Research Preprints · 2026

The Economics of
Trust-Minimized Money

Three companion papers proving that Proof-of-Work is a measurement instrument, a monetary stabilizer, and a foundation for decentralized communication — all without committees, oracles, or institutional trust.

Read the Argument Download All (15 PDFs)
3 Papers
5 Languages
11 Theorems
1 Network
The Core Argument

Every monetary system in history has had a trust problem.

Gold required trust in assayers. Paper required trust in central banks. Bitcoin solved the issuance problem but left monetary policy — the question of how much currency should exist — to a fixed schedule written in 2009.

These three papers answer a harder question: can a cryptographic protocol manage its own monetary policy, responding to economic reality without trusting any committee, oracle, or institution?

The answer is yes. The proof runs through three steps.

01

PoW is a measurement instrument.

When miners compete for block rewards, the difficulty they encounter is a live, adversarially-revealed reading of how much the network is worth securing. No comparable instrument exists in Proof-of-Stake — expenditure is displaced into opaque channels the protocol cannot observe.

02

That instrument drives a stable feedback controller.

Tail emission tracks the work signal. A burn mechanism provides countervailing demand. Together they form a two-loop control system that is provably Lyapunov-stable — convergent by construction, oracle-free by design, manipulation-resistant by the mathematics of sublinear response.

03

The burn demand has a natural source.

Burn-to-speak pricing for decentralized messaging creates exactly the endogenous coin demand the monetary mechanism requires — while simultaneously solving the oldest problem in distributed systems: how to prevent spam without a moderator.

The chain closes. No oracle enters. No committee votes. The argument is complete.

🪷
Why Lotus

Hoa Sen. कमल. The Lotus.

The lotus is Vietnam's national flower — hoa sen — rising clean from muddy water, a symbol of purity emerging from difficult conditions. In India it is kamal, sacred to Lakshmi and Saraswati, the flower of prosperity and knowledge. In both cultures it represents the same idea: something beautiful and uncorrupted growing from an imperfect world.

That is what this network is trying to be. Money that rises clean from the mess of institutional capture, committee governance, and oracle dependency. A protocol that works because the mathematics forces it to — not because anyone is trusted to maintain it.

🇻🇳 Tiếng Việt
🇮🇳 हिन्दी
🇨🇳 中文
🇬🇧 English
Paper Dependencies
01
Consensus & Energy
Establishes $\sigma_t := \mathcal{H}_t/\Pi_t$ as a protocol-visible security signal unique to PoW
enables
02
Adaptive Monetary Policy
Uses $\sigma_t$ to build oracle-free feedback; stable iff $\phi \in (0,\, 2+2\gamma)$
requires
03
CashWeb Protocol
Burn-to-speak demand closes the loop; optimal burn $B^* = \sqrt{D\sigma/\alpha}$
burn demand feeds back into price stability
01 — Consensus Theory
EN · 6pp 中文 Tiếng Việt हिन्दी العربية

Security Expenditure, Energy, and Issuance Legibility in Permissionless Consensus

Shammah Chancellor — Preprint, 2026

Proof-of-Stake does not eliminate energy expenditure — it displaces it into channels the protocol cannot see. Proof-of-Work alone makes security costs legible, enabling algorithmic monetary policy.
Theorem
Equilibrium Security Expenditure

In any permissionless system offering an externally priced block reward, rational defenders expend resources proportional to expected value at risk — regardless of consensus mechanism.

$\mathbb{E}[C^{\mathrm{def}}_t] \gtrsim \alpha\,\mathbb{E}[V_t]$
Theorem
Protocol-Visible Security Density

PoW protocols compute $\sigma_t$, the expected irreversible work backing each unit of issuance. No equivalent quantity is computable from PoS consensus state.

$\sigma_t \;:=\; \mathcal{H}_t \,/\, \Pi_t$
Corollary
PoS Displaces, Not Eliminates

Expenditure shifts into validator infrastructure duplication, MEV optimization, governance capture, and institutional overhead — heterogeneous, opaque, unmeasurable.

Remark
Long-Range Attack Asymmetry

Old PoS validator keys enable history rewriting at near-zero cost. PoW requires re-expending energy for every block rewritten — an irreducibly physical guarantee.

Full Abstract

Proof-of-Stake (PoS) systems are commonly described as environmentally efficient alternatives to Proof-of-Work (PoW) on the basis that they avoid continuous hashing. This paper analyzes consensus security from an equilibrium, expectation-based perspective and shows that for any permissionless system offering an externally valued block reward, rational attackers and defenders are incentivized to expend real resources proportional to the expected value at risk. Proof-of-Work expresses this expenditure directly and legibly via energy consumption, while Proof-of-Stake displaces it into heterogeneous and opaque channels such as infrastructure duplication, validator identity proliferation, MEV-driven optimization, governance capture, and institutional overhead. We further show that PoW uniquely provides a protocol-visible measure of security expenditure per unit of issuance, enabling algorithmic reasoning about monetary policy without reliance on social or institutional oracles.

Cite as
Chancellor, S. (2026). Security Expenditure, Energy, and Issuance Legibility in Permissionless Consensus. Preprint.
02 — Monetary Mechanism Design
EN · 14pp 中文 Tiếng Việt हिन्दी العربية

Adaptive PoW Monetary Policy Without Oracles: A Constructive Mechanism for Pseudo-Stability via Work-Coupled Tail Emission and Burn

Shammah Chancellor — Preprint, 2026

A Bitcoin-style chain can achieve price pseudo-stability using only its own difficulty signal and market-driven burn demand. No committees. No oracles. Provably convergent.
Theorem — Lyapunov Stability
Two-Loop Mechanism is Formally Stable

If price sensitivity $\phi$ lies in the stability region, the tail-emission and burn-feedback system satisfies a discrete Lyapunov condition and converges geometrically.

$\phi \in (0,\, 2+2\gamma) \;\Longrightarrow\; \Delta V_n \leq -\eta\, V_n$
Construction
Sublinear Homomorphic Emission Rule

Tail subsidy updates multiplicatively from observable block headers alone. Sublinear exponent $\gamma \in (0,1)$ provides both stability and manipulation resistance.

$R^{\mathrm{tail}}_{n+1} = \mathrm{clip}\!\left(R^{\mathrm{tail}}_n \cdot \left(\frac{W_n}{W_{n-1}}\right)^{\!\gamma},\; R_{\min}, R_{\max}\right)$
Proposition
Oracle-Free Demand Sink

With $N$ advertisers holding fixed fiat budget $b$, coin-denominated burn demand rises as price falls — the sink strengthens in exactly the direction required for stability.

$B^{\mathrm{b2s}}_n \approx Nb\,/\,P_n$
Analysis
Manipulation Resistance

A miner controlling fraction $\mu$ finds suppression profitable only when the gain exceeds the cost of foregone rewards. The threshold tightens as $\gamma \to 0$.

$\mu\gamma R^{\mathrm{tail}}_n \;\leq\; P_n(R_n + (1-\beta)F_n)$
Full Abstract

This paper proposes a constructive alternative to Bitcoin that retains Proof-of-Work while enabling pseudo-stability without reliance on discretionary governance or external price oracles, offering an adversarial alternative to committee-managed indices such as CPI. Building on the observation that PoW exposes protocol-visible security expenditure through difficulty, we specify a two-loop mechanism: (i) an adaptive, work-coupled tail emission rule defined entirely from header-observable variables and prior consensus state, and (ii) a market-driven burn mechanism that provides an endogenous demand sink without any oracle. We prove formal Lyapunov stability of the two-loop mechanism under linearized dynamics, characterize the stability region $\phi \in (0, 2+2\gamma)$, and discuss implementability within Bitcoin-style daemon and validation architecture.

Cite as
Chancellor, S. (2026). Adaptive PoW Monetary Policy Without Oracles. Preprint.
03 — Protocol Design
EN · 21pp 中文 Tiếng Việt हिन्दी العربية

CashWeb: Federated Messaging with Cryptocurrency-Based Economic Anti-Spam

Shammah Chancellor — Preprint, 2026

Spam is solved the same way every economic problem is solved: price it. CashWeb uses cryptographic burn payments to make abuse irrational, without moderators, platforms, or trust.
Theorem
Optimal Burn Rate in Closed Form

The welfare-maximizing burn rate balances spam deterrence against legitimate-user accessibility. Higher spam damage $D$ or propensity $\sigma$ raises $B^*$.

$B^* = \sqrt{D\sigma \,/\, \alpha}$
Theorem
Fee Recycling Resistance

Under partial fee burn (fraction $\beta$ burned), an attacker controlling fraction $\mu$ of hashpower recovers at most $(1-\beta)\mu$ of attack costs.

$\mathrm{Cost}_{\mathrm{net}} > 0 \;\Longleftrightarrow\; \mu < \beta$
Proposition
Sybil Attack Bound

Sybil attacks scale linearly with attacker budget, not computational resources. Economic anchoring eliminates the asymmetry that makes spam viable on legacy networks.

$N_{\mathrm{sybil}} \;\leq\; \mathcal{B} \,/\, (v_{\mathrm{reg}} + k\,v_{\mathrm{msg}})$
Protocol Spec
Proof-of-Payment (POP)

Complete specification linking on-chain value destruction to off-chain messaging via OP_RETURN outputs. Verifiable, unrecoverable burns with no trusted intermediaries. Deployable on Lotus today.

Full Abstract

We present CashWeb, a comprehensive protocol suite that integrates cryptocurrency-based economic mechanisms with federated messaging infrastructure to enable spam-resistant communication without centralized moderation. The protocol employs a novel "burn-to-speak" anti-spam mechanism where message senders attach small cryptocurrency payments that are cryptographically verifiable but do not require trusted intermediaries. We provide formal specifications for three core components: (1) a Proof-of-Payment (POP) protocol that links on-chain value to off-chain actions, (2) federated messaging with cryptographic identity management, and (3) a publish-subscribe system for topic-based broadcasting. Our economic analysis demonstrates that the burn mechanism creates optimal deterrence against spam while preserving accessibility for legitimate communication.

Cite as
Chancellor, S. (2026). CashWeb: Federated Messaging with Cryptocurrency-Based Economic Anti-Spam. Preprint.

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