Formation, Persistence, and Spin-Compatible Recurrence of Bounded Supports in Entanglement–Algebraic Spacetime

This paper is archived as a speculative research work. Entanglement–Algebraic Spacetime (EAS) takes the Scalar Fields (SFs) as a primitive, non-metric, rank–3 relational ontology and develops physical structure as consequences of that ontology rather than importing geometrical or field-theoretic primitives. This paper develops M1, a sufficient formation theory for persistent bounded supports built on the established F1 scalar-field ontology and F2 contextual recurrence formalism. Exact phase-resolved Second-Order Ordering (SOO) removes unsupported same-point phase- K distinctions without requiring an incoherence energy or global variational principle. Same-phase recurrence compatibility together with actual same-point cross-phase closure yields, under connectivity and a nonfree settlement witness, one common contextual recurrence class K= <4 throughout the admitted support. A support-relative membership rule combined with phase-complete reachability forces exactly three boundary members, each with two internal fixed association targets and one exterior-facing target. Exact boundary–exterior SOO permits scalar exchange while preserving bounded identity as an organization rather than as a confined scalar inventory. The three binary exterior contexts admit a scope-assembled effective recurrence representation T_B=I_3 T( ) ; for 0< <4 , this yields an elliptic C^3_ rec carrier, a projective CP^2_ rec representation, and a positive recurrence form. The certified recurrence action is the common scalar action e^iω_BI_3 , so the ambient identity End_ C( C^3_ rec) M_3( C) does not itself select a finite spectral algebra. Persistent bounded recurrence not exhausted as free path accommodation supplies the SF antecedent for massive-rest capability and a representation-ready input to downstream massive Dirac and finite-NCG mass sectors, without selecting a numerical mass. For the established nine-point electron-like motif, exhaustive enumeration of all 6^9=10,077,696 ordered schedules and all eight three-phase A/B recurrence words uniquely selects the reflection-equivalence antireturn class R_ AR=ABA,BAB/reflection , with Φ -Φ Φ . This native antireturn structure admits the standard spin- 12 SU(2) interface representation and massive Dirac embedding while remaining distinct from the recurrence and finite-NCG carriers. M1 therefore exports representation-ready SF consequences while preserving their native provenance. M1 does not itself select a numerical mass, adjudicate the status of any SF-to-electromagnetic- U(1) representation map in the controlling downstream theorem stack, construct an optional direct SF-side electromagnetic interaction law, or complete formation/release dynamics; these are separately typed downstream or research-extension questions rather than missing primitive foundations of M1.