Lemma 95.1
Two useful kinds of choice
B_total = 120 + 6 = 126
The main web combines mathematical continuation with direct entry into real place pages.
Mathematical depth 95
Six real places, with a deeper way through.
The six place choices are real pages from the live archive. The mathematical doors underneath keep the journey inside Discover Alone, add one to its depth and open another changing set of six places.
- Start here: Nehemia AzazPlace of death · Oxfordshire
- Try this: Simon CookBirthplace · Oxford
- Try this: Children's playgroundChildren's playground · Oxford
- Try this: Hurst HouseListed building · Rother
- Try this: Pendrell HallListed building · South Staffordshire
- Try this: Children's playgroundChildren's playground · West Oxfordshire
The mathematics of finding without an ending
These lemmas describe what the page really does. The formulas change with the carried depth and the live archive total; the facts underneath them do not.
Lemma 95.2
One map point
P = (latitude, longitude)
A trustworthy coordinate pair lets one real record appear at its saved position on the map.
Lemma 95.3
The complete archive
N = 1,118,481
N is read from the same live place database that makes the public pages.
Lemma 95.4
Real-page share
6 / 126 = 4.7619%
Six of the main choices open real records, so the archive remains part of every Fractal page.
Lemma 95.5
Distance on the earth
a = sin^2(delta_lat/2) + cos(lat_1) cos(lat_2) sin^2(delta_long/2)
The map uses positions on a globe, so nearby means surface distance rather than a flat drawing.
Lemma 95.6
Wrapped selection
row = ((start + offset - 1) mod N) + 1
When a chosen position passes the end of the database, it continues from the beginning without inventing a record.
Lemma 95.7
Continuation share
120 / 126 = 95.2381%
Most main choices deepen the mathematical web instead of ending the journey after one page.
Lemma 95.8
Four-country whole
N = Ireland + England + Scotland + Wales
The four country parts add back to the complete live archive rather than creating four separate totals.
Lemma 95.9
Far-apart starting offsets
offsets = {1, 97, 997, 10,007, 50,021, 100,003}
The six choices are taken from widely separated positions rather than six neighbouring database rows.
Lemma 95.10
Possible labelled routes
routes after k mathematical steps = 120^k
The formula counts possible sequences of labelled doors; it does not pretend that extra database records exist.
Lemma 95.11
One row, one public address
public page = page(saved record identifier)
A saved database row and its public page remain the same thing; no second made page is required.
Lemma 95.12
No repeated card
|chosen record identifiers| = 6
A record already selected for the current six is not shown a second time in that same set.
Continue through 120 mathematical doors
Every door below remains inside Discover Alone, carries depth 96 and opens six more real place pages.