A BEIChip/BEILogic trusted-execution system binds a behavioral event envelope, an identity anchor, and a trusted time anchor within a hardware security module, trusted execution environment, secure element, cloud enclave, or software-defined chip. A nonce-protected TimeChip includes an event digest, identity reference, trusted-time reference, validity window, policy hash, TimeFlux weighting vector, rollback boundary pointer, audit pointer, and cryptographic signature. A BEILogic state machine applies identity, time, behavior, policy, anti-replay, mapping, medical-admission, namespace-provisioning, endpoint-classification, and compliance checks before producing a signed BEI asset-state record. Domain-node asset plots, rooted cellular endpoint networks, signed endpoint records, PUFShield attestation, configurable mapping tables, Green Flux evidence, BEI Node provisioning, and medical-health gate embodiments support minting, indexing, exchange, authorization, compliance, namespace provisioning, industry adapters, and bounded rollback through chip-attested PUFShield verification and signed BEI asset-state records.