dynamicsystemsarchitecture.org

Version.002: State Separation and Causal Write Ordering in Multi-Source Estimation

Oct 4, 2026 · Gregory Lacefield

PurposeA revision of Version.001 that states a criterion for what a channel is instead of asserting four channels.
StatusCurrent — a separate document. Version.001 is unchanged. A structural argument only: not tested by an outside party, not peer reviewed.
Built from← Version.001
AttributionDrafted with Claude (Anthropic) at the author’s direction. Cites no figures from the lab’s own testing.
ReferencesThe reference list was written from memory and has not been checked against the sources. Verify each entry before relying on it.

Version.002 replaces the fixed four-channel claim of Version.001 with a stated criterion for what a channel is. It separates what happens in a system from what an estimator records about it, limits the separation guarantee to a single time slice, and adds a read-only coupling monitor. Version.001 is unchanged. Nothing in this document has been tested by an outside party, and it cites no figures from the lab's own testing.

What changed from Version.001

Version.001 (dated June 27, 2026, recorded in this project on October 4, 2026) stays as it is. This version is a separate document.

Area Version.001 Version.002
Channel count Four, asserted Set by a stated criterion. Four is the default template; the count is open per domain
Meaning of I Interface design in section 2, anxiety in the examples and section 6 Instrument and presentation parameters only. Subject affect is a candidate channel of its own
What S, D, I, C name Treated as the same thing as the estimate Process variables and estimator records kept apart
D feeding I Written into the update rule without comment Declared as a control edge, not a causal edge
Time Acyclic graph, with a time-delay fix listed as a stress case Two-slice model is the base. The guarantee is scoped to one slice
Correlation between channels Mentioned as a diagnostic residual Rule E: a read-only monitor over a window of slices
Provenance Source label Value-level provenance (Rule F)
Earlier multiplier claim Quoted and retracted in section 10 Not restated. This document cites no figures from lab testing

The problem

A test score, a sensor reading or a decision log is one number produced by several sources at once: the conditions the subject is in, the subject's own state, the instrument that elicited the response, and the act of responding. An estimator that sees only that number cannot recover the subject's state when different combinations of sources can produce the same value, because the information that would separate them was never recorded separately. A better estimator does not repair this. The information is gone before the estimator runs.

The remedy is at the input stage. Record the sources as separate variables with separate update rules before any inference. Whether a given system can do that depends on how well its apparatus isolates each source. That is an engineering condition, and this document treats it as one.

What a channel is

A channel is a set of variables with exactly one write authority, placed in an order of arrival. The world exists before the subject in it, the subject exists before the instrument that assesses it, and a measurement exists only after the instrument has acted. Two sets of variables belong in the same channel only if the same source writes them. If different sources write them, merging them destroys the record of which source did what, which is the original problem again.

This is the criterion. The number of channels is whatever the criterion yields for a given domain. Four is the default template for estimating the state of a subject:

Channel Role Written by Arrives
S Conditions acting on the subject and the instrument: noise, time of day, load The environment First
D The subject's state, the quantity being estimated: capability, belief, condition The subject's own dynamics, influenced by S After S
I The instrument: how the subject is probed and presented to (difficulty, format, timing, probe design) The assessor or designer After the subject exists
C The trace: what was observed when the subject responded through the instrument The subject acting through the instrument, under S After I acts

Within one time slice the order is S before D before I before C.

The diagnostic is not a channel in this template. It is the set of operators that read all four records and decide what the estimator may believe: the gate (Rule D), the monitor (Rule E), and alignment against a reference. Some framings promote the diagnostic to a channel and fold the trace into the instrument. Under the criterion, that is a legitimate alternative only if the diagnostic's output has a write authority no other channel has. That question is open (see Channel count).

Process variables and estimator records

The letters S, D, I and C name two different kinds of thing, and Version.001 treated them as one.

The causal order is a statement about process variables. Write isolation is a statement about records. The two fail independently. A record can be contaminated while the process is clean, for example when a computation blends two sources into one stored value. A process can be coupled while the records stay cleanly separated, and that separation is what lets the monitor see the coupling instead of finding it buried in a mixed number.

So "independent at source" (a claim about S*, D*, I*, C*) and "write-isolated" (a claim about S, D, I, C) are separate statements, and each needs its own justification. Claims below are about records unless a star says otherwise.

Adaptive systems add a third kind of dependence, the control edge: one record is chosen from another, such as next-problem difficulty chosen from the record D. A control edge is a decision by the operator of the system. It is not a causal effect of the subject on the instrument. Control edges are allowed in the update rules and must be declared, so they are not mistaken for process coupling.

Snapshots and dynamics

State estimation takes a snapshot. Within one time slice, the claim is that the four sources do not contaminate each other: the probe is designed, and the sampling interval is short enough, that no source's value is a function of another's during the slice. Across slices, real systems couple. Performance changes what the subject knows, affect changes capability, practice changes the subject.

The model is therefore two-slice. Within a slice, the dependence structure is acyclic and ordered. Across slices, an edge from any channel to any later channel is allowed, with a delay of at least one slice. This is the standard form of a dynamic Bayesian network (Murphy, 2002).

Three consequences follow.

  1. A strictly lower-triangular operator on n channels is nilpotent with index at most n. That holds for the within-slice operator only. It says nothing about influence across slices.
  2. "No cross-contamination in the instant" is an assumption (A1). The probe and sampling design must earn it. A latency measured over an interval already integrates several sources, so a slice is only as clean as the apparatus is short and selective.
  3. Coupling across slices has to be measured, not assumed away. That is the job of the monitor.

The coupling monitor

The monitor estimates how strongly channels co-vary over time. Correlation alone cannot show the direction of influence, so reading it takes care.

The monitor is read-only and writes to no channel. Its output is a coupling report. When a declared tolerance is exceeded, it raises a flag that A1 is in doubt for that domain. The response is a graph revision: re-declare the edge set and re-argue every guarantee under the new graph. How to do that revision while the system is running is an open problem (time-varying graphs).

Rules

The rules apply to records. Under the default template they read as follows.

Rule A. Write authority. Each record has exactly one writer, and no other code path can write it. This is enforced at the data layer, not only in application code.

Rule B. Order. Within a slice, update dependencies are acyclic under S before D before I before C. Across slices, delayed edges from any channel to any later channel are allowed and must be declared. Control edges must be declared too.

Rule C. Observation sources. Each channel has designated observation sources. The probe that feeds D must be designed to be insensitive to S and I. Where possible, use several independent probes taken under different S and I conditions, and treat agreement among them as higher confidence in D.

Rule D. Gate. D changes only when a gate passes. Telemetry may suppress an update. It may never supply an update's value. During a hold, D stays at its last confirmed value.

Rule E. Monitor. A read-only process estimates coupling between channels over a window of slices, conditioning on S, and reports it against a tolerance declared for the domain. It writes to no record.

Rule F. Provenance. Every value written to a record carries the provenance of the sources used to compute it, not only the label supplied by the caller. A value computed from a source the record may not read is rejected even when its label is allowed. The mechanism comes from information-flow control (Denning, 1976; Sabelfeld and Myers, 2003) and noninterference (Goguen and Meseguer, 1982).

Update equations for the default template:

S(t+1) = f_S(S(t), obs_S(t))
D(t+1) = D(t) + alpha * gate(probe(t), history, telemetry(t)) * delta_d(t)
I(t+1) = f_I(I(t), design(t), control(D(t)))    # control edge, declared
C(t)   = append-only observation log             # no state-update equation

In the linear case, recovering S, D and I from the observations requires the stacked observation operator, probes included, to have full column rank over the records to be estimated. If it does not, no arrangement of the records recovers them.

What this claims and does not claim

Claims. If probes can be designed to separate the sources, then records with exclusive writers keep information that a mixed record destroys. Within a slice, under A1 to A4, the rules prevent contamination of one record by another. Both are structural arguments. They are conditional on the assumptions below.

Does not claim.

Assumptions.

Label Assumption Who must establish it
A1 Within a slice, no source's value is a function of another's. The probe and sampling design, per domain
A2 Rules A and F are enforced at the data layer. The implementation
A3 Gate thresholds are calibrated for the domain and population. The operator, with domain data
A4 The monitor's tolerance is declared, and its estimator's own assumptions (for example, no unmeasured common cause) are stated. The operator

Evidence status. Structural argument only. No outside test, no field data.

Channel count: open and domain-dependent

This specification does not fix the number of channels. The right count depends on the domain and on what is being estimated. No argument or experiment here shows four to be optimal, and none shows it to be wrong. The criterion in "What a channel is" decides, one domain at a time.

For each proposed change to the channel set, apply three tests.

  1. Writer. Does the new set of variables have a write authority that no existing channel has?
  2. Order. Where does it arrive, and does placing it keep the within-slice order strict?
  3. Merge. If it were folded into an existing channel, would the quantity being estimated become unrecoverable from the merged record? This is the same logic as the non-recoverability argument for mixed signals. It can only be answered with data from the domain, and none exists yet.

Candidates raised so far. None is adopted.

Candidate Written by How current lab documents place it Arrives Status
Subject's regulatory or affective state (anxiety, motivation, tilt) The subject's own regulation, driven by S, I and earlier C Assigned to I in some documents, to a sub-component of D in others, to no channel in the proof After D, before C Strongest candidate: it is already split across definitions
Goals and interests The subject and a profile data bank Not a channel. At most a sub-component of D ("values") Before I, because it selects content May be a sub-record of D with a write rule (it may write I, never D) rather than a channel
Reference reality, or verifier External outcomes confirmed by a party outside the loop Folded into S in some framings. Named as "Reality" and "Verifier" in later parts of the proof without a definition After C, because outcomes are known later Candidate. Judging an estimate needs a reference that no template channel writes
Trace separate from instrument The subject, through the instrument In framings where the interface is the checker and the diagnostic is the fourth channel, the observed trace has no channel Not applicable Not an addition. A mapping gap between two four-channel readings

Two common readings together name five roles: the world, the subject, the instrument, the trace and the verdict. The default template has four channels and treats the verdict as operators over the records. The alternative reading keeps the verdict as a channel and folds the trace into the instrument. Under the criterion, the choice turns on write authority: does the trace have a different writer from the instrument's designer, and does the verdict write anything no other channel writes? The first answer looks like yes. The second is open.

Where it breaks

Feedback faster than the slice. The two-slice model handles feedback that runs across slices. If influence between channels runs within a slice, A1 fails, and no write rule restores it. The remedy is a shorter slice or a sharper probe.

Latent environment. Some of S cannot be observed directly, such as socioeconomic context or fatigue. S then has to be inferred from residuals, which makes a dual-estimation problem with its own identifiability limits.

No clean probe. If every available assessment of D is sensitive to S or I, separation of D is not achievable in that domain. Rule C's mitigation is several independent probes taken under different conditions. Agreement among them is evidence. Disagreement is information about S and I.

Blind monitor. A monitor whose baseline was set while coupling was already present absorbs that coupling and reports clean. A slow drift can do the same. The baseline has to be established under conditions verified as clean, and drift has to be tested for.

Contamination inside a legitimate write. A writer that is allowed to write D can still compute its value from a source it may not read. A source label cannot catch that. This is why Rule F requires provenance of the value, not of the caller.

Process and record confused. An argument that proves something about records is not an argument about the world. Where a result is stated about S*, D*, I*, C*, it needs its own justification.

Domain declaration and a worked example

Before applying the architecture to a domain, fill in one declaration. The channel count falls out of it.

Field What to write
Quantity estimated The thing the system exists to estimate, and who or what holds it
Channels One row per set of variables with a single writer
Writer The one source allowed to write each record
Arrives after What must exist before this channel can
Control edges Any record chosen from another, declared
Observation source How each record is observed, and the probe that feeds D
Slice length How long a slice is, and why A1 plausibly holds within it
Monitor tolerance The coupling level that triggers a graph revision

Worked example, illustrative only and not run with real students: a tutoring system estimating capability on a prerequisite graph of skills. The split between what an assignment is about and how hard it is was the first separation this application required.

Channel Variables Writer Arrives after Declared edges
S Time of day, noise, session length, device Environment observations None None
D Mastery estimate per skill node Gated update from the probe S None
I Difficulty tier, format, scaffolding, topic The assignment designer D, S Difficulty is chosen from D (control edge). Topic is chosen from G
C Answers, latency, edits Append-only observation log I None
G (candidate) Interests and goals The student and a profile data bank S May write I (topic). May not write D

Whether G is a fifth channel or a sub-record of D with a write rule is the open question in "Channel count". The monitor would test it: if G and D show coupling beyond the declared tolerance across slices, the write rule alone is not enough.

References