e7Day MegaTable — All Axioms, Theorems, and GrowthGarden Candidates#
Model: e7Day — Generalized System Construction
Version: dv_ClaOp46Max_OOv1_2026m03d27
Purpose: Comprehensive registry of every axiom, theorem, and candidate ever considered for e7Day. Includes selected (OOv1) and unselected (GrowthGarden) items. Anyone may chip away at GrowthGarden candidates and update their status.
Legend:
Sel = Selected for OOv1 (Y/N)
Type = axiom / theorem / theorem(conj.)
Cred = Credence (subjective probability of being true and useful)
VVN = Who proposed it
Con-Pro = Known objections and defenses
Cross-Day Meta-Axioms#
ID |
Statement |
Sel |
Type |
Cred |
Con-Pro / Notes |
|---|---|---|---|---|---|
mc.ax1 |
Every submodel produces a constructive fixpoint (distributed aggregation yield). fix(result(mk)) = result(mk). |
Y |
ax |
95% |
Pro: Grounded in type theory. Con: “Constructive” may be too strong for m0 (does VOID have a constructive witness?). |
mc.ax2 |
OK ↔ fixpoint convergence + scope-creep-excluded. |
Y |
ax |
90% |
Pro: Clean formalization of “it was good.” Con: “scope-creep-excluded” needs formal definition. |
mc.ax3 |
Evening-first: process(mk) = evening ▷ morning (via negativa before commitment). |
Y |
ax |
80% |
Pro: Connects to HELL methodology. Con: May be a design principle (theorem?) rather than axiom. Could be derivable from optimization theory (R6). |
mc.ax4 |
Construction cascade: input(mk) ⊇ ∪{result(mj) | j < k}. |
Y |
ax |
95% |
Pro: Straightforward filtered sequence. Con: m5 depends on m3 AND m4 (multi-dependency), so “j < k” may need refinement to a DAG rather than linear order. |
Submodel Axioms#
ID |
Statement |
Sel |
Type |
Cred |
Con-Pro / Notes |
|---|---|---|---|---|---|
m0.ax1 |
VOID: ∃Ω with H(Ω) = Hmax ∧ no types in Ω. |
Y |
ax |
85% |
Con: Does Ω “exist” constructively? Tension with mc.ax1. |
m1.ax1 |
TYPE: Ω = L ⊎ D, irrevocable, all construction within L. |
Y |
ax |
95% |
Pro: Clean, foundational. |
m2.ax1 |
EQUAL: Types(L) = Int(L) ⊎ Real(L). |
Y |
ax |
90% |
Pro: Standard CS distinction. |
m2.ax2 |
Every Real→Int mapping is lossy (∀φ: info-loss(φ) ≥ ε > 0). |
Y |
ax |
95% |
Pro: Known result in numerical analysis. |
m2.th1 |
PERFECT ∧ PERFIDE cannot hold universally. (Reclassified from m2.ax3 at TEMPER: derivable from m2.ax1 + m2.ax2. Proof sketch: applying PERFECT to Real types requires Real→Int mapping, which is lossy by m2.ax2, destroying what PERFECT tries to preserve. Applying PERFIDE to Int types requires Int→Real mapping, adding spurious precision. Neither direction preserves both.) |
Y |
th |
90% |
Pro: Maps to known dichotomies (nominal/structural typing, Kant/utilitarian, Arrow’s Impossibility). Derivability from m2.ax1+m2.ax2 strengthens the claim. AA: Formalize proof (AA-TEMPER-a8). Iron Maiden: HELD (9 OK, 1 OKO). |
m3.ax1 |
VALUE: Values(L) = Ground(L) ⊎ Ocean(L). |
Y |
ax |
90% |
Pro: Follows from m2 residual uncertainty. |
m3.ax2 |
Programs: finite decision trees rooted in Ground, taking Water input, producing Ground output. |
Y |
ax |
90% |
Pro: Curry-Howard pair. Note: “Water” (not “Ocean”) leaves open the circulation mechanism (RoL?). |
m3.ax3 |
Water Circulation: Water must cycle Ocean → Trees → Ocean. Without circulation, Ground dries and Ocean stagnates. (Promoted from R1.) |
Y |
ax |
85% |
Pro: Biologically fundamental. Con: Circulation mechanism (RoL?) unspecified. Note: Promoted from GrowthGarden R1 by user request. |
m4.ax1 |
LOGIC: Processes(L) = DAY(L) ⊎ NIGHT(L). |
Y |
ax |
90% |
Pro: Standard foreground/background distinction. |
m4.ax2 |
Time is a first-class entity with measurable progress. |
Y |
ax |
85% |
Con: “First-class” is vague. Needs sharper type-theoretic definition. |
m5.ax1 |
CARE: Conditional-data machines are self-managing and self-replicating. |
Y |
ax |
85% |
Con: Self-replication is a strong biological claim. Needs formal specification of replication mechanism. |
m5.ax2 |
UMP: noise > θ → channel-capacity-for-signal → 0. |
Y |
ax |
90% |
Pro: Grounded in Shannon. |
m6.ax1 |
HOPE-p1: Special-purpose world complete but no general intelligence. |
Y |
ax |
90% |
Pro: Descriptive, well-supported by construction cascade. |
m6.ax2 |
HOPE-p2: Balospe exists with general intelligence, responsible for Balance(L) OLT, recursively endowed. |
Y |
ax |
85% |
Con: Recursive endowment (“shares Creator’s abilities”) is the boldest claim. Pro: Self-hosting compiler analogy is precise. |
m6.ax3 |
HOPE-p3: OKO(m2) ∧ OKO(m6.2) ∧ designed-to-resolve(m6.2,m2) → OK+(system). Matched OKO pair = self-correcting architecture. |
Y |
ax |
75% |
Con: The multiplication metaphor (−1 × −1 = +1) is suggestive but not a proof. Needs rigorous justification. Most vulnerable axiom in the set. |
m6.ax4 |
Self-assessment bifurcation (asymmetric): self-assesses(B,OK) → BABL (sufficient; self-reinforcing trap). ZION → self-assesses(B,OKO) (necessary but not sufficient; a free agent can stop at any time, cf. Gen.18 Abraham). OKO enables but does not guarantee ZION. |
Y |
ax |
82% |
Pro: Candidate deepest finding. OK→BABL is modally necessary (analytic: “blindly assuming” entails OK). The asymmetry (BABL is stable attractor, ZION requires perpetual maintenance) is realistic. Con: OKO→ZION direction weakened to necessity at TEMPER (free agency means any agent can stop). Iron Maiden: HELD (8 OK, 2 OKO). |
m6.th1 |
OSCR Collapse: OKO(m2) ∧ self-assesses(B,OK) → ¬self-corrects(B) → ¬designed-to-resolve(B,m2) → KO(system). (Reclassified from m6.ax5 at TEMPER: derivable from m6.ax3 + m6.ax4 in 6 steps. See TEMPER Entry a10, Test II.) |
Y |
th |
90% |
Pro: The negative case is MORE defensible than the positive (m6.ax3), because the causal chain (complacency → no correction → system failure) is empirically well-documented. Derivability from m6.ax3+m6.ax4 strengthens the claim. AA: Formalize derivation (AA-TEMPER-a10). Iron Maiden: HELD (8 OK, 2 OKO). |
m7.ax1 |
TRUST: result(m7) = ∪{result(mk) | k=0..6}. Null operation. |
Y |
ax |
95% |
Pro: Definitional. |
m7.ax2 |
Time = WorkTime ⊎ RestTime (type distinction). |
Y |
ax |
90% |
Pro: Heschel’s “cathedral in time.” Clean. |
m7.ax3 |
Fractal periodicity: 6+1 integer-day ratio is the constrained optimum for Earth-like systems, given: circadian biology (integer-day batching), lunar alignment (28÷7=4), innovation-cycle isomorphism (e7Ch, pending), and Schelling-point resistance to BABL erosion. |
Y |
ax |
75% |
Con: Universality across non-Earth-like systems unproven. Depends on e7Ch being well-founded. Pro: Numerology objection answered (constrained optimization, not cargo cult). Schelling-point argument provides game-theoretic stability. Iron Maiden: initially BREACH, rescued to HELD (7 OK, 3 OKO) after user defense. |
Theorems#
ID |
Statement |
Sel |
Type |
Cred |
Con-Pro / Notes |
|---|---|---|---|---|---|
th1 |
W = L (scope produces the world). PET connection. |
Y |
th |
90% |
Pro: Straightforward if e7Day models creation. Con: Only applies when constructor = God. |
th2 |
Lossiness: Complex(L) → all Real→Int mappings lose info. |
Y |
th |
95% |
Pro: Follows directly from m2.ax2. |
th3 |
BABL originates in self-assessment (OK→BABL; OKO necessary for ZION). Mechanism behind th8. |
Y |
th |
85% |
Pro: Definitional argument (BABL = “blindly assuming” analytically entails OK). Substantially addresses Con-11. Con: OKO→ZION weakened to necessity (consistent with m6.ax4 reformulation). Iron Maiden: HELD (9 OK, 1 OKO). |
th4 |
System requires Balospe for OLT survival. General intelligence necessary because special-purpose machines cannot handle novel PERFECT/PERFIDE trade-offs. |
Y |
th |
87% |
Pro: Derivable from m2.th1 + m5.ax1 + m6.ax1. Substantially addresses Con-22 (volunteer requirement). Con: Assumes continuous novelty generation (needs explicit axiom or derivation). Iron Maiden: HELD (8 OK, 2 OKO). |
th5 |
Rest (periodic consolidation) is structurally necessary. Omitting consolidation → error accumulation → BABL. |
Y |
th |
80% |
Pro: Three defense lines (information-theoretic, thermodynamic, computational). Motivates ax25 (Jubilee). Addresses Con-31 with refinement (concurrent GC still redirects resources). Con: Error-accumulation model needs formalization. Iron Maiden: HELD (8 OK, 2 OKO). |
th6 |
Dual-Nothing: VOID (max entropy) and TRUST (min new-entropy) are formally dual. e7Day is entropy-reduction arc. (Promoted from R2.) |
Y |
th |
80% |
Pro: Follows from m0.ax1 + m7.ax1. Elegant. Con: “Formal duality” needs categorical specification (initial/terminal object?). Iron Maiden: HELD (9 OK, 1 OKO). |
th7 |
Compassion Capacity Theorem (five-gate form): Gate 1: repair-history prerequisite (OKO provides, OK does not). Gate 2: scope limitation (finite agents ⊂ F_all). Gate 3: other-awareness (state + context + trajectory). Gate 4: channel quality / Compassion UMP (noise > θ → help → 0). Gate 5: perpetual scope-expansion commitment (hero who stops → irrelevant/supervillain; ASON trap; “arrived” = deadlock). God: all gates non-binding. (Major rescue from original single-arrow form at TEMPER.) |
Y |
th |
70–80% |
Pro: Connects to 12+ axioms/theorems across PET, JUB, e7Day. Partially derives th8 mechanism. Provides mechanism for m2.th1. Supervillain theorem, eternal-life corollary. Con: Gate 5 depends on e7He (unspecified). Game-theoretic stability defensible but not proven. h* transition vulnerability (potential Con-45). VVN: iv_LLoL_OOv1 / dv_ClaOp46Max_OOv1. Iron Maiden: HELD (7 OK, 3 OKO). |
GrowthGarden (GG) — Candidates Not Selected for OOv1#
POST code: GG (GrowthGarden). Content that may be valuable but didn’t make the cut. Worth revisiting in future rounds or models.
GG# |
Statement |
Type |
Cred |
VVN |
Notes / Why not selected |
|---|---|---|---|---|---|
GG-a1 |
Monotonic Complexity. Each day strictly increases structural complexity in some well-defined measure. |
th |
75% |
dv_ClaOp46Max |
Unsure which complexity measure. Intuitively obvious but needs the right metric. |
GG-a2 |
PERFECT/PERFIDE Conservation. Gain in one requires expenditure from the other; total budget conserved. |
ax |
70% |
dv_ClaOp46Max |
Needs economic formalization not yet in model. |
GG-a3 |
Sabbatical Convergence. 6:1 is the unique optimal ratio for error accumulation vs. consolidation. |
th(conj.) |
65% |
dv_ClaOp46Max |
No proof sketch. May be empirical. |
GG-a4 |
Evening-First Efficiency. Via negativa converges faster than morning-first processes. |
th |
60% |
dv_ClaOp46Max |
Plausible from optimization theory but no formal model. |
GG-a5 |
Sky-to-Ocean Depletion. Sky machines converting potential→existing can exhaust future potential. |
th |
55% |
dv_ClaOp46Max |
Needs dynamics model. Connects to ax24 life-friendly cord. |
GG-a6 |
Constructor-Agnosticism. Same structural result regardless of constructor identity. |
th |
55% |
dv_ClaOp46Max |
Hard to define equivalence class of constructors. |
GG-a7 |
UMP-BABL Equivalence. UMP = BABL at info scale; BABL = UMP at system scale. |
th |
50% |
dv_ClaOp46Max |
May be analogy not formal equivalence. |
GG-a8 |
Blind Evolution Insufficiency. Above threshold C*, evolution too slow to prevent BABL. |
th |
50% |
dv_ClaOp46Max |
Threshold C* undefined. Connects to th8 CTMC. |
GG-a9 |
Verdict Counting. OK count per day is a formal invariant encoding structural information. |
ax |
45% |
dv_ClaOp46Max |
May be coincidence. Needs more models to confirm. |
GG-b10 |
Heschel Theorem. RestTime has its own internal modality (contemplation, integration, celebration). |
ax |
40% |
dv_ClaOp46Max |
Needs richer time theory. Beautiful if formalizable. |
GG-b11 |
4Be Completeness. Four capacities are necessary AND sufficient for OLT innovation economy. |
ax |
35% |
dv_ClaOp46Max |
Belongs to e4Be model, not e7Day. Scope boundary. |
GG-b12 |
EDEN Stability. All 4 EDEN properties must hold to resist BABL. |
ax |
35% |
dv_ClaOp46Max |
EDEN not yet elaborated. Premature to formalize. |
GG-b13 |
WoLC Duality. e7Day and WoLC are categorically dual. |
th(conj.) |
25% |
dv_ClaOp46Max |
May be poetic not categorical. Needs functor definition. |
GG-b14 |
Balospe Incompleteness. By Goedel, Balospe always has blind spots (necessary OKO). |
th(conj.) |
20% |
dv_ClaOp46Max |
Goedel-for-agents is contested. High risk of overreach. |
GG-b15 |
Information-Entropy Mirror. Total info content = H(VOID) - H(m6.3), conserved under trust test. |
th(conj.) |
15% |
dv_ClaOp46Max |
Probably oversimplifies real entropy dynamics. |
GG-b16 |
Scope Expansion Prohibition. D→L boundary is formally impermeable within a cycle. |
th |
15% |
dv_ClaOp46Max |
May already follow from m1.ax1. |
GG-b17 |
Strange Attractor Periodicity. ZION frequencies are discrete and 7-based. |
ax |
10% |
dv_ClaOp46Max |
Could be numerology rather than dynamics. |
GG-b18 |
RoL Circulation Axiom. Distinguished river cycle transporting Water from Ocean through Ground. |
ax |
8% |
dv_ClaOp46Max |
Almost no formal content yet. May grow with RoL model. |
GG-b19 |
Day 2 / Day 6.2 Resonance. Bidirectional feedback between EQUAL and Balospe. |
th(conj.) |
5% |
dv_ClaOp46Max |
Needs coupling constant/operator. At the junk boundary. |