A structural framework for interpreting what is necessary to maintain future selectability.
Not about efficiency, optimization, or higher returns — but about the structures required to avoid collapse.
Does a given phenomenon reduce the set of reachable future options, or not? A framework for making that judgment structurally.
I_min ≡ ∃t'>t : O(x_t') ≠ ∅
There must remain at least one reachable future state with options. Not an optimization target — a maintenance criterion.
| # | Name | Definition |
|---|---|---|
| D0 | Existence | Ω ≠ ∅ — the state space is non-empty |
| D1 | Distinction | Ω partitions into non-overlapping parts |
| D2 | Relation | R ⊆ Ω × Ω — states are connected |
| D3 | Transition | T ⊆ R — some relations are state changes. Time ≡ order of transitions |
| # | Name | Key Point |
|---|---|---|
| D4 | Indeterminacy | If |Ω| > 1, which state is realized is undetermined |
| D5 | Observation | Observation is lossy mapping. Information always decreases |
| D6 | Constraint | Repeated transition patterns become constraints |
| D7 | Evaluation | Evaluation is a multi-dimensional vector, not a single score |
| D8 | Boundary | Inside/outside distinction. No boundary, no agent |
| D9 | Selection | Selection irreversibly shrinks Ω |
| D10 | Attribution | Attribution of selection — self-model |
| D11 | Integrated Selection | Integration of multiple selections. Functional definition only |
| D11' | Experiential Condition | Whether integrated selection manifests as experience — structurally undecidable [OPEN] |
| # | Name | Key Point |
|---|---|---|
| D12 | Stability | Attractors exist. Systems persist near them |
| D13 | Option Shrinkage | Every selection reduces the option space |
| D14 | Meta-Evaluation | Evaluating the evaluation criteria. Without it, no calibration |
| D15 | Threshold | Below Θ, collapse risk |
| D16 | Restoration | Without restoration attempts, every system eventually collapses |
| D17 | Cost | Every action has cost > 0 |
| D18 | Delay | Effects lag behind causes. No instantaneous causation |
| D19 | Closure Boundary | No system can access the full Ω |
| # | Name | Key Point |
|---|---|---|
| D20 | Overheating | Single goal + acceleration → approaching Θ |
| D21 | Buffering | Dispersal, deferral, diversification → option preservation |
| D22 | Autonomy | Operates only through structure. No external intervention |
| D23 | Termination | Ending as completion, not collapse |
Not choices but necessities. Inescapable consequences for any selection system maintaining I_min.
| SC | Statement |
|---|---|
| SC-1 | No goal fixation — fixation shrinks options toward collapse |
| SC-2 | No omniscient optimization — would require violating D19 |
| SC-3 | Selection speed limit — too fast leads to collapse |
| SC-4 | Diversity required — monoculture converges to Θ |
| SC-5 | Failure cannot be eliminated — elimination blocks restoration paths |
| SC-6 | Distributed judgment — centralization is fragile |
| SC-7 | Identity non-fixation — fixation constrains action → collapse |
| SC-8 | Combination theorem — four collapse types |
| SC-9 | Descriptive incompleteness — no system fully describes Ω |
This repository contains the Core layer (6 documents).
This repo (Core)
d-arch-reference.txt — Compressed overview
D-Arch_Index.txt — Document hierarchy and branching rules
D-Arch_Core.txt — Axioms, maintenance criterion, structural chain
D-Arch_Core_formal — Formal definitions
D-Arch_SC_Detail.txt — Structural consequences (SC-1–9)
D-Arch_SC_Formal.txt — SC formal proofs
D-Arch_OC_Detail.txt — Operating conditions (OC-1–10)
Full version (29 documents) — available at voidafter.com
Core + Physics + Applied
Matter → Field → Life → Regulation → Civilization
→ Consciousness → Intelligence → ⛔ Termination Line
No extension beyond the termination line.
| Symbol | Definition |
|---|---|
| Ω | Total state space |
| T | Permitted transitions |
| O(x) | Reachable options from state x |
| Θ | Collapse threshold pattern |
| I_min | ∃t'>t : O(x_t') ≠ ∅ |
| J | Evaluation function (vector) |
| B | Boundary operator |
| M | Attribution mapping |
| R | Restoration action |
- Website: voidafter.com
- Framework: voidafter.com/app/framework
- Full download (29 docs): voidafter.com/app/download
SC-9 applies to this document itself.