# Clarity Validation Pilot

**Spectral Grammar as a Screening Signal for Psychological Displacement**

Diego Rincón · Phronesis · Draft protocol, v1

---

## 1. Background & Rationale

Clarity (phronesis.world/clarity) computes a coherence score from free-written text using a fully deterministic, non-ML pipeline: sentences become nodes in a graph weighted by content-word overlap and positional proximity, the graph Laplacian is formed, and its eigenspectrum is extracted via the Jacobi eigenvalue algorithm. The theoretical claim, laid out in *From Grammar to Coherence* (Rincón, 2026 — zenodo.org/records/21403447), is that grammatical/discourse structure is itself a legible readout of a person's underlying coherence state — that displacement in language mirrors displacement in the coupled-oscillator dynamics of the nervous system.

That claim has never been tested against a validated clinical instrument. This protocol is that test.

**What is actually being validated:** not "Clarity diagnoses depression," but the much narrower and falsifiable question — does a purely structural, content-free property of a short writing sample (its eigenspectrum) carry statistically detectable information about a person's psychological state, as indexed by standard self-report screeners? A positive result would be evidence for the coherence framework generally, independent of whether the tool is ever used clinically. A null result would be informative too — it would tell us the metric, as currently defined, isn't picking up what the theory predicts.

## 2. Objectives / Hypotheses

**H1 (primary).** `displacementIndex` correlates positively with PHQ-9 total score (depression severity).

**H2 (primary).** `displacementIndex` correlates positively with PCL-5 total score (PTSD symptom severity).

**H3 (secondary).** `coherenceScore` correlates negatively with PHQ-9 and PCL-5 totals. (Not a redundant restatement of H1/H2 — `displacementIndex` and `coherenceScore` are not perfect inverses; see §6.)

**H4 (exploratory).** The proportion of eigenvalues in the lowest quartile band (`theta`, interpreted as slow/repetitive structure) correlates with rumination-adjacent PHQ-9 items (items 2, 3: anhedonia, sleep) and with PCL-5's intrusion cluster.

**H5 (exploratory, tests the dyadic-coupling claim specifically).** `coherenceScore` correlates negatively with a loneliness/connection measure (UCLA-3), independent of depression score — i.e., the coherence signal tracks *isolation* even after controlling for mood.

**Pre-specified thresholds.** r ≥ .30 — signal worth a fully-powered follow-up. r ≥ .50 — strong enough to justify building toward a screening-tool development track. r < .20 with this N — treat as a null result for the current metric definition, not for the underlying theory; report and revise the metric.

## 3. Design

Cross-sectional, correlational, single-session pilot. Fully online, no in-person visit required.

**Sample size.** Two tiers, both using the Fisher z approximation for detecting a Pearson r at α = .05 (two-tailed), power = .80:

| Target effect (r) | Required N |
|---|---|
| .40 | ~47 |
| .35 | ~62 |
| .30 | ~85 |

**Recommendation: N = 60 as a feasibility/effect-size-estimation pilot** (adequately powered only down to r ≈ .35), explicitly framed as Phase 1. If the observed effect is in the .25–.35 range — plausible for a first-generation proxy measure — Phase 1 will be underpowered to confirm it at conventional significance, and the right move is a pre-registered Phase 2 at N ≈ 85–90, not p-hacking the Phase 1 sample. State this in the protocol itself so it isn't a post-hoc excuse.

## 4. Participants

**Sample.** Community adults (18+), recruited online (Prolific or a university subject pool). Deliberately *not* a clinical-diagnosis-only sample — restricting to diagnosed participants would compress variance on the outcome measures and bias the correlation toward zero. The goal is a sample with a full range of PHQ-9/PCL-5 scores, which a general community pool with typical base rates of distress will provide.

**Inclusion.** 18+, fluent English writer, able to provide informed consent, access to a computer or phone with a working microphone (only needed if breath-channel data is added in a later phase — not required for Phase 1).

**Exclusion / safety.** PHQ-9 item 9 (suicidal ideation) is scored immediately upon submission. Any endorsement above "not at all" triggers an automatic on-screen message with crisis resources (988 Suicide & Crisis Lifeline, Crisis Text Line) before the participant proceeds, and flags the case for researcher follow-up per standard IRB practice for online mental-health-adjacent research. This is a floor requirement, not optional.

## 5. Measures

**Predictor — Clarity spectral output**, computed client-side, all fields logged:

- `fiedler` (λ₁, algebraic connectivity — primary structural-coherence signal)
- `spectralGap` (λ₂ − λ₁ — robustness of the coherence estimate)
- `spectralRadius` (λₙ — discourse complexity ceiling)
- `bands` (theta/alpha/beta/gamma — quartile proportions of the eigenvalue distribution)
- `coherenceScore` = 0.6 × fiedlerNorm + 0.3 × gapNorm + 0.1 × (1 − fragmentationIndex), where fiedlerNorm and gapNorm are normalized by sentence count
- `displacementIndex` = 0.7 × (1 − coherenceScore) + 0.3 × (1 − contentWordDensity)
- `fragmentationIndex` (proportion of near-zero eigenvalues — isolated/disconnected sentences)
- `sentenceCount`, `contentWordDensity`, `wordCount`

Note for analysis: `displacementIndex` is a weighted composite of structural coherence *and* lexical density (content-word ratio), not structure alone. If H1/H2 are supported, a planned secondary analysis decomposes which component — `coherenceScore` or `contentWordDensity` — is carrying the correlation, since prior psycholinguistic literature (e.g., absolutist-word and function-word research in depression text) would predict the lexical component alone might already correlate with PHQ-9, independent of the graph-theoretic claim. This needs to be ruled out, not assumed away.

**Outcome measures:**

- **PHQ-9** — 9-item depression severity screener, validated, public domain.
- **PCL-5** — 20-item PTSD Checklist for DSM-5, validated.
- **UCLA Loneliness Scale (3-item short form)** — tests H5 (the connection/coupling claim) directly, separate from mood.

**Covariates (planned, not optional):** `wordCount` and `sentenceCount`. The eigenvalue metrics are text-length-sensitive even after the tool's internal per-sentence normalization (`n * 0.1`, `n * 0.15` — heuristic constants, not empirically calibrated), so length must be entered as a covariate rather than assumed to be controlled for by the tool itself.

## 6. Procedure

Single online session, ~15–20 minutes:

1. Consent
2. Demographics (age, gender, English fluency, device type)
3. PHQ-9
4. PCL-5
5. UCLA-3
6. Clarity writing task — standardized prompt (**"your week"**, chosen over "free write" to reduce topic-driven variance across participants), minimum 150 words / ≥ 5 sentences enforced before submission is allowed (the tool's near-zero-sentence branch returns a degenerate fixed value and must not be allowed to enter the dataset)
7. Debrief screen with study purpose and crisis resources (shown to all participants, not just flagged ones)

**Infrastructure requirement before this can run:** the current Clarity implementation stores sessions in browser `localStorage` only, with no participant-ID linkage and no server-side persistence. Running an actual study requires a small consented data-capture backend — a Cloudflare Worker + D1 table, matching the stack already used for `redtooth-worker` — that writes `{participantId, spectralResult, PHQ9, PCL5, UCLA3, timestamp}` server-side under explicit consent. This is a half-day build, not a redesign, but it has to happen before recruitment opens.

## 7. Analysis Plan

- **Primary:** Pearson correlation (Spearman if outcome distributions are non-normal, which PHQ-9/PCL-5 often are in community samples) between `displacementIndex` and PHQ-9 total; same for PCL-5 total.
- **Covariate-adjusted:** partial correlation controlling for `wordCount` and `sentenceCount`.
- **Secondary:** multiple regression, PHQ-9 ~ `coherenceScore` + `contentWordDensity` + `wordCount`, to decompose the composite per §5.
- **H5:** partial correlation of `coherenceScore` with UCLA-3, controlling for PHQ-9 total (isolating the connection signal from general mood).
- **Exploratory:** band proportions (`theta`/`alpha`/`beta`/`gamma`) against PHQ-9 and PCL-5 subscales.
- All tests two-tailed, α = .05, uncorrected for the primary pair (H1/H2 pre-registered as co-primary); Holm correction applied across the exploratory H4/H5 set.

## 8. Risks & Data Privacy

**Risk level:** minimal. Both outcome instruments are standard, widely-used clinical screeners already administered to general populations in research and primary care. The writing task ("tell me about your week") is lower-risk than trauma-focused prompts, chosen deliberately over "a relationship" or "stuck place" for this reason.

**Data handling:** participant ID decoupled from any identifying information at the point of analysis; raw free-text responses accessible only to the PI; text retained only as long as needed for scoring verification, then the raw text (not the derived spectral metrics) is deleted. This should be stated explicitly in the consent form, since IRBs weigh free-text retention heavily.

## 9. Limitations

- The core predictor is a novel, previously unvalidated metric — this study is a first test, not a confirmation of anything.
- Single time point: no test-retest reliability data yet. Should be a named Phase 1.5 if Phase 1 shows signal, before investing in Phase 2.
- Convenience/online sample — self-selected, English-only, skews toward younger and more tech-familiar populations; findings won't generalize to clinical populations without a follow-up in that setting.
- Self-report outcome measures carry their own known biases (social desirability, recall).
- N = 60 is powered for effect sizes ≥ .35; a true effect in the .20–.30 range (plausible and still theoretically meaningful) will not reach significance here and should not be reported as "no effect" — report the point estimate and confidence interval, not just the p-value.

## 10. Pre-registration

Recommend pre-registering hypotheses, sample size justification, and the analysis plan above on OSF before data collection begins. For an independent researcher without institutional affiliation, pre-registration is the single highest-leverage credibility move available — it's free, it's fast, and it's exactly what a skeptical reviewer or IRB will ask about first.

The full pre-registration, formatted to OSF's standard template fields and ready to submit, is in [`osf-preregistration.md`](osf-preregistration.md).

## 11. Feasibility & Next Steps

- **Build requirement:** consented backend for Clarity sessions (§6) — ~half a day of work on the existing Cloudflare stack.
- **Recruitment:** Prolific, ~$4–6/participant × 60 ≈ $240–360, plus platform fees. 2–3 week data collection window at typical Prolific throughput.
- **Analysis:** R or Python, open-sourced alongside the pre-registration.
- **If Phase 1 clears r ≥ .30:** proceed to the hyperscanning study — does Clarity's `displacementIndex`, measured pre-session, predict real inter-brain coupling measured during a real conversation? That is the study that would actually test the dyadic-eigenspectrum consciousness claim, not just the single-person screening claim. Phase 1 is the cheap, fast gate that determines whether the expensive study is worth running. The full protocol, including a phased access plan and multiple pre-registered coupling metrics learned directly from the ds007471 null result, is in [`phase2-hyperscanning-protocol.md`](phase2-hyperscanning-protocol.md).
- **A prototype of the coupling-metric side already ran on open data**, before committing to any new hyperscanning collection — see [`ds007471-hyperscanning-note.md`](ds007471-hyperscanning-note.md). Result: a simple alpha-band coupling metric did not predict joint agency or synchronization performance in that dataset, which narrows what a real hyperscanning study should test rather than starting from nothing.