.. meta:: :description: Symbol dictionary for e7Day axioms and theorems: entities, type partitions, operators, verdicts, and named concepts used in the 30 formal statements. :keywords: e7Day symbols, notation, L, D, Omega, Int, Real, Ground, Ocean, fix, OK, OKO, BABL, ZION, PERFECT, PERFIDE, UMP :author: LLoL as Laurence Loewe of Laodicea and Claude Opus 4.6 **************************************************** e7Day Symbol Dictionary **************************************************** This page defines all symbols used in the e7Day formal statements (axioms and theorems). Only resolved definitions are listed here. For unresolved acronym alternatives, see ``dict/ambiguities-to-decide.rst``. For the axioms, see :doc:`axioms`. For the theorems, see :doc:`theorems`. .. E7DAY-SYMBOLS-CONTENT-START Entities and Constants ======================== .. list-table:: :widths: 12 22 41 25 :header-rows: 1 * - Symbol - Name - Meaning - Used in * - :math:`\Omega` - Total domain - Pre-partition domain (VOID state) before scope partition - m0.ax1, m1.ax1 * - :math:`L` - Light / in-scope - The domain within which all construction occurs - m1.ax1 and throughout * - :math:`D` - Dark / out-of-scope - Complement of L; excluded from construction - m1.ax1 * - :math:`W` - World - The system produced by the construction (W = L) - th1 * - :math:`B` - Balospe - Balance-o-stat species; agent with general intelligence - m6.ax2, m6.ax4 * - :math:`h^*` - Maximally influential agent - The agent with maximal causal influence (per PET ax19) - th7 (Gate 5) * - God - God - Distinguished divine entity (boundary condition for th7) - th7 Type Partitions ================= .. list-table:: :widths: 12 22 41 25 :header-rows: 1 * - Symbol - Name - Meaning - Used in * - :math:`\text{Int}(L)` - Integer types - Indivisible types within L - m2.ax1, m2.ax2 * - :math:`\text{Real}(L)` - Real types - Divisible types within L - m2.ax1, m2.ax2 * - :math:`\text{Ground}(L)` - Ground values - Unconditionally known values - m3.ax1, m3.ax2 * - :math:`\text{Ocean}(L)` - Ocean values - Conditionally known values - m3.ax1, m3.ax3 * - Water - Water - Circulation medium (Ocean through programs and back) - m3.ax2, m3.ax3 * - :math:`\text{DAY}(L)` - DAY processes - Directed foreground activity - m4.ax1 * - :math:`\text{NIGHT}(L)` - NIGHT processes - Nondeterministic background guidance - m4.ax1 * - WorkTime - Work time - Active construction time - m7.ax2 * - RestTime - Rest time - Periodic consolidation time - m7.ax2 Operators and Functions ========================= .. list-table:: :widths: 12 22 41 25 :header-rows: 1 * - Symbol - Name - Meaning - Used in * - :math:`\text{fix}(\cdot)` - Fixpoint operator - "It was good" convergence; fix(result(mk)) = result(mk) - mc.ax1 * - :math:`\text{result}(m_k)` - Submodel result - Output of submodel k - mc.ax1, mc.ax4, m7.ax1 * - :math:`\text{process}(m_k)` - Submodel process - The evening-then-morning process of submodel k - mc.ax3 * - :math:`\text{input}(m_k)` - Submodel input - Input to submodel k (includes all prior results) - mc.ax4 * - :math:`\text{info-loss}(\varphi)` - Information loss - Information lost by mapping :math:`\varphi` - m2.ax2 * - :math:`\text{scope}(\cdot)` - Scope - Experiential scope of an agent's compassion - th7 (Gates 2, 5) * - :math:`\text{repair-history}(a, F)` - Repair history - Agent a's repair experience for fault class F - th7 (Gates 1, 2) * - :math:`\text{awareness}(a, \cdot)` - Awareness - Agent a's information about another's state/context/trajectory - th7 (Gate 3) * - :math:`\text{noise}(\cdot)` - Noise level - Noise on a compassion or information channel - m5.ax2, th7 (Gate 4) Verdicts ========== .. list-table:: :widths: 12 22 41 25 :header-rows: 1 * - Symbol - Name - Meaning - Used in * - OK - OK - Fixpoint convergence; scope-creep-excluded; "it was good" - mc.ax2, m6.ax4 * - OKO - OKO - Structurally necessary indeterminacy; requires external resolution - m6.ax3, m6.ax4 * - KO - KO - System failure - m6.th1, th7 * - :math:`\text{OK}^+` - OK-plus - Self-correcting architecture from matched OKO pair - m6.ax3 Named Concepts ================ .. list-table:: :widths: 12 22 41 25 :header-rows: 1 * - Symbol - Name - Meaning - Used in * - PERFECT - PERFECT - Preserve Existence Rights of Functionally Existing Copies of Types - m2.th1, th3 * - PERFIDE - PERFIDE - Preserve Exchangeability of Resource Functionality in Diverse Environments (double meaning deliberate) - m2.th1 * - BABL - BABL - Blindly Assuming Blind Leveraging (collapse attractor) - m6.ax4, m6.th1, th3, th5 * - ZION - ZION - Zoning Investigating Organizing Navigating (innovation attractor) - m6.ax4, th3 * - UMP - UMP - Unimportant Message Problem (noise threshold for signal collapse) - m5.ax2, th7 (Gate 4) * - ASON - ASON - Ambiguous Semantics Of Nothing (semantic trap at VOID) - th7 (Gate 5) * - OSCR - OSCR - OK Self-assessment Collapse Route - m6.th1 Mathematical Symbols ====================== .. list-table:: :widths: 12 22 41 25 :header-rows: 1 * - Symbol - Name - Meaning - Used in * - :math:`H(\cdot)` - Entropy - Shannon entropy function - m0.ax1 * - :math:`H_{\max}` - Maximum entropy - Upper bound of entropy (VOID state) - m0.ax1 * - :math:`\varepsilon` - Epsilon - Minimum information loss bound (strictly positive) - m2.ax2 * - :math:`\theta` - Theta - Noise threshold for channel collapse - m5.ax2, th7 * - :math:`F_{\text{all}}` - All fault classes - The set of all problem/fault classes in the system - th7 (Gates 1, 2, 5) * - :math:`\uplus` - Disjoint union - Type partition operator (exhaustive, non-overlapping) - m1.ax1, m2.ax1, m3.ax1, m4.ax1, m7.ax2 * - :math:`\triangleright` - Sequential composition - Evening before morning ordering - mc.ax3 .. E7DAY-SYMBOLS-CONTENT-END