Lemma 1.1
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.
Mathematical depth 1
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: Whitehill CopseWood · East Hampshire
- Try this: The Sustainability CentreHeritage attraction · East Hampshire
- Try this: Hunsdonbury lower churchyardChurch, cross or graveyard · East Hertfordshire
- Try this: Under The Pier ShowHeritage attraction · East Suffolk
- Try this: Pair of bowl barrows 720m SSE of Westmeston Farm forming part of Western Brow round barrow cemeteryScheduled monument · Lewes
- Try this: The MountMountain / peak · North Kesteven
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 1.2
Saved total depth
D_total = sum(d_i)
The saved total is the sum of the carried depth on each recorded page opening.
Lemma 1.3
Depth survives a handoff
carried d = explicit depth, otherwise depth inside the carried seed
A journey arriving from Dagmor or AI ContactCentre keeps its existing depth instead of restarting at zero.
Lemma 1.4
A bounded spread
0 <= different records after v openings <= min(N, 6v)
Six pages per opening can broaden coverage quickly, while the real database total remains the firm upper limit.
Lemma 1.5
Average saved depth
D_average = D_total / page openings
This is the average journey number on an opening, not the number of different people.
Lemma 1.6
The next depth
d_next = 1 + 1 = 2
Every mathematical continuation adds exactly one to the carried journey number.
Lemma 1.7
Mathematical continuations
B_math = 120
These doors stay inside the Discover Alone Fractal and each one carries the next depth.
Lemma 1.8
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 1.9
Six real records
R = 6
Each opening keeps six real place pages from the live archive in front of the reader.
Lemma 1.10
Two useful kinds of choice
B_total = 120 + 6 = 126
The main web combines mathematical continuation with direct entry into real place pages.
Lemma 1.11
One map point
P = (latitude, longitude)
A trustworthy coordinate pair lets one real record appear at its saved position on the map.
Lemma 1.12
The complete archive
N = 1,118,481
N is read from the same live place database that makes the public pages.
Continue through 120 mathematical doors
Every door below remains inside Discover Alone, carries depth 2 and opens six more real place pages.