e7Day Overview

This is version dv_ClaOp46Max_OOv1_2026m03d27.

For the axioms, see e7Day Axioms. For the theorems, see e7Day Theorems. For the symbol dictionary, see e7Day Symbol Dictionary.

Scope

Model: e7Day — Generalized System Construction.

Central question: What is the minimal formal structure for constructing a self-correcting, scope-expanding system over the long term (OLT)?

Zone: Universal. The model applies to any system construction process that follows a phased, fixpoint-producing architecture. The primary instantiation is the seven-day creation narrative (Genesis 1), but the formal structure is independent of any specific tradition.

Method: Each submodel (day) defines a partition, operator, or constraint on the domain under construction. The cross-day meta-axioms govern how submodels compose. The cascade is cumulative: each submodel’s input includes all prior submodels’ results.

Submodel Summary

e7Day envisions 10 submodels (m0–m9). OOv1 defines m0–m7 plus cross-day meta-axioms; m8–m9 remain open.

Cross-Day Meta-Axioms (mc)

Four axioms governing the composition of all submodels: constructive fixpoints (mc.ax1), OK convergence criterion (mc.ax2), evening-first ordering (mc.ax3), and the construction cascade (mc.ax4). These are not tied to any single day but constrain the entire arc.

m0 — VOID

Pre-partition maximum-entropy state. No types, no structure — only the raw potential from which construction begins. Tohu va-vohu (formless and void). 1 axiom.

m1 — TYPE

Binary scope partition: L (light, in-scope) vs. D (dark, out-of-scope). Irrevocable within a construction cycle. All subsequent construction operates within L. 1 axiom.

m2 — EQUAL

Type structure within L: integers (indivisible) and reals (divisible). Every mapping from Real to Int is lossy. This creates the foundational tension between PERFECT (preserve existence rights of types) and PERFIDE (preserve exchangeability of resource functionality). The PERFECT/PERFIDE impossibility (m2.th1) follows as a theorem. Verdict: OKO. 2 axioms + 1 theorem.

m3 — VALUE

Value structure within L: Ground (unconditionally known) and Ocean (conditionally known). Programs are finite decision trees rooted in Ground, taking Water input, producing Ground output. Water must circulate (Ocean → Trees → Ocean). 3 axioms.

m4 — LOGIC

Process structure within L: DAY (directed foreground activity) and NIGHT (nondeterministic background guidance). Time is a first-class entity with measurable progress. 2 axioms.

m5 — CARE

Conditional-data machines that are self-managing and self-replicating (Ocean machines, Sky machines, Ground machines). The Unimportant Message Problem (UMP): when noise exceeds threshold, channel capacity for signal collapses to zero. 2 axioms.

m6 — HOPE

Two-part construction. Part 1 (m6.1): the special-purpose world is complete but contains no general intelligence. Part 2 (m6.2): Balospe (Balance-o-stat species) is introduced with general intelligence, responsible for Balance(L) OLT and recursively endowed. The matched OKO pair (m2 × m6.2) produces a self-correcting architecture (OK+). Self-assessment bifurcation: OK → BABL (sufficient, self-reinforcing trap); OKO necessary for ZION but not sufficient. OSCR Collapse (m6.th1) follows as a theorem. 4 axioms + 1 theorem.

m7 — TRUST

Null operation: TRUST aggregates all prior results. Time splits into WorkTime and RestTime. Fractal periodicity: the 6+1 integer-day ratio is the constrained optimum for Earth-like systems (circadian batching, lunar alignment, Schelling-point resistance to BABL erosion). 3 axioms.

m8 — (Open)

Boundary explorer / ToL-ToK. Formal content to be defined.

m9 — (Open)

Ergodic traverser. Formal content to be defined.

System-Level Theorems

Seven general theorems span the model: W = L (th1), Lossiness (th2), BABL origin (th3), Balospe necessity (th4), Rest necessity (th5), Dual-Nothing (th6), and the Compassion Capacity Theorem in five-gate form (th7). See e7Day Theorems for formal statements.