BA-01 · LESSON 02

Ledgers and double spending

A ledger records who can spend each scarce digital unit. A shared order prevents two conflicting payments from both becoming final.

45 min Difficulty 1/5 Not started

VISUAL MODEL

See the whole mechanism before going step by step

Use the diagrams to orient yourself. Then the guided explanation below teaches every part in depth.

4 explanatory views

CONCEPT-SPECIFIC MAP · state machineOne valid action transforms a known stateSelect any state to inspect its exact role.

RELATIONSHIP MAPOrdered mechanism flow

01
BEFOREKnown state
Identify the facts and objects that exist before the action.
02
ACTIONLedgers and double spending
The Ledgers and double spending lesson isolates the event that proposes a change.
03
RULEDeterministic check
The enforcing rule accepts or rejects the proposed transition.
04
AFTERSuccessor state
Accepted work creates a new state without silently changing the prior facts.
05
FAILUREState unchanged
A failed condition must not produce a partially accepted successor.

Rule shown: A valid transition names the prior state, action, enforcing rule, and successor state.

STAGE 1 OF 5BEFORE: Known state

Identify the facts and objects that exist before the action.

Governing relationship: A valid transition names the prior state, action, enforcing rule, and successor state. Complete path: 1. BEFORE, Known state. Identify the facts and objects that exist before the action. 2. ACTION, Ledgers and double spending. The Ledgers and double spending lesson isolates the event that proposes a change. 3. RULE, Deterministic check. The enforcing rule accepts or rejects the proposed transition. 4. AFTER, Successor state. Accepted work creates a new state without silently changing the prior facts. 5. FAILURE, State unchanged. A failed condition must not produce a partially accepted successor.

1. State transitionWhat exists, what changes, and what results

BEFORE

Alice controls output X worth 10 units. She signs transaction P paying Bob 10 and transaction Q paying Carol 10.

MECHANISM

Assume a ledger records one output worth 10 units that Alice can authorize. Its identifier makes that exact claim distinguishable from every other claim.

AFTER

Double-spend prevention requires a shared ordering and state update, not merely unforgeable signatures.

Text equivalent: Starting from Alice controls output X worth 10 units. She signs transaction P paying Bob 10 and transaction Q paying Carol 10. The mechanism begins when Assume a ledger records one output worth 10 units that Alice can authorize. Its identifier makes that exact claim distinguishable from every other claim. The resulting lesson is Double-spend prevention requires a shared ordering and state update, not merely unforgeable signatures.

2. Mechanism pathSelect a stage to inspect its job

STAGE 1 OF 5

Create one spendable claim

Assume a ledger records one output worth 10 units that Alice can authorize. Its identifier makes that exact claim distinguishable from every other claim.

Complete path: 1. Create one spendable claim: Assume a ledger records one output worth 10 units that Alice can authorize. Its identifier makes that exact claim distinguishable from every other claim. 2. Reference the prior claim: A valid transfer names the claim it consumes and creates replacement claims for recipients. It cannot merely copy a number into another message. 3. Detect conflicts: If Alice creates two transfers that both reference the same claim, nodes can see that the inputs conflict even if both signatures are valid. 4. Agree on an order: The system needs an ordering rule so one conflicting transfer can become part of accepted history. Bitcoin uses blocks with proof of work and validates only the accepted chain's first valid spend. 5. Update the live set: After accepting one transfer, nodes remove the consumed claim and add its new outputs. The competing transfer now points to something already spent.

3. Rule and failure boundaryWhat accepts the result and where it can stop

ACCEPTED PATH

Nodes accept a candidate only when its named input is still in the live unspent set, authorization succeeds, and value is conserved.

CHANGED CONDITION

After P consumes X, Q fails at the state check even if Alice's second signature is mathematically valid; the accepted state remains unchanged.

Important distinction: A valid digital signature proves that a payment has not been double spent. A signature proves authorization. The ledger's accepted order and current unspent state determine whether the authorized input is still available.

Text equivalent: The accepted path is enforced by Nodes accept a candidate only when its named input is still in the live unspent set, authorization succeeds, and value is conserved. If the required condition changes, After P consumes X, Q fails at the state check even if Alice's second signature is mathematically valid; the accepted state remains unchanged.

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Learn the idea

A ledger is a record of ownership or spendable claims. Digital information can be copied, so a digital bearer asset needs a rule that orders competing transfers. Double spending is the attempt to make two recipients accept transfers that consume the same prior claim.

GUIDED EXPLANATION1/5 ideas inspected

Create one spendable claim

Assume a ledger records one output worth 10 units that Alice can authorize. Its identifier makes that exact claim distinguishable from every other claim.

The worked example follows the explanation

Inspect every idea above to open it.

Important distinction“A valid digital signature proves that a payment has not been double spent.”

A signature proves authorization. The ledger's accepted order and current unspent state determine whether the authorized input is still available.

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