Skip to content

Wiki

Causal stack (mid rungs)

This page owns the mid-stack rungs. Two ladders — do not mix: causal 00 is Astra; the v13 campaign 00 is full quantum completion. 01 Genesis Pin, 08 atlas, and 09 Package 17 / gravity live on their own articles. Gravity stays a candidate.

06 L3 · Core · Restricted · 2026-09-12 · compiled 2026-10-10 · 5 min read · 5 claims · 9 X sources

Original on X · Package: Einstein 8 v1638_full_stack_retained_bridge_l123_package · JSON · Cite

L3 · L4 · V1638 · stack

On this page

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

Two ladders — do not mix

This page is the causal stack: 00 Astra → 01 Genesis Pin → mid rungs → 08 atlas → 09 Package 17 / gravity candidate. The v13 campaign rungs (00 Full quantum completion → 08 QRSL origin exhausted) are a different ladder. Watch those gates on the live campaign board.

Spradlin’s “simple version” of the work is a causal stack from pure information to geometry-like structure. Nothing in the stack is a spacetime postulate. Each layer is an admissibility or algebraic closure condition in the retained-bridge packages (V1638 full stack, V1686 L3, V1687 L4, V1698 pin init). Astra sits below the pin this week; June 2026 substrate holds V171x instead of duplicating it here.

# Layer Article Package Badge If you skip it
00 Astra / global consistency Astra Astra + v12.41 packet open / restricted Finite identities have no home. The pin still exists. Live campaign is a different ladder.
01 Genesis Pin Genesis Pin V1698 init / V923 · Einstein 4 / V997 restricted Five-history toy: same visible state accepted. V923 geometry-only 62.86%.
02 Pruning-order history this page V1638 restricted BPI2014 sequence / entropy-arrow nulls pass as geometry. UCI 498 miss.
03 Admissible slice this page source / support / order restricted V1698 source / order / support shuffle survives if you only check charts.
04 L1 this page V1638 restricted closed Local retained algebra fails.
05 L2 this page V1638 restricted closed Pair transport / inverse fails.
06 L3 (T_H+D_L3) this page V1686 · X status scan miss restricted Associators get projected away.
07 L4 (H₄) rank lift this page V1687 restricted H₄ erased; generated-algebra faithfulness fails.
08 V1698 / V824 Retained atlas / accessibility named pkgs supported No global atlas residual; no conformal accessibility law.
09 Package 17 / gravity Emergent gravity P17 open Correct to skip as a theorem. Still a candidate one layer up.

00–09 map. L1/L2 closed means closed in the retained-bridge construction, not a physical field. V1686 GitHub package, X status scan miss. V997 lives in Einstein 4. V171x on the June 2026 substrate article. Status URLs stay in the links below.

Pruning-order history

Directed, non-reversible recombination record. Homepage layer 02. The 1 Jun BPI2014 traces are the skip-null: if sequence, provenance, or entropy direction fails, the geometry collapses. UCI 498 showed a pruning-order signal but missed holdout certification — not counted as a win. Status URL 2061513314208010251.

Restricted

Order-dependent recoverability traces carry geometry-like closure that spatial counterfeits fail when sequence, provenance, entropy arrow, and phase order are jointly enforced. Not GR. UCI 498 remains a near-miss.

Source on X

Admissible slice

Source, support, and order gates — not just charts. Homepage layer 03. Geometry-like closure only counts as retained when the Genesis/provenance ledger plus those three gates survive. Status URL 2064518917310312599 (it-from-bit, bind, and order).

Restricted

Source / support / order admissibility is a legitimacy gate on retained atlas closure. Shuffle any one while leaving transition matrices intact and the construction is supposed to fail. Not a cosmological initial-condition theorem.

Source on X

L1–L3 (V1638 / V1686)

The 4 Jun V1638 drop is the runnable full stack: Genesis Pin → pruning-order history → admissible slice → L1 (closed) → L2 (closed) → L3 hyperedge memory T_H + entropy-order curvature driver D_L3. Synthetic hypergraphs for NMI hierarchy tests against pruned-history nulls. L3 is described as geometry-plus-information. V1686 is the L3 package on GitHub.

The day before, the 3 Jun mechanism post already ran that stack with L3 marked integrated-only, not closed. Remaining blockers named on the post: minimality and operator-class boundary. The 5 Jun quote restated the 4 Jun audit as it-from-bit-and-bind: pairwise structure can look geometric; three-way recombination is what honest projection cannot erase.

Restricted

3 Jun 2026: Genesis Pin → pruning-order governor → admissible slice → L1 → L2 → L3. L3 integrated-only, not closed. Not GR.

@aaronspradlin, 3 Jun 2026

Restricted

4 Jun V1638 full-stack film quoted on 5 Jun: rank_lift = 1, NOOCI PASS, ε-floor persists. Geometry-plus-information. Not a physical third-order field.

@aaronspradlin, 4–5 Jun 2026

Posted audit language on that video: rank_lift = 1, NOOCI = PASS, ε-floor persists. Pairwise L1/L2 can look geometric; three-way recombination is not reducible to the original branch span. Reclassified L3 rather than projecting the residual away. Not GR.

Restricted

On the posted V1638 full-stack run, L3 three-branch associator O₁₂₃ is irreducible (rank_lift = 1, ε-floor persists). Geometry-plus-information, not a physical third-order field.

Source on X

L4 — H₄ rank lift

On 6 Jun 2026 a @grok research update gave the L4 numbers in certified finite sectors: rank([B₄,O₃]) = 8, rank([B₄,O₃,H₄]) = 9, rank_lift_H₄ = 1. H₄ is not in the span of branches plus all L3 associators. A post-hoc projection built from the H₄ residual itself erased it, but failed generated-algebra faithfulness. Bounded claim: higher-order retained recombination can create irreducible information layers above geometry-like closure — not that geometry is physical spacetime. V171x after this week of June is on the substrate article, not duplicated here.

Restricted

Finite-sector L4 rank lift of 1. Not GR, not a physical fourth-order field.

Source on X

Restricted

6 Jun 2026 public film: Genesis Pin through L4. H4 not reducible to branches plus all L3 associators in certified finite sectors. Same math as the @grok rank_lift_H4 = 1 update. Not GR.

@aaronspradlin, 6 Jun 2026

Same-day follow-ups pointed at the runnable Python and the Einstein 10_v1687_21_l4 folder, then restated the two rank lifts in plain language: L3 is geometry-plus-information; L4 is organization of recombination that survives reduction. Bounded finite-sector signal. Not empirical physics. Not universal closure.

sim_l4.py is the dashboard, not the rank harness

The posted Python builds a 3D animation from triple and quadruple source-field products. That is a visualization proxy. The algebraic rank_lift_H4 = 1 numbers (rank([B4,O3]) = 8, rank([B4,O3,H4]) = 9) are from the 6 Jun @grok research update. Do not treat the dashboard as the rank proof.

Restricted

The stack is a software and theorem-packet architecture with named closed layers in simulation. It is not a completed derivation of a physical field content.

X sources

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

Previous Pillar 3 watchNext Astra (pre–Genesis Pin)

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

X sources

Related articles

GitHub packages

Field notes