The vacuum of a free lattice scalar field carries entanglement entropy that scales with a region's boundary, not its volume: fitted 3D exponent 2.09±0.01 (area predicts 2, volume 3), 2D 1.05 (perimeter), 1D flat to 9 digits. Bekenstein–Hawking-like area scaling emerges from a bare field theory with no gravity input (Srednicki 1993, independently recomputed).
The load-bearing input to Jacobson/Verlinde/Ryu–Takayanagi arguments — vacuum entanglement natively carries area scaling — comes out of a bare lattice with no gravity in it. Machinery check; says nothing about whether nature's gravity emerges this way.
Falsify-box — how to kill this claim
Verification record — every quoted number, re-run 2026-07-26
| quantity | measured | verdict |
|---|---|---|
| 3D scaling exponent | 2.0895 ± 0.0062 (fit s.e.); window-shift moves it −0.009 | MATCH |
| 2D scaling exponent | 1.0538 ± 0.0051 (perimeter law = 1) | MATCH |
| 1D saturation | |S(64) − S(8)| = 8.8e-9 (flat, as a two-point boundary demands) | MATCH |
| discriminator audit | NO DISCRIMINATOR — reproduces GR/QFT by construction | MATCH |
Provenance
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-4d6af727c9 | 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.
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.
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AREA LAW SCALING TEST (Srednicki 1993 reproduction -- known result)
Free scalar lattice ground state, m = 1.0, exact Gaussian method
scipy: available (not required; pure-numpy path used)
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[3D] 14x14x14 torus (2744 sites), centered s x s x s cubes
s = 2 boundary sites 6s^2 = 24 S = 0.275013
s = 3 boundary sites 6s^2 = 54 S = 0.651009
s = 4 boundary sites 6s^2 = 96 S = 1.190797
s = 5 boundary sites 6s^2 = 150 S = 1.894496
s = 6 boundary sites 6s^2 = 216 S = 2.762119
s = 7 boundary sites 6s^2 = 294 S = 3.793668
s = 8 boundary sites 6s^2 = 384 S = 4.989141
3D exponent, fit window s=2..8 : p = 2.0895 +/- 0.0062 (fit s.e.)
3D exponent, fit window s=3..7 : p = 2.0803 +/- 0.0048 (fit s.e.)
window shift moves p by -0.0093
AREA law predicts p = 2 ; VOLUME law predicts p = 3
[2D] 32x32 torus (1024 sites), centered s x s squares
s = 2 boundary sites 4s = 8 S = 0.179604
s = 3 boundary sites 4s = 12 S = 0.281368
s = 4 boundary sites 4s = 16 S = 0.383072
s = 5 boundary sites 4s = 20 S = 0.484752
s = 6 boundary sites 4s = 24 S = 0.586428
s = 7 boundary sites 4s = 28 S = 0.688103
s = 8 boundary sites 4s = 32 S = 0.789777
s = 9 boundary sites 4s = 36 S = 0.891452
s = 10 boundary sites 4s = 40 S = 0.993126
s = 11 boundary sites 4s = 44 S = 1.094801
s = 12 boundary sites 4s = 48 S = 1.196475
2D exponent, fit window s=2..12: p = 1.0538 +/- 0.0051 (fit s.e.)
2D exponent, fit window s=3..10: p = 1.0462 +/- 0.0035 (fit s.e.)
AREA (perimeter) law predicts p = 1 ; VOLUME (bulk) law predicts p = 2
[1D] periodic chain, N = 200, centered interval of length s
area law in 1D = boundary is 2 points = S saturates for s >> 1/m
s = 2 S = 0.110097766
s = 4 S = 0.111773556
s = 8 S = 0.111800800
s = 16 S = 0.111800809
s = 32 S = 0.111800809
s = 64 S = 0.111800809
saturation check: |S(64) - S(8)| = 8.841e-09 (relative 7.908e-08)
volume (extensive) scaling would have grown S by 8x over that range
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HEADLINE NUMBERS
p3 (3D, s=2..8) = 2.0895 +/- 0.0062 [area=2, volume=3]
p3 (3D, s=3..7, robust.) = 2.0803 +/- 0.0048
p2 (2D, s=2..12) = 1.0538 +/- 0.0051 [area=1, volume=2]
p2 (2D, s=3..10, robust.)= 1.0462 +/- 0.0035
1D saturation |S(64)-S(8)| = 8.841e-09 (flat = area law)
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STATUS: reproduced-known-result; validates machinery, not nature.
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