Workstream A · Research dossier

Record
formation.

How can a specified physical process produce a definite record, and how reliably can that record persist?

Mathematical result

Established starting point

The exact exclusion construction

For orthogonal projectors $P_j$ and an active set $S$ of $m \ge 2$ labels, R05 uses

K_{S,r} = \frac{P_S - P_r}{\sqrt{m-1}}, \qquad \sum_{r\in S} K_{S,r}^{\dagger}K_{S,r} = P_S.

With initial populations $\tfrac12, \tfrac13, \tfrac16$ , the six ordered exclusion histories have probabilities summing to 1, and the terminal survivor probabilities equal the supplied populations. The terminal operation for survivor $j$ is the projective instrument $\rho \mapsto P_j \rho P_j$ .

The construction gives an exact last-survivor representation of a supplied quantum instrument. Its physical application requires a specified preparation, apparatus interaction and record interpretation.

Theorem R05.1 statement Full worked example and history table

Physical questions

What the construction leaves open

01
Does the apparatus implement the specified instrument?
Requires an interaction model and measured frequencies compared with the instrument within stated tolerances.
02
What changes under calibration errors and noise?
Requires an explicit noise model. Exact zero effects are not robust against unrestricted full-rank perturbations (Theorem R05.4).
03
How is the record stored?
Requires a physical memory model and its stability over the relevant time, as a separate claim from the construction.
04
What are the energy and reservoir requirements?
Requires accounting of energy exchanged with the apparatus and reservoir, consistent with total stress in any joint model.
05
Does a proposed model predict anything different from a conventional quantum model?
Requires a calculated, quantitative difference. None is presently established.

Exact zero exclusion is not robust against every arbitrarily small full-rank perturbation. A protected error class or tolerance-based record rule requires its own definition and tests.

A numerical threshold or rounded probability is not a derived physical realisation law.

Optional illustration

A chosen timing model

For $n \ge 2$ candidate labels, assume $n-1$ independent exponential waiting times with a supplied constant rate $\gamma > 0$ , measured in inverse units of an identified clock time. The total time is their sum:

T = \sum_{k=1}^{n-1} \tau_k, \qquad \mathbb{E}[T] = \frac{n-1}{\gamma}.

This is the chosen timing model for the jump implementation in R05. A physical rate requires a clock identification (R08). It is not a universal PDT prediction and is not a demonstrated difference from ordinary quantum mechanics.

Dossier summary

Model, evidence and criteria

Specified model

R05 exclusion instrument applied to a supplied projective measurement.

Inputs and assumptions

A specified preparation, apparatus interaction, noise model, record storage mechanism, energy and reservoir accounting, and a clock identification for any timing claim.

Calculated outputs

History probabilities and survivor totals for the three-label example; expected completion time under the chosen timing model.

Proposed measurements

Outcome frequencies, post-measurement states, record lifetime and energy exchange for a specified apparatus.

Evidence currently available

The construction and its worked example are mathematical results. No apparatus model has yet been tested against data.

Comparison or rejection criterion

A specified apparatus model reproduces the instrument within stated calibration and noise tolerances, with its record rule and energy accounting defined in advance. Comparator: an appropriate conventional quantum model of the same apparatus.

Reproducibility

The example uses exact fractions and can be checked by hand on the mathematics page. No code, dataset or apparatus specification has been published.

Current foundational references

R03 R04 R05 Theorem R03.1 statement Theorem R05.1 statement Theorem R05.4 statement

Recordformation.

The exact exclusion construction

What the construction leaves open

A chosen timing model

Model, evidence and criteria

Record
formation.