Obex Engine I is a formally specified Sybil-deterrent entry protocol for distributed consensus. It instantiates a verifiable-random-function-anchored proof-of-eligibility mechanism combined with a deterministic, large-scale, memory-bound Merkle structure to enforce honest participation at constant verification cost. Let \mathsf{VRF}{\text{R255}}\colon \{0,1\}^* \to \{0,1\}^{64}\times\{0,1\}^{80} denote the RFC 9381-compliant Ristretto255 ECVRF returning output y and proof \pi=(\gamma,c,s). For chain identifier C\in\{0,1\}^{32}, epoch index e\in\mathbb{Z}{\ge0}, and epoch nonce n\in\{0,1\}^{32}, the VRF input is \alpha = \text{tag} \,\|\, C \,\|\, \text{LE}{64}(e) \,\|\, n . Participants compute (y,\pi)=\mathsf{VRF}{\text{R255}}(sk,\alpha) and derive the epoch hash E=\mathsf{BLAKE3}\!\bigl(\text{tag}\,\|\,\text{“VRFOUT”}\,\|\,C\,\|\,\text{LE}_{64}(e)\,\|\,n\,\|\,y\,\|\,\pi\bigr)\in\{0,1\}^{32}. Identity binding uses Ed25519 signatures: with verifying key pk, message M=\text{tag}\,\|\,\text{“EPOCH”}\,\|\,E\,\|\,n\,\|\,pk is signed to produce \sigma. Seed and dataset key are deterministically derived \text{SEED}=\mathsf{BLAKE3}(\text{tag}\,\|\,\text{“SEED”}\,\|\,M\,\|\,\sigma),\quad K=\mathsf{BLAKE3}(\text{tag}\,\|\,\text{“KDF”}\,\|\,\text{SEED}). From K each leaf i\in[0,N-1] (with N=2^{26}) is computed as L_i=\mathsf{BLAKE3}K(\text{LE}{64}(i))\in\{0,1\}^{32}, forming a perfect binary Merkle tree of depth 26 with root R. Challenge seed C_\text{chal}=\mathsf{BLAKE3}(\text{tag}\,\|\,\text{“CHAL”}\,\|\,E\,\|\,n\,\|\,pk\,\|\,R) drives uniform rejection-sampled indices \mathcal{I}\subset[0,N-1]. The prover returns \{(i,L_i,\text{path}_i):i\in\mathcal{I}\}. Verification is logarithmic: check \pi with pk, recompute E, verify \sigma, recompute K and R, then for each i verify Merkle authentication path \text{path}_i\to R. All cryptographic primitives are constant-time, domain-separated by the fixed tag [Iota]_|::"v1", and achieve 128-bit security under standard assumptions.