless dark component can be constructed from persistent collective modes, with its stress, abundance and clustering calculated explicitly.", "category": "cosmos", "apps": [ "gauge", "comparison" ], "status": "example", "inner": "Persistent collective source modes could store energy without coupling strongly to ordinary electromagnetic records.", "outer": "Their gravitational response would appear through clustering, lensing and structure formation.", "potential": "The structured source could potentially supply an unseen gravitating component with properties tied to its formation dynamics.", "result": "A rapidly oscillating scalar example illustrates a nearly pressureless averaged component in its stated regime.", "gap": "That illustrative field is not yet a source-derived dark-matter species with a predicted abundance and full observational fit.", "next_step": "Derive the mode, stress tensor and production history, then test background evolution and perturbations together.", "exercise": "Inspect finite collective modes for a controlled example. Generic curve fitting does not replace lensing or structure-formation analysis.", "targets": [ "matter-spectrum", "gravitational-limit" ], "kind": "foundation", "level": "introductory", "url": "problems/dark-matter.html", "modified": "2026-11-09" }, { "slug": "dark-energy", "title": "Dark energy and complementary temporal structure", "order": 20, "original_minutes": 6, "description": "Developing the original (0,c) proposal into a conserved smooth component, with a worked negative-pressure mechanism and observable expansion history.", "summary": "The central idea A component whose energy grows in proportion to physical volume has negative pressure and can accelerate expansion. The DTT task is to derive that response, its magnitude and any evolution from the complementary source structure.", "category": "cosmos", "apps": [ "constants", "comparison" ], "status": "example", "inner": "A complementary source sector could contribute energy whose response depends on the generated physical volume.", "outer": "Completed clocks and distances measure the resulting pressure, expansion and any time variation.", "potential": "A source-selected volume response could explain accelerated expansion while linking it to other vacuum properties.", "result": "The supplied extensive-energy model gives negative pressure when its energy density is fixed.", "gap": "The density, physical stress tensor and evolution must be calculated rather than inserted to reproduce acceleration.", "next_step": "Derive energy and pressure from one source functional and check conservation, stability and cosmological observables.", "exercise": "Inspect the constants explorer’s vacuum assumptions and normalization steps before interpreting any numerical value.", "targets": [ "vacuum-selection", "gravitational-limit" ], "kind": "foundation", "level": "introductory", "url": "problems/dark-energy.html", "modified": "2026-11-09" }, { "slug": "cosmological-constant", "title": "The cosmological constant: source averaging and gravitational response", "order": 21, "original_minutes": 6, "description": "The Single Monad proposal to average source states, developed through an explicit energy normalization and the distinction between vacuum shifts and observable excitation energy.", "summary": "The central idea Source averaging can remove an unjustified multiplicity factor when labels describe alternatives of one state. A cosmological-constant mechanism must also fix the physical energy density, its response to constant energy shifts and its small residual value.", "category": "cosmos", "apps": [ "constants" ], "status": "example", "inner": "Different source labels may represent alternatives within one normalized state rather than independent physical copies.", "outer": "Gravity responds to the completed energy–momentum content and its dependence on the metric.", "potential": "Source averaging could correct an inappropriate state count, while a deeper selection law could determine the gravitating residual.", "result": "The guide calculates normalized averaging and shows explicitly how a constant Hamiltonian shift survives it.", "gap": "Normalization alone does not remove the absolute vacuum-energy ambiguity or predict a small cosmological constant.", "next_step": "Construct a metric-sensitive vacuum functional and prove that its selected residual is stable under admissible microscopic changes.", "exercise": "Trace the cosmological-constant dependency map and distinguish a normalization choice from a predicted gravitational value.", "targets": [ "vacuum-selection", "gravitational-limit" ], "kind": "foundation", "level": "introductory", "url": "problems/cosmological-constant.html", "modified": "2026-11-09" }, { "slug": "measurement-problem", "title": "The measurement problem: when does an inner process become a record?", "order": 22, "original_minutes": 6, "description": "Develop an operational DTT measurement programme using completion flags, quantum instruments, pointer stability, outcome probabilities and a measurable memory-dependent test.", "summary": "The central idea A complete measurement model must explain which observable is recorded, how an outcome becomes stable, why its probability follows the required law and how the apparatus retains the result.", "category": "time", "apps": [ "quantum", "memory" ], "status": "example", "inner": "The source and apparatus evolve together, retaining phase and correlations before a stable record is available.", "outer": "Completion must have an operational criterion: an outcome is registered, can be read again and enters later predictions.", "potential": "This could replace an unexplained observer boundary with a physical account of when a generative process becomes a usable event.", "result": "Quantum instruments describe outcome probabilities and conditional states; the article separates recording, stability and outcome selection.", "gap": "A completion label or decoherence calculation alone does not derive unique outcomes and their probability law.", "next_step": "Specify the complete instrument, including unfinished/rejected trials, and derive record stability and any proposed delay relation.", "exercise": "Compare interference with retained path information, then test whether a proposed record preserves the information needed for future outcomes.", "targets": [ "phase-and-composition", "joint-source-dynamics" ], "kind": "investigation", "level": "introductory", "url": "problems/measurement-problem.html", "modified": "2026-11-09" }, { "slug": "black-hole-information", "title": "Black-hole information: retained memory and outward release", "order": 23, "original_minutes": 6, "description": "A new SMM/DTT research route to black-hole information, separating coarse-grained loss from quantum unitarity and giving an explicit isometric completion model with a Page-shaped entropy example.", "summary": "The central idea Information hidden from an observer is not the same as information destroyed by the full evolution. SMM/DTT can address the distinction by treating each completion as an isometry from retained source memory to new memory and radiation, then deriving its entropy, energy and causal behavior.", "category": "time", "apps": [ "memory", "quantum" ], "status": "example", "inner": "The full source state can retain correlations absent from the outward description of a black hole.", "outer": "Successive completions could transfer those correlations into emitted radiation and accessible records.", "potential": "The distinction between hidden generation and accessible completion offers a language for information storage and release within one evolution.", "result": "A finite isometry model preserves total information and produces an illustrative rising-and-falling radiation entropy.", "gap": "A Page-shaped example does not establish realistic evaporation, horizon dynamics, energy balance or a gravitational solution.", "next_step": "Couple a memory-preserving radiation map to a source-derived energy and causal model, and calculate their joint consistency.", "exercise": "Explore predictive memory and quantum correlations as separate ingredients; the labs do not simulate black-hole evaporation.", "targets": [ "gravitational-limit", "phase-and-composition" ], "kind": "investigation", "level": "introductory", "url": "problems/black-hole-information.html", "modified": "2026-11-09" }, { "slug": "lorentz-symmetry", "title": "Lorentz symmetry from completed records", "order": 24, "original_minutes": 6, "description": "An explicit split-complex boost, a common propagation cone and a worked discrete-mode calculation connect inner generation with relativistic observations.", "summary": "The central idea Split-complex algebra gives an exact 1+1-dimensional Lorentz boost. A physical DTT realization must also derive a shared propagation cone and show how the dynamics of matter and clocks respect it.", "category": "space", "apps": [ "geometry", "timing" ], "status": "conditional", "inner": "Inner generation supplies transport and the interactions from which matter and physical clocks are built.", "outer": "Observers compare completed displacements and clock readings, so a shared cone must govern those measurements.", "potential": "A single source could explain why clock and matter laws agree on the same limiting speed and transformation structure.", "result": "The guide gives an exact split-complex boost and conditional cone and discrete-dispersion examples.", "gap": "An algebraic boost does not force all material devices to obey it; common dynamics and the relevant limiting regime remain essential.", "next_step": "Derive a common propagation and clock law across multiple material realizations without separate frequency tuning.", "exercise": "Compare geometric dimension and clock response; test what changes when an independent inner-activity coupling is introduced.", "targets": [ "universal-clock-law", "joint-source-dynamics" ], "kind": "investigation", "level": "technical", "url": "problems/lorentz-symmetry.html", "modified": "2026-11-09" }, { "slug": "spatial-dimensions", "title": "Why three spatial dimensions?", "order": 25, "original_minutes": 6, "description": "Connect the six nested generative roles of SMM/DTT to three observable directions, stable locality and independently measurable dimensional scaling.", "summary": "The central idea Three dimensions can enter through a local readout, the growth of spatial regions, or the spectrum of a propagation operator. A convincing source model should make these independent measurements agree over an identified physical range.", "category": "space", "apps": [ "geometry" ], "status": "conditional", "inner": "Six nested inner roles represent dependent formation stages whose completed relations may admit several distinguishable directions.", "outer": "An outward readout defines position; volume growth and propagation provide independent measurements of effective dimension.", "potential": "A generation law could explain three-dimensional space if it selects and stabilizes agreement between these different measurements.", "result": "A three-component quaternionic readout and a refinement dimension are exact within their specified constructions.", "gap": "A local rank of three does not by itself prove three-dimensional extended locality or universal dimensional scaling.", "next_step": "Calculate readout rank, neighbourhood growth and propagation dimension from one stable family of source states.", "exercise": "Compare nested roles, the 64-to-27 address example and refinement dimensions without identifying their different counts.", "targets": [ "stable-locality", "joint-source-dynamics" ], "kind": "investigation", "level": "introductory", "url": "problems/spatial-dimensions.html", "modified": "2026-11-09" }, { "slug": "testable-predictions", "title": "From a proposed mechanism to a testable prediction", "order": 26, "original_minutes": 7, "description": "Develop SMM/DTT experiments through independently calibrated clocks, complete quantum records, reserved spectroscopy data and a common source model.", "summary": "The central idea Specify the source, apparatus, observable and comparator before evaluating agreement. Clock comparisons, phase-sensitive registration and spectroscopy provide concrete ways to turn a temporal interpretation into a quantitative research programme.", "category": "time", "apps": [ "comparison", "timing", "hydrogen" ], "status": "target", "inner": "One source law should restrict several internal responses with a fixed set of parameters.", "outer": "Completed experiments measure independently calibrated observables at settings reserved before comparison.", "potential": "The shared temporal origin gains predictive power when a calibration in one channel fixes a relation in another.", "result": "The guide formulates clock-ratio and cross-transition consistency tests with explicit calibration and reserved observations.", "gap": "A flexible fit, a familiar quantum effect or a synthetic example alone does not discriminate the proposed mechanism.", "next_step": "Declare one source-derived relation, a conventional comparator, nuisance effects and a held-out measurement protocol.", "exercise": "Fit only the training rows in the comparison tool, inspect frozen predictions on test rows and export inputs and residuals.", "targets": [ "joint-source-dynamics", "normalized-coupling" ], "kind": "investigation", "level": "introductory", "url": "problems/testable-predictions.html", "modified": "2026-11-09" }, { "slug": "joint-source-dynamics", "title": "Open problem: one dynamics for geometry, clocks and matter", "order": 27, "original_minutes": 8, "description": "Define the central SMM/DTT source problem: one autonomous update that constrains independently measured geometry, clock readings and propagation.", "summary": "The central connection A decisive next theorem would derive a relation between record refinement, a physical clock and matter transport across a family of settings, while accounting for retained memory and completion resources.", "category": "space", "apps": [ "geometry", "timing", "memory" ], "status": "target", "inner": "A single autonomous interaction must create record relations, retain memory and drive the matter and clock sectors.", "outer": "Independent instruments read geometry, physical duration and propagation after completion.", "potential": "This is the central opportunity: agreement among space, time and matter could become a consequence of shared generation.", "result": "A declared one-charge model locks phase and dilation under its interaction restriction.", "gap": "Separate capacity, scale, material-clock and matter interfaces still need dynamical selection and a full resource account.", "next_step": "Construct a nonempty source family and prove a joint relation stable under admitted perturbations and all completion branches.", "exercise": "Compare refinement outputs and clock laws while changing independent controls; identify exactly which agreement is imposed.", "targets": [ "stable-locality", "universal-clock-law" ], "kind": "target", "level": "technical", "url": "problems/joint-source-dynamics.html", "modified": "2026-11-09", "prerequisites": "Source state, update, retained memory and independently specified instruments.", "deliverable": "A working source family with a joint geometry–clock–matter identity and a complete resource budget.", "test": "Vary a source parameter without retuning the instruments; test whether the identity survives." }, { "slug": "stable-locality", "title": "Open problem: selecting and preserving spatial locality", "order": 28, "original_minutes": 8, "description": "Stable locality requires a dynamical propagation bound, a persistent neighbourhood structure, and a justified connection to physical distance.", "summary": "The central connection Existing finite constructions prove lattice neighborhoods and local support bounds under explicit operation rules. A stronger source law must prepare those rules with accounted resources and preserve them under perturbations.", "category": "space", "apps": [ "geometry", "gauge" ], "status": "target", "inner": "Source operations must prepare and preserve the relations that define neighbouring records.", "outer": "Controllable influence measured between completed records must obey a bound in the generated distance.", "potential": "Locality could be a stable outcome of temporal generation, explaining why a common source appears as an extended world.", "result": "Finite constructions provide neighbourhood and support bounds for explicitly admitted operations.", "gap": "Preparing the structure, preventing nonlocal shortcuts and controlling larger systems require additional estimates.", "next_step": "Prove a preparation-and-stability theorem with accounted memory, operation range and size-independent constants.", "exercise": "Inspect spatial addresses and local loop transport; document the neighbourhood each model assumes.", "targets": [ "joint-source-dynamics", "gravitational-limit" ], "kind": "target", "level": "technical", "url": "problems/stable-locality.html", "modified": "2026-11-09", "prerequisites": "Generated adjacency, physical distance and the admitted operation range.", "deliverable": "A locality theorem including preparation cost, stability and constants uniform in system size.", "test": "Introduce graph defects and local perturbations; test for unaccounted shortcuts." }, { "slug": "universal-clock-law", "title": "Open problem: why material clocks should share one law", "order": 29, "original_minutes": 8, "description": "Use the protected-clock theorem and its countermodel to define a source-derived, stable and operationally universal DTT clock law.", "summary": "The central connection Branch invisibility is exactly a commutant condition in the finite clock model. A universal DTT law must derive that condition, or a different common response, for an independently defined physical class of clocks.", "category": "space", "apps": [ "timing", "geometry" ], "status": "target", "inner": "Different material clocks contain internal processes that may couple differently to inner generative activity.", "outer": "A universal outward time law requires independently built clocks to agree after fixed calibration.", "potential": "DTT could explain physical clock universality if completion selects or protects the same response across a real class of devices.", "result": "The finite clock model gives an exact commutant criterion for invisibility of specified inner branches.", "gap": "Protection of a chosen device does not establish a universal material-clock class or its physical selection.", "next_step": "Derive the allowed clock interactions for at least two material realizations and test delayed as well as immediate readouts.", "exercise": "Vary the inner-work coupling in the geometry–clock comparison and compare it with the declared timing model.", "targets": [ "joint-source-dynamics", "stable-locality" ], "kind": "target", "level": "technical", "url": "problems/universal-clock-law.html", "modified": "2026-11-09", "prerequisites": "An independently defined material-clock class and its readout algebra.", "deliverable": "A shared clock-response theorem for distinct devices, including failed and delayed completions.", "test": "Vary inner activity after fixed calibration and compare immediate and delayed readings." }, { "slug": "phase-and-composition", "title": "Open problem: deriving phase-compatible quantum composition", "order": 30, "original_minutes": 8, "description": "Extend real-dynamical phase selection into a source-derived rule for composing systems, retaining joint coherence and producing completed records.", "summary": "The central connection The polar phase calculation and balanced tensor construction are exact conditional starting points. The open problem is to make their compatibility, observable algebra and completion rule consequences of one source dynamics.", "category": "time", "apps": [ "quantum", "memory" ], "status": "target", "inner": "Oriented inner dynamics can select a compatible phase structure on its dynamic sector under the representation hypotheses.", "outer": "Joint preparations and completed instruments must use a consistent composition and probability rule.", "potential": "A common source might connect quantum phase, entanglement and records through one operational structure.", "result": "Published phase-selection mathematics supplies a conditional phase construction; the standard composite additionally uses a balanced tensor rule.", "gap": "Local phase selection alone does not select all composite-system and measurement assumptions.", "next_step": "Derive a physically admitted operation algebra whose joint evolution preserves the required composition and completion rules.", "exercise": "Use the phase laboratory to test the resulting probabilities, and explicitly state which quantum composition rules are supplied.", "targets": [ "joint-source-dynamics", "matter-spectrum" ], "kind": "target", "level": "technical", "url": "problems/phase-and-composition.html", "modified": "2026-11-09", "prerequisites": "A real representation, oriented dynamics and an explicit joint-operation algebra.", "deliverable": "A source-selected composition and instrument rule compatible with phase and retained records.", "test": "Test joint coherence and all outcome probabilities across several preparations." }, { "slug": "normalized-coupling", "title": "Open problem: fixing a normalized physical coupling", "order": 31, "original_minutes": 8, "description": "Specify the missing response-normalization theorem between the structural 137 receiver and a physically identified SMM/DTT electromagnetic coupling.", "summary": "The central connection The open target is the dimensionless primitive response gprim=scont/(4πac). Proving an inverse-rank factor does not fix this remaining quantity; a source-selected relation would make the ideal coupling a physical model output.", "category": "matter", "apps": [ "constants", "hydrogen" ], "status": "target", "inner": "Generative structure fixes candidate record sectors, while the same source must also determine their stiffness and response to charge.", "outer": "Outward force, phase and spectroscopic measurements identify a dimensionless physical coupling.", "potential": "Structural counts could become physical constants if source dynamics fixes the response normalization and electromagnetic identification.", "result": "The declared grammar yields 137 records, and conditional response models isolate an inverse-rank factor.", "gap": "The primitive dimensionless response remains free; a structural 137 alone does not determine measured alpha.", "next_step": "Compute normalized charge, action and field response from one model, then reserve an independent atomic observable.", "exercise": "Inspect the alpha dependency map and vary response assumptions before checking their consequences for atomic scales.", "targets": [ "joint-source-dynamics", "matter-spectrum" ], "kind": "target", "level": "technical", "url": "problems/normalized-coupling.html", "modified": "2026-11-09", "prerequisites": "Normalized carrier charge, action scale and source response.", "deliverable": "A dimensionless coupling relation whose normalization is fixed without fitting the target constant.", "test": "Calibrate independent quantities and reserve a force or spectral measurement." }, { "slug": "matter-spectrum", "title": "Open problem: a source-derived spectrum of matter", "order": 32, "original_minutes": 8, "description": "Define a common SMM/DTT spectral problem for stable carriers, mass, spin, charge and dispersion, with an exact finite-walk diagnostic.", "summary": "The central connection Finite eigenmodes, protected auxiliary sectors and local quantum walks provide exact benchmarks. A physical matter spectrum requires source-selected carriers and a common energy–momentum dictionary that survives interactions and limits.", "category": "matter", "apps": [ "hydrogen", "gauge" ], "status": "target", "inner": "Persistent formation patterns and their interactions define candidate excitations of the source.", "outer": "Completed energy, momentum, charge and transition measurements identify the properties attributed to particles.", "potential": "One spectral law could connect particle identities and mass relations to the same structure that generates space and clocks.", "result": "Finite spectral, singlet and quantum-walk examples provide explicitly calculable benchmark sectors.", "gap": "Physical species, their representations and the common energy scale have not been uniquely selected.", "next_step": "Follow one mode through preparation, dispersion and an independently predicted transition, then extend to a second species.", "exercise": "Compare exact finite loop spectra with atomic scale relations; retain the distinct physical identifications of each model.", "targets": [ "normalized-coupling", "phase-and-composition" ], "kind": "target", "level": "technical", "url": "problems/matter-spectrum.html", "modified": "2026-11-09", "prerequisites": "Source-selected carriers, physical observables and a common clock/energy dictionary.", "deliverable": "One stable mode with jointly calculated dispersion, charge and transition data.", "test": "Predict a second mode or transition without giving it an independent coupling." }, { "slug": "gravitational-limit", "title": "Open problem: a gravitational limit of temporal generation", "order": 33, "original_minutes": 8, "description": "Formulate the source-to-gravity problem through geometric response, universal matter coupling, a weak-field example and controlled limiting equations.", "summary": "The central connection The target is a controlled effective action and universal matter coupling from the same source update. A curvature coefficient can be matched to G only after those physical interfaces and the limiting regime are established.", "category": "space", "apps": [ "geometry", "constants" ], "status": "target", "inner": "The source must generate geometric response and the interactions read by matter and clocks.", "outer": "Completed weak-field and propagation measurements identify a common effective metric and gravitational strength.", "potential": "Gravitation could follow from the response of the same formation process that supplies material measurements.", "result": "Conditional curvature and coefficient dictionaries describe how a candidate effective action would be matched.", "gap": "Universal coupling, the effective equations and a controlled limiting construction remain open.", "next_step": "Derive one weak-field source response and compare its effects on several independently defined probes.", "exercise": "Inspect geometric readouts and the gravitational-constant dependency map; separate matched inputs from predicted coefficients.", "targets": [ "joint-source-dynamics", "vacuum-selection" ], "kind": "target", "level": "technical", "url": "problems/gravitational-limit.html", "modified": "2026-11-09", "prerequisites": "A stable geometry, matter action and metric-sensitive source response.", "deliverable": "A controlled effective action with common coupling to independently defined probes.", "test": "Compare weak-field clock, light and matter responses and monitor regulator dependence." }, { "slug": "vacuum-selection", "title": "Open problem: selecting a gravitating vacuum contribution", "order": 34, "original_minutes": 7, "description": "Identify what a DTT vacuum mechanism must calculate beyond normalized response, with exact offset, averaging and relaxation tests.", "summary": "The central connection The task is to derive a metric-sensitive vacuum functional and a stable relation between its constant term and curvature response. Exact offset and relaxation tests distinguish a selection mechanism from normalization or averaging.", "category": "cosmos", "apps": [ "constants" ], "status": "target", "inner": "The source vacuum has retained states and responses whose absolute contribution must be selected by a physical rule.", "outer": "Completed gravitational measurements depend on metric variation, including the vacuum’s constant contribution.", "potential": "A source-derived selection mechanism could connect a small gravitating vacuum term to the same dynamics fixing other responses.", "result": "Offset and auxiliary-relaxation calculations expose the ambiguity left by normalized observables.", "gap": "Averaging and normalization do not by themselves fix a radiatively stable gravitational vacuum value.", "next_step": "Specify the metric-dependent functional and test its selected residual under constant shifts and microscopic perturbations.", "exercise": "Follow the vacuum matching steps and identify every free scale, subtraction and normalization in the constants explorer.", "targets": [ "gravitational-limit", "normalized-coupling" ], "kind": "target", "level": "technical", "url": "problems/vacuum-selection.html", "modified": "2026-11-09", "prerequisites": "A physical metric variation and an absolute source-energy prescription.", "deliverable": "A selected gravitating residual with a stability estimate under microscopic changes.", "test": "Apply constant-offset and parameter-perturbation tests to the same functional." } ] }