Master ledger — self-audit (exact rationals)

Generated by recomputing every identity from the seed values using Python’s fractions.Fraction. PASS = exact match; CLOSE = within typical repeating-decimal noise (5.555 vs 50/9); FAIL = real discrepancy.

§1 Cardinal scalars + factorisations

PASS | AETHER = product of factors {2: 7, 3: 2, 5: 3} | claim=144000 | computed=144000
PASS | SUN = product of factors {2: 8, 3: 3, 5: 3} | claim=864000 | computed=864000
FAIL | TIME = product of factors {2: 7, 3: 4, 5: 2} | claim=518400 | computed=259200
PASS | MATTER = product of factors {2: 10, 3: 3, 5: 3} | claim=3456000 | computed=3456000
PASS | GREAT_YEAR = product of factors {2: 6, 3: 4, 5: 1} | claim=25920 | computed=25920
FAIL | SANSKRIT_TIME = product of factors {2: 7, 3: 5, 5: 1} | claim=311040 | computed=155520
PASS | RFEU = product of factors {2: 6, 3: 4, 5: 2} | claim=129600 | computed=129600

§1 Mutual relations between cardinals

PASS | SUN / 5.555 (50/9) = 155,520 | claim=155520 | computed=155520
PASS | SUN / 4.444 (40/9) = 194,400 | claim=194400 | computed=194400
PASS | SUN / 3.333 (10/3) = 259,200 | claim=259200 | computed=259200
PASS | SUN / 2.222 (20/9) = 388,800 | claim=388800 | computed=388800
PASS | SUN / 1.111 (10/9) = 777,600 | claim=777600 | computed=777600
PASS | SUN / 11.111 (100/9) = 77,760 | claim=77760 | computed=77760
PASS | MATTER / 11.111 = 311,040 | claim=311040 | computed=311040
PASS | AETHER / 5.555 = 25,920 | claim=25920 | computed=25920
PASS | AETHER / 11.111 = 12,960 (RFEU/10) | claim=12960 | computed=12960
PASS | MATTER / 6.666 = 518,400 | claim=518400 | computed=518400
PASS | MATTER / 16 = 216,000 | claim=216000 | computed=216000
PASS | MATTER / 144,000 = 24 | claim=24 | computed=24
PASS | MATTER / 266.666 (800/3) = 12,960 | claim=12960 | computed=12960
PASS | SUN / 25,920 = 33.333 | claim=100/3 | computed=100/3
PASS | SUN / 518,400 = 1.666 | claim=5/3 | computed=5/3
PASS | SUN / 129,600 = 6.666 | claim=20/3 | computed=20/3

§2 Dimension fractions ladder

PASS | d1 = n*10/9 | claim=10/9 | computed=10/9
PASS | d2 = n*10/9 | claim=20/9 | computed=20/9
PASS | d3 = n*10/9 | claim=10/3 | computed=10/3
PASS | d4 = n*10/9 | claim=40/9 | computed=40/9
PASS | d5 = n*10/9 | claim=50/9 | computed=50/9
PASS | d6 = n*10/9 | claim=20/3 | computed=20/3
PASS | d7 = n*10/9 | claim=70/9 | computed=70/9
PASS | d8 = n*10/9 | claim=80/9 | computed=80/9
PASS | d9 = n*10/9 | claim=10 | computed=10
FAIL | d11 = n*10/9 | claim=110/9 | computed=100/9

§5 Octave-sequence base values

PASS | LOS base 144 -> AETHER /1000 | claim=144 | computed=144
PASS | MOS C = 24 * 11.111 = 800/3 Hz | claim=800/3 | computed=800/3
PASS | POS Sun base 864 -> SUN/1000 | claim=864 | computed=864
PASS | TOS TIME 518,400 / 60 = 8,640 | claim=8640 | computed=8640
PASS | RFEU 129,600 = AETHER * 9/10 | claim=129600 | computed=129600
PASS | VOS torus 16 | claim=16 | computed=16

§8 Music tuning C = 800/3

PASS | C = 24 * 11.111 = 266.666... | claim=800/3 | computed=800/3
PASS | C decimal repr | claim=800/3 | computed=800/3
PASS | C/2 octave down | claim=400/3 | computed=400/3
PASS | C*2 octave up | claim=1600/3 | computed=1600/3

§9 Cross-quadrant ratios

PASS | SUN / AETHER = 6 | claim=6 | computed=6
PASS | TIME / AETHER = 3.6 | claim=18/5 | computed=18/5
PASS | MATTER / AETHER = 24 | claim=24 | computed=24
PASS | RFEU / AETHER = 0.9 | claim=9/10 | computed=9/10
PASS | GY / AETHER = 9/50 = 0.18 | claim=9/50 | computed=9/50
PASS | GY * 100 = 2,592,000 (Mayan?) | claim=2592000 | computed=2592000
PASS | GY / 12 = 2,160 | claim=2160 | computed=2160
PASS | GY / 4 = 6,480 | claim=6480 | computed=6480
PASS | TIME / GY = 20 | claim=20 | computed=20
PASS | TIME * 60/100 = 311,040 | claim=311040 | computed=311040

§3 Body diameters

PASS | Sun radius = D/2 = 432,000 | claim=432000 | computed=432000
PASS | Earth radius = D/2 = 3,960 | claim=3960 | computed=3960
PASS | Moon radius = D/2 = 1,080 | claim=1080 | computed=1080
PASS | Earth+Moon dia = 10,080 | claim=10080 | computed=10080
PASS | Sun_square = 4 * Sun_D | claim=3456000 | computed=3456000
PASS | Sun_square / 16 = 216,000 (Moon×100) | claim=216000 | computed=216000

§4 Element digit-product² (decimal point ignored)

PASS | H mp=-259.2 -> digits product=180 -> V=p^2 | claim=32400 | computed=32400
PASS | He mp=-272.2 -> digits product=56 -> V=p^2 | claim=3136 | computed=3136
PASS | Ne mp=-248.6 -> digits product=384 -> V=p^2 | claim=147456 | computed=147456
PASS | Ar mp=-189.4 -> digits product=288 -> V=p^2 | claim=82944 | computed=82944
PASS | Kr mp=-157.4 -> digits product=140 -> V=p^2 | claim=19600 | computed=19600
PASS | Xe mp=-111.8 -> digits product=8 -> V=p^2 | claim=64 | computed=64
PASS | Rn mp=-71.15 -> digits product=35 -> V=p^2 | claim=1225 | computed=1225

§4 Hydrogen right-triangle cascade (target 0.5184 = TIME/1e6)

PASS | 3-side = mp/3 = 86.4 | claim=432/5 | computed=432/5
PASS | 4-side = (mp/3)*4 = 345.6 | claim=1728/5 | computed=1728/5
PASS | 5-side = (mp/3)*5 = 432.0 | claim=432 | computed=432
FAIL | triangle area = (a*b)/2 = 44,789.76 | claim=373248/25 | computed=1119744/25
FAIL | area /24 = 1,866.24 | claim=15552/25 | computed=46656/25
FAIL | /60 = 31.104 | claim=1296/125 | computed=3888/125
FAIL | /60 = 0.5184 (= TIME / 1e6) | claim=108/625 | computed=324/625
FAIL | step3 * 1e6 = 518,400 (TIME) | claim=172800 | computed=518400
FAIL | /60 = 0.00864 | claim=9/3125 | computed=27/3125
FAIL | /60 = 0.000144 (= LIGHT/1e6) | claim=3/62500 | computed=9/62500
FAIL | step5 * 1e6 = 144 (LIGHT) | claim=48 | computed=144

§4 Hydrogen / noble-gas value ratios (PART 15 lines 130-146)

CLOSE | H/He claim 10.33163265306122 | claim=2025/196 | computed=1291454081632653/125000000000000
PASS | H/Ne claim 0.2197265625 | claim=225/1024 | computed=225/1024
PASS | H/Ar claim 0.390625 | claim=25/64 | computed=25/64
CLOSE | H/Kr claim 1.653061224489796 | claim=81/49 | computed=413265306122449/250000000000000
PASS | H/Xe claim 506.25 | claim=2025/4 | computed=2025/4
CLOSE | H/Rn claim 26.44897959183673 | claim=1296/49 | computed=2644897959183673/100000000000000

§7 Mirror-set / shuffle (sanity check on the 864-family)

Six digit permutations of {8,6,4} present in PART 15 line 84: [864, 846, 684, 648, 486, 468]
PASS | permutations are 6 distinct | claim=6 | computed=6
PASS | digit-sum of 864 mod 9 = 0 | claim=0 | computed=0
PASS | digit-sum of 846 mod 9 = 0 | claim=0 | computed=0
PASS | digit-sum of 684 mod 9 = 0 | claim=0 | computed=0
PASS | digit-sum of 648 mod 9 = 0 | claim=0 | computed=0
PASS | digit-sum of 486 mod 9 = 0 | claim=0 | computed=0
PASS | digit-sum of 468 mod 9 = 0 | claim=0 | computed=0

Red-flag scan

§9 line SUN_DIAMETER^2 / 1000 = SUN_SQUARE = 4 · SUN_DIAMETER · 1000 → SUN_DIAMETER = 4,000 ? ❌ is correctly flagged in the ledger; the actual definition SUN_SQUARE = 4 · SUN_D = 3,456,000 is used everywhere else and is consistent.
§6 says torus is 8 planes × 16 sectors at base, then 4-fold subdivided to 32 × 64. Subdivision factor: 32/8 = 4 ✓, 64/16 = 4 ✓. Total cells: 8×16=128 → 32×64=2,048. Subdivision ratio 2,048/128 = 16 = 4². ✓
§6 ‘Plasmoid: 7,200° / 0 (= 20 full 360° rotations)’: 20×360 = 7,200 ✓.
§5 RFEU = 129,600 (also written 1,296): 129,600 / 1,296 = 100 ✓ (the ‘1,296’ form is shorthand × 100).
§1 SANSKRIT_TIME = 311,040: factorisation 2^7 * 3^5 * 5 = 128 * 243 * 5 = 155,520. ❌ FAIL — this gives 155,520, not 311,040. Real factorisation: 311,040 = 2^8 * 3^5 * 5 = 256 * 243 * 5 = 311,040. ✓ So my note has 2^7 where it should be 2^8.
§1 MATTER factorisation 2^10 * 3^3 * 5^3: 1024 * 27 * 125 = 3,456,000 ✓.
§1 SUN factorisation 2^8 * 3^3 * 5^3: 256 * 27 * 125 = 864,000 ✓.
§1 AETHER factorisation 2^7 * 3^2 * 5^3: 128 * 9 * 125 = 144,000 ✓.
§1 TIME factorisation 2^7 * 3^4 * 5^2: 128 * 81 * 25 = 259,200. ❌ FAIL — gives 259,200, not 518,400. Real factorisation: 518,400 = 2^8 * 3^4 * 5^2 = 256 * 81 * 25 = 518,400. ✓ Off-by-one again — should be 2^8 not 2^7.
§1 GREAT_YEAR factorisation 2^6 * 3^4 * 5: 64 * 81 * 5 = 25,920 ✓.
§1 RFEU factorisation 2^6 * 3^4 * 5^2: 64 * 81 * 25 = 129,600 ✓.

Self-audit · Python Fraction · 08_self_audit.md