A bonding curve is a smart con… new circulation numerically. Since the full redeploy of 6 October 2026 on Stokenet, each caper's own state component checks the reserve after every buy and sell. It computes the XRD the curve should hold for the tokens in circulation and refuses any trade that leaves the vault below that figure (assert_reserve, contracts/core/src/caper_dao.rs), failing with the message listed on Why a transaction failed (/wiki/help/why-a-transaction-failed) . A vampire caper is the one exception: a migration issues tokens against escrowed origin tokens rather than XRD, so the reserve may sit below the curve by the shortfall migrations created, never further. The state component cannot be swapped by a logic upgrade, so every holder's ability to sell back along the curve does not depend on the swappable trading logic pricing correctly. Every trade in either directio…how the proceeds are deployed.

Which of these are still runni…ll shutdown proposal (https://web.archive.org/web/20260202102232/https://forum.tecommons.org/t/tec-shut… implementation plan (https://web.archive.org/web/20260113072249/https://forum.tecommons.org/t/tec-toke…foundations/what-is-a-caper) .

The cap is an asymptote, not a…10−12 (CURVE_S_MAX, contracts/logiccommon/src/lib.rs), and the reserve …n the arithmetic never needed.

What you actually pay The cur…the first buy, half that by 1.0199% sold, 1% by 10.821.4%, and a halving every 120% of the supply from there on…e curve price; it is about 1.098% by 120% sold and 0.5% by 240%, and halves every 120% sold after that. There is n…ar zero at launch, peaks near 0.741.49% sold, falls while the halvin…run the price, and from about 8462% sold climbs again as the pri… 0.945c ) ÷ ( 1 − 0.055c )0%2%4%6%8%14%8%12%16%20%half the peakwhat you paycur…ch trade at launch, half by 1.0199% sold, 1% by 10.821.4%, and a halving every 120% of the supplyfrom there on,…es with the price until about 0.741.49% sold, falls while the halvings outrun it, and from about 8462%sold climbs again as the pric…AUNCH+105.8%HALF THE PEAK BY1.0199% soldHALVES EVERY120% soldSkim 100% at launch, 1% by 10.821.4% sold, halving every 120% after, on buys and sells al…ughout – earliest is cheapest.

Type Perpetual AMM (continuous…d sells) Peak 100%, half by 1.0199% sold, 1% by 10.821.4%, halving every 120% sold · 94.5% XRD, 5.5% toke… (/wiki/markets/raising-funds)

A bonding curve is a smart con… × (1 − s) × x10) for x = 2−s/120%, with s the fraction sold: half the peak by 1.0199% sold, 1% by 10.821.4%, and a halving every 120% of the supply after that. A…how the proceeds are deployed.

A bonding curve is a smart con…of the rate is taken in XRD – the rise in the curve's backed potential across the stretch the trade moves throughon every XRD the curve takes from a buy, out of the payment on a buy before it funds the curve, or out of then every XRD it pays out ton a sell, out of the payout. It splits 11:10: 49.5% of th…d 45% banked for the founder. It is charged at each token's own poEach trade reads one rate, a buy where it starts and a sell at the bottom it would reach if every token handed int rather than as a share of one gross figetired, so a trade pays at least what the same trade cut into pieces would; the pieces approach the rate's integral along the curve, which is what makes a trade cut into pieces pay exactly what it pays wholeand since 30 September 2026 that integration is the trader's to do, a transaction per piece, rather than the contract's. - 5.5% is a slice of the tok…how the proceeds are deployed.

Which of these are still runni…2026 and re-taken on 27 August, 8 September, 14 September and on 8, 14, 21 and 217 September 2026, keylessly, fr…ill the head when re-read on 217 September 2026, with neither …ved: false and a pushed_at of 1823 September 2026 through the Gi…hed_at still read 4 September, on 21 September it read 18 September, and on 217 September it read 1823 September. The repository's o…5 August, 4 September, then 16, 18 and 1823 September 2026 – landing on t…, and its freshest repository is canton-dev-fundon 27 September 2026 was ocp-canton-sdk (https://github.com/Fairmint/ocp-canton-dev-fundsdk) , pushed on 20 September 2026, while the two the API ranks immediately behind it –two days earlier, while the last pushes to c-org-js (https://github.com…th a continuous organization, on 19 September, and to c-org itself, both on 1823 September –, are the same bot on the same …foundations/what-is-a-caper) .

Type Perpetual AMM (continuous….8%, halving every 10% sold · ⅔ XRD to founder · ⅓ tokens (30/31 founder · 1/31 Commo94.5% XRD, 5.5% tokens · 49.5% to this caper's treasury (XRD) · 50% to founder (45% XRD, 5% tokens) · 0.5% to Commons (tokens) Coined 2017 — Simon de l… (/wiki/markets/raising-funds)

A bonding curve is a smart con…irection also carries a skim, paid in the curve's own composition. A curve whose price rises as the n-th power of supply holds 1/(n+1) of its market value as reserve; this one is a square root at the origin, so two thirds of a young caper is reserve and one third is claim on future buyers. The skim splits along that line: - Two thirdsthe only trade charge. It is paid 94.5% in XRD and 5.5% in tokens, to three recipients: - 94.5% of the rate is taken in XRD –…or out of the payout on a sell – and. It splits 11:10: 49.5% of the skim to the traded caper's own treasury and 45% banked for the founder. It is…exactly what it pays whole. - One third5.5% is a slice of the tokens the … tokens handed in on a sell – tithed 30/31split 10:1: 5% of the skim to the founder and 1/310.5% to the Caper Commons —, the protocol-wide treasury, d…The live peak is 100%, so the tokenXRD leg peaks at 33.3394.5% of the tokens a tradecurve XRD a trade moves and the token leg at 5.5% of the tokens it moves. The rate falls as circ… ones it retires. Most of the founder and Commons rewardsskim arrives early: a caper that stops by 20% of its supply sold paid 90about 85% of its skim XRD on the first…how the proceeds are deployed.

Curve shapes The choice of fun…le curve in both directions – a 0.5% trade fee on buysthe skim on either leg, not a curve spread, is what the protocol charges, plus the founder skim on either leg, at a rate that falls with circulation. That rate's peak is a field written into the …neither route can shorten it. The fee49.5% of the skim is deposited, in XRD, into the treasury of the caper being boughttraded, so a curve funds its own DAO on the way in. A sell pays noevery trade in either direction; there is no separate trade fee ( Raising funds (/w…9) for the design trade-offs.

History The continuous-token i…lic goods — the same shape as Caper's 1/31the shares of Caper's skim that go to each caper's own treasury and to the Caper Commons slice. The underlying theory frames…mic-games-as-estimators-3/) ).

Which of these are still runni… only where it sits. The curve, the founder skim and the trade fee and the skim are parameters of each caper'…foundations/what-is-a-caper) .

What you actually pay The curve sets the base price; the founder reward skims a share of every trade, and the skim takes a share of every trade for this caper’s treasury, the founder and the $CAPER treasury. On a buy it bites in two places – two thirdsits $XRD part, 94.5% of the rate, on top of each $XRD the curve takes, one thirdand its token part, 5.5%, off the tokens the curve mint…% of the supply from there on —– never zero, and never settling. With the trade fee off the gross first, tThe markup on the price you pay starts near 15106%, so the first buyers pay about 2.506 times the curve price; it is about 1.609% by 10% sold and 1.010.5% by 20%, and what it adds over the 0.5% trade fee halves every 10% sold after that. There is no other trade charge. A sell pays the founder rewardskim on the same schedule on the way out, and no trade fee. The reward'taken off the payout the curve computes rather than off a payment. The skim’s value reads the other way: b…cause price starts near zero, ithe founder's take per token is near zero …sold climbs again as the price'’s pole outruns them. Either wa…what you pay = P(s) × ( 1 + ⅔0.945c ) ÷ ( 1 − fee )( 1 − ⅓0.055c )0%2%4%6%8%10%half the peakw… paycurve price P(s)the gap = founderthe skimsupply sold (% of cap)pri…10% of the supplyfrom there on — there is, with no floor. Two thirds94.5% is paid in $XRD, one third and 5.5% in tokens –, about a 151%06% markup at thefirst buy, fee included; there is no other trade charge. Sells pay the same schedule on the way out.The take peaks laterPrice sta…he cheapest.MARKUP AT LAUNCH+151.305.8%HALF THE PEAK BY1.01% soldHALVES EVERY10% soldFounder sSkim 100% at launch, 1% by 10.8… sold, halving every 10% after; 0.5% trade fee on buys, on buys and sells alike.caper.networkThe skim'’s share is front-loaded and paid ⅔94.5% in $XRD, ⅓5.5% in the coin; its value peaks …ughout – earliest is cheapest.

Caper’s bonding curve Every c…FORMULA, NOT AN ORDER BOOKBuy —– send XRD; the curve mints new…s and the price ticks up.Sell —– return tokens; the curve pays… the price ticks down.Reserve —– always covers the circulating supply —– you never need a counterparty.Cap —– as supply nears 100bn the pri…0.001SUPPLY CAP100,000,000,000BUY FEE0.5%FIRST BUY PAYS2.06 × P(s)Every caper trades against its…covers the circulating supply.

A bonding curve is a smart con…along that line: - Two thirds of the rate is taken in XRD off– the trade's gross –rise in the curve's backed potential across the stretch the trade moves through, out of the payment on a buy, before it funds the curve, or out of the payout on a sell – and banked for the founder. It is charged at each token's own point rather than as a share of one gross figure, which is what makes a trade cut into pieces pay exactly what it pays whole. - One third is a slice of the…how the proceeds are deployed.

Curve shapes The choice of fun…a fresh logic component and a governed UPGRADE (/wiki/governance/execution) of the registry's current_mainrepointing of the registry's current_main – either a governed UPGRADE (/wiki/governance/execution) passed in the $CAPER caper or the operator backstop the protocol admin badge holds (propose_main, then activate_main), which is the route every swap so far has taken. Both run through the same internal step and the same timelock, whose length is fixed when the registry is instantiated and which no method can rewrite, so neither route can shorten it. The fee is deposited into th…9) for the design trade-offs.

Which of these are still runni… and re-taken on 27 August, 8 September, 14 September and 214 September 2026, keylessly, fr…till the head when re-read on 214 September 2026, with neither repository archived. Maintained is not the same a…ved: false and a pushed_at of 418 September 2026 through the Gi…r 2026 pushed_at still read 4 September, and on 21 September it read 18 September. The repository's own event stream attributes all fourevery one of them to renovate[bot] —– 13, 21 and 25 August, 4 September, then 16 and 418 September 2026 —– landing on twohree unmerged dependency branches,…novate/major-eslint-monorepo) and, renovate/papaparse-5.x, neither of which anyone has merged and renovate/prettier-3.x, none of which anyone has merged (33 branches, 29 of them the bot's). So the API's freshness figur…at, and its freshest repositories are Canton tooling pushed on 7 Septy is canton-dev-fund (https://github.com/Fairmint/canton-dev-fund) , pushed on 20 September 2026, while the two the API ranks immediately behind it – c-org-js (https://github.com/Fairmint/c-org-js) , the NPM module for interacting with a continuous organization, on 19 September, and c-org itself on 18 September – are the same bot on the same unmerged branches, c-org-js's master head being 6ed5ee2 (https://github.com/Fairmint/c-org-js/commit/6ed5ee2) of 10 December 20260 – and neither "bonding" nor "…foundations/what-is-a-caper) .

Type Perpetual AMM (continuous…d sells) Peak 100%, half by 1.301% sold, 1% by 10.8%, never below 0.5%halving every 10% sold · ⅔ XRD to founder · ⅓ tokens… (/wiki/markets/raising-funds)

A bonding curve is a smart con…as circulation grows, peak × (0.005 + 0.995 × (1 − s) × e−52s)2% × x + 98% × (1 − s) × x10) for x = 2−s/10%, with s the fraction sold: half the peak by 1.301% sold, 1% by 10.8%, and a floor of 0.5%halving every 10% of the supply after that. A sell's token le…how the proceeds are deployed.

What you actually pay The cur…the first buy, half that by 1.301% sold, 1% by 10.8%, and never below 0.5%a halving every 10% of the supply from there on — never zero, and never settling. With the trade fee off the g…bout 2.5 times the curve price, and settles towards 1%; it is about 1.6% by 10% sold and 1.01% by 20%, and what it adds over the 0.5% trade fee halves every 10% sold after that. A sell pays the founder rewa…ar zero at launch, peaks near 10.74% sold, falls while the rate does, and then climbs with the price on the floorhalvings outrun the price, and from about 84% sold climbs again as the price's pole outruns them. Either way the price you pay…ch trade at launch, half by 1.301% sold, 1% by 10.8%, and never below 0.5%a halving every 10% of the supplyfrom there on — there is no floor. Two thirds is paidin $XRD, one third in tokens – about a 151%markup at the first buy, fee included. Sells pay thesame schedule.The take peaks l…es with the price until about 10.74% sold, falls while the rate doeshalvings outrun it, and from about 184%sold climbsagain withas the price on the 0.5% floor’s pole outruns them.Still cheapest earlyEither wa…AUNCH+151.3%HALF THE PEAK BY1.301% soldNEVER BELOW0.5%100% founder skim on buys and sellsHALVES EVERY10% soldFounder skim 100% at launch, 1% by 10.8% sold, never below 0.5%, plus ahalving every 10% after; 0.5% trade fee on buys.caper.…ughout – earliest is cheapest.

Type Perpetual AMM (continuous…n Skim (buys and sells) Peak 5100%, half by 6.751.3% sold, 1% by 10%, never below 0.745% · ⅔ XRD to founder · ⅓ token… (/wiki/markets/raising-funds)

A bonding curve is a smart con…d in $CAPER. The live peak is 5100%, so the token leg peaks at 1.6733.33% of the tokens a trade moves.…ls as circulation grows, peak / √(1 + s / COLLATERALIZATION_SCALE) with s the fraction sold, and never reaches zero× (0.005 + 0.995 × (1 − s) × e−52s) with s the fraction sold: half the peak by 1.3% sold, 1% by 10%, and a floor of 0.5% after that. A sell's token leg changes h…only for the ones it retires. FMost of the founder and Commons rewards scale with curve activity rather than being front-loadedarrive early: a caper that stops by 20% of its supply sold paid 90% of its skim XRD on the first 10%. Vampire capers (bound to an …how the proceeds are deployed.

What you actually pay The cur… in two places – two thirds off the $XRD before it reachesrate on top of each $XRD the curve takes, one third off the tokens the…. That share is front-loaded: 5100% at the first buy, fhalling as the curve fills and never reaching zero. The trade fee and the $XRD leg both come off the same gross, so as af that by 1.3% sold, 1% by 10%, and never below 0.5%. With the trade fee off the gross first, the markup on the price you pay the two starts near 5.7%151%, so the first buyers pay about 2.5 times the curve price, and settles towards 1.3%. A sell pays the founder rew…r token is near zero at launch and rises with the price, the falling rate only slowing the rise, so it scales with activity rather than being front-loaded, peaks near 1% sold, falls while the rate does, and then climbs with the price on the floor. Either way the price you pay…IVE PRICEwhat you pay = P(s) × ( 1 + ⅔c ) ÷ ( 1 − fee − ⅔c )( 1 − ⅓c )0%10%20%30%40%52%4%6%8%10%half the peakwhat you paycur…of cap)price / tokenTHE SHARE IS FRONT-LOADED, THE TAKE IS NOTThe share is front-loaded5PEAKS AT LAUNCH, THE TAKE A LITTLE LATERThe share peaks at launch100% of each trade at launch, half by 6.751.3% sold, 0.74% with the whole supply sold1% by 10%, and never below 0.5%. Two thirds comesoff theis paidin $XRD, one third off thein tokens – about a 5.7151% markup at the first buy, fee included. Sellspay thesame schedule.The take is notpeaks laterPrice starts near zero, so a l…n the takerises with the price; the falling rate only slows until about 1% sold, falls while the rate does, and from about 14% sold climbsagain with the prisece on the 0.5% floor.Still cheapest earlyEither wa…the cheapest.MARKUP AT LAUNCH+5.7151.3%HALF THE PEAK BY6.751.3% soldNEVER BELOW0.74%55%100% founder skim on buys and sells, half by 6.751% by 10% sold and, never below 0.745%, plus a 0.5% trade fee on bu…XRD, ⅓ in the coin; its value peaks early, dips, then rises with the price. The pric…ughout – earliest is cheapest.

Curve shapes The choice of fun… directions – a 0.5% trade fee on buys, not a curve spread, is what … the registry's current_main. Where that fee lands is not symmetric: the buy leg stays in the caper you are buying, while the sell leg leaves it altogether for the root $XRD caper's treasury (/wiki/markets/trading) The fee is deposited into the treasury of the caper being bought, so a curve funds its own DAO on the way in and the base layer on the way out. A sell pays no trade fee ( Raising funds (/wiki/markets/raising-funds) sets out both legsworks it through). Choosing a curve's exponent…9) for the design trade-offs.

What you actually pay The cur…towards 1.3%. A sell pays the founder reward on the same schedule on the way out, and no trade fee. The reward's value reads the…w 0.74%, plus a 0.5% trade fee on buys.caper.networkThe skim's share…ughout – earliest is cheapest.

Caper’s bonding curve Every c…0.001SUPPLY CAP100,000,000,000TRADEBUY FEE0.5%Every caper trades aga…covers the circulating supply.

Type Perpetual AMM (continuous…n Skim (buys and sells) Peak 7.5%, zero by 30% soldhalf by 6.75% sold, never below 0.74% · ⅔ XRD to founder · ⅓ tokens… (/wiki/markets/raising-funds)

A bonding curve is a smart con… new circulation numerically. While a caper is under 30% sold, eEvery trade in either direction…d in $CAPER. The live peak is 7.5%, so the token leg peaks at 2.51.67% of the tokens a trade moves, and t. The rate tapers to zero by 30% soldfalls as circulation grows, peak / √(1 + s / COLLATERALIZATION_SCALE) with s the fraction sold, and never reaches zero. A sell's token leg changes hands rather than retiring, so below that line a sell retires fewer tokens th…how the proceeds are deployed.

Curve shapes The choice of fun…the founder skim on either leg until 30% of supply is sold, at a rate that falls with circulation. That rate is a field writte…9) for the design trade-offs.

What you actually pay The cur…o places – two thirds off the $XRD before it reaches the curv…k what you end up holding per $XRD spent. That share is front-loaded: 7.5% at the first buy, tapering straight to zero by 30% soldfalling as the curve fills and never reaching zero. The trade fee and the $XRD leg both come off the same…ce you pay the two start near 8.55.7% and fade to the 0.5% fee alonesettle towards 1.3%. A sell pays the same schedul…arts near zero, the founder's actual take is a hump thattake per token is near zero at launch and peaks around 11% sold, scalingrises with the price, the falling rate only slowing the rise, so it scales with activity rather than bei…c )( 1 − ⅓c )0%10%20%30%40%50%skim → 0skim peaks ~11% soldhalf the peakwhat you paycurve price P(s)th…y sold (% of cap)price / tokenFRONT-LOADED RATE, HUMPED TAKETHE SHARE IS FRONT-LOADED, THE TAKE IS NOTThe share is front-loaded7.5% of each trade at launch, tapering to zero by 30%half by 6.75% sold, 0.74% with the whole supply sold. Two thirds comesoff the $XRD, one thirdoff the tokens – about an 8.5 5.7% markup at the first buy, fee included. Sellspay the same schedule.The take…ly nothing is nearly nothing. The take humps,peaking near 11% soldPer token the takerises with the price; the falling rate only slows the rise.Still cheapest earlyEither wa…climbs faster than the skim fadells, so the earliest buyis the cheapest.MARKUP AT LAUNCH+8.5%FOUNDER’S TAKE PEAKS~11% soldBOTH GONE BY30% sold7.5% founder skim on buys and sells, zero by 30% sold5.7%HALF THE PEAK BY6.75% soldNEVER BELOW0.74%5% founder skim on buys and sells, half by 6.75% sold and never below 0.74%, plus a 0.5% trade fee.caper.…e skim's share is front-loaded (7.5% at launch, zero by 30% sold, on buys and sells) and paid ⅔ in $XRD, ⅓ in the coin; its value ris a hump peaking near 11% soldes with the price. The price you pay rises throughout – earliest is cheapest.

Type Perpetual AMM (continuous…onic in circulating fraction Per-buy skim Skim (buys and sells) Peak 7.5%, zero by 30% sold · ⅔ XRD to founder · ⅓ tokens (3… (/wiki/markets/raising-funds)

A bonding curve is a smart con… new circulation numerically. Every buyWhile a caper is under 30% sold, every trade in either direction also carries a skim, paid in …hirds is taken in XRD off the paymenttrade's gross – the payment on a buy, before it funds the curve, or the payout on a sell – and banked for the founder. -…rd is a slice of the tokens that buy mints,e trade moves – the mint on a buy, the tokens handed in on a sell – tithed 30/31 to the founder a…y, denominated in $CAPER. The token leg thereforelive peak is 7.5%, so the token leg peaks at 2.5% of each mint, and since it is a fixed fraction of every mint, the founder's share of the coin is the average of that fraction over the curve travelled — never above its own peakthe tokens a trade moves, and the rate tapers to zero by 30% sold. A sell's token leg changes hands rather than retiring, so below that line a sell retires fewer tokens than the seller handed in, and the curve pays only for the ones it retires. Founder and Commons rewards …gin token) earn this same per-buytrade slice; in addition, holders o…how the proceeds are deployed.

Curve shapes The choice of fun…, is what the protocol charges, plus the founder skim on either leg until 30% of supply is sold. That rate is a field writte…9) for the design trade-offs.

What you actually pay The cur…reward skims a share of every buy. The skimtrade. On a buy it bites in two places – two thi…. That share is front-loaded: 17.5% at the first buy, tapering straight to zero by 30% sold. The trade fee and the XRD leg both come off the same gross, so as a markup on the price you pay ithe two starts near 178.5% and fades to the 0.5% trade feefee alone. A sell pays the same schedule on the way out. The reward's value reads the…ou pay = P(s) ÷ ( 1 − fee )( 1 − ⅔c )( 1 − ⅓c )0%10%20%30%40%… TAKEThe share is front-loaded17.5% of each buytrade at launch, tapering to zero b…s comes off the XRD, one thirdoffthe tokens – about a 17n 8.5% markup at the first buy, fee included. Sells pay the same schedule.The take is notPrice starts n…the cheapest.MARKUP AT LAUNCH+178.5%FOUNDER’S TAKE PEAKS~11% soldBOTH GONE BY30% sold17.5% founder skim, tapering to on buys and sells, zero by 30% sold, plus a 0.5%…skim's share is front-loaded (17.5% at launch, zero by 30% sold, on buys and sells) and paid ⅔ in XRD, ⅓ in the …ughout – earliest is cheapest.

Which of these are still runni…on was taken on 13 August 2026, and re-taken on 27 August 2026 and re-taken again on 8, 8 September and 14 September 2026, keylessly, fr…n from commentary about them. Across all thrBetween probes exactly one figureonly freshness dates hasve moved; it is the same figure each time, and it moves, and the section below explains why a freshness date ins the direction this section warns aboutweakest of these readings. Bancor smart tokens Maintai…ner on 29 July 2026, and both awere still the head six weeks and three probes laterwhen re-read on 14 September 2026. Maintained is not the same a…it that changed a contract is 11 December 2020 0861378 (https://github.com/Fairmint/c-org/commit/0861378) , "Fix/sell no lock", on 6 December 2020 – the 2.4.24 release five days later touched only package.json files. The repository carries 33 b…t push was 7 August 2026, and every re-probe since has found a later onethe next two re-probes each found a later one; on 14 September 2026 pushed_at still read 4 September. The repository's own event s…readings are three years apart, and the gap widens on every probewhenever the bot next runs. A dormant repository does no…en confess; it reads fresher eachvery time you lookits bot runs, which is why one reading of …never settle the question and threeseveral can. The Vyper sibling, c-or… are Canton tooling pushed on 12 August 2026 – but the words "continuous", "bonding" and "CAFE" no longer appear on it7 September 2026 – and neither "bonding" nor "CAFE" appears on it, while "continuous" survives only as "Continuous settlement", a cap-table transfer feature. The model this page calls Ca…foundations/what-is-a-caper) .

What you actually pay The cur…ach buy at launch, tapering tozero by 30% sold. Two thirds comes off theXRD, one third offthe tokens – about a17.5% markup at the first buy.…ts near zero, so a large shareof nearly nothing is nearly nothing. Thetake humps,peaking near 11% sold.Still ch…way your price only rises: thecurve climbs faster than the skim fades,so the earliest buyis the cheapest.MARKUP AT LAUN…S~11% soldBOTH GONE BY30% soldProtocol defaults: 15% founder skim, tapering to zero by 30% sold – paid ⅔ in XRD, ⅓ in the coin –, plus a 0.5% trade fee.caper.n…ughout – earliest is cheapest.

Caper’s bonding curve Every c…the curve mints new tokens andthe price ticks up.Sell — retu…s; the curve pays XRD from itsreserve and the price ticks do…s the circulating supply — younever need a counterparty.Cap …y nears 100bn the price curvestoward infinity.CURVE CONSTANT…covers the circulating supply.

Which of these are still runni…on was taken on 13 August 2026 and, re-taken on 27 August 2026 and re-taken again on 8 September 2026, keylessly, from each pro…n from commentary about them. OnAcross all three probes exactly one figure has moved; int is the fortnight between themsame figure each time, and it moveds in the direction this section…Bancor smart tokens Maintained., on the reading that discriminates rather than the one below it. Neither contracts-solidity (https://…protocol/contracts-solidity) andnor contracts-v3 (https://github…bancorprotocol/contracts-v3) were both pushedis archived, and their freshness survives the test the next row fails: the head of master is 78c5736 (https://github.com/bancorprotocol/contracts-solidity/commit/78c5736) , the release commit 0.7.15, and the head of dev (https://github.com/bancorprotocol/contracts-v3/commits/dev) is 97d7905, "updated mainnet artifacts" — both landed by a maintainer on 29 July 2026, and neither is archboth are still the head six weeks and three probes later. Maintained is not the same as actived. Aragon Fundraising Retired.…ved: false and a pushed_at of 25 August4 September 2026 through the GitHub API. …reshest push was 7 August 2026; renovate[bot] has force-pushed three times since — 13, 21 and 25 August — so pushed_at has advanced eighteen days while 781d1ed has stayed exactly where it was in September 2023, and every re-probe since has found a later one. The repository's own event stream attributes all four to renovate[bot] — 13, 21 and 25 August and 4 September 2026 — landing on two unmerged dependency branches, renovate/major-eslint-monorepo (https://github.com/Fairmint/c-org/commits/renovate/major-eslint-monorepo) and renovate/papaparse-5.x, neither of which anyone has merged. So the API's freshness figure has walked out of August and into September while 781d1ed has stayed exactly where it was in September 2023: the two readings are three years apart and the gap widens on every probe. A dormant repository does no…en confess; it reads fresher everyach time the bot runsyou look, which is why one reading of it can never settle the question and three can. The Vyper sibling, c-org-vy…foundations/what-is-a-caper) .

The cap is an asymptote, not a… clamps its search at s_max = 0.999999 (compute_tokens_bought_inner1 − 10−12 (CURVE_S_MAX, contracts/logic/src/lib.rs),…tays finite on the boundary a partia full migration could otherwise(/wiki/foundations/migrating-an-existing-token) lands on as its ordinary starting state. The buy path then asserts th… Cap Exceeded if it is not. Threewo figures follow from that inte…ve to the clamp takes roughly 1.322.70bn XRD of reserve;, and the spot price there is about 1,000bn XRD per token, – some 707,000 billion times the price at half the supply sold; and the last 100,000 tokens, one ten-thousandth of one percent of the cap, cannot be minted by buying at any price. Every caper therefore keeps inventory it can never sell through the curve. That is a property of the shape rather than a policy choice: it is the same 1 − s denominator that makes the price asymptotic in the first place, and it is what the chart below draws as the gap between where the curve leaves the plot and the cap line. That steepness is a property of the shape rather than a policy choice: it is the same 1 − s denominator that makes the price asymptotic in the first place, and it is what the chart below draws as the gap between where the curve leaves the plot and the cap line. Where the bound sits is a solvency question, not a rounding one, and it moved on 29 August 2026. A clamp does not merely bound the domain – it flattens the reserve integral above it, so every circulation past the bound returns one and the same reserve figure. A seller is paid the difference between that figure before their sale and after it, so a sell that begins and ends inside the flattened region succeeds and pays exactly zero: real tokens surrendered for nothing. The dead region is (1 − bound) × cap tokens wide. At the 0.999999 bound this curve used until 29 August it was 100,000 tokens wide – comfortably large enough for a real trade to fall inside – and at 1 − 10−12 it is 0.1 of a token, below anything anyone can trade. The new bound is set by where Decimal's eighteen places stop resolving 1 − √s, not by caution, and tightening it is what let the vampire migration ceiling be removed rather than kept as buy margin the arithmetic never needed.

Curve shapes The choice of fun…, is what the protocol charges, and t. That rate is a configured field (/wiki/help/faq) rather than a constant of the contractfield written into the logic component (/wiki/help/faq) when the platform is instantiated rather than a constant compiled into it, so the app reads it off the gateway and fails loudly on drift – but nothing can rewrite it in place. The deployed CaperMain exposes no fee setter of any kind, so moving the rate takes a fresh logic component and a governed UPGRADE (/wiki/governance/execution) of the registry's current_main. Where that fee lands is not …9) for the design trade-offs.

Which of these are still runni…ection was taken on 13 August 2026 and re-taken on 27 August 2026, keylessly, from each pro…an from commentary about them. Only one figure moved in the fortnight between them, and it moved in the direction this section warns about. Bancor smart tokens Maintain…ved: false and a pushed_at of 725 August 2026 through the GitHu… 2020. The repository carries 330 branches (https://github.com/Fairmint/c-org/branches/all) , 289 of them automated dependency bumps, and the 7 August 2026freshest push was one of those bots raising a lforce-pushing an ESLinter major version ton a branch nobody merged. pushe…ing that discriminates is the head commit of the default branch, and even that can be a README edit (https://github.com/Fairmint/c-org/commits/master) , and even that can be a README edit. Re-probing on 27 August 2026 made the point a second time rather than merely confirming it. When this page first read the repository the freshest push was 7 August 2026; renovate[bot] has force-pushed three times since — 13, 21 and 25 August — so pushed_at has advanced eighteen days while 781d1ed has stayed exactly where it was in September 2023. A dormant repository does not read as dormant for a fortnight and then confess; it reads fresher every time the bot runs. The Vyper sibling, c-org-vy…foundations/what-is-a-caper) .

The cap is an asymptote, not a target Circulation is capped at 100bn tokens, and because the price divides by 1 − s, that cap is a limit the curve approaches rather than a supply it ever reaches. The contract enforces it in two places. The Newton solver that prices a buy clamps its search at s_max = 0.999999 (compute_tokens_bought_inner, contracts/logic/src/lib.rs), and the reserve integral clamps at the same point so that it stays finite on the boundary a partial migration could otherwise land on. The buy path then asserts that the new circulation is still at or below the cap and reverts with Curve Cap Exceeded if it is not. Three figures follow from that integral at the protocol's K = 0.001 and a 100bn cap. Filling the curve to the clamp takes roughly 1.32bn XRD of reserve; the spot price there is about 1,000 XRD per token, some 707,000 times the price at half the supply sold; and the last 100,000 tokens, one ten-thousandth of one percent of the cap, cannot be minted by buying at any price. Every caper therefore keeps inventory it can never sell through the curve. That is a property of the shape rather than a policy choice: it is the same 1 − s denominator that makes the price asymptotic in the first place, and it is what the chart below draws as the gap between where the curve leaves the plot and the cap line.

Caper’s bonding curve Every c…TOCOLThe bonding curvePRICE = f(SUPPLY)price P(s) = K · √s / (1 − s) …covers the circulating supply.

Further reading - Tokens 2.0:…onomic-games-as-estimators-3/) - The Standing Counterparty (/blog/the-standing-counterparty) – why a curve is the market maker a specialist could never be

Curve shapes The choice of fun… curve in both directions – a flat 0.5% trade fee, not a curve sp…, is what the protocol charges, and that rate is a configured field (/wiki/help/faq) rather than a constant of the contract. Where that fee lands is not …9) for the design trade-offs.

Curve shapes The choice of fun…ngle curve in both directions —– a flat 0.5% trade fee, not a curve spread, funds each caper's treasuryis what the protocol charges. Where that fee lands is not symmetric: the buy leg stays in the caper you are buying, while the sell leg leaves it altogether for the root $XRD caper's treasury (/wiki/markets/trading) , so a curve funds its own DAO on the way in and the base layer on the way out ( Raising funds (/wiki/markets/raising-funds) sets out both legs). Choosing a curve's exponents…9) for the design trade-offs.

Which of these are still runni…e Token Engineering Commons (https://te/wiki/daos/public-goods/token-engineering-commons.org/) – the commons the Commons S…foundations/what-is-a-caper) .

Further reading - Tokens 2.0:…/components/bonding-curve.md) (repository archived 8 March 2023) - Introducing Continuous Org…onomic-games-as-estimators-3/)

Which of these are still running The designs above are usually described in the present tense. They are not equally alive. Every reading in this section was taken on 13 August 2026, keylessly, from each project's own repositories, forum and governance venue rather than from commentary about them. Bancor smart tokens Maintained. contracts-solidity (https://github.com/bancorprotocol/contracts-solidity) and contracts-v3 (https://github.com/bancorprotocol/contracts-v3) were both pushed on 29 July 2026 and neither is archived. Aragon Fundraising Retired. aragon/fundraising (https://github.com/aragon/fundraising) was archived on 8 March 2023, the same day as aragon-apps (https://github.com/aragon/aragon-apps) – the sunset of the Aragon client, not of Aragon (/wiki/dao-governance/tooling/frameworks/aragon) , which still ships a DAO framework. Continuous Organizations (DAT) Dormant since 2020, although the GitHub API reports the repository as fresh. See below. Augmented bonding curve Its flagship deployment has been wound down and redeemed. Eleven voters closed it in August 2025. The augmented bonding curve's flagship commons voted itself closed. The Token Engineering Commons (https://tecommons.org/) – the commons the Commons Stack design was built for – resolved to end. "Proposal: Initiate the Sunsetting Process for the $TEC Token" (https://snapshot.box/#/s:tecommons.eth/proposal/0xec36a9a998e84dd79196d49f830e7eba81f51ea9be641a757ad55268a0049438) ran on Snapshot (https://snapshot.box/#/s:tecommons.eth) from 30 July to 4 August 2025 and closed with 11 voters, 264,496.79 TEC for against 6,773.42 opposed. Queried through Snapshot's GraphQL hub (https://hub.snapshot.org/graphql) , it is still the most recent of the space's 28 proposals. A full shutdown proposal (https://forum.tecommons.org/t/tec-shutdown-proposal/1520) followed in October 2025, describing the TEC as the first explicit economic commons on a blockchain and arguing for closing it deliberately rather than letting it drift, and the final implementation plan (https://forum.tecommons.org/t/tec-token-sunset/1531) of 2 December 2025 set each holder's redemption at the lower of their balance on 23 July 2025, the day the wind-down was announced, or their balance at dissolution – so that neither buying in nor selling out after the announcement could change a claim. The organisation's GitHub (https://github.com/CommonsBuild) carries the sequence in its repository names: TECsunsetcomingsoon, TECredeem and tec-shutdown, all created in the closing weeks of 2025. The front page of tecommons.org still reads as an open invitation to join, which is the ordinary condition of a wound-down DAO: the code and the governance record move on before the website does. One repository reads fresh while being dormant, which is worth knowing before trusting any freshness check. Fairmint/c-org (https://github.com/Fairmint/c-org) , the reference implementation of the Decentralized Autonomous Trust, reports archived: false and a pushed_at of 7 August 2026 through the GitHub API. Both readings mislead. The head of master is 781d1ed, dated 5 September 2023, and its commit message is "Update README.md"; the last commit that changed a contract is 11 December 2020. The repository carries 30 branches, 28 of them automated dependency bumps, and the 7 August 2026 push was one of those bots raising a linter major version on a branch nobody merged. pushed_at records a push to any branch, so on a repository with a dependency bot attached it is the bot's heartbeat rather than the project's; the reading that discriminates is the head commit of the default branch, and even that can be a README edit. The Vyper sibling, c-org-vyper (https://github.com/Fairmint/c-org-vyper) , is archived outright. Fairmint itself is busy: its homepage (https://www.fairmint.com/) now sells onchain cap tables built on the Open Cap Table Format, and its freshest repositories are Canton tooling pushed on 12 August 2026 – but the words "continuous", "bonding" and "CAFE" no longer appear on it. The model this page calls Caper's ancestor was left behind by the company that named it. None of this makes the curve a weak primitive – Bancor's contracts are maintained, and new launchpads keep shipping on the same idea. It does mean that "X uses a bonding curve" is a claim with a date on it, and that the thing most likely to end a curve is not its mathematics but the organisation around it. Caper's own curve is described above; what is worth noting here is only where it sits. The curve, the founder skim and the trade fee are parameters of each caper's deployed contract rather than of a front end an operator can retire, and the sell side carries no pause, no owner gate and no schedule – see Trading (/wiki/markets/trading) and What is a caper (/wiki/foundations/what-is-a-caper) .

History The continuous-token i…am, Paruch & Shorish (https://epubresearch.wu.ac.at/7433/1/zargham_paruch_shorish.pdfen/publications/economic-games-as-estimators-3/) ).

Relationship to automated mark…MM such as Uniswap (https://docevelopers.uniswap.org/concepts/protocol/concentrated-liquiditydocs/get-started/concepts/how-uniswap-works) prices two pre-existing ass…iterally free of price impact.

Further reading - Tokens 2.0:…orish (BlockScience) (https://epubresearch.wu.ac.at/7433/1/zargham_paruch_shorish.pdfen/publications/economic-games-as-estimators-3/)

The mathematics Two quantities…r formula (https://github.com/AaragonBlack/fundraising/blob/master/docs/…at approaches the full supply.

Further reading - Tokens 2.0:…ndraising (https://github.com/AaragonBlack/fundraising/blob/master/docs/…/1/zargham_paruch_shorish.pdf)

What you actually pay The cur…rd skims a share of every buy. The skim bites in two places – two thirds off the XRD before it reaches the curve, one third off the tokens the curve mints – and both shrink what you end up holding per XRD spent. That share is front-loaded –: 15% at the first buy, tapering straight to zero by 30% sold –, so as a markup on the price you pay it starts near 187.5% and fades to the 0.5% trade …at you pay = P(s) ÷ ( 1 − 0.5% fee − founder skim c(s)fee )( 1 − ⅔c )( 1 − ⅓c )0%10%20%30%40%50%skim → 0ski… tapering tozero by 30% sold. On the price you pay,that isTwo thirds comes off theXRD, one third off the tokens – about an 1817.5% markup at the firstbuy.The take is notPrice start…he cheapest.MARKUP AT LAUNCH+18.37.5%FOUNDER’S TAKE PEAKS~11% sold…m tapering to zero by 30% sold, – paid ⅔ in XRD, ⅓ in the coin – plus a 0.5% trade fee.caper.n…% at launch, zero by 30% sold) and paid ⅔ in XRD, ⅓ in the coin; its value is a hump peaking …ughout – earliest is cheapest.

Type Perpetual AMM (continuous…irculating fraction Per-buy slice kim ⅔ XRD to founder · ⅓ tokens (30/31 founder · 1/31 Caper Commons) Coined 2017 — Simon de la R… (/wiki/markets/raising-funds)

A bonding curve is a smart con… new circulation numerically. On eEvery buy, an additional small slice of the buyer's curve-dlso carries a skim, paid in the curve's own composition. A curve whose price rises as the n-th power of supply holds 1/(n+1) of its market value as reserve; this one is a square root at the origin, so two thirds of a young caper is reserived tokens is taken from the inventory vault and split: - and one third is claim on future buyers. The skim splits along that line: - Two thirds is taken in XRD off the payment, before it funds the curve, and banked for the founder. - One third is a slice of the tokens that buy mints, tithed 30/31 goes to the founder vault. - 1/31 goesand 1/31 to the Caper Commons — the pr…asury, denominated in $CAPER. The token leg therefore peaks at 5% of each mint, and since it is a fixed fraction of every mint, the founder's share of the coin is the average of that fraction over the curve travelled — never above its own peak. Founder and Commons rewards sc…how the proceeds are deployed.

Applications - Automated marke…ce or revenue token (/wiki/daos-governance/concepts/treasury/dao-tokenom… before migrating it to a DEX.

Risks and criticisms - Front-r… under mass selling (/wiki/daos-governance/concepts/analysis/how-daos-fa…serve ratios and magnify risk.

Applications - Automated marke…ce or revenue token (/wiki/daos/concepts/treasury/dao-tokenomics) , replacing fi… before migrating it to a DEX.

Risks and criticisms - Front-r… under mass selling (/wiki/daos/concepts/analysis/how-daos-fail) . - Parameter …serve ratios and magnify risk.

What you actually pay The curve sets the base price, but; the founder reward skims a share of every buy – 15% at launch, tapering to nothing by the time 30% of supply has sold. Stacked on the curve, that skim is a shrinking. That share is front-loaded – 15% at the first buy, tapering straight to zero by 30% sold – so as a markup on the price you pay: it starts near 18% at the first buy, gone by 30%. It never opens a cheaper entry later, because the curve underneath always rises faster than the skim fades –nd fades to the 0.5% trade fee. The reward's value reads the other way: because price starts near zero, the founder's actual take is a hump that is near zero at launch and peaks around 11% sold, scaling with activity rather than being front-loaded. Either way the price you pay only ever rises, so the earliest buy is always…(s) )0%10%20%30%40%50%skim → 0skim peaks ~11% soldwhat you paycurve price P(s)th…y sold (% of cap)price / tokenA SHRINKING MARKUP, NOT A DIPWidest at launchAround 18% over the curve price at thefirst buy, fading to the 0.5% feeFRONT-LOADED RATE, HUMPED TAKEThe share is front-loaded15% of each buy at launch, tapering tozero by 30%sold.Never a cheaper entryThe markup shrinks, but the curveunderneath climbs fast On the price you pay,that is about an 18% markup at the firstbuy.The take is notPrice starts near zero, so your priceonly ever rises. The earliest buy is thecheapest.Split a big buyThe skim rate locks to circulation themoment your order landa large shareof nearly nothing is nearly nothing. Thetake humps, peaking near 11% sold.Still cheapest earlyEither way your price only rises: thecurve climbs faster than the skim fades,so splitting alargethe earliest buy letis the rate taper across thefill.MARKUP AT LAUNCH+18.3%SKIM GONE BY30% soldTHEN ONLY0.5% feecheapest.MARKUP AT LAUNCH+18.3%FOUNDER’S TAKE PEAKS~11% soldBOTH GONE BY30% soldProtocol defaults: 15% founder skim tapering to zero by 30% sold, plus a 0.5% trade fee.caper.networkEffective price sits above the curve by the founder skim – largest as a share near launch, closing to the 0.5% trade fee by 30% soldThe skim's share is front-loaded (15% at launch, zero by 30% sold); its value is a hump peaking near 11% sold. The price you pay rises throughout – earliest is cheapest.

What you actually pay The curve sets the base price, but the founder reward skims a share of every buy – 15% at launch, tapering to nothing by the time 30% of supply has sold. Stacked on the curve, that skim is a shrinking markup on the price you pay: near 18% at the first buy, gone by 30%. It never opens a cheaper entry later, because the curve underneath always rises faster than the skim fades – so the earliest buy is always the cheapest. CAPER PROTOCOLWhat you actually payEFFECTIVE PRICEwhat you pay = P(s) ÷ ( 1 − 0.5% fee − founder skim c(s) )0%10%20%30%40%50%skim → 0what you paycurve price P(s)the gap = founder skimsupply sold (% of cap)price / tokenA SHRINKING MARKUP, NOT A DIPWidest at launchAround 18% over the curve price at thefirst buy, fading to the 0.5% fee by 30%sold.Never a cheaper entryThe markup shrinks, but the curveunderneath climbs faster, so your priceonly ever rises. The earliest buy is thecheapest.Split a big buyThe skim rate locks to circulation themoment your order lands, so splitting alarge buy lets the rate taper across thefill.MARKUP AT LAUNCH+18.3%SKIM GONE BY30% soldTHEN ONLY0.5% feeProtocol defaults: 15% founder skim tapering to 30% sold, 0.5% trade fee.caper.networkEffective price sits above the curve by the founder skim – largest as a share near launch, closing to the 0.5% trade fee by 30% sold.

Applications - Automated marke…ermanent primary market for a governance or revenue token (/wiki/dao/concepts/dao-tokenomics) , replacing fixed sales with … before migrating it to a DEX.

Risks and criticisms - Front-r… "value" is reflexive and can evaporate under mass selling (/wiki/dao/concepts/how-daos-fail) . - Parameter and composition…serve ratios and magnify risk.

Caper’s bonding curve Every caper’s token trades against its own bonding curve: the price is a formula of how much supply has sold, so there is always a live market and never a need for a counterparty. The reserve backs every token in circulation. CAPER PROTOCOLThe bonding curvePRICE = SUPPLYprice P(s) = K · √s / (1 − s) s = supply sold / cap0%25%50%75%100%cap = 100bnBUY → price rises← SELL price fallssupply sold (% of cap)price / tokenA PRICE FORMULA, NOT AN ORDER BOOKBuy — send XRD; the curve mints new tokens andthe price ticks up.Sell — return tokens; the curve pays XRD from itsreserve and the price ticks down.Reserve — always covers the circulating supply — younever need a counterparty.Cap — as supply nears 100bn the price curvestoward infinity.CURVE CONSTANT K0.001SUPPLY CAP100,000,000,000TRADE FEE0.5%Every caper trades against its own bonding curve.caper.networkPrice rises as supply sells; the reserve always covers the circulating supply.

A bonding curve is a smart con…ther than being front-loaded. For vVampire capers (bound to an origin token) earn this same per-buy slice; is forced to zero — the founder's bootstrap is the migration vault populated when origin holders migraten addition, holders of the origin token can migrate into the caper — a free mint that draws from the inventory vault and advances circulation without an XRD buy, with the resulting reserve gap backfilled by a fee on later direct buys. See Trading (/wiki/markets/…how the proceeds are deployed.

Curve shapes The choice of fun…on & Parametrization (https://blog.medium.com/relevant.-community/bonding-curves-in-de…89) for the design trade-offs, and Dynamic Token Bonding Curves (https://tokeneconomy.co/dynamic-token-bonding-curves-41d36e43befa) for curves whose parameters adjust over time.

Further reading - Tokens 2.0:…— Relevant Community (https://blog.medium.com/relevant.-community/bonding-curves-in-de…s-token-models-a167f5ffef89) - Token Bonding Curves in Practice — Token Economy (https://tokeneconomy.co/token-bonding-curves-in-practice-3eb904720cb8) - Dynamic Token Bonding Curves — Token Economy (https://tokeneconomy.co/dynamic-token-bonding-curves-41d36e43befa) - Economic Games as Estimator…/1/zargham_paruch_shorish.pdf)

Type Perpetual AMM (continuous token model) Price Monotonic in circulating fraction Per-buy slice 30/31 founder · 1/31 Caper Commons Coined 2017 — Simon de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) / Zap, on Bancor (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) Also powers Curation markets · continuous organizations · AMMs Related Trading (/wiki/markets/trading) , Raising funds (/wiki/markets/raising-funds)

A bonding curve is a smart contract that sets a token's price as a mathematical function of its circulating supply: it mints new tokens when buyers arrive and burns them when holders sell, so a market is always open without an order book or a matching counterparty. Caper uses one as the permanent, built-in market for every caper's governance token. This page covers Caper's implementation first, then the wider idea it descends from. Caper's curve The curve is a perpetual AMM whose price is a smooth, monotonically increasing function of the fraction of supply in circulation. Price starts at zero with nothing sold and goes asymptotic as circulation approaches the full 100bn. Buying moves XRD into the curve vault and tokens out of the inventory vault; selling reverses both. The cumulative XRD held by the curve has a closed-form integral, so sells price out exactly; buys solve for the new circulation numerically. On every buy, an additional small slice of the buyer's curve-derived tokens is taken from the inventory vault and split: - 30/31 goes to the founder vault. - 1/31 goes to the Caper Commons — the protocol-wide treasury, denominated in $CAPER. Founder and Commons rewards scale with curve activity rather than being front-loaded. For vampire capers (bound to an origin token) this slice is forced to zero — the founder's bootstrap is the migration vault populated when origin holders migrate. See Trading (/wiki/markets/trading) for the buy/sell panel and Raising funds (/wiki/markets/raising-funds) for how the proceeds are deployed.

How bonding curves work More generally, a bonding-curve contract holds a reserve (or collateral) pool of a base asset — XRD on Radix, historically ETH on Ethereum — and issues its own token against it: - Buying / minting. A buyer deposits reserve assets; the contract mints new tokens, adds the deposit to the reserve, and the spot price rises because supply has increased. - Selling / burning. A seller returns tokens; the contract burns them, releases the corresponding reserve, and the spot price falls. The result is what Yos Riady (https://yos.io/2018/11/10/bonding-curves/) calls a continuous token: it has a deterministic price (set by the formula, not negotiation), a continuous price (token n+1 always costs more than token n), and instant liquidity (any amount can be bought or sold at any time). Deposited funds stay locked in the contract, so the token is always backed by collateral that can be reclaimed by burning — the same property that lets every caper holder cash out (/wiki/markets/trading) at any time.

The mathematics Two quantities are easy to confuse. The bonding curve itself, P(S), gives the spot price of the next token at supply S. The reserve held by the contract — and therefore the cost of a finite purchase — is the area under that curve, its integral. As Slava Balasanov (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) illustrates with a simple quadratic curve: spot price: P(S) = S² reserve: R(S) = ∫₀ˢ P(s) ds = ⅓ · S³ cost to mint: ΔR = ⅓·(S + n)³ − ⅓·S³ (to add n new tokens)Because a buyer pays the integral rather than the final spot price, a large order pays a progressively higher average price as it climbs the curve. Each curve therefore has a characteristic reserve ratio — the share of the token's notional market capitalisation actually held as collateral: reserveRatio = reserveBalance / (price × supply)A linear curve P(S) = m·S has a reserve ratio of ½; the quadratic curve above has ⅓. The Bancor protocol (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) generalises this by holding the reserve ratio (its "connector weight") constant, giving the widely reused Bancor formula (https://github.com/AragonBlack/fundraising/blob/master/docs/components/bonding-curve.md) : price = reserveBalance / (supply × reserveRatio) purchaseReturn = supply × ((1 + reserveAdded / reserveBalance) ^ reserveRatio − 1) saleReturn = reserveBalance × (1 − (1 − tokensSold / supply) ^ (1 / reserveRatio))A reserve ratio between 0% and 100% tunes the curve's steepness: 100% gives a flat, fully-collateralised price (a stable peg), while smaller ratios produce steeper curves that reward early buyers more. Caper's curve, P(s) = K · √s / (1 − s) in the circulating fraction s, is a steep variant: the price is zero at genesis (so there is no sniper floor) and rises to a pole as the float approaches the full supply.

Curve shapes The choice of function shapes a token's incentives. Common forms, catalogued by BonDeFi (https://medium.com/@bondefi/bonding-curves-anti-snipe-1cf47220d3bc) and others (https://yos.io/2018/11/10/bonding-curves/) , include: - Linear — P = m·S + b. Constant-rate price growth; simple and predictable. - Polynomial / quadratic — e.g. P = S². Faster appreciation that rewards early participants. - Exponential — P = a·e^(b·S). Steep, speculative growth. - Sigmoid / logarithmic — S-shaped or flattening curves that model adoption slowing as supply matures, damping late-stage volatility. A contract may also use separate buy and sell curves; the gap between them forms a bid–ask spread that can fund the protocol or reward long-term holders. Caper instead uses a single curve in both directions — a flat trade fee, not a curve spread, funds each caper's treasury.

History The continuous-token idea entered crypto with the Bancor protocol (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) (2017), whose "smart tokens" used a constant reserve ratio to stay continuously convertible into their reserve. Later that year Simon de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) published "Tokens 2.0: Curved Token Bonding in Curation Markets" (21 November 2017), framing curved bonding as the pricing engine for curation markets — markets that "reduce information asymmetry through the use of tokenized signals." He credits the Zap team with coining the term "bonding curves." In 2018 Thibauld Favre (https://hackernoon.com/introducing-continuous-organizations-22ad9d1f63b7) introduced Continuous Organizations, using a Decentralized Autonomous Trust (DAT) and a bonding curve to mint and burn "FAIR" tokens that represent claims on an organisation's future cash flows — giving projects continuous fundraising and guaranteed liquidity instead of a one-off sale. Caper is a direct descendant of this model: an organisation whose token lives on a permanent curve. Around 2019–2020 the Commons Stack (https://commonsstack.org/) , with research firm BlockScience, generalised the design into the augmented bonding curve (https://blog.giveth.io/deep-dive-augmented-bonding-curves-3f1f7c1fa751) , which diverts a share of every purchase into a "common pool" to fund public goods — the same shape as Caper's 1/31 Caper Commons slice.

Relationship to automated market makers Bonding curves and automated market makers (AMMs) are close cousins. A single-reserve bonding curve is effectively a one-sided AMM that mints and burns the token itself, whereas a constant-function AMM such as Uniswap (https://docs.uniswap.org/concepts/protocol/concentrated-liquidity) prices two pre-existing assets against each other along an invariant — the constant-product rule x · y = k. Bancor's price = reserveBalance / (supply × reserveRatio) is the bonding-curve generalisation of that idea. A common claim is that bonding curves have "zero slippage." That is imprecise. Because a purchase pays the area under the curve between the old and new supply, a large order still pays a progressively higher average price — a price impact functionally like slippage, which is exactly why Caper's Trading (/wiki/markets/trading) guide notes that "slippage is implicit in the curve shape." The genuine distinction is that this impact is fully deterministic: it depends only on the trade size and the fixed curve, not on the fluctuating ratio of two pooled assets, and the curve can never run out of the token it mints. Liquidity is always available and its price impact is knowable in advance — but it is not literally free of price impact.

Applications - Automated market making. Continuous, reserve-backed pricing underpins Bancor's smart tokens (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) and the broader family of on-chain AMMs. - Curation markets. Bonding curves let participants stake on the quality or relevance of information, rewarding early curators as a signal gains support ( de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) ). - Continuous organizations & DAOs. A curve becomes a permanent primary market for a governance or revenue token, replacing fixed sales with continuous fundraising and guaranteed exit liquidity (https://hackernoon.com/introducing-continuous-organizations-22ad9d1f63b7) — the pattern Caper is built on. - Public-goods funding. Augmented bonding curves (https://blog.giveth.io/deep-dive-augmented-bonding-curves-3f1f7c1fa751) route part of each buy into a common pool, turning token demand into a funding stream for open-source and charitable work. - Token launchpads. On Radix, BonDeFi (https://medium.com/@bondefi/bonding-curves-anti-snipe-1cf47220d3bc) uses a batched bonding curve to launch tokens fairly; on Solana, Pump.fun (https://www.solflare.com/ecosystem/pump-fun-where-memes-meet-markets-on-solana/) popularised the "fair launch," pricing a token up the curve as buyers arrive before migrating it to a DEX.

Risks and criticisms - Front-running / MEV. Because price depends only on supply, an adversary who sees a pending buy can buy first and sell into it. Both Balasanov (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) and Riady (https://yos.io/2018/11/10/bonding-curves/) flag bonding curves as "susceptible to front-running attacks"; batched curves and ordering protections aim to mitigate it. - Reflexivity and volatility. Tying price to supply creates a feedback loop — buying raises the price, which attracts more buying. Steep curves amplify this into pump-and-dump dynamics where a rush to exit can collapse the price as fast as it rose. - Market cap is not collateral. Because the reserve is the area under the curve, a token's notional market capitalisation (price × supply) is typically several times the reserve backing it. Every holder can still redeem along the curve, but the headline "value" is reflexive and can evaporate under mass selling. - Parameter and composition risk. The wrong curve shape or reserve ratio can make a token too volatile or too illiquid, and deeply nested curves (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) (a curve collateralised by another curved token) compound reserve ratios and magnify risk.

Further reading - Tokens 2.0: Curved Token Bonding in Curation Markets — Simon de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) - How to Make Bonding Curves for Continuous Token Models — Slava Balasanov (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) - Bonding Curves Explained — Yos Riady (https://yos.io/2018/11/10/bonding-curves/) - Bonding Curve component docs — Aragon Fundraising (https://github.com/AragonBlack/fundraising/blob/master/docs/components/bonding-curve.md) - Introducing Continuous Organizations — Thibauld Favre (https://hackernoon.com/introducing-continuous-organizations-22ad9d1f63b7) - Deep Dive: Augmented Bonding Curves — Commons Stack / Giveth (https://blog.giveth.io/deep-dive-augmented-bonding-curves-3f1f7c1fa751) - Bonding Curves & Anti-Snipe — BonDeFi (https://medium.com/@bondefi/bonding-curves-anti-snipe-1cf47220d3bc)

Type Perpetual AMM (continuous token model) Price Monotonic in circulating fraction Per-buy slice 30/31 founder · 1/31 Caper Commons Coined 2017 — Simon de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) / Zap, on Bancor (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) Also powers Curation markets · continuous organizations · AMMs Related Trading (/wiki/markets/trading) , Raising funds (/wiki/markets/raising-funds)

A bonding curve is a smart contract that sets a token's price as a mathematical function of its circulating supply: it mints new tokens when buyers arrive and burns them when holders sell, so a market is always open without an order book or a matching counterparty. Caper uses one as the permanent, built-in market for every caper's governance token. This page covers Caper's implementation first, then the wider idea it descends from. Caper's curve The curve is a perpetual AMM whose price is a smooth, monotonically increasing function of the fraction of supply in circulation. Price starts at zero with nothing sold and goes asymptotic as circulation approaches the full 100bn. Buying moves XRD into the curve vault and tokens out of the inventory vault; selling reverses both. The cumulative XRD held by the curve has a closed-form integral, so sells price out exactly; buys solve for the new circulation numerically. On every buy, an additional small slice of the buyer's curve-derived tokens is taken from the inventory vault and split: - 30/31 goes to the founder vault. - 1/31 goes to the Caper Commons — the protocol-wide treasury, denominated in $CAPER. Founder and Commons rewards scale with curve activity rather than being front-loaded. For vampire capers (bound to an origin token) this slice is forced to zero — the founder's bootstrap is the migration vault populated when origin holders migrate. See Trading (/wiki/markets/trading) for the buy/sell panel and Raising funds (/wiki/markets/raising-funds) for how the proceeds are deployed.

How bonding curves work More generally, a bonding-curve contract holds a reserve (or collateral) pool of a base asset — XRD on Radix, historically ETH on Ethereum — and issues its own token against it: - Buying / minting. A buyer deposits reserve assets; the contract mints new tokens, adds the deposit to the reserve, and the spot price rises because supply has increased. - Selling / burning. A seller returns tokens; the contract burns them, releases the corresponding reserve, and the spot price falls. The result is what Yos Riady (https://yos.io/2018/11/10/bonding-curves/) calls a continuous token: it has a deterministic price (set by the formula, not negotiation), a continuous price (token n+1 always costs more than token n), and instant liquidity (any amount can be bought or sold at any time). Deposited funds stay locked in the contract, so the token is always backed by collateral that can be reclaimed by burning — the same property that lets every caper holder cash out (/wiki/markets/trading) at any time.

The mathematics Two quantities are easy to confuse. The bonding curve itself, P(S), gives the spot price of the next token at supply S. The reserve held by the contract — and therefore the cost of a finite purchase — is the area under that curve, its integral. As Slava Balasanov (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) illustrates with a simple quadratic curve: spot price: P(S) = S² reserve: R(S) = ∫₀ˢ P(s) ds = ⅓ · S³ cost to mint: ΔR = ⅓·(S + n)³ − ⅓·S³ (to add n new tokens)Because a buyer pays the integral rather than the final spot price, a large order pays a progressively higher average price as it climbs the curve. Each curve therefore has a characteristic reserve ratio — the share of the token's notional market capitalisation actually held as collateral: reserveRatio = reserveBalance / (price × supply)A linear curve P(S) = m·S has a reserve ratio of ½; the quadratic curve above has ⅓. The Bancor protocol (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) generalises this by holding the reserve ratio (its "connector weight") constant, giving the widely reused Bancor formula (https://github.com/AragonBlack/fundraising/blob/master/docs/components/bonding-curve.md) : price = reserveBalance / (supply × reserveRatio) purchaseReturn = supply × ((1 + reserveAdded / reserveBalance) ^ reserveRatio − 1) saleReturn = reserveBalance × (1 − (1 − tokensSold / supply) ^ (1 / reserveRatio))A reserve ratio between 0% and 100% tunes the curve's steepness: 100% gives a flat, fully-collateralised price (a stable peg), while smaller ratios produce steeper curves that reward early buyers more. Caper's curve, P(s) = K · √s / (1 − s) in the circulating fraction s, is a steep variant: the price is zero at genesis (so there is no sniper floor) and rises to a pole as the float approaches the full supply.

Curve shapes The choice of function shapes a token's incentives. Common forms, catalogued by BonDeFi (https://medium.com/@bondefi/bonding-curves-anti-snipe-1cf47220d3bc) and others (https://yos.io/2018/11/10/bonding-curves/) , include: - Linear — P = m·S + b. Constant-rate price growth; simple and predictable. - Polynomial / quadratic — e.g. P = S². Faster appreciation that rewards early participants. - Exponential — P = a·e^(b·S). Steep, speculative growth. - Sigmoid / logarithmic — S-shaped or flattening curves that model adoption slowing as supply matures, damping late-stage volatility. A contract may also use separate buy and sell curves; the gap between them forms a bid–ask spread that can fund the protocol or reward long-term holders. Caper instead uses a single curve in both directions — a flat trade fee, not a curve spread, funds each caper's treasury. Choosing a curve's exponents and constants is a parametrization problem in its own right — see Bonding Curves In Depth: Intuition & Parametrization (https://blog.relevant.community/bonding-curves-in-depth-intuition-parametrization-d3905a681e0a) and On Single Bonding Curves for Continuous Token Models (https://medium.com/thoughtchains/on-single-bonding-curves-for-continuous-token-models-a167f5ffef89) for the design trade-offs, and Dynamic Token Bonding Curves (https://tokeneconomy.co/dynamic-token-bonding-curves-41d36e43befa) for curves whose parameters adjust over time.

History The continuous-token idea entered crypto with the Bancor protocol (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) (2017), whose "smart tokens" used a constant reserve ratio to stay continuously convertible into their reserve. Later that year Simon de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) published "Tokens 2.0: Curved Token Bonding in Curation Markets" (21 November 2017), framing curved bonding as the pricing engine for curation markets — markets that "reduce information asymmetry through the use of tokenized signals." He credits the Zap team with coining the term "bonding curves." In 2018 Thibauld Favre (https://hackernoon.com/introducing-continuous-organizations-22ad9d1f63b7) introduced Continuous Organizations, using a Decentralized Autonomous Trust (DAT) and a bonding curve to mint and burn "FAIR" tokens that represent claims on an organisation's future cash flows — giving projects continuous fundraising and guaranteed liquidity instead of a one-off sale. Caper is a direct descendant of this model: an organisation whose token lives on a permanent curve. Around 2019–2020 the Commons Stack (https://commonsstack.org/) , with research firm BlockScience, generalised the design into the augmented bonding curve (https://blog.giveth.io/deep-dive-augmented-bonding-curves-3f1f7c1fa751) , which diverts a share of every purchase into a "common pool" to fund public goods — the same shape as Caper's 1/31 Caper Commons slice. The underlying theory frames a bonding curve as an economic estimator of a token's value ( Zargham, Paruch & Shorish (https://epub.wu.ac.at/7433/1/zargham_paruch_shorish.pdf) ).

Relationship to automated market makers Bonding curves and automated market makers (AMMs) are close cousins. A single-reserve bonding curve is effectively a one-sided AMM that mints and burns the token itself, whereas a constant-function AMM such as Uniswap (https://docs.uniswap.org/concepts/protocol/concentrated-liquidity) prices two pre-existing assets against each other along an invariant — the constant-product rule x · y = k. Bancor's price = reserveBalance / (supply × reserveRatio) is the bonding-curve generalisation of that idea. A common claim is that bonding curves have "zero slippage." That is imprecise. Because a purchase pays the area under the curve between the old and new supply, a large order still pays a progressively higher average price — a price impact functionally like slippage, which is exactly why Caper's Trading (/wiki/markets/trading) guide notes that "slippage is implicit in the curve shape." The genuine distinction is that this impact is fully deterministic: it depends only on the trade size and the fixed curve, not on the fluctuating ratio of two pooled assets, and the curve can never run out of the token it mints. Liquidity is always available and its price impact is knowable in advance — but it is not literally free of price impact.

Applications - Automated market making. Continuous, reserve-backed pricing underpins Bancor's smart tokens (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) and the broader family of on-chain AMMs. - Curation markets. Bonding curves let participants stake on the quality or relevance of information, rewarding early curators as a signal gains support ( de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) ). - Continuous organizations & DAOs. A curve becomes a permanent primary market for a governance or revenue token, replacing fixed sales with continuous fundraising and guaranteed exit liquidity (https://hackernoon.com/introducing-continuous-organizations-22ad9d1f63b7) — the pattern Caper is built on. - Public-goods funding. Augmented bonding curves (https://blog.giveth.io/deep-dive-augmented-bonding-curves-3f1f7c1fa751) route part of each buy into a common pool, turning token demand into a funding stream for open-source and charitable work. - Token launchpads. On Radix, BonDeFi (https://medium.com/@bondefi/bonding-curves-anti-snipe-1cf47220d3bc) uses a batched bonding curve to launch tokens fairly; on Solana, Pump.fun (https://www.solflare.com/ecosystem/pump-fun-where-memes-meet-markets-on-solana/) popularised the "fair launch," pricing a token up the curve as buyers arrive before migrating it to a DEX.

Risks and criticisms - Front-running / MEV. Because price depends only on supply, an adversary who sees a pending buy can buy first and sell into it. Both Balasanov (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) and Riady (https://yos.io/2018/11/10/bonding-curves/) flag bonding curves as "susceptible to front-running attacks"; batched curves and ordering protections aim to mitigate it. - Reflexivity and volatility. Tying price to supply creates a feedback loop — buying raises the price, which attracts more buying. Steep curves amplify this into pump-and-dump dynamics where a rush to exit can collapse the price as fast as it rose. - Market cap is not collateral. Because the reserve is the area under the curve, a token's notional market capitalisation (price × supply) is typically several times the reserve backing it. Every holder can still redeem along the curve, but the headline "value" is reflexive and can evaporate under mass selling. - Parameter and composition risk. The wrong curve shape or reserve ratio can make a token too volatile or too illiquid, and deeply nested curves (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) (a curve collateralised by another curved token) compound reserve ratios and magnify risk.

Further reading - Tokens 2.0: Curved Token Bonding in Curation Markets — Simon de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) - How to Make Bonding Curves for Continuous Token Models — Slava Balasanov (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) - Bonding Curves Explained — Yos Riady (https://yos.io/2018/11/10/bonding-curves/) - Bonding Curve component docs — Aragon Fundraising (https://github.com/AragonBlack/fundraising/blob/master/docs/components/bonding-curve.md) - Introducing Continuous Organizations — Thibauld Favre (https://hackernoon.com/introducing-continuous-organizations-22ad9d1f63b7) - Deep Dive: Augmented Bonding Curves — Commons Stack / Giveth (https://blog.giveth.io/deep-dive-augmented-bonding-curves-3f1f7c1fa751) - Bonding Curves & Anti-Snipe — BonDeFi (https://medium.com/@bondefi/bonding-curves-anti-snipe-1cf47220d3bc) - Bonding Curves In Depth: Intuition & Parametrization — Relevant Community (https://blog.relevant.community/bonding-curves-in-depth-intuition-parametrization-d3905a681e0a) - On Single Bonding Curves for Continuous Token Models — thoughtchains (https://medium.com/thoughtchains/on-single-bonding-curves-for-continuous-token-models-a167f5ffef89) - Token Bonding Curves in Practice — Token Economy (https://tokeneconomy.co/token-bonding-curves-in-practice-3eb904720cb8) - Dynamic Token Bonding Curves — Token Economy (https://tokeneconomy.co/dynamic-token-bonding-curves-41d36e43befa) - Economic Games as Estimators — Zargham, Paruch & Shorish (BlockScience) (https://epub.wu.ac.at/7433/1/zargham_paruch_shorish.pdf)

Type Perpetual AMM (continuous token model) Price Monotonic in circulating fraction Per-buy slice 30/31 founder · 1/31 Caper Commons Coined 2017 — Simon de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) / Zap, on Bancor (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) Also powers Curation markets · continuous organizations · AMMs Related Trading (/wiki/markets/trading) , Raising funds (/wiki/markets/raising-funds)

A bonding curve is a smart contract that sets a token's price as a mathematical function of its circulating supply: it mints new tokens when buyers arrive and burns them when holders sell, so a market is always open without an order book or a matching counterparty. Caper uses one as the permanent, built-in market for every caper's governance token. This page covers Caper's implementation first, then the wider idea it descends from. Caper's curve The curve is a perpetual AMM whose price is a smooth, monotonically increasing function of the fraction of supply in circulation. Price starts at zero with nothing sold and goes asymptotic as circulation approaches the full 100bn. Buying moves XRD into the curve vault and tokens out of the inventory vault; selling reverses both. The cumulative XRD held by the curve has a closed-form integral, so sells price out exactly; buys solve for the new circulation numerically. On every buy, an additional small slice of the buyer's curve-derived tokens is taken from the inventory vault and split: - 30/31 goes to the founder vault. - 1/31 goes to the Caper Commons — the protocol-wide treasury, denominated in $CAPER. Founder and Commons rewards scale with curve activity rather than being front-loaded. For vampire capers (bound to an origin token) this slice is forced to zero — the founder's bootstrap is the migration vault populated when origin holders migrate. See Trading (/wiki/markets/trading) for the buy/sell panel and Raising funds (/wiki/markets/raising-funds) for how the proceeds are deployed.

How bonding curves work More generally, a bonding-curve contract holds a reserve (or collateral) pool of a base asset — XRD on Radix, historically ETH on Ethereum — and issues its own token against it: - Buying / minting. A buyer deposits reserve assets; the contract mints new tokens, adds the deposit to the reserve, and the spot price rises because supply has increased. - Selling / burning. A seller returns tokens; the contract burns them, releases the corresponding reserve, and the spot price falls. The result is what Yos Riady (https://yos.io/2018/11/10/bonding-curves/) calls a continuous token: it has a deterministic price (set by the formula, not negotiation), a continuous price (token n+1 always costs more than token n), and instant liquidity (any amount can be bought or sold at any time). Deposited funds stay locked in the contract, so the token is always backed by collateral that can be reclaimed by burning — the same property that lets every caper holder cash out (/wiki/markets/trading) at any time.

The mathematics Two quantities are easy to confuse. The bonding curve itself, P(S), gives the spot price of the next token at supply S. The reserve held by the contract — and therefore the cost of a finite purchase — is the area under that curve, its integral. As Slava Balasanov (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) illustrates with a simple quadratic curve: spot price: P(S) = S² reserve: R(S) = ∫₀ˢ P(s) ds = ⅓ · S³ cost to mint: ΔR = ⅓·(S + n)³ − ⅓·S³ (to add n new tokens)Because a buyer pays the integral rather than the final spot price, a large order pays a progressively higher average price as it climbs the curve. Each curve therefore has a characteristic reserve ratio — the share of the token's notional market capitalisation actually held as collateral: reserveRatio = reserveBalance / (price × supply)A linear curve P(S) = m·S has a reserve ratio of ½; the quadratic curve above has ⅓. The Bancor protocol (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) generalises this by holding the reserve ratio (its "connector weight") constant, giving the widely reused Bancor formula (https://github.com/AragonBlack/fundraising/blob/master/docs/components/bonding-curve.md) : price = reserveBalance / (supply × reserveRatio) purchaseReturn = supply × ((1 + reserveAdded / reserveBalance) ^ reserveRatio − 1) saleReturn = reserveBalance × (1 − (1 − tokensSold / supply) ^ (1 / reserveRatio))A reserve ratio between 0% and 100% tunes the curve's steepness: 100% gives a flat, fully-collateralised price (a stable peg), while smaller ratios produce steeper curves that reward early buyers more. Caper's curve, P(s) = K · √s / (1 − s) in the circulating fraction s, is a steep variant: the price is zero at genesis (so there is no sniper floor) and rises to a pole as the float approaches the full supply.

Curve shapes The choice of function shapes a token's incentives. Common forms, catalogued by BonDeFi (https://medium.com/@bondefi/bonding-curves-anti-snipe-1cf47220d3bc) and others (https://yos.io/2018/11/10/bonding-curves/) , include: - Linear — P = m·S + b. Constant-rate price growth; simple and predictable. - Polynomial / quadratic — e.g. P = S². Faster appreciation that rewards early participants. - Exponential — P = a·e^(b·S). Steep, speculative growth. - Sigmoid / logarithmic — S-shaped or flattening curves that model adoption slowing as supply matures, damping late-stage volatility. A contract may also use separate buy and sell curves; the gap between them forms a bid–ask spread that can fund the protocol or reward long-term holders. Caper instead uses a single curve in both directions — a flat trade fee, not a curve spread, funds each caper's treasury.

History The continuous-token idea entered crypto with the Bancor protocol (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) (2017), whose "smart tokens" used a constant reserve ratio to stay continuously convertible into their reserve. Later that year Simon de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) published "Tokens 2.0: Curved Token Bonding in Curation Markets" (21 November 2017), framing curved bonding as the pricing engine for curation markets — markets that "reduce information asymmetry through the use of tokenized signals." He credits the Zap team with coining the term "bonding curves." In 2018 Thibauld Favre (https://hackernoon.com/introducing-continuous-organizations-22ad9d1f63b7) introduced Continuous Organizations, using a Decentralized Autonomous Trust (DAT) and a bonding curve to mint and burn "FAIR" tokens that represent claims on an organisation's future cash flows — giving projects continuous fundraising and guaranteed liquidity instead of a one-off sale. Caper is a direct descendant of this model: an organisation whose token lives on a permanent curve. Around 2019–2020 the Commons Stack (https://commonsstack.org/) , with research firm BlockScience, generalised the design into the augmented bonding curve (https://blog.giveth.io/deep-dive-augmented-bonding-curves-3f1f7c1fa751) , which diverts a share of every purchase into a "common pool" to fund public goods — the same shape as Caper's 1/31 Caper Commons slice.

Relationship to automated market makers Bonding curves and automated market makers (AMMs) are close cousins. A single-reserve bonding curve is effectively a one-sided AMM that mints and burns the token itself, whereas a constant-function AMM such as Uniswap (https://docs.uniswap.org/concepts/protocol/concentrated-liquidity) prices two pre-existing assets against each other along an invariant — the constant-product rule x · y = k. Bancor's price = reserveBalance / (supply × reserveRatio) is the bonding-curve generalisation of that idea. A common claim is that bonding curves have "zero slippage." That is imprecise. Because a purchase pays the area under the curve between the old and new supply, a large order still pays a progressively higher average price — a price impact functionally like slippage, which is exactly why Caper's Trading (/wiki/markets/trading) guide notes that "slippage is implicit in the curve shape." The genuine distinction is that this impact is fully deterministic: it depends only on the trade size and the fixed curve, not on the fluctuating ratio of two pooled assets, and the curve can never run out of the token it mints. Liquidity is always available and its price impact is knowable in advance — but it is not literally free of price impact.

Applications - Automated market making. Continuous, reserve-backed pricing underpins Bancor's smart tokens (https://medium.com/@simondlr/bancors-smart-tokens-vs-token-bonding-curves-a4f0cdfd3388) and the broader family of on-chain AMMs. - Curation markets. Bonding curves let participants stake on the quality or relevance of information, rewarding early curators as a signal gains support ( de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) ). - Continuous organizations & DAOs. A curve becomes a permanent primary market for a governance or revenue token, replacing fixed sales with continuous fundraising and guaranteed exit liquidity (https://hackernoon.com/introducing-continuous-organizations-22ad9d1f63b7) — the pattern Caper is built on. - Public-goods funding. Augmented bonding curves (https://blog.giveth.io/deep-dive-augmented-bonding-curves-3f1f7c1fa751) route part of each buy into a common pool, turning token demand into a funding stream for open-source and charitable work. - Token launchpads. On Radix, BonDeFi (https://medium.com/@bondefi/bonding-curves-anti-snipe-1cf47220d3bc) uses a batched bonding curve to launch tokens fairly; on Solana, Pump.fun (https://www.solflare.com/ecosystem/pump-fun-where-memes-meet-markets-on-solana/) popularised the "fair launch," pricing a token up the curve as buyers arrive before migrating it to a DEX.

Risks and criticisms - Front-running / MEV. Because price depends only on supply, an adversary who sees a pending buy can buy first and sell into it. Both Balasanov (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) and Riady (https://yos.io/2018/11/10/bonding-curves/) flag bonding curves as "susceptible to front-running attacks"; batched curves and ordering protections aim to mitigate it. - Reflexivity and volatility. Tying price to supply creates a feedback loop — buying raises the price, which attracts more buying. Steep curves amplify this into pump-and-dump dynamics where a rush to exit can collapse the price as fast as it rose. - Market cap is not collateral. Because the reserve is the area under the curve, a token's notional market capitalisation (price × supply) is typically several times the reserve backing it. Every holder can still redeem along the curve, but the headline "value" is reflexive and can evaporate under mass selling. - Parameter and composition risk. The wrong curve shape or reserve ratio can make a token too volatile or too illiquid, and deeply nested curves (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) (a curve collateralised by another curved token) compound reserve ratios and magnify risk.

Further reading - Tokens 2.0: Curved Token Bonding in Curation Markets — Simon de la Rouviere (https://medium.com/@simondlr/tokens-2-0-curved-token-bonding-in-curation-markets-1764a2e0bee5) - How to Make Bonding Curves for Continuous Token Models — Slava Balasanov (https://medium.com/relevant-community/how-to-make-bonding-curves-for-continuous-token-models-3784653f8b17) - Bonding Curves Explained — Yos Riady (https://yos.io/2018/11/10/bonding-curves/) - Bonding Curve component docs — Aragon Fundraising (https://github.com/AragonBlack/fundraising/blob/master/docs/components/bonding-curve.md) - Introducing Continuous Organizations — Thibauld Favre (https://hackernoon.com/introducing-continuous-organizations-22ad9d1f63b7) - Deep Dive: Augmented Bonding Curves — Commons Stack / Giveth (https://blog.giveth.io/deep-dive-augmented-bonding-curves-3f1f7c1fa751) - Bonding Curves & Anti-Snipe — BonDeFi (https://medium.com/@bondefi/bonding-curves-anti-snipe-1cf47220d3bc)