First, the individual entries. The grid entry is listed first, then the clue answer in the appropriate column for its set. Following that is the letter to be extracted from the clue (by set) and where that letter is to be found in the clue. (I'm basing this file on my original planning spreadsheet.) Finally, you get the clue and its explanation. At the bottom of this table is the explanation of the answer extraction.
Across: | GRID ENTRY | SUB | N | QUASI | SIMPLE | +sub | +N | +q | +sim | Where | Across: | Clue | Explanation | |
1 | SAUNA | SAUNA | N | START | 1 | NASA uncertain about university’s social bath | anag. nasa around u | |||||||
4 | ISSUE | TISSUES | N | word 2 | 4 | McCourts narrative makes claim against network | tis+sues | |||||||
7 | OILER | BOILERPLATE | C | word 2 | 7 | Legal copy revised liable trope | anag. liable trope | |||||||
11 | COOING | COOING | I | START | 11 | Inamoratas sweet talk with soulless subordinate holding love-in | co(oin)g | |||||||
12 | PINOCHLE | PINOCHLE | V | START | 12 | Varied lone chip for card game | anag. lone chip | |||||||
13 | INDIE | WINDIER | H | word 2 | 13 | More howling, Be victorious! Lose ignominiously! and Run! | win+die+r | |||||||
16 | IDEAL | AILED | N | LAST | 16 | Computer brain took control, suffered from infection | ai+led | |||||||
17 | SARONGS | SARONGS | E | START | 17 | Exotic grass on garments from Polyneisia | anag. grass on | |||||||
19 | CRONE | MICRONESIA | E | word 3 | 19 | Island-filled expanse in Pacific Ocean rim is variegated | anag. Ocean rim is | |||||||
20 | KIMONO | KIMONO | R | START | 20 | Robe obtained from Basinger and Yoko | kim+ono | |||||||
21 | ROUTED | DETOUR | I | LAST | 21 | Change course, down around visitor from Alpha Centauri | d(et)our | |||||||
24 | ASIMOV | ASIMOV | S | START | 24 | SF giant, like yours truly, with short turn | as+i+mov[e] | |||||||
25 | ERROR | TERRORIZE | C | word 2 | 25 | Panic coming from mislabeled "Retro Award" eschewing past | anag. retro + [p]rize | |||||||
30 | SNAILS | SAILS | N | 2 | 30 | Unmoored Lisas yachts | anag lisas | |||||||
32 | DONOR | DOOR | D | 3 | 32 | Medico declining Eastern states opening | doctor – ct | |||||||
34 | EXCEL | SEX CELL | K | word 2 | 34 | Promote keeping former lover with hundred sperm, e.g. (2 wds.) | s(ex+c)ell | |||||||
35 | ELICIT | FELICITY | E | word 2 | 35 | Joyous experience is false! Untrue! Lie! (Nice, for one.) | f + anag. lie + city | |||||||
41 | SNEER | SEER | E | 2 | 41 | Jeanne Dixon, e.g., speaking of drought | homophone sere | |||||||
42 | NEARLY | EARLY | R | 1 | 42 | Real erratically, year is ahead of schedule | anag. real + y | |||||||
44 | SLEUTH | HUSTLE | C | LAST | 44 | Scam heroin and steal cattle, rubbing out leader of republic | h + [r]ustle | |||||||
46 | IMPART | ARMPIT | O | LAST | 46 | Arabic member of Parliament leading it to become unpleasant place to go to | ar + mp + it | |||||||
48 | PIANO | PIANO | I | START | 48 | Instrument in Utopian orchestra | hidden | |||||||
50 | SAUNTER | NATURES | D | LAST | 50 | Types Newton is growing older, losing head | N + [m]atures | |||||||
52 | AGAIN | AGAIN | T | START | 52 | Twice falls over, abandoning God | rev. niaga[ra] | |||||||
53 | IOTAS | IOTAS | Y | START | 53 | Yannis characters portrayed by flora and fauna from several regions (British excepted) | [b]iotas | |||||||
54 | COOLANTS | COOLANTS | O | START | 54 | Organofluorine compounds dispersed, lost: no A/C | anag. lost no a/c | |||||||
55 | TEEOFF | TOFFEE | E | LAST | 55 | Candy made from drop of theobroma and skimmed beverage | t + [c]offee | |||||||
56 | SNEED | SEED | L | 2 | 56 | Plant’s material matches declared yield | homophone cede | |||||||
57 | KNEEL | KEEL | I | 2 | 57 | Mirrorlike electromagnets clasping ships bottom | hidden | |||||||
58 | AMBER | CHAMBERS | D | word 3 | 58 | Cryptic resource described by radio operator interrupting radio operators | c(ham)bers | |||||||
Down: | Down: | |||||||||||||
1 | SNICK | SICK | N | 2 | 1 | Unclean! (said exactly that way) | homophone sic | |||||||
2 | ACNE | ACE | E | 3 | 2 | One Dirac equation derivative | hidden | |||||||
3 | NOISOME | MOONIES | H | LAST | 3 | How one functions: Ones divided by one equals ones, in a group. Thats cultish | mo + on(i)es | |||||||
4 | INTROVERT | INTROVERT | F | START | 4 | Following interest, Neville Longbottoms pet toad has flipped over shy person | int + rev. trevor | |||||||
5 | SPEND | SPED | D | 4 | 5 | Held by gas pedal! | hidden | |||||||
6 | ENDS | SEND | A | LAST | 6 | Post contents of Ibsen drama | hidden | |||||||
8 | ICARUS | ICARUS | H | LAST | 8 | High flyer from America following interstate with motorized transport | i+car+us | |||||||
9 | ELAN | MELANGE | O | word 2 | 9 | Combination of Alice’s Restaurant owner and WikiLeaks founder getting rid of obstinate jerk | mel + [ass]ange | |||||||
10 | RECEDE | DECREE | R | LAST | 10 | Condemn, mostly, East End edict from ruler | decr[y] + e + e | |||||||
14 | DEMI | ACADEMIC | N | word 4 | 14 | Mecca Aid disbanded, not producing any practical outcome | anag. Mecca Aid | |||||||
15 | MONET | MOET | O | 3 | 15 | Producer of champagne Simpsons barkeep and taverns opening | moe + t | |||||||
18 | GARB | BRAG | A | LAST | 18 | Bikinis top above strippers string is Grade A | bra + g | |||||||
19 | CORNER | CORER | L | 4 | 19 | Apple gadget is programmed after trades by R&D | coded substitute r for d | |||||||
22 | TRICK | STRICKEN | S | word 2 | 22 | Major Strasser’s killer, filling submachine gun, is wounded | st(rick)en | |||||||
23 | ELLEN | REPELLENT | O | word 4 | 23 | Truly disgusting agent on Chicago transit forty days before Easter | rep+el+lent | |||||||
24 | AIDE | MAIDEN | N | word 2 | 24 | Rookie’s name source of excitement among staff | ma(id+e)n | |||||||
26 | RAISE | PRAISED | A | word 2 | 26 | Receiving accolades dispelled despair | anag despair | |||||||
27 | MOLAL | MOLAL | I | START | 27 | Interrupting Ms. Flanders with answer about a solutions density | mol(a)l | |||||||
28 | SNIDE | SIDE | U | 2 | 28 | Current time-out started by soccers first-place team | s + [t]ide | |||||||
29 | ARISTO | RATIOS | C | LAST | 29 | Right at Jovian moon, syzygys first producing relationships arithmetic | r+at+io+s | |||||||
30 | SCHNITZEL | SCHNITZEL | C | START | 30 | Chen, Liszt improvised a Viennese specialty | anag chen liszt | |||||||
31 | LAY | LAY | A | START | 31 | Albany, without odd characters, is not professional | alternating letters | |||||||
36 | HERA | THERAPY | N | word 2 | 36 | Previously named ones taking blame for attempt to treat disorder | the(rap)y | |||||||
37 | ARENA | AREA | M | 4 | 37 | Geometric measure of topless Barenaked gal | [b]are+[g]a[l] [barenaked treated as two words] | |||||||
38 | TAPROOM | TAPROOM | G | START | 38 | Grad student who leads recitations and lecturer not permitted to finish physics unit without h-bar | ta+pro[f]+o[h]m [h-bar, presented as the symbol, contains the last letter of the wordplay “h” and the definition “bar”] | |||||||
39 | ASPICS | ASPICS | O | START | 39 | Oakland team snaps jelly molds | as+pics | |||||||
40 | BUNGLE | BUGLE | N | 3 | 40 | Annoy the French horn | bug+le | |||||||
43 | RANT | RAT | S | 3 | 43 | Rising pitch indicates scab | reverse tar | |||||||
45 | PURSE | SUPER | T | LAST | 45 | Dine with Eric’s better half – that’s great | sup+er | |||||||
47 | TASER | STARE | E | LAST | 47 | Eagerly at first, following celebritys gaze | star+e | |||||||
49 | ICON | LEXICONS | T | word 4 | 49 | Carelessly clone six tomes, like the OED | anag clone six | |||||||
50 | SINK | HELSINKI | S | word 4 | 50 | Brothel, sin, kinkiness supplying European capital | hidden | |||||||
51 | CAFE | FACE | R | LAST | 51 | Oppose inconclusive truth and error | fac[t] + e |
OK, so now you need to count the UNCHECKED CONSONANTS in the UNDERLINED COLUMNS and interpret them as UNICODE CHARACTERS. (And to complete things, Uc's PhD is from the UNIVERSITY OF CHICAGO, which of course is an urban campus.)
You should get 222A and 2282. (There's a hint that you'll need to work in hex in the instructions, where I talk about the 4016-1 clues.) Looking up these characters in the Unicode standard, you'll find that they are the characters for "set union" and "subset", ∪⊂ which are used throughout Uc's dissertation, and which also look like "UC".
Inserting these into the blank squares in the central entry, and reading the letters that are already there as though they were in the appropriate font to be set names, you get ℜ∪ℑ⊂ℂ, which means "the set of real numbers unioned with the set of imaginary numbers forms a proper subset of the set of complex numbers."