Adelphos: The Self-Organizing, fractal Trust Network

40 καὶ ἀποκριθεὶς ὁ βασιλεὺς ἐρεῖ αὐτοῖς, Ἀμὴν λέγω ὑμῖν, ἐφ' ὅσον ἐποιήσατε ἑνὶ τούτων τῶν ἀδελφῶν μου τῶν ἐλαχίστων, ἐμοὶ ἐποιήσατε.

The King will answer them, ‘Most certainly I tell you, because you did it to one of the least of these my brothers, you did it to me.’
- Matthew 25:40

Table of Contents

• What is Adelphos?
• Differences from Systems like LETS or Ripple
• Economy and Trust Within Families
• Level Zero (L0): The Family Unit
• Level One (L1): The Cohort
• Self-Organizing Nature of Adelphos
• Not a Ponzi Scheme
• Measuring Trust in Adelphos
• Money in Adelphos
• License

What is Adelphos?

Adelphos (from the ancient Greek word for "brother") is a system that enables users across regions or countries to exchange goods and services using a hybrid of real currency (cash or deferred payments) and virtual credit. It builds on natural human trust starting from small groups like families, scaling fractally to larger structures like neighborhoods or communities. This creates a self-organizing network where trust grows organically, reducing reliance on traditional banking.

Differences from Systems like LETS or Ripple

• LETS (Local Exchange Trading Systems): Uses purely virtual credits that cannot leave the system, limiting flexibility for real-world needs.
• Ripple: Relies on a mesh of interconnections for credit paths, but lacks Adelphos' fractal hierarchy, which mimics social structures for more intuitive scaling and risk management.

Economy and Trust Within Families

Families form the core of human trust and economy, regardless of culture. Key traits include:

• Mutual trust: Members rely on each other without constant tracking.
• Shared responsibility: Debts or obligations are collective.

Examples:

• Parents cover a child's mistakes (e.g., breaking a window).
• Spouses share financial liabilities, even with separate assets.

These principles underpin Adelphos' Level Zero (L0) Trust.

Level Zero (L0): The Family Unit

In Adelphos, an L0 group isn't limited to biological families—it's any small unit acting as one economically.

Characteristics:

• Shared ledger: No individual accounts; all transactions are group-wide.
• Full mutual responsibility: Members are liable for all debts, including Redeemable Money (RM) and Unredeemable Money (UM).
• External view: The group appears as a single entity to outsiders.

Each group enters with a fixed equity (risk limit), capping total debt to prevent overextension.

Level One (L1): The Cohort

L1 groups represent close friends or trusted allies—people you trust deeply but don't share daily finances with.

Key differences from L0:

• No shared living or joint accounts.
• Trust is limited: Informal for small exchanges, formal (e.g., IOUs) for larger ones.

Example:

Alice and Lucy are close friends. They exchange small gifts without tracking debts. But if Lucy sells school books to Alice for $200, she expects cash or a formal IOU.

In Adelphos, L1 cohorts pool equities from L0 groups, exposing a portion (e.g., 50%) externally while maintaining internal trust.

Self-Organizing Nature of Adelphos

Adelphos grows fractally: Higher levels (e.g., L2 neighborhoods) mimic lower ones, with admins, pooled equities, and shared responsibilities. This allows organic expansion from families to communities, using routing like DNS for efficient credit paths (O(log n) complexity in balanced trees).

Not a Ponzi Scheme

Adelphos is the opposite of a Ponzi scheme. In Ponzi models, the top exploits the bottom without responsibility. Here, higher levels are liable for lower ones' debts, distributing risk upward and encouraging accountability.

Measuring Trust in Adelphos

Trust defies simple definition but, in Adelphos, it's the credit you're willing to extend—quantified by amount and time.

What Is Trust?

If Alice sells Bob a $300 phone and accepts a 30-day IOU, she's trusting him for $300 over that period. Longer delays may include interest (e.g., $310 after a year for 3%).

Trust as a Measurable Concept

Trust is the delayed payment you're willing to accept. Example:

Selling a €4,000 car to a friend for €3,500 cash + €500 IOU yields a 12.5% trust ratio.

Adelphos records IOUs, making trust quantifiable and relational.

Philosophy of Trust

Adelphos shifts from scarcity-based money to credit-based exchange without fully replacing currencies. Users set personal trust thresholds to limit risk.

The Axiom of Adelphos

One unit of trust equals one unit of currency exchanged. We denote currency as τ (Tao).

The Human Unit

Currencies vary; the "human unit" (τ_HV) is the smallest meaningful amount (e.g., $1 in the US, 1,000 pre-Euro Lire in Italy).

📏 The Trust-bel: Unit of Trust

Trust is measured in trust-bel (tb):

trust-bel = 10 * log10(τ / τ_HV)

Where τ is postponed currency, τ_HV is the human unit.

Example 1 (USA):

Alice lends Bob $100 (τ_HV = $1).
tb = 10 * log10(100 / 1) = 20 tb.

Example 2 (pre-Euro Italy):

Anna lends Bruno 1,000,000 Lire (τ_HV = 1,000 Lire).
tb = 10 * log10(1,000,000 / 1,000) = 30 tb.

The logarithmic scale reflects how trust grows non-linearly.

Trust in Practice

Trust-bel standardizes comparisons across currencies (e.g., using USD exchange rates for Yen). It's used for credit limits and routing.

Money in Adelphos

Money is either real (external cash) or deferred (internal credit).

Deferred types:

• Redeemable Money (RM): IOU with a due date; may accrue interest.
• Unredeemable Money (UM): Credit without a repayment date; lower trust typically.

Redeemable Money (RM)

Users set RM trust levels, limiting acceptance.

Example:

Alice buys a $300 phone from Bob (20 tb trust).
RM_max = 10^(20 / 10) * $1 = $100.
She pays $200 cash + $100 RM IOU.

RM is spendable within limits.

Further Example:

Bob uses $60 RM for Lucy's lessons (she accepts up to $100). He has $40 left.

Observations:

• Trust is relational (Lucy trusts the IOU issuer).
• Credit accumulates; exceeding limits requires cash.

Unredeemable Money (UM)

Similar to RM but indefinite. Users set separate (often lower) trust levels.

Key Differences:

• RM may include interest; UM does not.
• Users are fully liable for their own RM/UM, but only RM from invited friends.

Defining Your Trust Levels

You’ll define two trust thresholds:

• RM (Redeemable Money) — credit with a due date
• UM (Unredeemable Money) — credit without a due date

Key Principle

You control how much personal money you allow into the system. But you are also responsible for converting it back to real money if you choose to leave.

🧾 Example: Bob Registers

Bob sets:

• RM trust: 20tb → 10^(20/10) × $1 = $100
• UM trust: 10tb → 10^(10/10) × $1 = $10

This means:

• Bob can receive up to $100 in RM and $10 in UM
• These limits also define how much credit he can extend to others

Bob Buys a Phone from Alice

Alice has:

• RM trust: 30tb → $1000
• UM trust: 20tb → $100

The phone costs $300. Even though Alice is willing to accept all $300 in RM, Bob’s RM limit is only $100.

So Bob pays:

• $100 in RM
• $10 in UM
• $190 in real money (cash)

Reciprocity Principle If a user sets low trust, others will offer them limited trust in return.

Two Ways to Enter ἀδελφός

1. Register independently

   • You build your trust network from scratch
   • You are responsible for those you invite

2. Join via invitation

   • You are not responsible for users who joined before you
   • You are responsible for those you invite

Your responsibility is always capped by the trust level you chose at registration. Invited users may choose high trust, but their effective trust is limited by their inviter’s endorsement.

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Example: Bob Invites Alice

Bob registers with:

• RM trust: 25tb → $316
• UM trust: 15tb → $31.6

If Alice issues a $100 RM cheque, Bob’s remaining liability is:

• $316 - $100 = $216

This reflects how endorsement creates responsibility. If Alice defaults, Bob is liable — up to his declared trust capacity.

License

Copyright (c) Lino Ferrentino 2025. This project is licensed under the GPLv3 License.

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