FROM PROPOSAL TO DEFINED DYNAMICS
Specify the model before deriving its consequences.
A source model becomes checkable when another reader can identify every state, operation, observation and physical calibration used by the argument.
The criterion for a joint explanation
Geometry, clocks and matter should arise as readouts of a stated common dynamics. Running independently selected algorithms on one controller does not establish why their physical laws agree. The useful question is which freedom the dynamics removes, and which freedoms still enter through the readouts or calibration.
Eight parts of a complete specification
| Part | Write down | Check |
|---|---|---|
| 1. State and preparation | A set, phase space or Hilbert space; admissible initial states; constraints; the prepared state or distribution. | Where are all registers, random seeds, ancillas and external controls represented? |
| 2. Retained memory | The variables carried from one update to the next and the equivalence relation used to discard distinctions. | Can states assigned the same record have different completed futures? Use the memory lab. |
| 3. Autonomous update | A map F, transition kernel, unitary, quantum channel or generator, together with its domain and fixed parameters. | If the update changes with a step counter, is that counter inside the state? Are environment couplings declared? |
| 4. Allowed local operations | The algebra of admissible operations and the adjacency or support relation they respect. | Is locality an input, an output, or a result in a specified limit? Do not assume the adjacency being derived. |
| 5. Clock observable | An independently readable clock variable, its coupling, monotonicity conditions and calibration. | Could another allowed clock change the proposed ratio while leaving the archive unchanged? |
| 6. Spatial and matter readouts | Rules assigning distances, adjacency, excitations and transport to source records. | Does readout rank give a metric? Does a propagation bound use the same clock and length units? |
| 7. Completion instrument | A deterministic output map, or outcome maps with explicit probabilities and state updates. | Are probabilities normalized? Are rejected outcomes counted? For quantum instruments, is the sum trace preserving? |
| 8. Resource budget | Memory size, update cost, preparation and reset, acceptance probability, and any reference system used. | Does the bound count all attempts and auxiliary resources, including unobserved failures? |
A compact specification template
Use this as a worksheet for a construction. Each placeholder should become a definition, a measured input, or an explicitly unresolved item.
Model name and version: State space S and constraints: Preparation p₀ or ρ₀: Retained variables and discarded distinctions: Autonomous update F or generator L: Fixed parameters and allowed variation: Allowed operations and locality relation: Completion outcomes, probabilities, and post-outcome state: Clock observable T and its independent calibration: Spatial readout X and distance rule: Matter observable M and propagation rule: Units, reference scales, and input constants: Resource cost per attempt and per accepted record: Claim to prove, including its quantified parameter range: Assumptions used by the proof: Countermodels or conditions where the claim fails: Independent observable reserved for comparison:
Declare how the six inner roles enter
In the SMM/DTT interpretation, the six inner generative roles are nested aspects of one construction; the seventh role is outer completion. A formal model must state their mathematical realization. If a hierarchy is used, declare its refinement maps. If an update factorization is used, declare the factors and their ordering, and explain why that factorization expresses the intended nesting.
A diagram with six boxes is not a derivation of six independent time coordinates. A clock duration for a role requires an observable and an interaction rule. If two descriptions are claimed to be equivalent, supply a map that preserves the records and dynamics being compared.
State the geometry–clock target without building it into a definition
Δu / Δτ = D, c = vgD
The count and scale equations determine a scaling exponent for the stated refinement. Identifying it with a geometric dimension requires the relevant construction and separation or regularity assumptions. Identifying it with a physical clock ratio requires separately defined clock readings.
Define u, τ, the distance measurement, and the matter-front speed independently of the desired equality. State their units; if the ratio is to equal a dimensionless D, use compatible temporal units or an explicit calibration. Then prove the relation on a nonempty family of settings (B,r), with one fixed measurement protocol. A countermodel that preserves the premises and changes the ratio identifies a missing selection condition.
Next: make the result reproducible.
Record the baseline, vary one input, and compare the exported result with a calculation that does not depend on the same implementation. Follow the protocol →