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Accessibility curvature law

V824: spatial compression of reachable-state accessibility generates conformal, curvature-like scalar structure. Scalar/conformal sector only. Not tensor Einstein.

08 Atlas / scalar · Result · Supported · 2026-05-20 · compiled 2026-10-10 · 1 min read · 1 X source

Original on X · Package: Einstein Phase 1 · JSON · Cite

V824 · curvature · conformal · accessibility

On this page

• Supported vs failed branches

Causal stack

1. 00 Astra / global consistency
2. 01 Genesis Pin
3. 02 Retained pruning-order history
4. 03 Admissible slice
5. 04 L1 (closed)
6. 05 L2 (closed)
7. 06 L3 hyperedge memory T_H + D_L3
8. 07 L4 H₄ rank lift
9. 08 Discrete atlas / scalar accessibility
10. 09 GEM-bridge / gravity

Author: Aaron Spradlin. Program: Recoverability Geometry / Accessibility Branch. Version V824, 20 May 2026. The paper asks whether ordered-update recoverability systems naturally generate geometry-like structure. The strongest validated branch was accessibility geometry, not tensor transport.

$$G_{\mathrm{proxy}}=2\alpha \Delta \log (A+\epsilon ),A=\exp (C-\mu +\eta \mathrm{repair})$$

With accessibility potential φ = −α log(A+ε) and G_proxy = −2Δφ, the effective conformal factor is Ω = exp(φ), g_eff = Ω² g₀. Held-out R² ≈ 0.879 (mean), correlation ≈ 0.938; compressed operator R² ≈ 0.917; direct perturbation δG R² = 1.000; adversarial nulls next-best ≈ 0.

Supported vs failed branches

• Supported: scalar/conformal accessibility-curvature law, Hamiltonian-like scalar closure, conformal geometry via Ω / g_eff.
• Not supported: full tensor Einstein closure, ADM momentum constraints, conserved vector current, physical spacetime interpretation, local PDE evolution law for A. Tensor-branch attempts failed.

Recoverability pressure creates reachable-state density. Spatial compression of log accessibility generates curvature-like scalar structure.

Accessibility Curvature Law paper, V824

X sources

Original posts this article was compiled from. The notebook copy is editorial; the status URL is the source.

• 2026-05-20

  V824 accessibility-curvature law locked

  In the notebook · Open original post

Previous Retained atlas closure (V1698)Next UQCF-GEM

Causal stack

1. 00 Astra / global consistency
2. 01 Genesis Pin
3. 02 Retained pruning-order history
4. 03 Admissible slice
5. 04 L1 (closed)
6. 05 L2 (closed)
7. 06 L3 hyperedge memory T_H + D_L3
8. 07 L4 H₄ rank lift
9. 08 Discrete atlas / scalar accessibility
10. 09 GEM-bridge / gravity

On this page

• Supported vs failed branches

X sources

Related articles

• Claim ledger
• Recoverability geometry
• Recoverability framework
• Emergent gravity (candidate)

GitHub packages

• Einstein Phase 1

Field notes

• V824 accessibility-curvature law locked

  2026-05-20

  On X