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92 lines
3.6 KiB
Markdown
92 lines
3.6 KiB
Markdown
# Appendix C: Bonding Curve Price Table & BTC Reserve Projections
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## Curve Formula
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$$
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\text{Price (BTC)} = k \times \sqrt{n}
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$$
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Where:
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- `k = 0.0000000006 BTC` (genesis constant)
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- `n` = total number of $ORAMA tokens sold from the curve
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## Total Cost Formula
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The cumulative BTC required to purchase the first N tokens from the curve:
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$$
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\text{Total BTC} = k \times \frac{2}{3} \times n^{3/2}
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$$
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## Detailed Price Table
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| Tokens Sold (n) | Price per $ORAMA (BTC) | Price (USD at $100K BTC) | Cumulative BTC Spent | Cumulative USD Spent |
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|---|---|---|---|---|
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| 1 | 0.0000000006 | $0.00006 | 0.0000000004 | $0.00004 |
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| 100 | 0.000000006 | $0.0006 | 0.0000004 | $0.04 |
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| 1,000 | 0.000000019 | $0.0019 | 0.000012 | $1.27 |
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| 10,000 | 0.00000006 | $0.006 | 0.0004 | $40 |
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| 50,000 | 0.000000134 | $0.0134 | 0.00447 | $447 |
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| 100,000 | 0.00000019 | $0.019 | 0.0127 | $1,265 |
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| 500,000 | 0.000000424 | $0.0424 | 0.141 | $14,142 |
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| 1,000,000 | 0.0000006 | $0.06 | 0.4 | $40,000 |
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| 2,000,000 | 0.000000849 | $0.0849 | 1.131 | $113,137 |
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| 5,000,000 | 0.00000134 | $0.134 | 4.47 | $447,214 |
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| 10,000,000 | 0.0000019 | $0.19 | 12.65 | $1,264,911 |
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| 15,000,000 | 0.00000232 | $0.232 | 23.24 | $2,323,790 |
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| 21,000,000 | 0.00000275 | $0.275 | 38.49 | $3,849,002 |
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## BTC Protocol Reserve Accumulation
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As tokens are purchased from the curve, BTC accumulates in the protocol reserve:
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| Milestone | BTC in Reserve | USD Value | What This Backs |
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|---|---|---|---|
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| First 100K tokens sold | 0.013 BTC | $1,265 | Minimal — early days |
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| First 1M tokens sold | 0.4 BTC | $40K | Small but growing reserve |
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| First 5M tokens sold | 4.47 BTC | $447K | Meaningful bridge backing |
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| First 10M tokens sold | 12.65 BTC | $1.27M | Substantial reserve |
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| Full curve (21M sold) | **38.49 BTC** | **$3.85M** | Full reserve capacity |
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## Curve Inventory Supply
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The curve's sell-side inventory comes from 20% of block rewards, **capped at 21,000,000 $ORAMA total**. Once the curve has accumulated 21M tokens (whether sold or unsold), the 20% share redirects to the block proposer.
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| Era | Daily Curve Inventory Added | Monthly | Era Total (2 years) |
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|---|---|---|---|
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| 1 (Years 1–2) | 288,000 $ORAMA | 8,640,000 | 21,024,000 |
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| 2 (Years 3–4)* | 144,000 $ORAMA | 4,320,000 | 10,512,000 |
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*The 21M cap will likely be reached during Era 1. Once reached, no further tokens flow to the curve regardless of era.*
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## Curve vs Order Book Interaction
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The curve and the order book coexist. The real market price is determined by organic supply and demand on the order book:
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**Scenario: Curve price > Order book price (typical early on)**
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- Miners sell on the order book at prices below the curve
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- Buyers purchase from the order book (cheaper)
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- The curve sits unused, accumulating inventory
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- This is normal — miners have surplus tokens and need to sell
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**Scenario: Order book price > Curve price (as demand grows)**
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- Order book is more expensive than the curve
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- Buyers purchase from the curve instead
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- BTC flows into the protocol reserve
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- The curve provides a price ceiling in this scenario
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**Scenario: After sunset**
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- Curve stops receiving new inventory
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- All trading happens on the order book
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- The curve may still have leftover inventory available at its last price point
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- Pure free market
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## Sunset Conditions
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The curve's 20% share of block rewards drops to 0% when:
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1. Average daily order book volume exceeds the governance-defined threshold
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2. This threshold is maintained for 30 consecutive days
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3. The change is automatic — no vote required
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After sunset, the 20% that previously went to the curve flows directly to block proposers (miners receive 100% of block rewards).
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