Solution Evaluation · Fee Layer

CIP-0082 — Improved Rewards Scheme

Margin swap + k-raises — inverts viability, regenerates 2020

CIP-0082 · Improved Rewards Scheme Parameters · 2022 · Tobias Fancee · 4-stage package · stage 2 hard fork required · No-go as a standalone — stage 2 inverts operator revenue, stages 3–4 fire in the wrong regime

official page · forum thread · stage 1 (minPoolCost 340 → 170) complete on mainnet at epoch 445 (2023/10/27)

CIP-0082 is the most ambitious of the four CIPs — a four-stage package touching three layers of the reward pipeline at once. Stage 1 (minPoolCost 340 → 170) is already retired on mainnet; the live content is stages 2–4: delete minPoolCost entirely and add minPoolRate = 3 % (stage 2, hard fork), then raise k: 500 → 750 → 1000 six epochs later (stages 3–4, parameter changes). The package targets the same diagnostic findings as CIP-0023 (OPE.O1.F4 hyperbola, OPE.O6.F1 operator-fleet asymmetry) plus the entity-level concentration POL.O5.F1 documents at the upper tail.

CIP-0082 is the cleanest delegator-side fix in the bundle, suboptimal as a standalone — stage 2 inverts operator revenue across the viability line, and stages 3–4 fire in the wrong regime. The flat 3 % rate compresses delegator dispersion from 38× to 1.00× — a genuine win on the headline §3.3 yield-equalisation claim — but the equalisation is funded by a transfer from sub-reliable pool operators (−9× per pool) to saturated pool operators (+4× per pool), captured most heavily by the 11+ pool MPO bracket (+200 K ADA/yr per entity).

Three findings frame the verdict:

The package gets the right targets and the right layers — but stage 2's revenue inversion lands on the very population V2 §3.1 names as the foundational priority, and stages 3–4 fire before the precondition that would make them constructive.

Table of Contents

1. What CIP-0082 proposes

CIP-0082 is a four-stage package that reforms the reward-sharing scheme in sequence:

  1. Floor halvingminPoolCost: 340 → 170 ADA. Complete on mainnet at epoch 445 (2023/10/27).
  2. Margin swap — delete minPoolCost entirely; add minPoolRate = 3 %. The fixed-ADA fee becomes a flat proportional rate. Hard fork required.
  3. First pool-count expansionk: 500 → 750. Saturation cap shrinks from ~77 M ADA to ~51 M.
  4. Second pool-count expansionk: 750 → 1000. Saturation cap shrinks to ~38.5 M.

The author frames the package as a fairness-and-decentralisation reform.

Stage 2 is mechanically the same as CIP-0023's paired variant — reduce minPoolCost, add a margin floor — at an extreme calibration: cost taken to zero, rate set to 3 %. The author credits CIP-0023 explicitly: "minPoolRate was originally proposed in CIP-0023."

Stages 3–4 leave the fee formula alone but halve the saturation cap each time, redistributing reward pressure across the top of the distribution.

Live content of CIP-0082 as a governance item is therefore stages 2–4. Stage 1 is documentation.

2. The problem it tries to fix

The CIP attacks two layers of the reward pipeline at once.

Fee side (stage 2).

A 100 k ADA delegator on mainnet today faces an effective fee rate of about 27 % in a 2 M ADA pool versus 0.7 % in a saturated pool — a 38× dispersion driven almost entirely by the 170 ADA fixed-cost floor.

The author's headline claim: stage 2 collapses this to a flat 3 % everywhere. Fee-driven differences in delegator return disappear.

Saturation side (stages 3–4).

The current cap leaves room for at most 500 saturated pools. The multi-pool population already controls 76.7 % of productive stake across 449 productive pools.

The author's argument: doubling k to 1000 splits saturated pools, "gets stale delegations moving", and amplifies the pledge bonus by shrinking $z_0 = \text{Supply}/k$.

3. Verdict — three reasons it fails as a standalone

1. Stage 2 collapses delegator dispersion from 38× to 1.00× — and inverts operator revenue across the viability line.

The flat 3 % rate equalises delegator yield to 2.21 % across the productive range — a clean delivery on the headline §3.3 yield-equalisation claim. The funding mechanism is a revenue reallocation underneath: saturated pool operators rise from 12 410 to 52 560 ADA/yr (+4×), sub-reliable pool operators fall from 12 410 to 1 365 ADA/yr (−9×). On the n-MPO axis the spread widens to a +200 K vs −11 K ADA/yr gap between an 11+ pool fleet and a sub-reliable single-pool operator.

The delegator-side equalisation is funded by the small-pool tail and captured by the large-fleet top — the inverse of the V2 §3.1 operator-viability target.Margin-swap revenue inversion

2. Stages 3–4 fire in the wrong regime — new slots feed the existing fleet.

The 2020 k: 150 → 500 raise produced today's multi-pool landscape (POL.O5.F1: 83 entities, 449 productive pools, 76.7 % of productive stake). CIP-0082 fires stages 3–4 just 6 epochs after stage 2 — no window to negotiate, vote, and activate a stake-cap layer in between — into the same weak-pledge regime, with the same near-zero registration cost (~500 ADA per pool) and the same near-horizontal MPO infrastructure. The new slots get absorbed by the existing fleet, not by new entrants.

The deconcentration target fails by re-running the script that created the current concentration.k-raises in the wrong regime

3. Stage 2 is the same primitive as CIP-0023, scaled up — voting both is incoherent.

Both stage 2 and CIP-0023's paired variant add a margin floor on top of a reduced minPoolCost; CIP-0082 takes the cost to zero and the rate to 3 %, CIP-0023 paired stops at 50 ADA and 1.5 %. The structural critique transfers one-for-one: operator revenue inverts across the viability line, with magnitudes roughly 2× larger on the pool axis and 4× larger on the n-MPO axis than CIP-0023's.

The coherent governance choice is stage 2 alone, deprecating CIP-0023 — the CIP-0082 author already credits the predecessor: "minPoolRate was originally proposed in CIP-0023."

The remainder of the document walks the package in three steps: §4 quantifies what each of the four stages does on mainnet today (delegator ROS, per-pool operator revenue, per-entity operator revenue by n-MPO bracket); Appendix A unpacks the four-stage formula change and re-runs the CIP's own 2022 calibration at today's parameters; Appendix B documents the per-finding evidence with verdict tags, with §B.3 providing the standalone k-lever deep dive that supports the verdict on stages 3–4.

4. What it does to mainnet today

The Margin swap (stage 2) acts on two axes at once and in opposite directions: delegator yield equalises at 2.21 %; operator revenue redistributes from small pools to large.

Delegator net ROS — flat across the productive range (today vs each stage):

Canonical tier Rep. σ Today Stage 2 — Margin swap Stage 3 — k → 750 Stage 4 — k → 1000
Dormant (50 K) 50 K 0 % 2.21 % 2.21 % 2.21 %
Sub-reliable (2 M) 2 M 1.65 % 2.21 % 2.21 % 2.21 %
Healthy (15 M) 15 M 2.19 % 2.21 % 2.21 % 2.21 %
Saturated (77 M) 77 M 2.26 % 2.21 % 1.47 % (now above $z_0$) 1.10 %

Table 4.1 — Delegator net ROS by tier across stages. The Margin swap rescues Dormant / Sub-block / Sub-reliable from the fee-consumption trap; stages 3–4 then degrade the top of the distribution by halving the saturation cap.

Operator annualised revenue — inverts across the viability line:

Canonical tier Rep. σ Today Stage 2 — Margin swap Δ Margin swap
Sub-reliable (2 M) 2 M 12 410 ADA/yr 1 365 −9×
Healthy (15 M) 15 M 12 410 10 242 −1.2×
Saturated (77 M) 77 M 12 410 52 560 +4×

Table 4.2 — Per-pool operator revenue by tier under the Margin swap. The flat 12 410 ADA/yr ceiling under today's minPoolCost = 170 is replaced by a stake-proportional take that inverts revenue at the viability line.

Operator revenue by fleet bracket — the transfer compounds with fleet size:

Reading aid — the n-MPO axis. n = number of pools the same entity runs. n = 1 means a single-pool operator; n ≥ 11 means an entity controlling 11 or more pools. The bracket measures how a reform's revenue impact compounds with fleet size.

n-MPO bracket Today Margin swap Δ per entity per year
Single-pool — Sub-reliable (< 3 M) 24 820 ADA/yr 13 644 −11 176
2-pool MPO 24 820 52 195 +27 375
6–10 pool MPO 92 319 179 599 +87 280
11+ pool MPO 239 387 439 850 +200 463

Table 4.3 — Per-entity revenue Δ by n-MPO bracket. A sub-reliable single-pool operator loses 11 K ADA/yr; an 11+ pool MPO entity gains 200 K. The amplification is mechanical — the proportional margin scales with both pool size and pool count.

In summary:

Without a stake-cap layer between stage 2 and stage 3, the new pool slots feed the existing multi-pool fleet.

5. Read more

Appendix A — Mechanism in detail

This appendix gives the four stages, the formula change at stage 2, the CIP's own worked calibration (epoch 385), and the updated calibration at current mainnet parameters. The opener summarises the conclusions; this appendix carries the derivations.

A.1. The four stages

CIP-0082 sequences four on-chain actions. Each has a distinct mechanical role:

# Stage name Action What it does mechanically Mainnet status
1 Floor halving minPoolCost: 340 → 170 ADA (parameter update) Halves the flat per-pool fee. First-order relief on the $1/\sigma$ hyperbola without changing the fee shape — every pool still owes a fixed ADA amount Complete on mainnet — Conway-era parameter-change action at epoch 445 (2023/10/27)
2 Margin swap Delete minPoolCost; add minPoolRate = 3 % (hard fork + ledger-rule change) Replaces the flat-ADA floor with a size-proportional floor via $poolRateEff = \max(poolRate, minPoolRate)$. The effective fee rate becomes constant at 3 % across every pool size. This is CIP-0023's paired variant at harsher calibration Pending HFC
3 First pool-count expansion k: 500 → 750 (parameter update) Shrinks saturation from $z_0 \approx 77$ M ADA to $\approx 51$ M ADA. Author's stated goal: "get stale delegations moving" by oversaturating large pools and amplifying the pledge benefit via $a_0$ on the reward curve Pending
4 Second pool-count expansion k: 750 → 1000 (parameter update) Further shrinks saturation to $\approx 38.5$ M ADA. Completes the concentration-relief programme: every current Large-healthy pool is reclassified as Near-saturation or beyond at the new cap Pending

Table A.1 — The four stages of CIP-0082. Stage 1 is mainnet-complete.

Per-stage role in one line each. Stage 1 shrinks the flat floor. Stage 2 replaces it. Stages 3 and 4 fragment the top of the distribution that the replaced floor was protecting — making them coherent only if the underlying pledge signal is simultaneously restored by a stake-cap layer (see Appendix B.2).

A.2. Stage-2 formula

Post-hard-fork pool-fee calculation (replacing the prior minPoolCost + poolRate × (R − minPoolCost) shape):

$$\text{take}(\sigma) = poolRateEff_{i} \times R_{\text{pool}}(\sigma), \qquad poolRateEff_{i} = \max(poolRate_{i},\ minPoolRate)$$

With minPoolCost removed, the fixed-per-pool component vanishes entirely. Stages 3–4 leave the fee formula unchanged and modify only $k$ (and therefore $z_0 = \text{Supply}/k$).

Design surface.

Property Value
New parameters minPoolRate (= 0.03), poolRateEff (derived)
Deleted parameters minPoolCost (at stage 2)
Changed parameters stakePoolTargetNum (500 → 750 → 1000 across stages 3–4)
Hard fork required Stage 2 only
Re-registration Not required — poolRateEff derived in ledger reward calc
Layer Fee (stages 1–2) + transversal (stages 3–4)
Reward curve shape Untouched
Pledge mechanics Untouched (amplified indirectly by k via $z_0$ shrinkage)

Table A.2 — Design surface of CIP-0082.

A.3. The CIP's epoch-385 worked calibration

The CIP's own 2022 worked example. Hollow pools (declared poolRate ≈ 0, minimum fees; total rewards ≈ 31.2 M ADA/epoch, saturation 64 M ADA at $k = 500$):

Pool Stake Pledge Current Stage 1 — Floor halving Stage 2 — Margin swap Stage 3 — k → 750 Stage 4 — k → 1000
Sybil 100 K ADA 100 K below viability below viability 1.52 ADA/ep, ROS 3.66 % 1.52 ADA/ep, ROS 3.66 % 1.52 ADA/ep, ROS 3.66 %
Sybil 1 M ADA 1 M 340 ADA/ep, ROS 1.23 % 170 ADA/ep, ROS 2.50 % 15.24 ADA/ep, ROS 3.66 % 15.24 ADA/ep, ROS 3.66 % 15.24 ADA/ep, ROS 3.66 %
Community 10 M ADA 100 K 340 ADA/ep, ROS 3.52 % 170 ADA/ep, ROS 3.65 % 152.4 ADA/ep, ROS 3.66 % 152.5 ADA/ep, ROS 3.66 % 152.5 ADA/ep, ROS 3.66 %
Community Saturated 1 M 340 ADA/ep, ROS 3.76 % 170 ADA/ep, ROS 3.77 % 1081 ADA/ep, ROS 3.68 % 720 ADA/ep, ROS 3.69 % 543 ADA/ep, ROS 3.69 %

Table A.3 — The CIP's own epoch-385 four-pool calibration across stages.

Headline figures (author's own). Three summary metrics distilling each stage's effect on the delegator side:

Headline Current Stage 1 — Floor halving Stage 2 — Margin swap Stage 3 — k → 750 Stage 4 — k → 1000
Viability point (pledge) ~670 K ADA ~335 K ADA 1 ADA 1 ADA 1 ADA
Competitive point (pledge) ~20 M ADA ~16.5 M ADA 1 ADA 1 ADA 1 ADA
Delegator ROS dispersion (100 K pool → saturated) 2.53 pp 1.28 pp 0.016 pp 0.024 pp 0.031 pp

Table A.4 — Delegator-side headline metrics across stages. The Margin swap collapses the dispersion ~160×; the k-raises let it drift back up to 0.031 pp because pledge differentiation activates more strongly as $z_0$ shrinks (intended).

The dispersion drift back up at stages 3–4 is the intended effect: the author states the k-raises are there to "increase the effect of the pledge benefit on rewards". The 0.016 → 0.031 pp drift is pledge differentiation activating more strongly, by design. The fee-regressivity component stays at zero throughout.

A.4. Updated calibration at current parameters (epoch 623)

Stage 1 is retired (mainnet minPoolCost = 170). Stages 2–4 are the forward-looking content. Calibration uses today's parameters: $z_0 = 77$ M ADA at $k = 500$, hollow-pool yield at saturation ≈ 2.275 %/yr (≈ 24 000 ADA/epoch at saturation), $a_0 = 0.3$, total reward pot $P \approx 12$ M ADA/epoch.

Saturation cap per stage:

Stage $k$ $z_0 = \text{Supply}/k$ Saturation-pinned reward $P/k$
Current / Margin swap 500 ~77 M ADA 24 000 ADA/ep
Stage 3 — k → 750 750 ~51.3 M ADA 16 000 ADA/ep
Stage 4 — k → 1000 1000 ~38.5 M ADA 12 000 ADA/ep

Table A.5 — Saturation cap and saturation-pinned per-pool reward at each stage.

Below saturation, per-ADA gross yield is constant at ≈ 2.275 %/yr regardless of σ or $k$. Above saturation the per-pool reward caps at $P/k$ — so every k-raise halves the effective reward-per-ADA for pools stranded above the new cap.

Delegator net ROS across the canonical nine-tier taxonomy (the diagnostic groups pools by stake size into nine canonical tiers from Dormant (~50 K) to Oversaturated; full definitions in pools-distribution §4.1.3):

Canonical tier Rep. σ Current (minPoolCost = 170) Stage 2 — Margin swap Stage 3 — k → 750 Stage 4 — k → 1000
Dormant 50 K 0 % (fee consumes pool) 2.21 % 2.21 % 2.21 %
Sub-block 500 K 0 % (fee consumes pool) 2.21 % 2.21 % 2.21 %
Sub-reliable 2 M 1.65 % 2.21 % 2.21 % 2.21 %
Healthy 15 M 2.19 % 2.21 % 2.21 % 2.21 %
Large healthy 50 M 2.25 % 2.21 % 2.21 % (still ≤ $z_0$) 1.70 % (now above $z_0$)
Near-saturation 67 M 2.26 % 2.21 % 1.69 % (now above $z_0$) 1.27 %
Saturated 77 M 2.26 % 2.21 % 1.47 % 1.10 %
Oversaturated 85 M 2.05 % 2.00 % 1.33 % 1.00 %

Table A.6 — Delegator net ROS by tier across stages at current mainnet parameters.

Per-pool operator annualised revenue (operator take × 73 epochs/yr, hollow pool):

Canonical tier Rep. σ Current (minPoolCost = 170) Stage 2 — Margin swap Stage 3 — k → 750 Stage 4 — k → 1000
Dormant 50 K 1 139 (pool absorbed) 34 34 34
Sub-block 500 K 11 373 (pool absorbed) 341 341 341
Sub-reliable 2 M 12 410 1 365 1 365 1 365
Healthy 15 M 12 410 10 242 10 242 10 242
Large healthy 50 M 12 410 34 128 34 128 (≤ $z_0$) 26 280 (above new $z_0$)
Near-saturation 67 M 12 410 45 735 35 040 (above new $z_0$) 26 280
Saturated 77 M 12 410 52 560 35 040 26 280
Oversaturated 85 M 12 410 52 560 35 040 26 280

Table A.7 — Per-pool operator annualised revenue by tier across stages.

Today's flat minPoolCost = 170 ADA caps every productive pool's operator revenue at 12 410 ADA/yr — the signature of the no-competitive-wage finding.

The Margin swap replaces that flat cap with a proportional share of the pool reward:

The operator-revenue curve inverts across the viability line. The delegator-side equalisation is funded by a transfer up the operator distribution.

What stages 3–4 do on top.

The pool-count expansions then compress operator revenue at the top of the distribution as $P/k$ shrinks: 52 560 → 35 040 → 26 280 ADA/yr at saturation.

Sub-reliable, Sub-block, and Dormant tiers are left at their Margin-swap values. Stages 3–4 do not help the small-pool tail at all — they redistribute revenue among large pools only.

Per-entity revenue by n-MPO bracket (sums per-pool take across the operator's pools using mean pools/entity and mean pool stake from operator-delegator §4.4, retail hollow segment, epoch 623; 73 epochs/yr):

n-MPO bracket Entities Pools/entity Mean stake/pool Current Margin swap Δ (Margin swap − Today) k → 750 k → 1000
2-pool MPO 17 2.00 38.24 M 24 820 52 195 +27 375 52 195 52 195
3–5 pool MPO 24 3.92 29.47 M 48 653 78 846 +30 193 78 846 78 846
6–10 pool MPO 9 7.44 35.37 M 92 319 179 599 +87 280 179 599 179 599
11+ pool MPO 7 19.29 33.41 M 239 387 439 850 +200 463 439 850 439 850

Table A.8 — Per-entity Δ by n-MPO bracket. The 11+ MPO bracket gains +200 K ADA/yr; the bracket-to-bracket amplification is 7.3× from 2-pool to 11+-pool.

At each bracket's mean pool stake, pools stay below $z_0$ at every k-raise. The pool-count expansions therefore do not erode multi-pool entity revenue — the Margin-swap uplift is preserved through all later stages.

The revenue trimming at the top of the nine-tier table applies to individual high-stake pools, not to the mean multi-pool fleet.

Appendix B — Findings

Two cards organise the analysis: the operator-revenue inversion driven by the Margin swap (S1), and the wrong-regime firing of the k-raises in stages 3–4 (S2).

Stage 2 is CIP-0023 paired, scaled up.

The Margin swap is mechanically the same instrument as CIP-0023's paired variant — reduce minPoolCost, add a margin floor — at a more extreme calibration:

The structural effect is the same: delegator dispersion collapses, operator revenue inverts across the viability line. The magnitudes here are roughly doubled on both sides.

Two reference tables anchor the cards below.

Pool-axis Δ across the canonical nine tiers (declared margin ≈ 0; column "Δ CIP-0023 paired" carries the CIP-0023 numbers for reference):

Canonical tier Rep. σ $R(\sigma)$ ₳/ep Current take (post-Floor-halving) Margin-swap take (3 % × R) Δ per pool, Margin swap Δ per pool, CIP-0023 paired
Dormant 50 K 15.6 15.6 0.47 −15.1 0
Sub-block 500 K 155.8 155.8 4.67 −151.1 −104.2
Sub-reliable 2 M 623 170 18.7 −151.3 −111.4
Healthy 15 M 4 675 170 140.3 −29.7 −50.6
Large healthy 50 M 15 584 170 467.5 +297.5 +113.0
Near-saturation 67 M 20 883 170 626.5 +456.5 +192.5
Saturated 77 M 24 000 170 720.0 +550.0 +239.3

Table B.2 — Per-pool Δ across the nine canonical tiers under the Margin swap, with CIP-0023 paired Δ for reference. Magnitudes are 2.0–2.5× larger on both sides of the viability line.

Sub-block pools were untouched by CIP-0023 standalone but lose −151 ADA/ep here. The reason: minPoolCost is gone entirely, so every productive pool becomes a proportional-margin contributor — including the tiers that previously kept the full pool reward as the fixed fee.

Per-entity Δ by n-MPO bracket (column "Δ CIP-0023 paired" for reference):

n-MPO bracket Entities Pools/entity Mean stake/pool $R(\sigma)$ ₳/ep Δ per entity per year — Margin swap Δ per entity per year — CIP-0023 paired
Single-pool — Sub-reliable (< 3 M) 155 1 1.81 M 564 −11 176 ADA/yr −8 198 ADA/yr
Single-pool — Healthy (3–38.5 M) 214 1 11.40 M 3 554 −4 628 ADA/yr −4 920 ADA/yr
Single-pool — Large healthy (38.5–62 M) 29 1 50.69 M 15 798 +22 185 ADA/yr +8 483 ADA/yr
Single-pool — Near-saturation (62–77 M) 16 1 69.38 M 21 623 +34 945 ADA/yr +14 863 ADA/yr
2-pool MPO 17 2.00 38.24 M 11 918 +27 375 ADA/yr +8 468 ADA/yr
3–5 pool MPO 24 3.92 29.47 M 9 183 +30 193 ADA/yr +4 865 ADA/yr
6–10 pool MPO 9 7.44 35.37 M 11 024 +87 280 ADA/yr +24 223 ADA/yr
11+ pool MPO 7 19.29 33.41 M 10 413 +200 463 ADA/yr +49 852 ADA/yr

Table B.3 — Per-entity Δ by n-MPO bracket. The transfer is ~4× larger than CIP-0023 paired on the operator-fleet axis (200 K vs 50 K ADA/yr for the 11+ pool MPO bracket).

Sub-reliable single-pool operators lose ~11 000 ADA/yr — roughly three months' operator cost floor stripped annually from the population the V2 §3.1 spec identifies as needing support.

The structural critique is the same as CIP-0023 paired, scaled up roughly 4×.

S1
Synthesis 01 · 3 findings

Margin swap inverts operator revenue across the viability line

3 findings

Delegator dispersion collapses, but the equalisation is funded by a transfer from small pool operators to large ones — with magnitudes roughly twice CIP-0023's. What looks like a clean delegator-side fix on the surface is a revenue reallocation underneath, and the reallocation runs the wrong way for V2's small-pool target.

Findings
  1. regresses#1S1.F2
    Per-pool operator revenue inverts across the viability line. Sub-reliable operators go from 12 410 to 1 365 ADA/yr (−9×); Saturated operators go from 12 410 to 52 560 ADA/yr (+4×). The CIP-0023 paired variant produces the same inversion with smaller magnitudes (~2× smaller each side). The delegator-side equalisation is funded by a transfer from small operators to large ones. See Table B.2 above for the per-tier breakdown.
  2. regresses#2S1.F3
    On the n-MPO fleet axis, the transfer compounds with fleet size. +27 K ADA/yr for a 2-pool MPO entity; +200 K ADA/yr for an 11+ pool MPO — a 7.3× bracket-to-bracket amplification. The transfer direction (up-distribution) is preserved through stages 3–4 because MPO mean pool stakes stay below $z_0$ at every k-raise. The Margin swap's delegator-side equalisation is funded primarily by the small-pool tail, and captured primarily by the large-fleet top. See Table B.3 above for the n-MPO breakdown.
  3. delivers#3S1.F1
    Delegator fee-rate dispersion collapses from 38× to 1.00×. Under the Margin swap, the net-ROS floor rises from 0 % / 1.65 % (Sub-reliable and below today) to 2.21 % (flat across the productive range). Direct delivery on the §3.3 delegator-yield claim — though the gain is concentrated in the tiers that currently attract the fewest delegators.

Stages 3–4 raise k from 500 → 750 → 1000 without changing the reward formula. The package-specific concern — that they fire six epochs after stage 2, in the regime the standalone analysis identifies as regressive — is captured in card S2 below. The deeper standalone analysis (what a k-raise does in isolation, why the amplified pledge bonus lands on no one, and why the bottom of the distribution is mechanically frozen) lives in §B.3 below.

S2
Synthesis 02 · 2 findings

k-raises fire in the wrong regime

2 findings

Stages 3–4 fire in the wrong regime — new pool slots get absorbed by the existing multi-pool fleet. With no stake-cap precondition between stage 2 and stage 3, and no redistribution back to small pools, the k-raises preserve the same regressive regime the standalone k-analysis warns against.

Findings
  1. regresses#1S2.F1
    No stake-cap precondition; k-raises fire in the regressive regime. CIP-0082 fires stages 3–4 6 epochs after the Margin swap — no stake-cap layer can be negotiated, voted, and activated in that window. The k-raise therefore fires in exactly the regime §B.3 below identifies as regressive: weak pledge, MPO-dominated fleet, empirically non-yield-following delegator base. CIP-0082 does not embed the precondition the lever needs to flip from regressive to constructive (an active stake-cap layer — CIP-0050's L or CIP-0037's dynamic saturation).
  2. regresses#2S2.F2
    Stages 3–4 do not redistribute back to the small-pool tail. The k-raises only trim the top: per-pool reward at saturation drops from 24 K to 16 K to 12 K ADA/ep across stages 2 → 4. Sub-reliable, Sub-block, and Dormant tiers see no change — they were already at the Margin-swap floor. Stages 3–4 redistribute revenue among large pools only, not back to the population the CIP's primary V2 §3.1 claim says to protect.

What the package needs.

Either acquire a stake-cap layer between stage 2 and stage 3, or drop stages 3–4. Firing them in the proposed sequence preserves the same regressive regime the standalone k-analysis below warns against.

B.3. Standalone k-lever deep dive

The S2 card above is the CIP-0082-specific finding: stages 3–4 fire 6 epochs after stage 2, in the regime the standalone analysis calls regressive. This sub-appendix is the standalone analysis itself — what happens when only k moves and the reward formula stays fixed. The same analysis applies to any future k-recalibration proposal that does not arrive bundled with a fee-layer or stake-cap reform.

Bottom line. Raising k standalone is a regressive lever in today's weak-pledge regime — it compresses the top tail without redistributing, amplifies a pledge bonus no operator profile is positioned to claim, and lets new slots feed the existing multi-pool fleet. Of the three structural thresholds in the diagnostic, k moves only saturation; production and viability are k-invariant.

B.3.1. What k moves and what it does not

A standalone k-raise changes only the scalar k. The reward formula is unchanged. A few derived quantities scale with k; most do not.

Quantity $k = 500$ $k = 750$ $k = 1000$ Nature of change
$z_0 = 1/k$ (relative) 0.2 % 0.133 % 0.1 % Halved at $k=1000$
$z_0$ absolute (×Supply ≈ 38.49 B ADA) 77 M 51.3 M 38.5 M Halved at $k=1000$
$P_{\max} = R/k$ (at $R \approx 15.53$ M ADA) 31 060 20 707 15 530 Halved at $k=1000$
Saturated hollow reward ($P_{\max} \cdot \lambda_{\text{size}}$) ≈ 23 885 ≈ 15 923 ≈ 11 942 Halved at $k=1000$

Table B.5 — Derived quantities at three k-values.

What k does NOT move. Three structural quantities are k-invariant — and this is the load-bearing mechanical result behind the bottom-line claim.

$$\hat f' = \bar p \cdot \frac{R}{k} \cdot \lambda_{\text{size}} \cdot \nu = \bar p \cdot \frac{R}{k} \cdot \lambda_{\text{size}} \cdot \frac{\sigma_{\text{abs}} \cdot k}{\text{CircSupply}} = \bar p \cdot R \cdot \lambda_{\text{size}} \cdot \frac{\sigma_{\text{abs}}}{\text{CircSupply}}$$

The k cancels. For any hollow pool staying below saturation at the new k, the absolute reward is invariant. This is the key mechanical result that refutes the "k-raise pushes the viability line up" framing.

The taxonomy rests on three thresholds: production, viability, saturation. A k-raise moves only saturation. The production line (~1 M, Sub-block) and the viability line (~0.54 M, hollow break-even) stay exactly where they are. Only the upper bound $z_0$ shifts — and only the upper tail with it.

B.3.2. The amplified pledge bonus lands on a population that does not exist on mainnet

For pools with meaningful self-pledge, the bonus $\lambda_{\text{pledge}} A(\nu, \pi)$ scales linearly in k. For a fully self-pledged 15 M pool:

$k$ $\nu$ $A(\nu, 1) = \nu^3$ Bonus = $\lambda_{\text{pledge}} \cdot A \cdot P_{\max}$
500 0.195 0.00739 28 ADA/ep
750 0.292 0.0250 108 ADA/ep
1000 0.390 0.0592 218 ADA/ep

Table B.6 — Pledge bonus for a fully self-pledged 15 M pool across k-values. 7.7× absolute amplification; annualised, +20 660 ADA/yr.

This is the only positive mechanical effect a standalone k-raise delivers. The catch is who fits the profile.

The implicit target — high pledge ratio + meaningful scale + retail delegation capture — does not exist on mainnet:

The amplified bonus is a larger prize for a profile no one currently fills.

B.3.3. Three findings — fleet absorption, narrow demand, top-tail-only mechanics

The cards below isolate the three reasons a standalone k-raise fails today: MPO fleet absorption (k.S3), narrow demand-side and unmoved supply-side (k.S2), and top-tail-only mechanical effect (k.S1).

k.S3
k-lever Synthesis 03 · 2 findings

MPO fleet absorption under weak pledge

2 findings

Under the current weak-pledge regime, new pool slots are absorbed horizontally by existing MPO fleets. The behavioural alternative to the amplified-pledge-signal channel is MPO fleet absorption — existing multi-pool operators register additional pools to capture the new slots regardless of pledge signal. Two anchors establish the pattern: one empirical, one structural.

Findings
  1. regresses#1k.S3.F1
    Historical k: 150 → 500 (Aug 2020) produced today's MPO landscape. The only previous k-raise in Cardano's live protocol history. Within two years of the raise, the MPO fleet pattern stabilised at the form the diagnostic now documents: 83 attributed entities controlling 76.7 % of productive stake across 449 productive pools. The raise did not produce a proportional increase in independent entities; it produced multi-pool expansion by existing operators. This is not a predictive model — it is the actual observed outcome of the one natural experiment Cardano has run on k at scale.
  2. regresses#2k.S3.F2
    Structural economics favour fleet expansion over new-entrant entry. Three quantitative anchors from the diagnostic, all directly observable on mainnet (no modelling required): (i) Pool registration cost is ~500 ADA per pool. Median retail MPO entity revenue: 25 K – 1 M ADA/yr depending on fleet size — an existing MPO can register a new pool at sub-0.05 % of annual revenue. (ii) Operational infrastructure scales near-horizontally: an operator already running $N$ pools has the relay topology, monitoring, keyset tooling, and ops capacity to run $N+1$ pools at near-zero marginal cost. (iii) Pledge is not binding on fleet expansion under the current formula — 42 of 48 saturation-scale MPOs already operate without meeting pledge targets. For a new-entrant operator to out-compete an existing MPO for a new slot, they would need to match the MPO's brand / wallet / marketing channel — a channel the k-raise does not amplify. The economic gradient favours expansion, not entry.
k.S2
k-lever Synthesis 02 · 2 findings

Narrow demand-side segment, insufficient operator-side mechanism

2 findings

A fine tool for a narrow delegator segment, insufficient on the operator side because the formula is unchanged. The CIP-0082 rationale frames stages 3–4 as a ROS-based redistribution claim — delegators choose pools partly on yield, oversaturation cuts yield at the top, therefore delegators migrate toward smaller pools. The diagnostic undermines both conditions.

Findings
  1. regresses#1k.S2.F1
    The ROS-focused delegator segment is a minority of productive stake. Decomposing the 21.57 B ADA of productive stake:
    Segment Stake Share Responsive to a ROS signal?
    Custodial (funds not discretionary) 4.55 B 21.1 % No — funds are custodied, reallocation is not a retail choice
    Retail, loyal tenure ≥ 2.7 yr ~7.15 B ~33 % No — 42 % of delegations have not moved in 2.7+ years
    Retail, volatile tenure < 25 d ~3.57 B ~17 % Potentially — but 50.5 % of switches land on yield-identical pools, and non-identical moves show visibility, not yield, asymmetry
    Retail, middle tenure ~6.30 B ~29 % Unclear
    The ROS-responsive segment that the k-raise redistribution mechanism actually targets is at most the subset of the retail-volatile tier whose switches are not yield-identical — at best ~8 % of productive stake. A single-digit-percent redistribution channel is not a network-level concentration reform.
  2. regresses#2k.S2.F2
    Changing k without revising the reward formula leaves the non-pledge equilibrium intact. Operators do not pledge today for a well-understood reason: pledge yield (0.68 %/yr at best) is structurally dominated by passive-delegation yield (~2.3 %/yr). 78 % of staked ADA sits in pools with pledge ratio < 1 %; 42 of 48 saturation-scale MPOs forfeit the bonus. A k-raise amplifies the pledge-bonus term roughly linearly in k for fully self-pledged pools below the new $z_0$, but keeps $A(\nu, 0) = 0$ — hollow pools (the overwhelming majority of productive stake) untouched — and leaves the surrounding formula that makes pledge a dominated strategy unchanged. The amplified bonus is a larger prize for a behaviour operators still have no reason to adopt.
k.S1
k-lever Synthesis 01 · 4 findings · the design-strength row

Top-tail compression with narrow pledge amplification, bottom unchanged

4 findings

Top-tail compression + narrow pledge amplification; bottom unchanged. The mechanical content of a standalone k-raise is the sum of four effects on the reward function — three regressive or blind, one delivery. The findings below isolate each one.

Findings
  1. regresses#1k.S1.F1
    Top-tail compression. At $k: 500 \to 1000$, every pool with $\sigma$ above the new $z_0 = 38.5$ M ADA converges to the same ceiling of ≈ 11 942 ADA/ep — a −50 % reward cut for today's Saturated-tier pools. The k-raise acts exclusively on the upper tail.
  2. blind spot#2k.S1.F4
    Of the three structural thresholds, k moves only saturation. Production threshold ($n \cdot S_{\text{active}} / (L \cdot f)$, Praos slot mechanics) and viability threshold ($c / (R \lambda_{\text{size}} / \text{CircSupply})$, hollow-pool break-even) contain no k. At mainnet today: 3-block threshold ≈ 2.92 M ADA, hollow-pool break-even ≈ 0.54 M ADA. Both are k-invariant. A k-raise does not rescue any pool at the production or viability boundary.
  3. blind spot#3k.S1.F3
    Hollow pools below saturation see zero mechanical change. The formula collapses to $\hat f' = \bar p \cdot R \cdot \lambda_{\text{size}} \cdot \sigma_{\text{abs}} / \text{CircSupply}$ — the scalar k disappears. Operator revenue (capped at minPoolCost) and delegator ROS are both invariant for the entire Sub-reliable, Sub-block, and Dormant populations. The "k-raise helps small pools" framing has no mechanical foundation.
  4. delivers#4k.S1.F2
    Pledge-bonus amplification for self-pledged pools. For self-pledged pools below the new saturation, the bonus $\lambda_{\text{pledge}} A(\nu, \pi)$ scales linearly in k in absolute terms. A fully self-pledged 15 M pool's bonus grows from 28 ADA/ep at $k = 500$ to 218 ADA/ep at $k = 1000$ — 7.7× amplification, +20 660 ADA/yr. This is the only genuinely positive mechanical effect a standalone k-raise delivers — but it lands on a population (Custodial-by-pledge) that does not capture retail delegation.

B.3.4. A common misreading, corrected

A recurring claim — in earlier drafts of this evaluation and in governance discussions — is that a k-raise "pushes the viability line up" and makes sub-threshold pools worse. The formula does not behave that way when only k moves.

What does push the viability line up is a change in the fee structure (minPoolCost) or the reward pot ($R$, e.g. reserve depletion). A k change leaves both untouched.

B.3.5. When a k-raise becomes a decentralisation tool

The regression is conditional on weak pledge. Once a stake-cap layer binds — CIP-0050's L, or CIP-0037's dynamic saturation — fleet expansion is no longer possible at the upper tail, and new pool slots have to go to new entrants.

In that order, a k-raise becomes a decentralisation tool. The correct sequence is therefore:

  1. fee-layer fix (so pledge is not a dominated strategy);
  2. stake-cap (so the upper tail cannot absorb new slots);
  3. k-recalibration.

A standalone k-raise before a stake-cap makes things worse, not better.

Appendix C — Origin and references

C.1. Identity card

Field Value
CIP number CIP-0082
Title Improved Rewards Scheme Parameters
Authors Tobias Fancee
Created 2022/01/03
Category Ledger
Status Proposed (as of 2026/04)
Official page cips.cardano.org/cip/CIP-0082
Source (GitHub) cardano-foundation/CIPs / CIP-0082
Forum thread forum.cardano.org/t/cip-improved-rewards-scheme-parameters/112409
Worked-calibration spreadsheet Context/CIPs-repo/CIP-0082/ImprovedRewardsSchemeParameters.xlsx

C.2. Origin and context

Authorship and moment. Written in early 2022 by Tobias Fancee. The worked calibration in the CIP uses epoch-385 parameters (minPoolCost = 340, a_0 = 0.3, k = 500, rewards ≈ 31.2 M ADA/epoch, saturation ≈ 64 M ADA). The author's central observation: a 10 M ADA community pool and a saturated pool both pay the same 340 ADA flat fee, and the effective fee rate hyperbola penalises small productive pools. The CIP aggregates into one package three reforms the community had been discussing separately — minPoolCost reduction, minPoolMargin / minPoolRate introduction (crediting CIP-0023 explicitly), and k raises to amplify the pledge benefit.

Stage 1 is already retired on mainnet. In the Conway era, a parameter-change governance action at epoch 445 (2023/10/27) halved minPoolCost from 340 to 170 ADA — the exact change proposed in stage 1. The live content of CIP-0082 as a governance item is therefore stages 2–4.

Hard-fork requirement. Stage 2 is the non-trivial change: a hard fork that deletes minPoolCost, introduces minPoolRate, and modifies the pool-fee calculation to $poolRateEff = \max(poolRate, minPoolRate)$ — a rule change preserving existing pool registration certificates without re-registration. Stages 3 and 4 are parameter updates only.

Historical placement. The CIP explicitly credits CIP-0023 for the margin-floor instrument: "minPoolRate was originally proposed in CIP-0023." CIP-0082 stage 2 is therefore mechanically equivalent to a paired variant of CIP-0023 (reduction of minPoolCost + introduction of a margin floor) — with the reduction taken to zero and the margin set to 3 % (vs CIP-0023's illustrative 50 ADA + 1.5 %).

The single empirical baseline for stages 3–4. k has been raised once in Cardano's live history: k: 150 → 500 in August 2020, about a year after Shelley launch. The argument was the same one heard today — more pools means more decentralisation. The observed outcome was the rise of the multi-pool-operator pattern that the diagnostic now documents (POL.O5.F1: 83 entities, 449 productive pools, 76.7 % of productive stake). This is the empirical anchor for the §B.3 standalone k-lever analysis. A k-raise also appears in two governance forms today: as stages 3–4 of this CIP, and as a standalone Parameter Change action outside the CIP-0082 package — both are covered by §B.3.

C.3. References

Status: Active 2026/04/23. Fee-layer reform (stages 1–2) + transversal k raise (stages 3–4). CIP identity and sources in Appendix C.1; evaluation references in Appendix C.3.

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