Precision fix 2026-08-19: the three-seal anchor minimum has been enforced since 2026-08-14 (the schedule step is at block 13,034,000 but an emergency ceiling held the effective minimum to one until then); anchors universal since block 13,889,296
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# AIP-4: On-Chain Post-Quantum Signature Verification Suite
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 every 32nd block also carries, under its block hash, a certificate of validator Falcon-512 seals, and since block 13,034,000 a node rejects such an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 anchor blocks (every 32nd block, on every one since block 13,889,296) also carry, under the block hash, a certificate of validator Falcon-512 seals, and since 2026-08-14 a node rejects an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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## Preamble
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# AERE consensus, machine-checked SAFETY + LIVENESS verification (with Falcon quorum extension)
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 every 32nd block also carries, under its block hash, a certificate of validator Falcon-512 seals, and since block 13,034,000 a node rejects such an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 anchor blocks (every 32nd block, on every one since block 13,889,296) also carry, under the block hash, a certificate of validator Falcon-512 seals, and since 2026-08-14 a node rejects an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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Date: 2026-07-12 · Scope: AERE QBFT / IBFT 2.0 (Hyperledger Besu, chain 2800) consensus and its
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staged Falcon-512 quorum-certificate extension (log-only + blocking).
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# anchor_blocking_quorum_smt.py
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#
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# MACHINE-CHECKED (z3) proof of ANCHOR-THRESHOLD SAFETY for the AERE post-quantum
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# anchor (every 32nd block, minimum K=3 seals since height 13,034,000).
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# anchor (every 32nd block, minimum K=3 seals since 2026-08-14).
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#
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# CORRECTION 2026-08-19: this file used to call the property "blocking-quorum safety
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# once the blocking fork is active (height >= 14,050,000)". The fork property
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# K=3 distinct valid seals on anchor blocks (f+1 of 9, not a quorum), none elsewhere.
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#
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# INVARIANT (the task target):
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# Since height 13,034,000, no ANCHOR block can be finalized with fewer
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# Since 2026-08-14, no ANCHOR block can be finalized with fewer
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# than K=3 valid Falcon seals from DISTINCT signers of the registry ACTIVE
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# at that height; and a NON-anchor block requires no seals at all.
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#
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("QBFT/IBFT 2.0 SAFETY (agreement)", "qbft_safety_smt.py"),
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("Falcon LOG-ONLY no-op", "falcon_logonly_noop_smt.py"),
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("Falcon BLOCKING safety/liveness/N>=7", "falcon_blocking_smt.py"),
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("Anchor THRESHOLD safety (K=3 of 9 on anchor blocks since 13,034,000, registry rotation)", "anchor_blocking_quorum_smt.py"),
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("Anchor THRESHOLD safety (K=3 of 9 on anchor blocks since 2026-08-14, registry rotation)", "anchor_blocking_quorum_smt.py"),
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("PQC ACTIVATION transition safety (log-only->blocking + contract-anchored registry)", "qbft_pqc_activation_smt.py"),
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("QBFT LIVENESS (partial synchrony)", "qbft_liveness_smt.py"),
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("QBFT explicit-Prepare counting (2026-07-14 2nd-client bug+fix)", "qbft_prepare_counting_smt.py"),
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# pqc-fork/pq-stark - PQ STARK-verify precompile 0x0AE8 (BabyBear/Plonky3 FRI/STARK verify skeleton)
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 every 32nd block also carries, under its block hash, a certificate of validator Falcon-512 seals, and since block 13,034,000 a node rejects such an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 anchor blocks (every 32nd block, on every one since block 13,889,296) also carry, under the block hash, a certificate of validator Falcon-512 seals, and since 2026-08-14 a node rejects an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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> **SCOPE CAVEAT (research finding, 2026-07-19; read before anything else).** The generic components
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> in this directory are real and conformance-confirmed, but they were confirmed against Plonky3
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# On-Chain Post-Quantum Signature Verification on an EVM Layer-1 (AERE, Chain 2800)
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 every 32nd block also carries, under its block hash, a certificate of validator Falcon-512 seals, and since block 13,034,000 a node rejects such an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 anchor blocks (every 32nd block, on every one since block 13,889,296) also carry, under the block hash, a certificate of validator Falcon-512 seals, and since 2026-08-14 a node rejects an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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## Abstract
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# AERE Anti-MEV Design: Threshold-Encrypted Mempool and Batch-Atomic Fair Settlement
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 every 32nd block also carries, under its block hash, a certificate of validator Falcon-512 seals, and since block 13,034,000 a node rejects such an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 anchor blocks (every 32nd block, on every one since block 13,889,296) also carry, under the block hash, a certificate of validator Falcon-512 seals, and since 2026-08-14 a node rejects an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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Subsystem specification. Status as of 2026-08-01 (re-measured at head block 11,810,041 on `https://rpc.aere.network`). Chain ID 2800 (Hyperledger Besu QBFT, 0.5-second blocks, seven validators, one operator).
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# AERE Network: Proven Results (status as of 2026-07-11)
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 every 32nd block also carries, under its block hash, a certificate of validator Falcon-512 seals, and since block 13,034,000 a node rejects such an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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> **Note added 2026-08-19.** Statements in this document that consensus on chain 2800 is (or remains) classical secp256k1 ECDSA QBFT were written before the post-quantum header anchor went live, and remain true for block-by-block finality. Since block 13,014,000 anchor blocks (every 32nd block, on every one since block 13,889,296) also carry, under the block hash, a certificate of validator Falcon-512 seals, and since 2026-08-14 a node rejects an anchor block with fewer than three valid seals (f+1 of nine; eight or nine are carried in practice). That is a post-quantum checkpoint about every 16 seconds, not a per-block quorum: the claim published on 2026-08-15 that from block 14,050,000 no block finalizes without a post-quantum quorum was wrong (the per-block rule armed at that height is retired in the shipped code in favour of the anchor rules) and was withdrawn on 2026-08-19. Details: https://aere.network/quantum.html and the aere-node repository, anchor/README.md.
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> **UPDATE (2026-07-16): two facts in this 2026-07-11 snapshot have since changed on
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> mainnet and are corrected inline below.** (1) The validator set has grown from 3 to
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