The score is called ΦR, or Phi-R. Higher means more next-step predictive structure belongs to the whole.
GARD-inspired predictive information in Flow Lenia
Before
the Replicator
Could the system's internal coordination warn us—before anything happened—which creatures would recover from a severe injury?
We ran the clean, prospective test on 288 fresh trajectories. The answer for this exact score, experiment, and three creature families was no.
01 / Question
What did we actually measure?
Four tracked founder lineages make up a changing composition. We asked whether their next composition was better predicted as one coordinated whole than as separate groups.
vs.
We tried every possible two-part split, following the central whole-versus-parts idea in the GARD paper.
02 / Design
Measure first. Injure later.
The feature code was not allowed to see the injury, the recovery label, or any later state. The complete protocol and analysis were frozen before the first trajectory ran.
Watch
Use exactly 65 composition states immediately before injury: 64 one-step transitions.
Measure
Compute the whole-versus-parts score using only that past window.
Injure
After fission number 8 (zero-based index 7), deplete 90% of the largest founder lineage.
Judge later
Require recovery at three consecutive post-injury division boundaries.
Recovery, in simple terms: the depleted lineage came at least halfway back and the four-founder mixture looked at least 90% like its pre-injury target—three divisions in a row. Runs that could not support a fair yes/no comparison were left unlabelled, not counted as failures.
03 / Accounting
Nothing was cherry-picked.
Every scheduled run stayed in the cohort. We did not rerun ugly cases, lower thresholds, extend convenient trajectories, or add fake noise when a founder coordinate was constant.
Fresh trajectories
288
ΦR measurable
262
Binary outcome
225
Complete final rows
211
Certified recoveryCertified no recoveryInapplicable under the frozen rule
The final comparison used 211 runs: 77 recovered and 134 did not. Of 26 unavailable Phi-R values, 25 had a founder coordinate absent or constant throughout the fit window; one was injured before 65 states existed.
04 / Injury
What the fixed injury looked like.
These are the first scheduled seed in each family, chosen by seed number—not by appearance or result. They show the intervention mechanics, not evidence for the statistical conclusion.
Mechanics example only · this run was later classified no recovery.
Mechanics example only · this run was later classified no recovery.
Mechanics example only · this run was later classified no recovery.
How to read these: each image shows total matter, not founder identity. The 512×512 arena was centered on the creature, reduced to 64×64, then shown with the same central 32×32 crop. Each frame is peak-normalized separately, so brightness does not show total matter loss; the mass numbers do. Pre and post were recentered independently.
05 / Result
Three ways the signal had to win.
The sample-size gates passed. The scientific signal tests did not.
Families disagreed.
Bars show recovered minus nonrecovered Phi-R, in within-family standard deviations. Our frozen rule required every family to point right.
c02+0.376
c03-0.520
c12+0.177
equal mean+0.011
lower before recoveryhigher before recovery
Permutation p = 0.4694 · not rare under shuffled labels
The disagreement remained.
We first removed what 14 simpler measurements could explain. c03 still pointed the other way.
c02+0.124
c03-0.188
c12+0.198
equal mean+0.045
lower before recoveryhigher before recovery
Permutation p = 0.3829 · still not convincing
Adding Phi-R made prediction slightly worse.
Each run was predicted by a model trained on other runs. Log loss is a penalty for wrong probability forecasts: lower is better.
14 ordinary controls0.686445
vs.
same controls + ΦR0.691239
Change: +0.004794 — worse overall. Bootstrap 95% interval: -0.001893 to +0.012045. Because it crosses zero, the tiny difference is also compatible with no real change.
c02+0.008
c03-0.003
c12+0.010
equal mean+0.005
Phi-R helpedPhi-R hurt
06 / Decision
The gates, at a glance.
Enough clean data existed to answer the question. The answer was negative.
Enough usable data
262 measurable Phi-R histories and 211 complete binary rows.
Raw direction
c03 pointed opposite to c02 and c12; p = 0.4694.
Beyond controls
The mixed direction remained; p = 0.3829.
Held-out prediction
Log loss rose by +0.004794; the interval crossed zero.
07 / Meaning
What can we honestly say?
A clean negative is useful because it closes one tempting explanation without pretending the larger question is settled.
We can say
- We built a prospective, zero-safe GARD-inspired whole-versus-parts measure for Flow Lenia.
- This exact W64 Phi-R did not reliably foretell later compositional recovery in c02, c03, and c12.
- It did not add useful held-out prediction beyond 14 ordinary pre-injury measurements.
- The result survived an independent from-scratch audit.
We cannot say
- “Lenia has no causal emergence.”
- “No information signal can precede replication or recovery.”
- “The reservoir does not work.” This experiment was not a reservoir comparison.
- “These creatures are—or are not—autonomous replicators.” Recovery was the fixed phenotype here.
The clean next move
Do not tune this cohort until it gives the wanted answer. Treat it as a sealed negative. A new prospective study can change one scientifically motivated thing—state description, timescale, or reproduction phenotype—and freeze that choice before new trajectories run. A causal claim would then require an intervention that deliberately moves the proposed precursor before the outcome.
08 / Receipts
Why trust the negative?
The experiment was designed so an answer could not be manufactured after seeing which runs recovered.
288 / 288completed with no retries or substitutions
200,268independently compared feature values
0feature-audit mismatches
1,000,000label permutations per association test
100,000bootstrap resamples for prediction uncertainty
622frozen files rechecked by independent audit
What “no peeking” meant
For an injury at step t, feature extraction read exactly the 65 states from [t−65, t). It excluded state t, the injured founder's identity, the reservoir contents, recovery timing, the label, and every later state. Features were written and independently audited before the outcome classifier was allowed to run. A synthetic mutation to the hidden suffix left every feature payload byte-identical.
The 14 ordinary measurements
- whole-state next-step predictability
- age
- mass
- recent growth
- fragmentation
- motion
- component count
- final founder-support deficit
- support-deficit exposure
- current founder fractions q0, q1, q2
- recent composition movement
- founder-labelled coverage
Extra held-out metrics
| Model | Log loss ↓ | ROC AUC ↑ | Brier ↓ |
|---|---|---|---|
| 14 controls | 0.686445 | 0.552796 | 0.244231 |
| Controls + ΦR | 0.691239 | 0.545411 | 0.246082 |
Sealed artifact hashes
| Freeze | 2ebf3a1d0b7ec5b41309968b19f824ec4b5c3b405039f78616f50becca90637d |
|---|---|
| Manifest | f0e4cecb554cc5f06d2a816deadcc9d398df46b6cec887c9971725bc0bbc2cdf |
| Protocol | 5c3effc16e70baad9d1b0ce1ca477ed05f724f4e7752ed0a4e88b191ac447e47 |
| Mechanical audit | 4a1ded6ce055a6466d405c68a4310a0a02c1584622bf2f8573b98b7901725989 |
| Features | f88140df0bdfe374423a1adf35ca3a741a1dcc2bd83588248a15cdeb46a35fff |
| Feature audit | cda38f10dd1018035117f3f43700b18fc3808dbfdd840d69d020877505e0507c |
| Outcome report | ea720da3f988827d7b95d6ff741d4b4e6f1f36135a54cd941a676aabb16aae1f |
| Association report | b75da09a98eaea4eaba03f7daf4f1ad31f4dc2d6032650ac6d314738e1e110a1 |
| Output tree | 2b40130fead1bd5a0af856cf0a323e2cdf31322e9571f6061b65f904784100af |
Output tree: 5,184 files · 76,432,538,023 bytes. The standalone page is explanatory output and is not itself part of the prospective freeze.