# Re-run of release/reproducibility from a fresh extraction of release/source.zip (sha256 f61eae3846de7df2a4e2cb55e905f7550082528926761b7664a5c0e16a3b23e4), 2026-09-30
# extracted to scratch; main.tex and references.bib in the zip are identical to paper/; certificate sha256 6d7130db...72943 (verifier/ and claimant/ copies identical)

== verifier/check_certificate.py (exit 0; output identical to recorded check_certificate_output.txt)
certificate file: certificate_Sigma_30_47_83.txt
  sha256 = 6d7130dbc0ecf948286ed5d2b7e51a2cdad322da0588a97f3c9ddf7a43f72943
  1707 turning points; indices 0..109230; min tau = -12755; max tau = 1
checks 1-4 passed (Seifert data, tau, symmetry/tail spot checks, certificate valid)
number of finite bars = 853 ; total rank = 4864
HF_red = T(16)^1 + T(14)^10 + T(13)^16 + T(12)^24 + T(11)^36 + T(10)^46 + T(9)^56 + T(8)^66 + T(7)^76 + T(6)^82 + T(5)^84 + T(4)^86 + T(3)^88 + T(2)^90 + T(1)^92
ell = 16 ; lengths in 1..ell that do not occur: [15]
RESULT: F[U]/U^15 is not a summand, so HF^-(Y) fails the strong geography restriction

== verifier/make_certificate.py: regenerated certificate is byte-identical (cmp) to verifier/certificate_Sigma_30_47_83.txt; also equal to this run's own turning points and to the Appendix A listing in main.tex

== verifier/scan2 -v 30,47,83 (built with cc -O2)
Sigma(30,47,83) A=117030 e0=-1 omega=(29,1,1) N0=109229 turning_points=1707 min_tau=-12755 bars=853 rank=4864 ell=16 sgr=FAILS
  HF_red = T(16)^1 T(14)^10 T(13)^16 T(12)^24 T(11)^36 T(10)^46 T(9)^56 T(8)^66 T(7)^76 T(6)^82 T(5)^84 T(4)^86 T(3)^88 T(2)^90 T(1)^92
  missing: 15

== pipeline_check_rerun
Sigma(30, 47, 83): A = 117030, e0 = -1, omega = [29, 1, 1], 32 vertices
  det(B) = 1, negative eigenvalues = 32 of 32, bad vertices = [0]
  (b) Laufer sequence on the lattice == closed formula on [0, N0+1] = [0, 109230]
      Nemethi Prop. 11.11 cycle == Laufer cycle and chi(full form) == tau at 110 samples
      semigroup form (Can-Karakurt) == closed formula on [0, N0]
  (c) K^2 + s = -102040, min tau = -12755, d = 0
  (d) union-find == stack: 853 bars, rank 4864
      HF_red = T(16)^1 + T(14)^10 + T(13)^16 + T(12)^24 + T(11)^36 + T(10)^46 + T(9)^56 + T(8)^66 + T(7)^76 + T(6)^82 + T(5)^84 + T(4)^86 + T(3)^88 + T(2)^90 + T(1)^92
      ell = 16, missing lengths: [15]
  (e) sigma(Milnor fibre) = -38912, sigma/8 = -4864, -(rank) - d/2 = -4864

real	0m7.410s
user	0m2.474s
sys	0m0.042s

== long_bars_rerun
min tau = -12755, attained on [(54390, 54420), (54480, 54510), (54720, 54750), (54810, 54840)]
  level min+0 : 4 components of {tau <= level}
  level min+1 : 12 components of {tau <= level}
  level min+2 : 16 components of {tau <= level}
  level min+3 : 20 components of {tau <= level}
  level min+4 : 24 components of {tau <= level}
  level min+5 : 24 components of {tau <= level}
  level min+6 : 30 components of {tau <= level}
  level min+7 : 30 components of {tau <= level}
  level min+8 : 30 components of {tau <= level}
  level min+9 : 30 components of {tau <= level}
  level min+10: 30 components of {tau <= level}
  level min+11: 28 components of {tau <= level}
  level min+12: 26 components of {tau <= level}
  level min+13: 24 components of {tau <= level}
  level min+14: 24 components of {tau <= level}
  level min+15: 24 components of {tau <= level}
  level min+16: 19 components of {tau <= level}
  level min+17: 19 components of {tau <= level}
bars: 853, rank 4864
HF_red = T(16)^1 + T(14)^10 + T(13)^16 + T(12)^24 + T(11)^36 + T(10)^46 + T(9)^56 + T(8)^66 + T(7)^76 + T(6)^82 + T(5)^84 + T(4)^86 + T(3)^88 + T(2)^90 + T(1)^92
bars of length >= 13: (length, index of the minimum born, birth level - min, death level - min)
   (16, 54720, 0, 16)
   (14, 50670, 67, 81)
   (14, 52080, 28, 42)
   (14, 53070, 10, 24)
   (14, 53400, 6, 20)
   (14, 54060, 1, 15)
   (14, 55050, 1, 15)
   (14, 55710, 6, 20)
   (14, 56040, 10, 24)
   (14, 57120, 28, 42)
   (14, 58530, 67, 81)
   (13, 46770, 263, 276)
   (13, 48180, 177, 190)
   (13, 49260, 123, 136)
   (13, 49590, 108, 121)
   (13, 51000, 56, 69)
   (13, 51750, 36, 49)
   (13, 52410, 21, 34)
   (13, 53730, 3, 16)
   (13, 55380, 3, 16)
   (13, 56790, 21, 34)
   (13, 57450, 36, 49)
   (13, 58200, 56, 69)
   (13, 59610, 108, 121)
   (13, 59940, 123, 136)
   (13, 61020, 177, 190)
   (13, 62430, 263, 276)

real	0m0.852s
user	0m0.314s
sys	0m0.012s

== crossval_rerun
tuples compared: 400 mismatches: 0

real	1m49.798s
user	0m38.360s
sys	0m2.491s

== family_rerun
p even: 106 members, 45 failures
p odd: 240 members, 2 failures
total: 346 members, 47 failures
odd-p failures: [(187, 317, 456), (207, 257, 1064)]
first even-p failures: [(30, 47, 83), (38, 55, 123), (46, 75, 119), (64, 81, 305), (68, 105, 193), (70, 99, 239), (72, 89, 377), (76, 129, 185), (80, 117, 253), (98, 115, 663), (100, 173, 237), (104, 133, 477)]

real	2m40.711s
user	0m57.271s
sys	0m0.534s

== further_rerun
Sigma(30,47,83) A=117030 e0=-1 omega=(29,1,1) N0=109229 turning_points=1707 min_tau=-12755 bars=853 rank=4864 ell=16 sgr=FAILS
  HF_red = T(16)^1 T(14)^10 T(13)^16 T(12)^24 T(11)^36 T(10)^46 T(9)^56 T(8)^66 T(7)^76 T(6)^82 T(5)^84 T(4)^86 T(3)^88 T(2)^90 T(1)^92
  missing: 15
Sigma(38,55,123) A=257070 e0=-1 omega=(37,1,1) N0=243541 turning_points=2779 min_tau=-28857 bars=1389 rank=10694 ell=22 sgr=FAILS
  HF_red = T(22)^1 T(20)^4 T(19)^10 T(18)^8 T(17)^22 T(16)^34 T(15)^44 T(14)^54 T(13)^64 T(12)^74 T(11)^84 T(10)^90 T(9)^92 T(8)^94 T(7)^96 T(6)^98 T(5)^100 T(4)^102 T(3)^104 T(2)^106 T(1)^108
  missing: 21
Sigma(46,75,119) A=410550 e0=-1 omega=(45,1,1) N0=392701 turning_points=4083 min_tau=-46971 bars=2041 rank=17088 ell=24 sgr=FAILS
  HF_red = T(24)^1 T(22)^10 T(21)^16 T(20)^28 T(19)^32 T(18)^46 T(17)^48 T(16)^58 T(15)^60 T(14)^74 T(13)^88 T(12)^98 T(11)^108 T(10)^118 T(9)^128 T(8)^134 T(7)^136 T(6)^138 T(5)^140 T(4)^142 T(3)^144 T(2)^146 T(1)^148
  missing: 23
Sigma(64,81,305) A=1581120 e0=-1 omega=(63,1,1) N0=1531711 turning_points=8031 min_tau=-185520 bars=4015 rank=65840 ell=48 sgr=FAILS
  HF_red = T(48)^1 T(46)^2 T(45)^14 T(44)^4 T(43)^26 T(42)^8 T(41)^38 T(40)^14 T(39)^52 T(38)^18 T(37)^66 T(36)^22 T(35)^80 T(34)^26 T(33)^94 T(32)^30 T(31)^108 T(30)^34 T(29)^116 T(28)^34 T(27)^118 T(26)^34 T(25)^120 T(24)^34 T(23)^122 T(22)^34 T(21)^124 T(20)^34 T(19)^126 T(18)^34 T(17)^128 T(16)^130 T(15)^132 T(14)^134 T(13)^136 T(12)^138 T(11)^140 T(10)^142 T(9)^144 T(8)^146 T(7)^148 T(6)^150 T(5)^152 T(4)^154 T(3)^156 T(2)^158 T(1)^160
  missing: 47
Sigma(72,89,377) A=2415816 e0=-1 omega=(71,1,1) N0=2348711 turning_points=10191 min_tau=-285482 bars=5095 rank=100610 ell=58 sgr=FAILS
  HF_red = T(58)^1 T(56)^2 T(55)^4 T(54)^14 T(53)^6 T(52)^8 T(51)^30 T(50)^10 T(49)^46 T(48)^14 T(47)^60 T(46)^18 T(45)^74 T(44)^22 T(43)^88 T(42)^26 T(41)^102 T(40)^30 T(39)^116 T(38)^34 T(37)^124 T(36)^34 T(35)^126 T(34)^34 T(33)^128 T(32)^34 T(31)^130 T(30)^34 T(29)^132 T(28)^34 T(27)^134 T(26)^34 T(25)^136 T(24)^34 T(23)^138 T(22)^34 T(21)^140 T(20)^34 T(19)^142 T(18)^34 T(17)^144 T(16)^146 T(15)^148 T(14)^150 T(13)^152 T(12)^154 T(11)^156 T(10)^158 T(9)^160 T(8)^162 T(7)^164 T(6)^166 T(5)^168 T(4)^170 T(3)^172 T(2)^174 T(1)^176
  missing: 57
Sigma(98,115,663) A=7472010 e0=-1 omega=(97,1,1) N0=7319521 turning_points=18979 min_tau=-896352 bars=9489 rank=311249 ell=97 sgr=FAILS
  HF_red = T(97)^1 T(95)^2 T(94)^2 T(93)^18 T(92)^4 T(91)^6 T(90)^34 T(89)^8 T(88)^10 T(87)^50 T(86)^14 T(85)^14 T(84)^68 T(83)^18 T(82)^18 T(81)^86 T(80)^22 T(79)^22 T(78)^104 T(77)^26 T(76)^26 T(75)^122 T(74)^30 T(73)^30 T(72)^140 T(71)^34 T(70)^34 T(69)^150 T(68)^34 T(67)^34 T(66)^152 T(65)^34 T(64)^34 T(63)^154 T(62)^34 T(61)^34 T(60)^156 T(59)^34 T(58)^34 T(57)^158 T(56)^34 T(55)^34 T(54)^160 T(53)^34 T(52)^34 T(51)^162 T(50)^34 T(49)^164 T(48)^34 T(47)^166 T(46)^34 T(45)^168 T(44)^34 T(43)^170 T(42)^34 T(41)^172 T(40)^34 T(39)^174 T(38)^34 T(37)^176 T(36)^34 T(35)^178 T(34)^34 T(33)^180 T(32)^34 T(31)^182 T(30)^34 T(29)^184 T(28)^34 T(27)^186 T(26)^34 T(25)^188 T(24)^34 T(23)^190 T(22)^34 T(21)^192 T(20)^34 T(19)^194 T(18)^34 T(17)^196 T(16)^198 T(15)^200 T(14)^202 T(13)^204 T(12)^206 T(11)^208 T(10)^210 T(9)^212 T(8)^214 T(7)^216 T(6)^218 T(5)^220 T(4)^222 T(3)^224 T(2)^226 T(1)^228
  missing: 96
Sigma(122,187,351) A=8007714 e0=-1 omega=(121,1,1) N0=7876441 turning_points=29395 min_tau=-968466 bars=14697 rank=333603 ell=67 sgr=FAILS
  HF_red = T(67)^1 T(65)^2 T(63)^6 T(62)^2 T(61)^8 T(60)^8 T(59)^14 T(58)^24 T(57)^30 T(56)^40 T(55)^44 T(54)^58 T(53)^72 T(52)^82 T(51)^92 T(50)^102 T(49)^112 T(48)^122 T(47)^132 T(46)^142 T(45)^152 T(44)^162 T(43)^172 T(42)^182 T(41)^192 T(40)^202 T(39)^212 T(38)^222 T(37)^232 T(36)^242 T(35)^252 T(34)^262 T(33)^272 T(32)^282 T(31)^292 T(30)^302 T(29)^312 T(28)^318 T(27)^320 T(26)^322 T(25)^324 T(24)^326 T(23)^328 T(22)^330 T(21)^332 T(20)^334 T(19)^336 T(18)^338 T(17)^340 T(16)^342 T(15)^344 T(14)^346 T(13)^348 T(12)^350 T(11)^352 T(10)^354 T(9)^356 T(8)^358 T(7)^360 T(6)^362 T(5)^364 T(4)^366 T(3)^368 T(2)^370 T(1)^372
  missing: 64 66
Sigma(144,233,377) A=12649104 e0=-1 omega=(143,1,1) N0=12473423 turning_points=41007 min_tau=-1537580 bars=20503 rank=526988 ell=76 sgr=FAILS
  HF_red = T(76)^1 T(74)^6 T(73)^4 T(72)^12 T(71)^4 T(70)^22 T(69)^20 T(68)^40 T(67)^36 T(66)^60 T(65)^52 T(64)^76 T(63)^72 T(62)^92 T(61)^88 T(60)^112 T(59)^104 T(58)^130 T(57)^120 T(56)^148 T(55)^136 T(54)^160 T(53)^148 T(52)^166 T(51)^160 T(50)^172 T(49)^172 T(48)^180 T(47)^196 T(46)^214 T(45)^232 T(44)^246 T(43)^256 T(42)^266 T(41)^276 T(40)^286 T(39)^296 T(38)^306 T(37)^316 T(36)^326 T(35)^336 T(34)^346 T(33)^356 T(32)^366 T(31)^376 T(30)^386 T(29)^396 T(28)^406 T(27)^412 T(26)^414 T(25)^416 T(24)^418 T(23)^420 T(22)^422 T(21)^424 T(20)^426 T(19)^428 T(18)^430 T(17)^432 T(16)^434 T(15)^436 T(14)^438 T(13)^440 T(12)^442 T(11)^444 T(10)^446 T(9)^448 T(8)^450 T(7)^452 T(6)^454 T(5)^456 T(4)^458 T(3)^460 T(2)^462 T(1)^464
  missing: 75
Sigma(187,317,456) A=27031224 e0=-1 omega=(186,1,1) N0=26742121 turning_points=69305 min_tau=-3307086 bars=34652 rank=1126228 ell=95 sgr=FAILS
  HF_red = T(95)^2 T(93)^10 T(92)^8 T(91)^22 T(90)^30 T(89)^36 T(88)^44 T(87)^58 T(86)^58 T(85)^68 T(84)^76 T(83)^84 T(82)^92 T(81)^108 T(80)^108 T(79)^126 T(78)^124 T(77)^144 T(76)^140 T(75)^162 T(74)^156 T(73)^180 T(72)^172 T(71)^198 T(70)^188 T(69)^216 T(68)^204 T(67)^234 T(66)^220 T(65)^252 T(64)^236 T(63)^270 T(62)^252 T(61)^288 T(60)^268 T(59)^306 T(58)^284 T(57)^323 T(56)^298 T(55)^330 T(54)^310 T(53)^336 T(52)^322 T(51)^342 T(50)^334 T(49)^348 T(48)^346 T(47)^354 T(46)^362 T(45)^380 T(44)^398 T(43)^416 T(42)^434 T(41)^451 T(40)^462 T(39)^472 T(38)^482 T(37)^492 T(36)^502 T(35)^512 T(34)^522 T(33)^532 T(32)^542 T(31)^552 T(30)^562 T(29)^572 T(28)^578 T(27)^580 T(26)^582 T(25)^584 T(24)^586 T(23)^588 T(22)^590 T(21)^592 T(20)^594 T(19)^596 T(18)^598 T(17)^600 T(16)^602 T(15)^604 T(14)^606 T(13)^608 T(12)^610 T(11)^612 T(10)^614 T(9)^616 T(8)^618 T(7)^620 T(6)^622 T(5)^624 T(4)^626 T(3)^628 T(2)^630 T(1)^632
  missing: 94
Sigma(207,257,1064) A=56603736 e0=-1 omega=(206,1,1) N0=56056841 turning_points=85185 min_tau=-6939542 bars=42592 rank=2358350 ell=162 sgr=FAILS
  HF_red = T(162)^4 T(160)^4 T(159)^6 T(158)^4 T(157)^8 T(156)^19 T(155)^10 T(154)^10 T(153)^34 T(152)^12 T(151)^14 T(150)^51 T(149)^16 T(148)^70 T(147)^20 T(146)^84 T(145)^24 T(144)^98 T(143)^28 T(142)^112 T(141)^32 T(140)^126 T(139)^36 T(138)^140 T(137)^40 T(136)^154 T(135)^44 T(134)^168 T(133)^48 T(132)^182 T(131)^52 T(130)^196 T(129)^56 T(128)^210 T(127)^60 T(126)^224 T(125)^64 T(124)^238 T(123)^68 T(122)^252 T(121)^72 T(120)^266 T(119)^76 T(118)^280 T(117)^80 T(116)^294 T(115)^84 T(114)^308 T(113)^88 T(112)^322 T(111)^92 T(110)^336 T(109)^96 T(108)^350 T(107)^100 T(106)^358 T(105)^100 T(104)^360 T(103)^100 T(102)^362 T(101)^100 T(100)^364 T(99)^100 T(98)^366 T(97)^100 T(96)^368 T(95)^100 T(94)^370 T(93)^100 T(92)^372 T(91)^100 T(90)^374 T(89)^100 T(88)^376 T(87)^100 T(86)^378 T(85)^100 T(84)^380 T(83)^100 T(82)^382 T(81)^100 T(80)^384 T(79)^100 T(78)^386 T(77)^100 T(76)^388 T(75)^100 T(74)^390 T(73)^100 T(72)^392 T(71)^100 T(70)^394 T(69)^100 T(68)^396 T(67)^100 T(66)^398 T(65)^100 T(64)^400 T(63)^100 T(62)^402 T(61)^100 T(60)^404 T(59)^100 T(58)^406 T(57)^100 T(56)^408 T(55)^100 T(54)^410 T(53)^100 T(52)^412 T(51)^100 T(50)^414 T(49)^416 T(48)^418 T(47)^420 T(46)^422 T(45)^424 T(44)^426 T(43)^428 T(42)^430 T(41)^432 T(40)^434 T(39)^436 T(38)^438 T(37)^440 T(36)^442 T(35)^444 T(34)^446 T(33)^448 T(32)^450 T(31)^452 T(30)^454 T(29)^456 T(28)^458 T(27)^460 T(26)^462 T(25)^464 T(24)^466 T(23)^468 T(22)^470 T(21)^472 T(20)^474 T(19)^476 T(18)^478 T(17)^480 T(16)^482 T(15)^484 T(14)^486 T(13)^488 T(12)^490 T(11)^492 T(10)^494 T(9)^496 T(8)^498 T(7)^500 T(6)^502 T(5)^504 T(4)^506 T(3)^508 T(2)^510 T(1)^512
  missing: 161

real	0m2.701s
user	0m0.897s
sys	0m0.014s

== surgery_rerun
spheres Sigma(p,q,pqn-1) with p*q*r <= 1000000: 102308 (102307 with HF_red != 0, 1 L-spaces); largest summand length 125; mismatches: 0

real	12m40.428s
user	6m7.411s
sys	0m3.356s

== minimal_rerun
Sigma(30,47,83): N0 = 109229  min tau = -12755  rank HF_red = 4864
HF_red = T(16)^1 + T(14)^10 + T(13)^16 + T(12)^24 + T(11)^36 + T(10)^46 + T(9)^56 + T(8)^66 + T(7)^76 + T(6)^82 + T(5)^84 + T(4)^86 + T(3)^88 + T(2)^90 + T(1)^92
ell = 16  summand lengths missing from 1..ell: [15]

real	0m0.827s
user	0m0.294s
sys	0m0.013s
