Specification · v1

Methodology

Formal definition of the index, the product decomposition, classification rule, survey instruments, and the limited X-profile estimator. Self-report model — not a clinical instrument.

1. Object of measurement

Let an individual report latent constructs related to partnership desire, realized outcomes, online immersion, involuntary framing, identity-content exposure, perceived deficits, and affective load. The Cel Index compresses these into a single scalar F ∈ [0, 1] via a multiplicative product. Gender path selects only the output label family (Femcel / Incel / Cel); it does not enter the product.

2. Variables

Sym	Construct	Domain
I	Online immersion	[0,1]
D	Desired partnership intensity	[0,1]
S	Realized relationship / dating success	[0,1]
B	Involuntary framing of the gap	[0,1]
C	Identity-content exposure	[0,1]
L	Perceived looks deficit	[0,1]
P	Perceived personality / social deficit	[0,1]
M	Perceived dating-market pressure	[0,1]
R	Affective charge (resentment, despair, etc.)	[0,1]
k, C₀	Identity logistic hyperparameters	fixed
τ	Classification threshold	fixed

3. Product model

F = I · (D − S)₊ · B · σ(k(C − C₀)) · ρ(L, P, M) · Ψ(R)

where

(x)₊ = max(0, x)

σ(x) = (1 + e⁻ˣ)⁻¹

ρ = clamp₀₁(0.22 + 0.36L + 0.22P + 0.20M)

Ψ = 0.32 + 0.68R

hyperparameters: k = 8, C₀ = 0.42, τ = 0.1

Multiplicativity encodes necessity: any factor near zero collapses F. The desire gap (D − S)₊ is the structural core; without an open gap the remaining terms cannot produce a high index.

4. Classification & display score

label_positive ⟺ F > τ

S_display = 100 · F ∈ [0, 100]

Tier bands on F (relative to τ):

High: F > 2.2τ
Elevated: τ < F ≤ 2.2τ
Borderline: 0.45τ < F ≤ τ
Low: F ≤ 0.45τ

Path label: woman → Femcel Index; man → Incel Index; other → Cel Index.

5. Survey instruments

Each construct is elicited with a continuous self-report control on [0, 1] (percent scale in the UI). Mapping is direct: slider value becomes the corresponding model variable (except ρ and Ψ, which are derived). Live gap (D − S)₊ is shown on the desire step.

6. X profile prefill (optional)

Scope: public profile aggregates only — post count, likes, media count, following, followers, bio text, account age. We do not ingest private data, DMs, or a full post-text corpus (authenticated timeline access is required for that and is not used here).

Estimator priors (all clamped to [0, 1]):

Î = 0.45·r + 0.25·v + 0.30·f — r log-scaled posts/day, v log lifetime posts, f log following
Ĉ from bio keyword hits + post volume + media/post ratio (content-mix proxy, not post NLP)
M̂ from follower level and following/follower asymmetry
R̂ from likes/day intensity + bio heat + post rate

Not estimated from X (must be self-reported): D, S, B, L, P. Every pre-filled slider is editable and flagged in the assessment UI with its source signals.

7. Limitations

Self-report bias and social desirability effects.
Multiplicative form is a structural assumption, not an empirical MLE fit.
Hyperparameters (k, C₀, τ, ρ weights) are fixed design choices.
X priors are coarse aggregate proxies — transparent, but not substitutes for honest self-report on D, S, B.
Not validated as a clinical, diagnostic, or psychometric instrument.

8. Reference form

F = I · (D − S)₊ · B · σ(k(C − C₀)) · ρ(L,P,M) · Ψ(R)

positive ⟺ F > τ

S_display = 100 · F

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