Gov/en/Portal:R&D/Innovations:Bonding Curve: Difference between revisions

Latest revision as of 12:07, 4 October 2026

💡 In simple words: Think of the very first people who chip in to build something new: they take the biggest chance, so they get the best subscription token. The Bonding Curve is the clear, public math rule that gives early supporters more Subscription Tokens per franc, with no guessing and no secret deals.

🎯 In 20 seconds (scientific summary): The Bonding Curve is a transparent algorithm intended to convert funding support into Subscription Tokens: the earlier the support, the higher the multiplier (up to ×100, around ×30 at mid-stage). It is non-speculative, publicly documented, and revisable prospectively through Open Calls with mathematical experts.

Type	Transparent algorithm
Purpose	Subscription Token generation from funding
Speculation	❌ None
Covered by	Real expenses + subscriptions
Expert review	Open Calls (math experts)
Early multiplier	Up to ×100
Growth multiplier	~×30 at mid-stage
See also	Subscription Tokens Explained
See also	Why Fund WikiDeal

Every new platform faces the same bootstrapping question: why would anyone support a project before it has proven itself? The first supporters carry the most uncertainty, so fairness suggests they should receive the most in return. The Bonding Curve is WikiDeal's answer: a public, verifiable formula that anyone can check, designed so that trust comes from transparency rather than from promises.

Summary

How the Bonding Curve is intended to work
No curve inside a donation: the jump comes after
The mathematical formula
Text-based visualization
Why a bonding curve?
Who does what
Relation to Subscription Tokens and Karma tokens
Transparency commitment
State of the art

How the Bonding Curve is intended to work

The bonding curve relates the current funding reserve level to the Subscription Tokens generated per CHF of support. The key principle: as the reserve grows, each CHF generates fewer Subscription Tokens. This recognizes early participants and creates a natural, non-speculative incentive to support early.

For a supporter, the experience is simple: Anna supports with CHF 100 when the reserve is nearly empty and would receive far more Subscription Tokens per franc than Ben, who supports the same amount a year later when the platform is established. Both can verify their calculation themselves, because the formula is public.

No curve inside a donation: the jump comes after

There is no "curve" running inside a given donation: a donated amount does not see its multiplier decrease along the way. The multiplier applied is the one in force at the moment of the donation, for the whole amount. What the curve describes is a jump (an adjustment) recalculated after each donation, according to the Bonding Curve and the Need-Driven Funding stabilizer.

Example: if the multiplier stands at ×65, a donation of CHF 1,000 is entirely multiplied by 65 (65,000 Subscription Tokens). After the transaction, the multiplier makes a jump, for instance down to ×63.8, which applies to the next donation only.

The mathematical formula

Subscription Tokens(CHF) = CHF × multiplier(R) where multiplier(R) is a decreasing function of Reserve R: multiplier(R) = M_max × e^(-k × R). M_max = maximum multiplier (at R=0, e.g. ×100); k = decay constant (determines how fast the multiplier drops); R = current reserve level (total CHF in fund); e = Euler's number (≈ 2.718...). Example at R=0 (first supporter): CHF 1 → 100 Subscription Tokens. Example at R=50,000 CHF (mid-stage): CHF 1 → ~30 Subscription Tokens. Example at R=500,000 CHF (growth stage): CHF 1 → ~5 to 8 Subscription Tokens.

⚠️ This calculation is intended to be discussed in Open Calls by mathematical experts. The exact constants (M_max, k) are subject to community review and may be adjusted through the Open Calls process. Updates would apply prospectively only: they would never reduce rights already attributed at the moment of a support.

Text-based visualization

The relationship between reserve and multiplier (illustrative):

Reserve (CHF) │ Multiplier (Subscription Tokens per CHF) ───────────────┼────────────────────────────── 0 │ ×100 ██████████████████████████ 5,000 │ ×80 ████████████████████ 20,000 │ ×50 █████████████ 50,000 │ ×30 ████████ 100,000 │ ×15 ████ 300,000 │ ×6 ██ 500,000+ │ ×2–5 █

Why a bonding curve?

The bonding curve addresses a fundamental bootstrapping problem: how to subscription token early supporters fairly without creating speculation or securities-law issues.

Early supporters take the highest risk (platform unproven) → highest multiplier
Later supporters take less risk (platform established) → lower multiplier
No external market price needed: the algorithm is self-contained
No speculation: Subscription Tokens are not tradeable on open markets
Transparent: everyone can see the curve and calculate their Subscription Tokens

Who does what

Supporters choose when and how much to support, and can verify their Subscription Tokens independently.
Mathematical experts review the constants through Open Calls.
The community oversees any change to the formula, which keeps governance in citizens' hands rather than in a closed boardroom.

Relation to Subscription Tokens and Karma tokens

The bonding curve determines the total Subscription Tokens generated. The Need-Driven Funding mechanism and the donor's own choice at donation time then determine how many of those Subscription Tokens the donor keeps and how much is left to the project as pure support (see the Subscription Tokens FAQ for the formulas currently proposed). Karma tokens are a separate, non-convertible form of Subscription Tokens, documented on their own page; the bonding curve does not determine them.

Transparency commitment

WikiDeal intends to publish the full bonding curve formula, constants, and historical data. Community members would be able to verify their Subscription Token calculations independently. The formula is defined, not opaque, and any change would go through an Open Call process with mathematical expert review. This reflects WikiDeal's broader aims of transparency, lower cost, flexibility and citizen participation.

State of the art

Algorithmic pricing curves and threshold-based collective funding have been studied in several strands of research. The works below provide scientific context for the bonding curve hypothesis; they do not guarantee its outcome.

Michael Zargham, Jamsheed Shorish and Krzysztof Paruch (2019), From Curved Bonding to Configuration Spaces, WU Vienna University of Economics and Business, Working Paper Series: open access paper.
Jiahua Xu, Krzysztof Paruch, Simon Cousaert and Yebo Feng (2023), SoK: Decentralized Exchanges (DEX) with Automated Market Maker (AMM) Protocols, ACM Computing Surveys, 55(11): doi:10.1145/3570639 · [{W}Automated_market_maker automated market maker on Wikipedia].
Robin Hanson (2003), Combinatorial Information Market Design, Information Systems Frontiers, 5(1): doi:10.1023/A:1022058209073 · prediction market on Wikipedia.
Paul Belleflamme, Thomas Lambert and Armin Schwienbacher (2014), Crowdfunding: Tapping the right crowd, Journal of Business Venturing, 29(5): doi:10.1016/j.jbusvent.2013.07.003 · crowdfunding on Wikipedia.
Ethan Mollick (2014), The dynamics of crowdfunding: An exploratory study, Journal of Business Venturing, 29(1): doi:10.1016/j.jbusvent.2013.06.005.

💡 Improve this concept: submit a proposal via Open Call

@@ Line 1: / Line 1: @@
-{{KidsIntro|Think of the very first people who chip in to build something new — they take the biggest chance, so they get the best reward. The Bonding Curve is the clear, public math rule that gives early supporters more Credits per franc, with no guessing and no secret deals.}}
+{{KidsIntro|Think of the very first people who chip in to build something new: they take the biggest chance, so they get the best subscription token. The Bonding Curve is the clear, public math rule that gives early supporters more Subscription Tokens per franc, with no guessing and no secret deals.}}
+{{ExpertIntro|The Bonding Curve is a transparent algorithm intended to convert funding support into Subscription Tokens: the earlier the support, the higher the multiplier (up to ×100, around ×30 at mid-stage). It is non-speculative, publicly documented, and revisable prospectively through Open Calls with mathematical experts.}}
-Wiki Core · Concept
-== The Bonding Curve ==
-Bonding Curve at a Glance
 {| class="wikitable"
@@ Line 13: / Line 8: @@
 |-
 | Purpose
-| Credit generation from funding
+| Subscription Token generation from funding
 |-
 | Speculation
 | ❌ None
 |-
-| Backed by
+| Covered by
 | Real expenses + subscriptions
 |-
 | Expert review
-| [[Gov/en/Portal:R&D/Open-Call:Main|Open Call]]s (math experts)
+| [[Gov/en/Portal:R&D/Open-Calls:Main|Open Call]]s (math experts)
 |-
 | Early multiplier
@@ Line 31: / Line 26: @@
 |-
 | See also
-| [[Gov/en/Portal:Economy/Rewards|Rewards Explained]]
+| [[Gov/en/Portal:Economy/Subscription Tokens|Subscription Tokens Explained]]
 |-
 | See also
@@ Line 37: / Line 32: @@
 |}
-The bonding curve is the core algorithm that converts funding contributions into Credits. It is a '''transparent, defined algorithm''' — not immutable (it can be updated through [[Gov/en/Portal:R&D/Open-Call:Main|Open Calls]] with mathematical experts), but consistent and publicly documented. It ensures that early funders are rewarded for taking on the highest risk.
+Every new platform faces the same bootstrapping question: why would anyone support a project before it has proven itself? The first supporters carry the most uncertainty, so fairness suggests they should receive the most in return. The Bonding Curve is WikiDeal's answer: a public, verifiable formula that anyone can check, designed so that trust comes from transparency rather than from promises.
-The bonding curve ensures early funders receive more Credits per CHF — recognizing the risk they take when the platform is unproven.
+{{ArticleSummary|
+* [[#how-it-works|How the Bonding Curve is intended to work]]
+* [[#jump-after-donation|No curve inside a donation: the jump comes after]]
+* [[#formula|The mathematical formula]]
+* [[#visualization|Text-based visualization]]
+* [[#why-a-bonding-curve|Why a bonding curve?]]
+* [[#roles|Who does what]]
+* [[#relation|Relation to Subscription Tokens and Karma tokens]]
+* [[#transparency|Transparency commitment]]
+* [[#state-of-the-art|State of the art]]
+}}
+__NOTOC__
-=== How the Bonding Curve Works ===
+<span id="how-it-works"></span>
+== How the Bonding Curve is intended to work ==
+The bonding curve relates the current funding reserve level to the Subscription Tokens generated per CHF of support. The key principle: '''as the reserve grows, each CHF generates fewer Subscription Tokens'''. This recognizes early participants and creates a natural, non-speculative incentive to support early.
-The bonding curve relates the current funding reserve level to the Credits generated per CHF contributed. The key principle: '''as the reserve grows, each CHF generates fewer Credits'''. This rewards early participants and creates a natural, non-speculative incentive to fund early.
+For a supporter, the experience is simple: Anna supports with CHF 100 when the reserve is nearly empty and would receive far more Subscription Tokens per franc than Ben, who supports the same amount a year later when the platform is established. Both can verify their calculation themselves, because the formula is public.
-=== The Mathematical Formula ===
+<span id="jump-after-donation"></span>
+== No curve inside a donation: the jump comes after ==
+There is no "curve" running inside a given donation: a donated amount does not see its multiplier decrease along the way. The multiplier applied is the one in force at the moment of the donation, for the whole amount. What the curve describes is a '''jump''' (an adjustment) recalculated '''after''' each donation, according to the Bonding Curve and the [[Gov/en/Portal:Economy/Need-Driven-Funding|Need-Driven Funding]] stabilizer.
-Credits(CHF) = CHF × multiplier(R) Where multiplier(R) is a decreasing function of Reserve R: multiplier(R) = M_max × e^(-k × R) M_max = maximum multiplier (at R=0, e.g. ×100) k = decay constant (determines how fast multiplier drops) R = current reserve level (total CHF in fund) e = Euler's number (≈ 2.718...) Example at R=0 (first funder): CHF 1 → 100 Credits Example at R=50,000 CHF (mid-stage): CHF 1 → ~30 Credits Example at R=500,000 CHF (growth stage): CHF 1 → ~5–8 Credits
+Example: if the multiplier stands at ×65, a donation of CHF 1,000 is entirely multiplied by 65 (65,000 Subscription Tokens). After the transaction, the multiplier makes a jump, for instance down to ×63.8, which applies to the next donation only.
-⚠️ This calculation will be discussed in Open Calls by mathematical experts. The exact constants (M_max, k) are subject to community review and may be adjusted through the Open Call process.
+<span id="formula"></span>
+== The mathematical formula ==
+Subscription Tokens(CHF) = CHF × multiplier(R) where multiplier(R) is a decreasing function of Reserve R: multiplier(R) = M_max × e^(-k × R). M_max = maximum multiplier (at R=0, e.g. ×100); k = decay constant (determines how fast the multiplier drops); R = current reserve level (total CHF in fund); e = [[wikipedia:E_(mathematical_constant)|Euler's number]] (≈ 2.718...). Example at R=0 (first supporter): CHF 1 → 100 Subscription Tokens. Example at R=50,000 CHF (mid-stage): CHF 1 → ~30 Subscription Tokens. Example at R=500,000 CHF (growth stage): CHF 1 → ~5 to 8 Subscription Tokens.
-=== Text-Based Visualization ===
+⚠️ This calculation is intended to be discussed in Open Calls by mathematical experts. The exact constants (M_max, k) are subject to community review and may be adjusted through the Open Calls process. Updates would apply prospectively only: they would never reduce rights already attributed at the moment of a support.
+<span id="visualization"></span>
+== Text-based visualization ==
 The relationship between reserve and multiplier (illustrative):
-Reserve (CHF) │ Multiplier (Credits per CHF) ───────────────┼────────────────────────────── 0 │ ×100 ██████████████████████████ 5,000 │ ×80 ████████████████████ 20,000 │ ×50 █████████████ 50,000 │ ×30 ████████ 100,000 │ ×15 ████ 300,000 │ ×6 ██ 500,000+ │ ×2–5 █
+Reserve (CHF) │ Multiplier (Subscription Tokens per CHF) ───────────────┼────────────────────────────── 0 │ ×100 ██████████████████████████ 5,000 │ ×80 ████████████████████ 20,000 │ ×50 █████████████ 50,000 │ ×30 ████████ 100,000 │ ×15 ████ 300,000 │ ×6 ██ 500,000+ │ ×2–5 █
-=== Why a Bonding Curve? ===
+<span id="why-a-bonding-curve"></span>
+== Why a bonding curve? ==
+The bonding curve addresses a fundamental bootstrapping problem: how to subscription token early supporters fairly without creating speculation or securities-law issues.
-The bonding curve solves a fundamental bootstrapping problem: how do you reward early funders fairly without creating speculation or securities law issues?
+* '''Early supporters take the highest risk''' (platform unproven) → highest multiplier
+* '''Later supporters take less risk''' (platform established) → lower multiplier
+* No external market price needed: the algorithm is self-contained
+* No speculation: Subscription Tokens are not tradeable on open markets
+* Transparent: everyone can see the curve and calculate their Subscription Tokens
-* '''Early funders take the highest risk''' (platform unproven) → receive highest multiplier
+<span id="roles"></span>
-* '''Later funders take less risk''' (platform established) → receive lower multiplier
+== Who does what ==
-* No external market price needed — the algorithm is self-contained
+* '''Supporters''' choose when and how much to support, and can verify their Subscription Tokens independently.
-* No speculation: Credits are not tradeable on open markets
+* '''Mathematical experts''' review the constants through [[Gov/en/Portal:R&D/Open-Calls:Main|Open Calls]].
-* Transparent: everyone can see the curve and calculate their Credits
+* '''The community''' oversees any change to the formula, which keeps governance in citizens' hands rather than in a closed boardroom.
-=== Relation to [[Gov/en/Portal:Economy/Rewards|Rewards]] and [[Gov/en/Portal:Economy/WIL-Tokens|WIL tokens]] ===
+<span id="relation"></span>
+== Relation to Subscription Tokens and Karma tokens ==
+The bonding curve determines the ''total'' [[Gov/en/Portal:Economy/Subscription Tokens|Subscription Tokens]] generated. The [[Gov/en/Portal:Economy/Need-Driven-Funding|Need-Driven Funding]] mechanism and the donor's own choice at donation time then determine how many of those Subscription Tokens the donor keeps and how much is left to the project as pure support (see the [[Gov/en/Portal:Economy/Subscription Tokens-FAQ|Subscription Tokens FAQ]] for the formulas currently proposed). [[Gov/en/Portal:Economy/Karma-Tokens|Karma tokens]] are a separate, non-convertible form of Subscription Tokens, documented on their own page; the bonding curve does not determine them.
-The bonding curve determines the ''total'' Credits generated. The [[Gov/en/Portal:R&D/Innovations:Need-Driven Funding|Need-Driven Funding]] then determines how those Credits are split between [[Gov/en/Portal:Economy/Rewards|Rewards]] (personal, P2) and the community pool. The bonding curve itself does not determine the Cash/WIL-token ratio — that is the Need-Driven Funding mechanism's job.
+<span id="transparency"></span>
+== Transparency commitment ==
+WikiDeal intends to publish the full bonding curve formula, constants, and historical data. Community members would be able to verify their Subscription Token calculations independently. The formula is defined, not opaque, and any change would go through an Open Call process with mathematical expert review. This reflects WikiDeal's broader aims of transparency, lower cost, flexibility and citizen participation.
-=== Transparency Commitment ===
+<span id="state-of-the-art"></span>
+== State of the art ==
+Algorithmic pricing curves and threshold-based collective funding have been studied in several strands of research. The works below provide scientific context for the bonding curve hypothesis; they do not guarantee its outcome.
-WikiDeal commits to publishing the full bonding curve formula, constants, and historical data. Community members can verify their Credit calculations independently. The formula is defined — not opaque — and any changes must go through an Open Call process with mathematical expert review.
+* Michael Zargham, Jamsheed Shorish and Krzysztof Paruch (2019), ''From Curved Bonding to Configuration Spaces'', WU Vienna University of Economics and Business, Working Paper Series: [https://epub.wu.ac.at/7385/ open access paper].
+* Jiahua Xu, Krzysztof Paruch, Simon Cousaert and Yebo Feng (2023), ''SoK: Decentralized Exchanges (DEX) with Automated Market Maker (AMM) Protocols'', ACM Computing Surveys, 55(11): [https://doi.org/10.1145/3570639 doi:10.1145/3570639] · [{W}Automated_market_maker automated market maker on Wikipedia].
+* Robin Hanson (2003), ''Combinatorial Information Market Design'', Information Systems Frontiers, 5(1): [https://doi.org/10.1023/A:1022058209073 doi:10.1023/A:1022058209073] · [https://en.wikipedia.org/wiki/Prediction_market prediction market on Wikipedia].
+* Paul Belleflamme, Thomas Lambert and Armin Schwienbacher (2014), ''Crowdfunding: Tapping the right crowd'', Journal of Business Venturing, 29(5): [https://doi.org/10.1016/j.jbusvent.2013.07.003 doi:10.1016/j.jbusvent.2013.07.003] · [https://en.wikipedia.org/wiki/Crowdfunding crowdfunding on Wikipedia].
+* Ethan Mollick (2014), ''The dynamics of crowdfunding: An exploratory study'', Journal of Business Venturing, 29(1): [https://doi.org/10.1016/j.jbusvent.2013.06.005 doi:10.1016/j.jbusvent.2013.06.005].
-'''See also:''' [[Gov/en/Portal:Economy/Rewards|Rewards Explained]] [[Gov/en/Portal:Economy/Rewards|Rewards]] [[Gov/en/Portal:Economy/WIL-Tokens|WIL tokens]] [[Gov/en/Portal:R&D/Innovations:Need-Driven Funding|Need-Driven Funding]] [[Gov/en/Portal:Economy/Main|Why Fund WikiDeal]] [[Gov/en/Portal:R&D/Open-Call:Main|Open Call Guide]]
+'''See also:''' [[Gov/en/Portal:Economy/Subscription Tokens|Subscription Tokens Explained]] · [[Gov/en/Portal:Economy/Subscription Tokens-FAQ|Subscription Tokens FAQ]] · [[Gov/en/Portal:Economy/Need-Driven-Funding|Need-Driven Funding]] · [[Gov/en/Portal:Economy/Revenue-Structure|Revenue Structure]] · [[Gov/en/Portal:Economy/Karma-Tokens|Karma tokens]] · [[Gov/en/Portal:Economy/Main|Why Fund WikiDeal]] · [[Gov/en/Portal:R&D/Open-Calls:Main|Open Call Guide]]
-💡 '''Improve this concept''' — submit a proposal via [[Gov/en/Portal:R&D/Open-Call:Main|Open Call]]
+💡 '''Improve this concept''': submit a proposal via [[Gov/en/Portal:R&D/Open-Calls:Main|Open Call]]
-[[Category:Migration June 2026]]
+[[Category:Funding]]
-<!-- visible -->
+[[Category:Innovation]]