Linearity of Blocks & Transactions

Linearity in blockchain systems refers to the strict ordering of blocks and transactions to maintain consistency, prevent double spending, and ensure deterministic state transitions. Celestium enforces linearity to guarantee all nodes reach consensus on the same transaction history.

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1. Concept of Linearity

Linearity ensures that:

• Blocks are arranged in a single, sequential chain.

• Each block references the hash of its predecessor, forming an immutable chain.

• Transactions within a block are ordered deterministically.

This structure prevents forks under normal conditions and ensures all network participants process transactions in the same sequence.

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2. Deterministic Block and Transaction Ordering

Celestium enforces deterministic block and transaction ordering through:

• Block Linearity: Each block has a unique height and follows its predecessor.

• Transaction Linearity: Transactions within a block are ordered based on:

  • Nonce (for transactions from the same account).

  • Priority Fee (tip) during mempool selection.

  • Time of arrival as a tie-breaker.

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3. Nonce and Sequential Transactions

Each account’s transactions are ordered using a nonce—a sequential number representing the number of transactions sent from an account.

Example:

Nonce	Transaction Hash	Status
0	0xabc123	Included
1	0xdef456	Included
2	0xghi789	Pending

If a transaction with nonce 1 is missing, the network will not process nonce 2 until nonce 1 is confirmed.

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4. Why Linearity Matters

• Double Spend Protection: Ensures a single transaction can alter an account’s state at a time.

• Consensus Finality: All validators agree on the exact order of blocks and transactions.

• Replay Protection: Nonces prevent transactions from being executed multiple times.

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5. Block Production and Finalization

Validators produce blocks sequentially, referencing the hash of the previous block. Each block is finalized upon consensus, ensuring no reordering can occur afterward.

Key Block Properties:

Property	Description
Height	Block number, starting from 0 (genesis block).
Parent Hash	Reference to the previous block’s hash.
State Root	Root hash representing the state after executing all transactions.

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6. Handling Gaps or Missing Transactions

If a transaction with a lower nonce is delayed:

• Higher nonce transactions from the same account are held in the mempool.

• Once the missing transaction is confirmed, pending transactions are processed sequentially.

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7. Celestium’s Approach to Linearity

Celestium’s consensus mechanism (PoA + AI and CelesBFT) reinforces linearity by:

• Assigning block production responsibilities to validators in a round-robin manner.

• Using AI-driven monitoring to prevent Byzantine behavior (e.g., block omission or reordering attempts).

• Achieving block finality in a single round of voting under normal network conditions.

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8. Summary

• Blocks and transactions follow a strict linear sequence.

• Nonces prevent reordering within accounts.

• Linear execution ensures consensus consistency and prevents state divergence.

• Validators adhere to linear block production under CelesBFT consensus.

Linearity is fundamental to Celestium’s performance and security, ensuring that all nodes maintain a unified state despite network latency or adversarial conditions.