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