Let's define the Collapsing-E notation that it should reach the Bachmann-Howard ordinal with the mind-blowing blasphemorgulus:
(1) blasphemorgulus = E100#{&}#100
= E100#{#{#{...#{#{#}#}#...}#}#}#100
w/ 100 #'s centered out (199 #'s total)
This equals to E100{#,#,1,2}100 in Hyper-Hyper-Extended Cascading-E notation by Sbiis Saibian.
He however defined {_,#,1,2} arrays only, along with {_,#+1,1,2} by his climbing theory.
However, he conclude that {_,#+2,1,2} doesn’t continue the nestings of {_,#+n,1,2} sequence in 4.3.12.
So, to continue. I have to think outside of the box! Remember the Extended Cascading-E Notation? This also fits 4-entry arrays also!
However, note that I am going to use & (ampersand) delimiters instead of arrays to make it more convenient and easier to reach the Bachmann-Howard ordinal.
Prepare for liftoff...
(2) blasphemorgulchime = E1,000#{&}#1,000
(3) blasphemorgultoll = E10,000#{&}#10,000
(4) blasphemorgulgong = E100,000#{&}#100,000
(5) blasphemorgulbong = E100,000,000#{&}#100,000,000
(6) blasphemorgulthrong = E100,000,000,000#{&}#100,000,000,000
...
(7) grand blasphemorgulus = E100#{&}#100#2
(8) grand grand blasphemorgulus = E100#{&}#100#3
(9) grand grand grand blasphemorgulus = E100#{&}#100#4
...
(10) grangol-carta-blasphemorgulus = E100#{&}#100#100
(11) greagol-carta-blasphemorgulus = E100#{&}#100#100#100
...
(12) gugolda-carta-blasphemorgulus = E100#{&}#100##100
(13) throogol-carta-blasphemorgulus = E100#{&}#100###100
...
(14) godgahlah-carta-blasphemorgulus = E100#{&}#100#^#100
(15) gridgahlah-carta-blasphemorgulus = E100#{&}#100#^##100
(16) godgathor-carta-blasphemorgulus = E100#{&}#100#^#^#100
(17) godtothol-carta-blasphemorgulus = E100#{&}#100#^#^#^#100
...
(18) tethrathoth-carta-blasphemorgulus = E100#{&}#100#^^#100
(19) Monster-Giant-carta-blasphemorgulus = E100#{&}#100(#^^#)^(#^^#)^#100
(20) terrible tethrathoth-carta-blasphemorgulus = E100#{&}#100(#^^#)^^#100
(21) tethriterator-carta-blasphemorgulus = E100#{&}#100#^^#>#100
(22) dustaculated-tethrathoth-carta-blasphemorgulus = E100#{&}#100#^^#>#^^#100
...
(23) tethracross-carta-blasphemorgulus = E100#{&}#100#^^##100
(24) tethracubor-carta-blasphemorgulus = E100#{&}#100#^^###100
...
(25) tethratope-carta-blasphemorgulus = E100#{&}#100#^^#^#100
(26) tethrarxitri-carta-blasphemorgulus = E100#{&}#100#^^#^^#100
(also called (27) tethrato-tethrathoth-carta-blasphemorgulus)
...
(27) pentacthulhum-carta-blasphemorgulus = E100#{&}#100#^^^#100
(28) hexacthulhum-carta-blasphemorgulus = E100#{&}#100#^^^^#100
...
(29) godsgodgulus-carta-blasphemorgulus = E100#{&}#100#{#}#100
(30) ohmygosh-ohmygosh-ohmygoosh-carta-blasphemorgulus = E100#{&}#100#{#{#}#}#100
...
(31) blasphemorgulatri = E100#{&}#100#{&}#100
(32) blasphemorgulatet = E100#{&}#100#{&}#100#{&}#100
...
(33) blasphemorgulus-by-hyperion = E100#{&}#*#100
(34) blasphemorgulus-by-deutero-hyperion = E100#{&}#*##100
...
(35) blasphemorgulus-by-godgahlah = E100#{&}#*#^#100
(36) blasphemorgulus-by-godgathor = E100#{&}#*#^#^#100
...
(37) blasphemorgulus-by-tethrathoth = E100#{&}#*#^^#100
(38) blasphemorgulus-by-tethracross = E100#{&}#*#^^##100
(39) blasphemorgulus-by-tethratope = E100#{&}#*#^^#^#100
...
(40) blasphemorgulus-by-pentacthulhum = E100#{&}#*#^^^#100
(41) blasphemorgulus-by-hexacthulhum = E100#{&}#*#^^^^#100
...
(42) blasphemorgulus-by-godsgodgulus = E100#{&}#*#{#}#100
(43) blasphemorgulus-by-ohmygosh-ohmygosh-ohmygoosh = E100#{&}#*#{#{#}#}#100
...
(44) deutero-blasphemorgulus = E100#{&}#*#{&}#100
(45) trito-blasphemorgulus = E100#{&}#*#{&}#*#{&}#100
(46) teterto-blasphemorgulus = E100#{&}#*#{&}#*#{&}#*#{&}#100
...
(47) blasphemorgulfact = E100(#{&}#)^#100
(48) grideuterblasphemorgulus = E100(#{&}#)^##100
...
(49) blasphemorgula-godgathor = E100(#{&}#)^#^#100
(50) blasphemorgula-godtothol = E100(#{&}#)^#^#^#100
...
(51) blasphemorgulus-ipso-tethrathoth = E100(#{&}#)^(#^^#)100
(52) blasphemorgulus-ipso-tethracross = E100(#{&}#)^(#^^##)100
(53) blasphemorgulus-ipso-pentacthulhum = E100(#{&}#)^(#^^^#)100
(54) blasphemorgulus-ipso-hexacthulhum = E100(#{&}#)^(#^^^^#)100
...
(55) blasphemorgulus-ipso-godsgodgulus = E100(#{&}#)^(#{#}#)100
(56) blasphemorgulus-ipso-ohmygosh-ohmygosh-ohmygoosh = E100(#{&}#)^(#{#{#}#}#)100
...
(57) dutetrated-blasphemorgulus = E100(#{&}#)^(#{&}#)100
(58) tritetrated-blasphemorgulus = E100(#{&}#)^(#{&}#)^(#{&}#)100
...
(59) terrible blasphemorgulus = E100(#{&}#)^^#100
(60) tethriterated blasphemorgulus = E100(#{&}#)^^#>#100
(61) terrisquared blasphemorgulus = E100(#{&}#)^^##100
(62) terricubed blasphemorgulus = E100(#{&}#)^^###100
(63) territesserated blasphemorgulus = E100(#{&}#)^^####100
...
(64) territoped blasphemorgulus = E100(#{&}#)^^#^#100
(65) tethrato-godgathoriated blasphemorgulus = E100(#{&}#)^^#^#^#100
...
(66) tethrathoth-tetrated blasphemorgulus = E100(#{&}#)^^#^^#100
(67) tethracross-tetrated blasphemorgulus = E100(#{&}#)^^#^^##100
(68) pentacthulhum-tetrated blasphemorgulus = E100(#{&}#)^^(#^^^#)100
(69) hexacthulhum-tetrated blasphemorgulus = E100(#{&}#)^^(#^^^^#)100
...
(70) godsgodgulus-tetrated blasphemorgulus = E100(#{&}#)^^(#{#}#)100
(71) ohmygosh-ohmygosh-ohmygoosh-tetrated blasphemorgulus = E100(#{&}#)^^(#{#{#}#}#)100
...
(72) dupentated-blasphemorgulus = E100(#{&}#)^^(#{&}#)100
(73) tripentated-blasphemorgulus = E100(#{&}#)^^(#{&}#)^^(#{&}#)100
...
(74) horrible blasphemorgulus = E100(#{&}#)^^^#100
(75) horrendous blasphemorgulus = E100(#{&}#)^^^^#100
...
(76) godsgoblasphemorgulus = E100(#{&}#){#}#100
(also called (77) grievous blasphemorgulus)
(78) ohmygosh-ohmygosh-ohmygooblasphemorgulus = E100(#{&}#){#{#}#}#100
Prepare for ordinal shifting problem...
We can show that the fundamental sequence of (#{&}#){#{#...{#{#}#}...#}#}# is not (#{&}#){&}#, but (#{&}#){#{&}#}#, since the ordinal α -> φ(1,0,0,0) in φ(α,0,φ(1,0,0,0)+1) is φ(φ(1,0,0,0),0,1), not φ(1,0,0,1) with respect to the finitary Veblen function.
Let's see that the fundamental sequence of (#{&}#){&}# should start from (#{&}#){#{&}#}# instead of (#{&}#){#{&}#}(#{&}#) since it alters the FGH ordinal fundamental sequence in a weird way.
So we have:
(79) blasphemorguldardyo = E100(#{&}#){#{&}#}#100
(80) blasphemorguldartria = E100(#{&}#){(#{&}#){#{&}#}#}#100
(81) blasphemorguldartessera = E100(#{&}#){(#{&}#){(#{&}#){(#{&}#){#{&}#}#}#}#}#100
On the other hand...
(82) blasphemormygosh-blasphemormygosh = E100(#{&}#){#{&}#}(#{&}#)100
(83) blasphemormygosh-blasphemormygosh-blasphemormygosh = E100(#{&}#){(#{&}#){#{&}#}(#{&}#)}(#{&}#)100
And hence...
(84) tweilasphemorgue = E100(#{&}#){&}#100
= E100(#{&}#){(#{&}#){...(#{&}#){(#{&}#){#{&}#}#}#...}#}#100
w/ 100 &'s
(85) frielasphemorgue = E100((#{&}#){&}#){&}#100
(86) fiorilasphemorgue = E100(((#{&}#){&}#){&}#){&}#100
Moving on...
(87) blasphemorguliterator = E100#{&}#>#100
(also called (88) hundrelasphemorgue)
(89) blasphemorgulgriditerator = E100#{&}#>##100
(also called (90) ludicriss)
(91) blasphemorgulspatialator = E100#{&}#>#^#100
(92) tethrathoth-turreted-blasphemorgulus = E100#{&}#>#^^#100
(93) pentacthulhum-turreted-blasphemorgulus = E100#{&}#>#^^^#100
(94) godsgodgulus-turreted-blasphemorgulus = E100#{&}#>#{#}#100
...
(95) dustaculated-blasphemorgulus = E100#{&}#>#{&}#100
(also called (96) blasphemorgudubbus)
(97) tristaculated-blasphemorgulus = E100#{&}#>#{&}#>#{&}#100
(also called (98) blasphemorgutrebbus)
(99) tetrastaculated-blasphemorgulus = E100#{&}#>#{&}#>#{&}#>#{&}#100
(also called (100) blasphemorguquabbus)
...
(101) blasphemorgulcross = E100#{&}##100
(comparable to agoraphobia)
(102) blasphemorgulcubor = E100#{&}###100
(comparable to astralthrathoth)
(103) blasphemorgulteron = E100#{&}####100
...
(104) blasphemorgultope = E100#{&}#^#100
(105) blasphemorgularxitri = E100#{&}#{&}#100
(106) blasphemorgularxitet = E100#{&}#{&}#{&}#100
Then...
(107) blasphemorgulhenus = E100#{&+1}#100
(also called (108) greesblasphemorgulus)
(109) blasphemous blasphemorgulhenus = E100(#{&+1}#){&}#100
(110) blasphemorgulhenaldubbus = E100(#{&+1}#){&+1}#100
(111) blasphemorgulhenaliterator = E100#{&+1}#>#100
(112) dustaculated-blasphemorgulhenus = E100#{&+1}#>#{&+1}#100
(113) blasphemorgulhenuecross = E100#{&+1}##100
(114) blasphemorgulhenuetope = E100#{&+1}#^#100
(115) blasphemorgulhenuarxitri = E100#{&+1}#{&+1}#100
...
(116) blasphemorguldeuterus = E100#{&+2}#100
(117) blasphemorgultritus = E100#{&+3}#100
(118) blasphemorgultetertus = E100#{&+4}#100
...
(119) blasphemorgulhyperius = E100#{&+#}#100
(120) blasphemorguldihyperius = E100#{&+#+#}#100
(121) blasphemorgulgridihyperius = E100#{&+##}#100
(122) blasphemorgulgodgahlahius = E100#{&+#^#}#100
(123) blasphemorgultethrathothius = E100#{&+#^^#}#100
...
(124) blasphemorgulversiadyon = E100#{&+#{&}#}#100
(125) blasphemorgulversed-blasphemorgulhenus = E100#{&+#{&+1}#}#100
...
(126) blasphemorgulversiatrion = E100#{&+#{&+#{&}#}#}#100
And making more fundamental sequences...
(127) blasphemordeus = E100#{&+&}#100
= E100#{&+#{&+#{...&+#{&+#{&}#}#...}#}#}#100
w/ 100 &'s
(128) blasphemortruce = E100#{&+&+&}#100
(129) blasphemorquad = E100#{&+&+&+&}#100
...
(130) blasphemorhyperiath = E100#{&#}#100
(131) blasphemoriasi-tethrathoth = E100#{&#^^#}#100
...
(132) blasphemoriadeusus = E100#{&#{&}#}#100
(133) blasphemoriatreusus = E100#{&#{&#{&}#}#}#100
...
(134) squariduagulus = E100#{&&}#100
= E100#{&#{&#{...&#{&#{&}#}#}#}#}#100
w/ 100 &'s
(135) squariduaguldeus = E100#{&&+&&}#100
(136) squariduagulhyperiath = E100#{&&#}#100
(137) squariduadiadeusus = E100#{&&#{&&}#}#100
...
(138) cubiculgulus = E100#{&&&}#100
(139) quarticulgulus = E100#{&&&&}#100
...
(140) hypericulgulus = E100#{&^#}#100
(141) hypericulastraduas = E100#{&^#{&}#}#100
(142) hypericulastratrias = E100#{&^#{&^#{&}#}#}#100
...
(143) spatialatigulus = E100#{&^&}#100
= E100#{&^#{&^#{...&^#{&^#{&}#}#...}#}#}#100
w/ 100 &'s
(144) dyalspatialatigulus = E100#{&^&&}#100
(145) tryalspatialatigulus = E100#{&^&&&}#100
...
(146) hyperialspatialatigulus = E100#{&^&^#}#100
(147) spatialatici-astraduas = E100#{&^&^#{&^&}#}#100
...
(148) spatialtritigulus = E100#{&^&^&}#100
(149) spatialtetertigulus = E100#{&^&^&^&}#100
(150) spatialpeptigulus = E100#{&^&^&^&^&}#100
(151) spatialextigulus = E100#{&^&^&^&^&^&}#100
...
(152) spatialdekatigulus = E100#{&^&^&^&^&^&^&^&^&^&}#100
And finally,
(153) blasteriagulus = E100#{&^^#}#100
(also called (154) spatialhecatigulus)
= E100#{&^&^&^&^...^&^&^&^&}#100
w/ 100 &'s
To be continued...