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Canonical Path v2.1: Foundation, Identification, and Survivability

The current research path after the foundations audit.

Purpose

This document describes the present canonical path through the repository. The path now begins with the Foundations Reconstruction. That audit found no independent mathematical role for an unqualified generator, rejected a generic forward/inverse complexity law, and made identity test-relative. The older Generator Question is retained as a legacy framing whose bounded identification questions survive.

After the foundation, two research arcs remain:

  • Model identification (the epistemic arc): under declared model families, evidence, intervention access, target equivalence, and cost measures, which candidate process models can an observer distinguish? Its phases are folded into From Trace to World-Binding and measured in the inverse-reconstruction benchmark.
  • The Viability Arc (the dynamical spine, this document): what happens to an emergent optimizing system over time, and what does it take to keep it alive? This runs emergence → optimization → constraint architecture → survivability and terminates in the Viable Corridor paper.

They share a compositional process language, not a universal law. One asks what evidence identifies; the other asks whether a specified optimizing process remains inside a declared viability region. This document maps their relationship and then follows the second.

The paper is a node, not the project. The Viable Corridor is one citable artifact produced by this repository — a stabilized synthesis at the sharp end of the arc. The repository remains the generative system: a map of related models, essays, simulations, narratives, and open problems. This path is written to keep the paper in proportion.

How the layers stack. Not everything is equally central, and the concepts should not compete for the throne. The working hierarchy:

  1. Foundation — Foundations Reconstruction: standard Borel interfaces, Markov kernels, composition, derivations, supplements, and limits.
  2. Research frontier — inverse reconstruction: bounded model identification under noise, observability, coverage, family search, and interventions.
  3. Identity layer — Mirror Problem, Chord/Arpeggio, IP, Δ-Kohärenz: competing test families and metrics for persistence. No absolute or generator-recovery identity is assumed. Consciousness is a separate boundary: functional architecture can be tested; experience is not derived (home).
  4. Safety / application layer — TEO, the Viable Corridor, the veto cluster: what happens when optimization pressure outruns the modeled constraints.
  5. Narrative layer — fiction, manifestos, logs: stress tests and concept generators, never evidence.

A concept that fits none of these layers, and has no home file, experiment, or open problem, is not part of the canonical claim structure. It may remain an explicitly unclassified seed in the Thinking Space without owing the project a promotion. Before it is used as a load-bearing claim, it needs a home, status, evidence path, and scope boundary — see What This Project Does NOT Claim and the Concept Registry for the term-by-term audit.

A note on tags. Each station below carries the status of its strongest content, using the project's vocabulary: [FOUNDATIONAL ASSUMPTION], [DEMONSTRATED], [HYPOTHESIZED], [FORMAL], [CONJECTURE], [HEURISTIC], [EMPIRICAL CONJECTURE], [MODEL ASSUMPTION], [SIMULATION ARTIFACT], [NARRATIVE STRESS TEST], [OPEN PROBLEM]. Mixed nodes are tagged per-claim, not globally.

1. Foundations Reconstruction — the shared language

The project begins with the smallest familiar classical basis adequate through prediction: measurable interfaces and stochastic processes, composed sequentially and in parallel. Structure, discrete dynamics, invariance, observation, information, and conditional prediction are derived. Identity, learning, and intelligence require declared supplements; phenomenal consciousness requires a bridge axiom that is not adopted.

The model-identification programme and the Viability Arc both pick up downstream of this language. Neither is implied merely by admitting processes.

2. Emergence and Self-Organization — [DEMONSTRATED] in selected models

Selected local processes produce measurable global structure in the repository's toy models. Their forward execution is tractable at the implemented scale; no universal cost claim follows.

3. Optimization and its Blindness — the hinge [HYPOTHESIZED]

The arc's pivot asks what happens when a system improves a declared objective while relevant effects remain outside its observations, constraints, or boundary. TEO supplies one conditional concentration-and-overshoot model; its two synthetic implementations also show a selected capability parameter loading more than one modeled constraint. Whether this pattern holds for a real optimizer is empirical.

(The hinge essay consolidates the existing material above; it asserts no new claim. The station is named because the arc is unintelligible without it: constraints answer a question, and this is the question.)

4. Constraint Architecture — TEO [HYPOTHESIZED] / [MODEL ASSUMPTION]

The repository's selected constraint model combines a regulatory brake, value coupling, and a substrate budget. Its research hypothesis is that some systems require a conjunction of constraints rather than one compensating scalar.

5. The Viable Corridor — the stabilized artifact [FORMAL] + [CONJECTURE] + [HEURISTIC]

The formal synthesis derived from the TEO branch — a paper-style node, not the whole project. It proves componentwise necessity results under its assumptions, defines viability as a conjunction, conjectures sufficiency, and advances a clearly hedged structural-mapping hypothesis. Its strongest current result is model-internal capability loading: in two synthetic models, the selected capability intervention pushes multiple boundaries and single-axis controls leave another modeled failure exposed.

  • The Viable Corridor — necessity theorem [FORMAL], sufficiency [CONJECTURE], isomorphism [HEURISTIC] / [EMPIRICAL CONJECTURE], derivations in Appendix A.
  • Evidence: Appendix C (TEO ODE, Class A) and Appendix D (agent-based ecology, Class C) — see §6.

6. Agent Ecology and Alignment-Veto Simulations — [SIMULATION ARTIFACT]

The executable side: do constraints actually matter? Two structurally independent models reproduce the regime claims (hard vs. soft budgets; capability loading; single-axis interventions failing at high capability).

7. Survivability: Substrate, Veto, and the Civilization Interpretation — [HYPOTHESIZED] / [EMPIRICAL CONJECTURE]

The arc's endpoint. The theory of survivability is the veto/viability cluster; its application to civilization is an explicitly heuristic interpretive layer, not a proven isomorphism.

8. Fiction and Narrative Stress Tests — [NARRATIVE STRESS TEST]

Fiction is the project's instrument for noticing when a clean formal claim is impossible to live with. It stays linked but separate from the formal layer.

  • fiction/README.md — full annotations. Substrate-limit pieces (Impedance Crash, The Vital Floor, Dashboard of the Commons) dramatize §3–§7.

9. Open Problems

The honest frontier — what the arc has not closed.

  • Proving sufficiency / deriving \(\gamma_c\) rigorously (not just single-trajectory existence). Paper §3.4, Appendix C.5.
  • Operationalizing \(\gamma_{\text{eff}}\), \(K_{\text{eff}}\), \(D_{\max}\) for real systems; \(K_c\) for societies. Paper §5.4.
  • A finite-\(N\) / general-network version of the coherence (Kuramoto) result. Paper §3.3.
  • Validating P7/P8 on real AI-agent systems (the Appendix D evidence is synthetic). Companion paper.
  • Genuine overshoot-collapse dynamics (delays, endogenous \(D_{\max}(t)\)) vs. the current rate-threshold self-arrest. Paper §6.4.
  • Whether the Viable Corridor should remain in this repo or become a spin-off. (Governance open problem.)
  • See also theory/reference/open-problems.md for the project-wide list (Mirror Problem, Co-Instantiation, Trace-to-Generator reconstruction).

Working Rule — keep the writing modes separate

Do not route everything through the paper. Per the Information Architecture:

  • papers/ — citable, compressed artifacts (the Viable Corridor).
  • theory/ — conceptual development and argument.
  • simulation-models/, lab/ — executable claims.
  • fiction/ — narrative stress tests.
  • logs/ — speculative architecture notes.
  • meta/ — repository governance and epistemic framing (this document).

One source of truth per concept; everything else links to it.