ParanO(1)d
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The network does not re-execute. It verifies.

Proof-Native
Statechain

Wallets prove ownership. Miners prove exact state transitions. Every node verifies the result. No signatures. No trusted setup. No replay from genesis.

O(1) SYNCno history. no archive nodes
SIGNATURELESShash-only ownership · PQ-ready
POW ORDERSproofs authorize every transition
01 / The dependency

Conventional blockchains
history from genesis.

Bitcoin, Ethereum and nearly every modern blockchain derive the present by executing history from genesis. More use creates more permanent bootstrap work for every future verifier.

Source of truth
The complete execution log
New full node
Downloads and re-executes the chain
Network age
Becomes an ever-growing hardware requirement
02 / The break with history

The present
proves itself.

ParanO(1)d separates validity from historical replay. Consensus carries a provable live UTXO state: spent outputs release their slots, and old activity does not remain a permanent burden for future nodes.

State growth
Live UTXOs—not lifetime transactions
Spent outputs
Slots clear and return to the allocator
Chain age
Adds no lifetime history or genesis replay
03 / Independent bootstrap

Bootstrap from proof.
Not from trust.

Peers provide data—not trust. A node receives the live UTXO state, its matching terminal and the latest 18 complete blocks. It authenticates the state, verifies the reorg window and becomes an independent full node. The procedure is the same in year one and year ten.

live state+πtip + 18 blocksindependent node ✓
04 / The paradigm shift

Prove where the
information lives.

In ParanO(1)d, proofs are built by whoever has the required data. The network receives the finished result, not another job to repeat the same work.

WWalletProves private authorization without revealing the spending secret.
MMinerProves public transaction logic and the exact state transition.
NNetworkVerifies proofs, applies proven slot writes and checks PoW.
05 / A living UTXO state

State grows with use.
Not with time.

Spending clears a slot. The allocator reuses empty positions before opening new state. Empty segments are virtual and disappear again when their last UTXO is spent.

Spend
Clear the indexed slot
Reuse
Issue a fresh creation_id in an empty position
Expand
Attach a canonical empty half at 75% occupancy — no pause
06 / Signatureless ownership

A secret is enough.
No keypair. No signature.

ParanO(1)d needs 256 bits of secret entropy—not a public-key pair or a mnemonic format. The wallet proves knowledge of that secret without revealing it; every spend produces a fresh ZK proof bound to the complete transaction.

Protocol
256-bit secret · no mnemonic format
On the wire
No public key · no transaction signature
Consensus
Hash-only ownership · PQ-ready from genesis
07 / PagedSpend

Many UTXOs.
One transaction.

Fixed proof pages are internal geometry. Up to 128 pages remain one indivisible user transaction with one txid, one fee, one capsule and one receipt.

1,020 inputs · 256 outputs
ATOMIC PAGEDSPEND
08 / Recursive history

History becomes
a fixed proof.

Every HistoryStep proves the current block and verifies the preceding terminal inside the same relation. Proof size and verification work do not increase with block height.

πh−1+blockh · statehπh
Active node
Live state + compact headers + latest 18 complete blocks
Chain age
Does not increase history verification
09 / Privacy by non-retention

Privacy
without privacy.

The live state is public, and transactions are visible while consensus carries them. ParanO(1)d does not make every node preserve the permanent transaction graph. Following an address across years requires an external tracker that records the stream continuously—and pays to store all of it.

Live state
Public values · public owners
Past graph
Not retained by consensus
External tracking
Record every transaction in real time
10 / Portable proof of payment

History expires.
The receipt does not.

When a payment confirms, the sender's wallet saves an exportable Merkle receipt. It carries the complete public payment data and a fixed-depth inclusion path. Any node verifies it against the canonical header—without the historical block body.

Authenticates
txid · recipients · amounts · fee · block time
Merkle path
Eight Poseidon2b levels
Old block body
Not required
11 / One binary proof stack

One arithmetic.
End to end.

Addresses, wallet authorization, transactions, state, recursive history and PoW share one binary proof stack. FROST-GKR folds repeated Poseidon2b structure into shared Boolean hypercubes; FRI-Binius closes the relation without a trusted setup.

ownership + txFROST-GKRstate + history + PoW
Field
GF(2^128) · one binary arithmetic
Prover
10.50× faster in the 59-permutation comparison
Algebraic proof
51.67× smaller
12 / Proof-Native PoW

Prove first.
Mine second.

PoW chooses the order of already-proven transitions. The miner completes the nonce-independent block proof, freezes an immutable template, then searches only the 128-bit nonce.

Block target
15-second mean · ASERT difficulty
Majority hashpower
May censor · reorder · reorg
Proof boundary
Cannot forge ownership or validate an invalid state
13 / Hardware-adaptive decentralization

The entire L1.
On your laptop.

Your laptop can hold the complete live state and independently verify the entire L1. ParanO(1)d adapts block capacity to available proving power: stronger hardware raises TPS; weaker hardware lowers it. Throughput changes. The network does not stop.

Your laptoplower TPS
Faster hardwarehigher TPS
Networkkeeps advancing
PARANO(1)D · PROOF-NATIVE STATECHAINtransparent L1 · proof of work