e7Day — Generalized System Construction

A formal model of generalized system construction, structured as 8 submodels (m0 VOID through m7 TRUST) plus cross-day meta-axioms. The model asks: What is the minimal formal structure for constructing a self-correcting, scope-expanding system over the long term?

Note

Version: dv_ClaOp46Max_OOv1_2026m03d27. All 30 OOv1 statements tested under Iron Maiden (TEMPER Round a2): 30 HELD, 0 BREACH.

Contents

• e7Day Overview
  • Scope
  • Submodel Summary
  • System-Level Theorems
• e7Day Axioms
  • Cross-Day Meta-Axioms
  • m0 — VOID
  • m1 — TYPE
  • m2 — EQUAL
  • m3 — VALUE
  • m4 — LOGIC
  • m5 — CARE
  • m6 — HOPE
  • m7 — TRUST
• e7Day Theorems
  • Submodel Theorems
  • System-Level Theorems
• e7Day Symbol Dictionary
  • Entities and Constants
  • Type Partitions
  • Operators and Functions
  • Verdicts
  • Named Concepts
  • Mathematical Symbols
• e7Day — AnyAims (Open Action Items)
  • New Model Dependencies
  • Formalization Tasks
  • Precision Improvements
  • Cross-Model Issues
  • Open Investigations
  • 7e Hairball Construction
• e7Day History
  • FORGE Session Sa2_2026m03d27
  • Session Files

Quick Overview

21 axioms in 9 groups:

• Cross-Day Meta (mc.ax1–4): Constructive fixpoints, OK convergence, evening-first ordering, construction cascade.

• m0 VOID (m0.ax1): Maximum-entropy pre-partition state.

• m1 TYPE (m1.ax1): Binary scope partition L ⊎ D.

• m2 EQUAL (m2.ax1–2): Integer/Real type split, lossy mappings.

• m3 VALUE (m3.ax1–3): Ground/Ocean values, programs as decision trees, water circulation.

• m4 LOGIC (m4.ax1–2): DAY/NIGHT process partition, first-class time.

• m5 CARE (m5.ax1–2): Self-managing conditional-data machines, UMP.

• m6 HOPE (m6.ax1–4): Special-purpose completion, Balospe with general intelligence, matched OKO self-correction, self-assessment bifurcation.

• m7 TRUST (m7.ax1–3): Null aggregation, WorkTime/RestTime, fractal periodicity.

9 theorems: PERFECT/PERFIDE impossibility (m2.th1), OSCR Collapse (m6.th1), W = L (th1), Lossiness (th2), BABL origin (th3), Balospe necessity (th4), Rest necessity (th5), Dual-Nothing (th6), Compassion Capacity five-gate theorem (th7).

GrowthGarden archive: 19 unselected candidates preserved in e7Day MegaTable — All Axioms, Theorems, and GrowthGarden Candidates.

Origin

Developed through FORGE session Sa2_2026m03d27 in two rounds: R1 produced OOv1; R2 (TEMPER) stress-tested all statements under Iron Maiden with 10 formal tests each. See e7Day History for details.

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