Mathematically Proven Claims — Provable Claims

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FSG-A // MATHEMATICS // PROVABLE CLAIMS

MATHEMATICALLY PROVEN CLAIMS
15 NUMERICAL CLAIMS BACKED BY EXECUTABLE CODE

Author: FSG-A — CC BY-SA 4.0

COMPLETE MATHEMATICS 2026-04-16

KEY TAKEAWAY

This page lists every numerical claim in the FSG-A wiki backed by executable mathematics. 15 claims from jammer range 11,150m to Weissberger vegetation loss to LiPo capacity at arctic temperatures. Each claim has a formula, a source (ITU-R, Dempster-Shafer, Friis), and a link to the code that calculates the value. Run python3 provable_claims.py to verify all 15 at once. Swedish Armed Forces/FMV can modify the parameters and reproduce the calculations themselves. This is the honest alternative to "trust us" claims: every number is a formula you can run.

How this works

Mathematical support is not the same as operational validation. If the wiki says "jammer range 11,150m", this can be supported at three levels:

Mathematically proven (this page): Friis formula run with concrete parameters gives 11,150m. Reproducible by anyone with a Python interpreter.
Simulated: ArduPlane SITL flight with virtual jammer shows realistic range effect. More credible but requires more resources.
Field-validated: Physical Fischer 26 with real jammer measured against real target sensor in forest terrain. Definitive proof.

FSG-A has only reached level 1 — mathematical proof. This page is transparency about exactly WHAT we have proven and WHAT we have not proven. Implementing agency must build prototype to reach level 3.

The 15 proven claims

RF Link Budget (1 claim)

ID	Claim	Formula	Result
JAM_RANGE_F26	2W jammer @ 2.4 GHz vs DJI drone (-80 dBm) reaches ~11,150m	Friis: d = 10^((P+G-S-20log(f)+147.55)/20)	11,150 m ✓

RF Vegetation Penetration (3 claims)

ID	Claim	Formula	Result
VEG_LOSS_VHF	140 MHz through 100m boreal forest: 11.4 dB loss	Weissberger ITU-R P.833-9	11.4 dB ✓
VEG_LOSS_5GHZ	5.8 GHz through 100m boreal forest: 32.9 dB loss	Weissberger ITU-R P.833-9	32.9 dB ✓
VEG_ADVANTAGE_RATIO	VHF gives ~140× more signal through forest than 5.8 GHz	ratio = 10^((L_5.8 - L_0.14)/10)	140× ✓

Important finding during this page's creation: Earlier versions of the wiki stated 11.2 dB and 31.5 dB for these values — incorrectly rounded down. provable_claims.py exposed these mathematical errors, and they have been corrected to 11.4 dB and 32.9 dB which give the exact mathematical output from the Weissberger formula. This illustrates the value of having executable mathematics instead of bare numbers.

Sensor Fusion (2 claims)

ID	Claim	Formula	Result
DS_FUSION_2	Two sensors 70% + 65% → 89.5% combined	m = 1-(1-m₁)(1-m₂)	0.895 ✓
DS_FUSION_3	Three sensors 70%+65%+60% → 95.8% combined	m = 1-∏(1-mᵢ)	0.958 ✓

Cryptography (1 claim)

ID	Claim	Formula	Result
HMAC_COLLISION_YEARS	HMAC-SHA256 56-bit requires ~2.28 million years at 1000 attempts/s	years = 2^56 / (1000 × 31.56M)	2.28 Myr ✓

Anti-Jam (2 claims)

ID	Claim	Formula	Result
CRPA_NULL_POWER_RATIO	25 dB null = 316× power reduction	ratio = 10^(dB/10)	316.2× ✓
FHSS_NARROWBAND_MISS	Narrowband jammer misses 99.98% of 4600 channels	miss_rate = (N-1)/N × 100	99.978% ✓

Antenna (2 claims)

ID	Claim	Formula	Result
BEAM_WIDTH_500M	30m CEP at 500m requires 6.87° beamwidth	θ = 2·atan(CEP/dist)	6.87° ✓
ANTENNA_GAIN_7DEG	7° beam gives ~28 dBi antenna gain	G ≈ 10·log10(32400/θ²)	28.2 dBi ✓

Arctic Operations (2 claims)

ID	Claim	Formula	Result
LIPO_CAPACITY_MINUS15	10Ah LiPo @ -15°C delivers ~6Ah (60%)	Tattu/Gens Ace datasheet interpolation	6000 mAh ✓
LIPO_CAPACITY_MINUS20	10Ah LiPo @ -20°C delivers 5Ah (50%)	Published cell chemistry literature	5000 mAh ✓

Energy Budget (2 claims)

ID	Claim	Formula	Result
FISCHER26_ENDURANCE	22.2V × 10Ah × 0.85 / 140W loiter = 1.35h (81 min)	t = (V·Ah·util) / P_avg	1.35 h ✓
FHSS_JAM_POWER_RATIO	Jamming 4600-channel FHSS requires 4600× more power	N_ch × P_per_ch	4600× ✓

Run the proof yourself

Download the code package. The verification harness is a plain Python script with no dependencies beyond the standard library plus NumPy:

# pip install numpy
# Reproduce the CRPA null-power claim from provable_claims.py
import numpy as np

def crpa_null_power_ratio(null_depth_db):
    """Return linear power reduction from dB null depth."""
    return 10 ** (null_depth_db / 10)

# Verified claim: a 25 dB CRPA null = 316x power reduction
ratio = crpa_null_power_ratio(25)
assert abs(ratio - 316.2278) < 0.01, "CRPA null claim failed"
print(f"CRPA 25 dB null = {ratio:.4f}x power reduction ✓")

# Run the full suite:
#   python3 provable_claims.py
# Expected output:
#   ✓ ALL 15 CLAIMS MATHEMATICALLY PROVEN
#   Verified: 15/15

The full harness output on a clean run:

$ python3 provable_claims.py
  Total 15 claims verified with executable code
  Verified: 15/15

  ▸ Anti-Jam
    [CRPA_NULL_POWER_RATIO] CRPA 25 dB null = 316× power reduction
      Formula:      ratio = 10^(dB/10)
      Calculated:   316.2278
      Expected:     316.2300
      Status:       ✓ VERIFIED

  [... 14 more ...]

  ✓ ALL 15 CLAIMS MATHEMATICALLY PROVEN

What this does NOT prove

Mathematical proof is not field validation. The following remain unproven:

That a physical Fischer 26 can actually carry 2W jammer + Yagi antenna and deliver the mathematically calculated range
That the Weissberger model actually applies to Swedish boreal forest specifically (the model is generic for "forested terrain")
That the sensors used in practice actually deliver the 70%/65%/60% levels assumed in Dempster-Shafer
That LiPo batteries in real arctic winter (with wind, humidity, battery aging) match the datasheet numbers

The mathematics is correct. The question is whether reality matches the mathematics. That is determined only by field validation, which FSG-A has not done.

License

Creative Commons Attribution-ShareAlike 4.0 International. Copy the code. Modify the parameters. Run in your own environment. Share improvements back if you wish.

MATHEMATICALLY PROVEN CLAIMS15 NUMERICAL CLAIMS BACKED BY EXECUTABLE CODE