BFEM v1.1 (HTML) — Bitcoin for Engineers S-Curve Model

A single-file, no-build, engineering-first Bitcoin valuation model.
Open index.html in a browser and play with the parameters.

• Adoption: stacked S-curves (Wave 1: retail/institutional; Wave 2: sovereign/settlement).
• Dynamic TAM: TAMᵢ(t) = TAMᵢ₀ · e^{gᵢ (t − t₀)} — expanding boundary condition.
• Price: P(t) = M(t) / S_free(t) where M(t) = Σ[TAMᵢ(t) · Aᵢ(t)^{γᵢ}].
• Free-float: S_free(t) = S_total(t) · (1 − h(t)), h(t) is a logistic withholding curve.

Defaults are calibrated to target ≈ $2.5M/BTC in 2028.

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Quick Start

1. Download this repo or copy index.html to any folder.
2. Double-click index.html to open it in your browser.
3. Tweak parameters in the cards; the chart updates live.
4. Optional: click Export CSV to download the time series.

No Node.js. No build. Just HTML + Chart.js from CDN.

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Parameters

Wave 1 (Retail/Institutional)

• TAM₁ ($T): starting store-of-value market size.
• TAM₁ Growth (%/yr): nominal growth (GDP + asset inflation).
• t50₁ (year): midpoint year when adoption ≈ 50%.
• k₁ (/yr): steepness of the adoption S-curve.
• γ₁: monetization intensity (>1 adds convexity).

Wave 2 (Sovereign/Settlement)

• Enable Wave 2: on/off.
• TAM₂ ($T), TAM₂ Growth, t50₂, k₂, γ₂: same meanings as above.

Supply & Free-Float

• Supply 2025/2028/2032 (M BTC): piecewise linear approximation of circulating supply.
• Free-Float Withheld at Saturation (%): max withheld share held by long-term/sovereigns.
• Withholding Midpoint (t_h): year when withholding ≈ 50% of max.
• Withholding Steepness (k_h): slope of the withholding curve.

Chart

• Y-Axis: log scale toggle (recommended).
  • Log scale uses a positive floor to remain valid.

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Model Equations

• Adoption (Wave i)
  Aᵢ(t) = 1 / (1 + e^{−kᵢ (t − t₅₀ᵢ)})

• Dynamic TAM (Wave i)
  TAMᵢ(t) = TAMᵢ₀ · e^{gᵢ (t − t₀)}

• Market Cap
  M(t) = Σ [TAMᵢ(t) · (Aᵢ(t))^{γᵢ}]

• Free-Float Supply
  S_free(t) = S_total(t) · (1 − h(t)) with h(t) = h_max / (1 + e^{−k_h (t − t_h)})

• Price
  P(t) = M(t) / S_free(t)

Engineering framing: multiple step responses (logistics) with a time-varying boundary condition (TAM growth) and an effective state constraint (free-float).

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Deploy (GitHub Pages)

1. Create a new GitHub repo (e.g., bfem-html).
2. Commit index.html and README.md.
3. In repo Settings → Pages, set Source to main branch and **/ (root)`.
4. Open the Pages URL (usually https://<user>.github.io/bfem-html/).

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Roadmap

• Optional historical price overlay (CSV drop-zone).
• Permalinked parameters via URL querystring.
• Free-float sourced from on-chain analytics (API hook).

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License

MIT — use freely with attribution to Bitcoin for Engineers (BFEM). Bitcoinforengineers.com