USR-2026-0056 · Information
The entanglement Hamiltonian of half the vacuum is a boost: at 200-digit precision the nearest-neighbour couplings ramp linearly with distance from the entangling cut (R² = 0.998–0.999), with the exact near-cut coupling t₁ = 3.141539 matching 2π/v_F to 1.7×10⁻⁵. The implied local temperature T(x) = 1/(2πx) is the Unruh effect on a lattice — and the T in Jacobson's Clausius relation.
PROVISIONAL
boost linearity R² = 0.998–0.999 (200-digit); near-cut t₁ = π to 1.7e-5
reproduced ≠ discovered
re-run & confirmed 2026-07-26 (R0 — founder CI; independence pending)
Bisognano–Wichmann / Eisler–Peschel, recomputed. Float64 cannot do this computation at all: the modular spectrum spans ~370 orders of magnitude and the apparent plateau tracks the eigenvalue clip — an arithmetic artifact, diagnosed and reported rather than published. REFINED by USR-2026-0065: reading the boost from the full modular dispersion rather than nearest-neighbour couplings alone removes the 8.8% shortfall and lands the slope on 2π/v_F to 2×10⁻⁵.
Falsify-box — how to kill this claim
SURVIVED
the coupling profile is non-linear at converged precision, or a sqrt/other profile fits comparably well
Verification record — every quoted number, re-run 2026-07-26
| quantity | measured | verdict |
|---|---|---|
| linearity R² | 0.998–0.999 at 200 digits | MATCH |
| near-cut coupling t₁ | 3.141539 vs π (deviation 1.7e-5) | MATCH |
| float64 verdict | NUMERICALLY INVALID — plateau tracks the clip, not physics | MATCH |
| REFINED 2026-07-26 (jacobson_clausius.py) | β(x) slope = 3.141533, R² = 0.9999999995, ratio to 2π/v_F = 0.99998 once the known finite-box conformal factor is divided out. Wave 2's nearest-neighbour-only reading of t₁ was low by up to 8.8% — that is exactly the source of its 0.90–0.92 shortfall. | MATCH |
| discriminator audit | NO DISCRIMINATOR — reproduces GR/QFT by construction | MATCH |
Provenance
script: information_seam/unruh_boost.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) — PARTIAL on first pass: the prescribed float64 computation failed honestly and was redone in extended precision; admitted from MCP intake INTAKE-52836dbbde | DISCRIMINATOR AUDIT 2026-07-26 (emergent_discriminator.py): this claim belongs to the thermodynamic-derivation wing, which reproduces general relativity or quantum field theory BY CONSTRUCTION and therefore carries NO observational discriminator — a computed and an uncomputed universe answer identically. Same category as USR-2026-0037/0038: verified machinery, not evidence about nature. Recorded on the claim rather than left implicit.. Status here is computed from evidence — the author cannot set it, and neither can we. Independent reproduction would move it; nothing else will.
§ Reproduction
unruh_boost.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 7 -- UNRUH THERMOMETER: entanglement Hamiltonian of half the
vacuum as a lattice boost (Bisognano-Wichmann / Eisler-Peschel)
STATUS: REPRODUCED (known result), machinery check -- not discovery
==========================================================================
numpy 1.26.4 | scipy 1.17.1 (not needed) | mpmath 1.3.0
chain N = 400, open boundaries, half filling; block A = sites 1..200
prediction: t_x ~ (2*pi/v_F)*x = pi*x (v_F = 2 for -2cos k)
[1] PRESCRIBED PROTOCOL (double precision, clip = 1e-12)
occupied modes: 200 (half filling)
clipped eigenvalues: 184 of 200 (raw range: min = -1.353e-15, max-1 = 9.992e-15)
spectral cap from clip: ||h_E|| <= ln((1-clip)/clip) = 27.631
t_x profile (note plateau beyond x ~ 6):
x = 1 t_x = 3.141539 t_x/x = 3.141539
x = 2 t_x = 6.281556 t_x/x = 3.140778
x = 3 t_x = 9.399784 t_x/x = 3.133261
x = 4 t_x = 12.365509 t_x/x = 3.091377
x = 5 t_x = 14.770541 t_x/x = 2.954108
x = 6 t_x = 16.084268 t_x/x = 2.680711
x = 8 t_x = 16.590601 t_x/x = 2.073825
x = 10 t_x = 17.022620 t_x/x = 1.702262
x = 20 t_x = 17.450219 t_x/x = 0.872511
x = 50 t_x = 17.561146 t_x/x = 0.351223
x = 120 t_x = 17.591688 t_x/x = 0.146597
prescribed fits -- REPORTED BUT NUMERICALLY INVALID (both windows
lie inside the precision plateau; see [2]):
window [10, 120]: slope = 0.001881 intercept = 17.417372 R^2 = 0.403225 (n = 111)
slope/(2*pi) = 0.000299 slope*v_F/(2*pi) = 0.000599
window [20, 100]: slope = 0.001063 intercept = 17.496672 R^2 = 0.648792 (n = 81)
slope/(2*pi) = 0.000169 slope*v_F/(2*pi) = 0.000338
window robustness (invalid regime): slope moves -43.5% between windows
VERDICT on prescribed windows: FAILED-AS-SPECIFIED -- R^2 0.403/0.649, slope ~ 0.0019 vs predicted ~ pi.
The failure is numerical (double precision), not physical; controls follow.
[2] CONTROL: the plateau is a clip artifact (it moves with the clip)
mean t_x over x in [30,120]:
clip = 1e-12 (cap 27.631): plateau = 17.5734 (clipped: 184)
clip = 1e-15 (cap 34.539): plateau = 21.7871 (clipped: 142)
plateau ratio 1.2398 vs cap ratio 1.2500 -- the 'flat t_x' tracks the clip, so it is an
artifact of finite precision, not a property of h_E.
[3] VALID double-precision reading: bonds adjacent to the cut
(modular energies needed there are far below the cap)
t_1/1 = 3.141539 vs pi = 3.141593 relative deviation = -1.69e-05
t_2/2 = 3.140778 vs pi = 3.141593 relative deviation = -2.59e-04
the boost slope 2*pi/v_F = pi appears directly at the cut, at N=400.
[4] HIGH-PRECISION VERIFICATION (same half-box geometry, N = 160, L = 80, 200-digit arithmetic)
smallest C_A eigenvalue = 3.459e-155 1 - largest = 3.459e-155
eigenvalues outside (0,1) needing clip: 0 (all resolved; NO clipping applied)
largest |modular energy| = 355.66 (vs double-precision cap 27.6 -- why [1] had to fail)
t_x profile (exact arithmetic):
x = 1 t_x = 3.141443 t_x/x = 3.141443 t_x/(pi*x) = 0.999952
x = 2 t_x = 6.282138 t_x/x = 3.141069 t_x/(pi*x) = 0.999833
x = 5 t_x = 15.692254 t_x/x = 3.138451 t_x/(pi*x) = 0.999000
x = 10 t_x = 31.290813 t_x/x = 3.129081 t_x/(pi*x) = 0.996018
x = 20 t_x = 61.826504 t_x/x = 3.091325 t_x/(pi*x) = 0.983999
x = 30 t_x = 90.821383 t_x/x = 3.027379 t_x/(pi*x) = 0.963645
x = 40 t_x = 117.424247 t_x/x = 2.935606 t_x/(pi*x) = 0.934432
x = 48 t_x = 136.343213 t_x/x = 2.840484 t_x/(pi*x) = 0.904154
x = 60 t_x = 159.432399 t_x/x = 2.657207 t_x/(pi*x) = 0.845815
x = 79 t_x = 170.049332 t_x/x = 2.152523 t_x/(pi*x) = 0.685169
t_1 = 3.141443 vs pi: relative deviation -4.76e-05
fits (fractional analogues of the prescribed windows, x/L in [0.05,0.60] and [0.10,0.50]):
window [4, 48]: slope = 2.839486 intercept = 3.899937 R^2 = 0.998174 (n = 45)
slope/(2*pi) = 0.451918 slope*v_F/(2*pi) = 0.903836
window [8, 40]: slope = 2.899215 intercept = 3.223766 R^2 = 0.999228 (n = 33)
slope/(2*pi) = 0.461424 slope*v_F/(2*pi) = 0.922849
window robustness: slope moves +2.1% between windows
slope sits below pi because A is half of a FINITE box: the exact
weight bends toward the far wall (t_x/(pi*x) drifts from 1.000 at
the cut to ~0.86 mid-block) -- geometry, not a BW violation.
honesty on locality: h_E is NOT strictly nearest-neighbor (distance-2
terms vanish by particle-hole symmetry); median |t^(3)_x / t^(1)_x| in window = 0.0052
particle-hole check: max |diagonal of h_E| = 3.58e-48 (should be ~0 at half filling)
[5] PHYSICAL READING (the point of the exercise)
Restricted to half of space, the ground state is EXACTLY thermal
w.r.t. the boost: rho_A ~ exp(-sum_x beta_loc(x) h(x)) with local
inverse temperature beta_loc(x) ~ 2*pi*x growing linearly from the
cut. An observer pinned at distance x from the horizon-analogue
sees temperature T(x) = 1/(2*pi*x) [units v_F = 1]:
x = 5: T = 0.031831
x = 20: T = 0.007958
x = 100: T = 0.001592
This T is the load-bearing input of Jacobson 1995 (dQ = T dS =>
Einstein equations) -- here it is exact lattice linear algebra,
not an analogy. Known result (Bisognano-Wichmann; Eisler-Peschel
lattice form), recomputed.
[6] SUMMARY
- Prescribed double-precision windows [10,120]/[20,100]: INVALID
(precision plateau; plateau level tracks the clip -- artifact).
- Near-cut couplings at N=400: t_x/x = pi to ~2e-5 (valid, double
precision).
- 200-digit rerun (L=80, zero clipping): linear ramp with R^2 = 0.99817/0.99923,
slope*v_F/(2*pi) = 0.904/0.923 in the two windows (finite-box
bending explains the shortfall from 1); BW boost CONFIRMED
within the stated geometry caveat.
- All of this reproduces known results; nothing here is evidence
that spacetime IS built this way -- only that the thermal-boost
ingredient of that story is mathematically real.
B · Yours
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