USR-2026-0054 · Information
In an exactly reversible HPP lattice gas (Loschmidt echo returns the initial state bit-for-bit), coarse-grained entropy rises in BOTH time directions away from a low-entropy initial state. The thermodynamic arrow of time lives in the boundary condition, not the dynamical laws (Boltzmann, demonstrated exactly).
PROVISIONAL
arrow in the state, not the laws — echo bit-exact, entropy rises both ways
reproduced ≠ discovered
re-run & confirmed 2026-07-26 (R0 — founder CI; independence pending)
The laws carry no arrow — reversal is bit-perfect. The arrow is a property of the special low-entropy state: time's direction is bookkeeping of the initial condition. Says nothing about why our universe started low-entropy.
Falsify-box — how to kill this claim
SURVIVED
the Loschmidt echo fails bit-exactness, or entropy fails to rise in the reversed time direction
Verification record — every quoted number, re-run 2026-07-26
| quantity | measured | verdict |
|---|---|---|
| Loschmidt echo bit-exact | True (a single flipped bit breaks it — verified adversarially) | MATCH |
| entropy forward, t=400 | 3.849 from S₀ = 1.385 | MATCH |
| entropy in REVERSED time, t=400 | 3.841 — rises in both directions | MATCH |
Provenance
script: information_seam/boltzmann_arrow.py
script status: PRESENT
datasets: information-seam-scripts (downloadable from /data — run it yourself)
re-run: 2026-07-26
script status: PRESENT
datasets: information-seam-scripts (downloadable from /data — run it yourself)
re-run: 2026-07-26
Status, honestly
verified by adversarial re-run (workflow, 2026-07-26); admitted from MCP intake INTAKE-8bba765fce. Status here is computed from evidence — the author cannot set it, and neither can we. Independent reproduction would move it; nothing else will.
§ Reproduction
boltzmann_arrow.py
The founder's own run of this script, captured verbatim. A match proves the result is reproducible; it is still R0 on this registry's independence rings — same code, so it cannot move a status. Only an outside run does that.
A · Recorded
founder's machine · 2026-08-02
========================================================================
TEST 5: boltzmann_arrow -- arrow of time is in the state, not the laws
HPP lattice gas, 64x64 torus, exactly reversible boolean dynamics
LABEL: reproduced (Boltzmann/Loschmidt), not discovered
========================================================================
particles : 800
S_max = ln(64) : 4.158883
S(0) (all in central 16x16) : 1.385407 [~ln(4) = 1.386294: block spans 4 coarse cells]
--- Run 1: FORWARD (400 steps) ---
t S(t)
0 1.385407
50 3.592780
100 2.826469
150 3.550822
200 3.379940
250 3.096985
300 3.713023
350 2.620387
400 3.849343
S(200) forward : 3.379940
S(400) forward : 3.849343
S band, t in [200,400] (fwd) : min=2.529618 max=3.856904 mean=3.302552
multinomial equilibrium ref : 4.119508 [ln(64) - (K-1)/(2N), NOT reached -- see caveat]
dip recurrence period (fwd) : 32.0 [~L/2 = 32: ballistic wrap-around refocusing, HPP artifact]
particle conservation (fwd) : True
--- Run 2: LOSCHMIDT ECHO (reverse at t=200, run 200 steps) ---
k S_echo(k) S_fwd(200-k)
0 3.379940 3.379940
50 3.550822 3.550822
100 2.826469 2.826469
150 3.592780 3.592780
200 1.385407 1.385407
EXACT bit-for-bit echo : True
max |S_echo(k)-S_fwd(200-k)| : 0
particle conservation (echo) : True
--- Run 3: BACKWARD (time run the other way, 400 steps) ---
t S(-t)
0 1.385407
50 3.609322
100 2.816176
150 3.566866
200 3.369001
250 3.101436
300 3.718333
350 2.658689
400 3.841238
S(400) backward : 3.841238
S band, t in [200,400] (bwd) : min=2.537823 max=3.870135 mean=3.307710
particle conservation (bwd) : True
========================================================================
HEADLINES
S(0) : 1.385407
S(400) forward : 3.849343 (S_max = 4.158883)
S mean t=[200,400] forward : 3.302552 (single-time values oscillate)
exact Loschmidt echo : True
S(400) backward : 3.841238
S mean t=[200,400] backward : 3.307710
========================================================================
Interpretation: the update rule is exactly reversible (proven
bit-for-bit by the echo), yet coarse-grained entropy rises in
BOTH time directions away from the initial state. The arrow of
time lives in the low-entropy boundary condition, not the laws.
Known physics since Boltzmann; reproduced here exactly. Nothing
here explains WHY the initial state was special.
Caveat: HPP's spurious invariants keep S below the multinomial
maximum, with a persistent period-32 refocusing oscillation --
the entropy RISE is robust, the saturation LEVEL is model-limited.
B · Yours
not runnable in-browser
This script needs data files, a heavy dependency, or more time than a browser tab should take. Download it from /data and run it locally.