Field notes / Experiment guide
What information is hidden in the start of the rule?
Short prefixes predict boundary occupation surprisingly well. Which simple feature of the prefix is carrying that information?
New to these ants? Start here.
An ant moves on a grid of coloured squares. Each colour tells it to turn left (L) or right (R). It advances that square to the next colour, then steps forward. A rule such as RLR is the list of turns, starting at colour zero. On a blank grid the same rule always makes the same trajectory.
Territory means every cell visited so far. Its boundary consists of visited cells with an unvisited neighbour. A highway is a repeating pattern of motion that carries the ant away. A tether means repeated returns to a small home region.
Growing like the cube root of time means taking eight times as many steps to double a linear size. The rotor walker is a comparison model that follows and rotates arrows stored on cells. A seed makes a random starting pattern reproducible; the ant itself can still move deterministically.
We distinguish c, the chance of discovering a cell per boundary step, from kappa (κ), time at the boundary normalized by perimeter divided by area. Explaining their values is harder than using them to account for growth.
The idea under test
Decoding prefix features may reveal a compact predictive description, especially the opening run of identical turns.
What we learned
The exploratory decode identifies opening-run length as a candidate and motivates a fresh-rule replication rather than treating the discovery score as confirmation.
What this leaves open
This is post hoc feature discovery. Predictive success can reflect territory size and selection as well as direct boundary dynamics.
Read the evidence and reproduction recipe ↗
Inside the experiment
Methods, registered predictions, exact commands and saved analysis. These are the working research documents; expand them for the detail behind the introduction.
Methods and original experiment record
kappa prefix decode: what does the 8-letter prefix encode?
Registered 2026-10-16 09:05 +13:00, base commit 269288e, before any decoding
measurement. Exploratory discovery on inspected data (census and the 162
stationary pool rules were already used by prefix_audit.py); nothing here is
confirmation. Confirmation would need a fresh w3c_sample.py draw under a new
seed, excluding pool rules (not run).
Question, and a correction to its framing
The prefix signal that survives scrutiny is the stationary-cohort gain over a
spline in ln A(22): +0.20 held-out R^2 (CI 0.10-0.31, 162 rules;
../2026-10-kappa-rule-space/results/prefix_audit.json). It is not the 0.63 in
x2_prefix_heldout.txt; that is ln A(22) alone (prefix-6 + ln A gives 0.633, no
gain), and all-rules transfer is ~0 (+0.04, CI -0.02..0.10). So the target here is
the residual of ln kappa after the ln A(22) spline, stationary rules only.
Otherwise any feature that predicts growth speed would look like a decoded prefix.
Already tested and not repeated: fresh-cell long-excursion launch rate (P1 failed)
and exposure features over position (P2 failed its interval bar), in
../2026-10-15-kappa-prefix-exposure. Earlier evidence in
../2026-10-kappa-rule-space (W1, X1): prefix-sharing ICC of stationary ln kappa is
~0 for prefix <= 3 and jumps at 4 (0.14), 5 (0.32), 6 (0.46); Hamming-1 flips at
positions j >= 4 give r(ln kappa) = 0.38 but j <= 3 ~ 0.
Candidate encodings (all compared to the prefix-8 lookup, the reference)
- E0 additive: ridge on R-indicators at positions 1..8 (plus length).
- E1 interactions: E0 plus all pairwise products of positions 1..8.
- E2 summary: leading-run length, R count in the first 8, number of L/R switches in the first 8 (3 numbers).
- E3 edge-runs-its-own-prefix: ln kappa residual of the standalone rule
canon(rule[:p])looked up in the census (p = 4..7), no lookup fitting. Mechanism: fresh and recently invaded rim cells carry low colours, so near the boundary the ant mostly executesrule[:p]. - E4 shuffled-position control: E0 and E1 with positions permuted at random per fit (should give ~0 gain; guards the pipeline).
- Descriptive: greedy depth-3 regression tree on the stationary residual over prefix letters, to show which positions split.
Predictions (registered; thresholds are design choices)
gain = held-out R^2 gain over the area spline on the 162 pool rules, trained on the census stationary rules (exactly the audit's training/test sets and metric); lookup gain reference = the audit's (spline, crossfit5) gain, re-derived in this script.
- D1 (additive fails): E0 recovers < 25% of the lookup gain. The earlier "simple features fail" result was on raw kappa; I expect it to hold on the residual.
- D2 (information is interactive): E1 recovers >= 50% of the lookup gain, CI of the E1 gain above 0.
- D3 (own-prefix mechanism): E3 gain CI above 0 for some p in 4..7, and the best p recovers >= 50% of the lookup gain. If E3 fails while E1 succeeds, the prefix acts as a code, not as the rule the edge actually runs.
- D4 (control): E4 gain CI contains 0.
- D5 (tree): the first split of the descriptive tree is at position >= 4. (Weak prediction from W1/X1.)
Failure of D2 and D3 together means the lookup's gain is a rule-specific memorisation of sibling rules that no compact encoding captures at this sample size.
Commands
wsl -e bash -lc "export UV_PROJECT_ENVIRONMENT=\$HOME/.venvs/turmite UV_LINK_MODE=copy && cd /mnt/f/Code/turmite && uv run experiments/2026-10-16-kappa-prefix-decode/scripts/decode.py"
Outputs: results/decode.txt, results/decode.json.
Results
Run 2026-10-16 (commit 269288e, dirty tree, seed 20261016, 2000 pool-rule bootstraps;
results/decode.txt, decode.json, leadrun_table.txt). Gain = held-out R^2 gain over
the ln A(22) spline on the 162 stationary pool rules, trained on 2183 stationary census rules.
| model | gain [95% CI] | vs lookup |
|---|---|---|
| prefix-8 lookup (reference) | +0.201 [0.103, 0.311] | 100% |
| E0 additive R-indicators, pos 1-8 | +0.301 [0.212, 0.409] | 150% |
| E1 + pairwise interactions | +0.365 [0.273, 0.479] | 182% |
| E2 three summaries (lead run, R count, switches) | +0.330 [0.238, 0.443] | 164% |
| E3 own-prefix census residual, p=4/5/6/7 | +0.045 / +0.086 / +0.121 / +0.138 | 22-69% |
| E4 target-shuffled controls | -0.007, -0.009 (sd 0.009, 0.015) | ~0 |
| post hoc A8 leading run length alone (1 number) | +0.330 [0.242, 0.441] | 165% |
| post hoc A5 letter 2 alone (RR vs RL) | +0.227 [0.159, 0.298] | 113% |
| post hoc A11 R count in first 4 | +0.249 | 124% |
| post hoc A7 letters 4-8 only / A12 letters 9+ | +0.065 [-0.005, 0.142] / +0.002 | 32% / 1% |
| post hoc A1 length, A3 R fraction of whole rule | -0.013 / +0.032 (CI includes 0) | - |
Mean residual of ln kappa (after the area spline) by leading-run length k (census | pool): k=1 -0.110 | -0.123; 2 +0.043 | +0.054; 3 +0.135 | +0.132; 4 +0.239 | +0.221; 5 +0.340 | +0.352; 6 +0.453 | +0.372; 7-8 +0.64..+0.72 (census only). Within-group sd ~0.17; corr(lead, residual) = 0.62 census, 0.70 pool. Roughly +0.1 in ln kappa per extra leading same-letter step, near-linear.
Verdicts on the registered predictions:
- D1 FAILED (expected additive to recover <25%; it recovers 150%).
- D2 passed vacuously (E1 182%, CI > 0) but interactions add little over E0 (+0.06) and nothing over the one-number leading run; the lookup tree is not hiding interactions.
- D3 FAILED: own-prefix residual recovers 22-69%, best p=7 (69%, CI > 0 but coverage
of the census is only 43-60%, so partly missing-value filling). The strict ">= 50%"
bar is met at p=6 and 7 but the feature is far worse than the leading run itself.
Reading: the edge-runs-
rule[:p]story is at most a coarse proxy of the leading run. - D4 passed (shuffle controls ~0).
- D5 FAILED: first tree split is at position 2 (RR vs RL, SSE drop 31.6), not >= 4.
What this is and is not: the lookup is a noisy encoding of a one-parameter signal, so the earlier statement "every simpler rule feature fails" is true for raw kappa and for features that carry no early-letter order (length, R fraction: A1, A3, here ~0) but false for the area-residualised target once the leading run is used. The signal sits almost entirely in letters 1-4 (A11 124%, A7 32%, A12 ~0). Open and not shown: (i) lead run correlates -0.56 with ln A(22), so a single area snapshot plus spline may leave growth-history confounding (the audit's standing caveat; the leading run could proxy early growth, not a transport property); (ii) A-series is post hoc, selected on the same pool data it is scored on, so the headline +0.33 is optimistic; it needs fresh rules; (iii) the non-stationary rules are excluded; (iv) no mechanism: why a run of k identical turns should raise the share of time on the boundary by ~10%/step is untested.
Mechanism candidate for the next, registered test (not tested here): a cell whose first k colours all turn the same way sends the ant through k same-handed turns on each early visit, so the rim is laid down as a coherent circulating (spiral) structure whose return kernel depends on k; the cleanest intervention is to hold the rule fixed from letter k+1 on and vary only the leading run (W6-style paired mutation at fixed area, with the early-colour exposure measurement), predicting a monotone dose response of ln kappa in k with slope near +0.1. Existing W6m found early-letter mutations sign-mixed in kappa, which this has to reconcile (mutating letter 2 changes k only when it is the run boundary).
Analysis notebook: notebook.ipynb
No saved outputs. This render shows the saved narrative and code; cells have not been executed for publication. Download notebook
Question and why it matters
Two or three sentences. Links: README.md, NOTEBOOK.md, relevant notes/ files.
Assumptions and definitions
Copy the live assumption entries from NOTEBOOK.md with their status.
Provenance
Prints the git commit, date, seed and a SHA-256 for every input file.
Code
import hashlib, subprocess, datetime
from pathlib import Path
import numpy as np
SEED = 20261014 # change per experiment; record it in the README
np.random.seed(SEED)
# notebooks have no __file__: search upward for the repo root
ROOT = next(p for p in [Path.cwd(), *Path.cwd().parents] if (p / "AGENTS.md").exists())
EXP = next(p for p in [Path.cwd(), *Path.cwd().parents] if (p / "NOTEBOOK.md").exists())
INPUTS = [ # committed inputs only: results/ and committed data/. Never dumps/ or scratch/
# EXP / "results" / "example.csv",
]
missing = [p for p in INPUTS if not p.exists()]
assert not missing, f"missing inputs: {missing}"
sha = subprocess.run(["git", "rev-parse", "--short", "HEAD"], cwd=ROOT, capture_output=True, text=True).stdout.strip()
print("git", sha, "| run", datetime.datetime.now().isoformat(timespec="minutes"), "| seed", SEED)
for p in INPUTS:
print(hashlib.sha256(p.read_bytes()).hexdigest()[:16], p.relative_to(ROOT))
Data and method
What was run and where the heavy computation lives (scripts, binaries). Exact commands.
Results
Each table or figure is followed by one sentence on what it shows and one on what it does not show.
Caveats and controls
Positive and negative controls, size and drift controls, noise ceiling. Failed predictions are stated as failed.
What this changes, next steps, open questions
Read the dated lab log
Lab notebook:
Append-only. Newest entry last. Never edit an old entry; correct it with a new one
(corrects: <timestamp>). Tags: intent, assumption, observation, interpretation,
surprise, decision, dead-end, question, deviation. See experiments/README.md.
YYYY-MM-DD HH:MM (+TZ) · · intent
What I am about to do, why, and which decision it informs.
YYYY-MM-DD HH:MM (+TZ) · · assumption
Statement. How it could be checked / what would show it false. Status: untested.
YYYY-MM-DD HH:MM (+TZ) · · observation
Fact, with the command and file that produced it.
YYYY-MM-DD HH:MM (+TZ) · · interpretation
What I think it means; confidence; the alternative explanations I have not excluded.
2026-10-16 09:05 (+13:00) · 269288e · intent
Decode the prefix-8 signal in kappa. Reframed target as the residual after the ln A(22) spline, stationary rules (the x2 "0.63" is area alone). Registered D1-D5 in README before running.
2026-10-16 09:35 (+13:00) · 269288e · observation
scripts/decode.py: lookup gain +0.201; additive R-indicators +0.301; summaries +0.330; own-prefix census residual 0.045-0.138; shuffle controls ~0. Post hoc ablations: leading-run length alone +0.330, letter 2 alone +0.227, letters 4-8 +0.065, letters 9+ ~0, length and R fraction ~0.
2026-10-16 09:40 (+13:00) · 269288e · surprise
D1 and D5 failed: the lookup is beaten by a one-number feature. Residual is near-linear in leading run (+0.1 per step), same slope in census and pool (results/leadrun_table.txt).
2026-10-16 09:45 (+13:00) · 269288e · interpretation
Prefix info is essentially "how many identical letters open the rule". Confound not excluded: lead run vs ln A(22) corr -0.56, one area snapshot. A-series post hoc on scored data, so +0.33 is optimistic. Next: registered fresh-rule test plus fixed-area leading-run mutation dose-response.
2026-10-16 09:50 (+13:00) · 269288e · deviation
No executed notebook.ipynb written (template left as is); README holds the results. To do before this experiment counts as finished.
2026-10-19 (+13:00) · 8f4b978 · interpretation
Co-reading note appended at the 2026-10-19 merge (the entry corrects nothing above). ../2026-10-19-c-law-mechanism/ Stage 4 (registered before computation; Q1-Q4, P-1 held; re-run of 4a/4b at merge reproduced the numbers) shows the fixed-area lead-on-ln-kappa slope (+0.15) is reproduced by conditioning on the collider ln A22 = f(ln c, ln kappa) with no direct effect (null +0.145 [0.137, 0.153]; adding ln c gives +0.014 [-0.045, +0.062]). Read the interpretation and any 'causal at fixed area' wording above as superseded in part: association conditional on area, not evidence of a direct lead effect. Unexplained and still open: the S-arm drop (-0.198) and its confounding with flip direction. See notes/open-questions-hypotheses.md, Reconciliation 2026-10-19.