Lemma 94.1
The next depth
d_next = 94 + 1 = 95
Every mathematical continuation adds exactly one to the carried journey number.
Mathematical depth 94
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: Boundary stone on Heanton VillasMonument or public art · Cornwall
- Try this: Old Milestone just south of the A390, north of TresawleMonument or public art · Cornwall
- Try this: Children's playgroundChildren's playground · Cornwall
- Try this: Devil's DungeonWood · Coventry
- Try this: Prior's WoodWood · Forest of Dean
- Try this: Charles WordsworthBirthplace · Lambeth
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 94.2
Mathematical continuations
B_math = 120
These doors stay inside the Discover Alone Fractal and each one carries the next depth.
Lemma 94.3
Positive-depth share
P_positive = openings with d > 0 / all page openings
This shows what share of the complete page-opening pie certainly followed an earlier page.
Lemma 94.4
Six real records
R = 6
Each opening keeps six real place pages from the live archive in front of the reader.
Lemma 94.5
Two useful kinds of choice
B_total = 120 + 6 = 126
The main web combines mathematical continuation with direct entry into real place pages.
Lemma 94.6
One map point
P = (latitude, longitude)
A trustworthy coordinate pair lets one real record appear at its saved position on the map.
Lemma 94.7
The complete archive
N = 1,118,481
N is read from the same live place database that makes the public pages.
Lemma 94.8
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 94.9
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 94.10
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 94.11
Continuation share
120 / 126 = 95.2381%
Most main choices deepen the mathematical web instead of ending the journey after one page.
Lemma 94.12
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.
Continue through 120 mathematical doors
Every door below remains inside Discover Alone, carries depth 95 and opens six more real place pages.