Research Lines — Tamesis Program

The Sator Square is not the destination. It is the proof of concept.

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Program Status

ID	Title	EXP	Key Result	Status
RL1	Physical-Informational Reversibility	EXP-11	Local $H(S)$ more ordered than global $H(U)$	Complete
RL2	Symmetry-Protected Information	EXP-10	$d_{\min}^{\text{orb}}=4$ achieves $\rho\geq99.6%$	Complete
RL3	Universal Entropy Invariance Class	EXP-08	13/13 groups in $\mathcal{F}$ — universal	Complete
RL4	Variational Information Principle	EXP-12	$\mathcal{A}[M,G]$ exact identity, 14 groups	Complete
RL5	Local Arrow of Time Breaking	EXP-13	$d_{\min}^{\text{orb}}$ predicts $t^*$, $r=+0.87$	Complete
RL6	Fundamental Compression Limit	EXP-09	Burnside LB violated — refined conjecture	Complete
RL7	Symbolic Codes and Physical Information	EXP-14	Holographic comparison	Pending

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★ Cross-Cutting Discovery

See full document: DISCOVERY_universal_invariant.md

Emerged from EXP-15: $d_{\min}^{\text{orb}}$ predicts all structural metrics simultaneously.

$$d_{\min}^{\text{orb}}(G) = \min_{\substack{O \in \text{orbits}(G) \ |O|>1}} |O|$$

Correlation	Value
$\text{corr}(d_{\min}^{\text{orb}},;\rho(t=1))$	$+0.868$
$\text{corr}(d_{\min}^{\text{orb}},;t^*)$	$+0.868$
$\text{corr}(d_{\min}^{\text{orb}},;\mathcal{A})$	$+0.825$
$\text{corr}(d_{\min}^{\text{orb}},;\kappa)$	$-0.825$

Higher $d_{\min}^{\text{orb}}$ → better recovery, longer coherence, more action, lower compression ratio.

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Escalation Path (updated)

Sator (combinatorial result)
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RL3: Entropy invariance generalize?    ✓ 13/13 groups in F
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RL6: Universal compression bound?      ✓ Burnside violated — refined conjecture
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RL2: Symmetry protect info passively?  ✓ d_orb=4 → ρ≥99.6%
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RL1: Physical subsystems stable?       ✓ H(S) < H(U) confirmed
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RL4: Variational principle?            ✓ A[M,G] = (n²-k)·log₂σ exact
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RL5: Local arrow of time?              ✓ d_orb predicts t* (r=0.87)
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★ UNIVERSAL INVARIANT: d_min_orb
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RL7: Physical codes / holography?      → Pending (EXP-14)

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Shared Infrastructure

• Core results: ../simulations/ (EXP-01 to EXP-07) — Sator foundation
• RL results: figures/, results/ — EXP-08 to EXP-15
• Synthesis: figures/SYNTHESIS/15_universal_invariant.png
• Theoretical framework: ../ajuste_fino/
• Published paper: ../index.html

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Files per Research Line

Each RL folder contains:

RL*/
├── readme.md      — core question, framing, open tasks
├── checklist.md   — live progress tracker
├── roadmap.md     — milestones and publication targets
└── simulations/   — Python scripts (EXP-NN_*.py)