WWN Test Procedures

Overview
URL Normalization
- Out-of-Range w Correction
  - Test N1: Negative overflow
  - Test N3: Positive overflow
Next Transitions
Prev Transitions
Auto-Navigation
Edge Cases
Wrap Function Verification
Bot Fingerprinting Signatures
References

Overview

This document contains test procedures for verifying WWN state transitions, boundary behavior, and URL normalization. The implementation uses:

W_MAX = 8191 = 2¹³ - 1 (Mersenne prime)
Modulus = 16383
State space: Z_ord × Z₁₆₃₈₃ (discrete torus)

URL Normalization

Out-of-Range w Correction

Visitors arriving with w outside [-8191, 8191] should have their URL silently corrected via history.replaceState.

Test	Input w	Expected w	Behavior
N1	-8192	8191	Wrap via torus
N2	-8193	8190	Wrap via torus
N3	8192	-8191	Wrap via torus
N4	10000	-6383	Wrap via torus
N5	0	0	No change
N6	8191	8191	No change (boundary)
N7	-8191	-8191	No change (boundary)

Test N1: Negative overflow

LOAD:  ?ord=1&k=1&w=-8192&t=2&d=p&utm_source=ring&utm_medium=webring&utm_campaign=literate-web

EXPECTED: Address bar changes to w=8191 (no redirect, no reload)
          Page renders with w=8191 displayed

Test N3: Positive overflow

LOAD:  ?ord=1&k=1&w=8192&t=0&d=p

EXPECTED: Address bar changes to w=-8191

Next Transitions

Normal next (no wrap)

Position increments without winding change.

LOAD:    ?ord=7&k=3&w=5&t=0&d=p
ACTION:  Click "next →"
RESULT:  ?ord=7&k=4&w=5&t=0&d=p

k: 3 → 4
w: unchanged (no boundary crossing)
t: unchanged (no direction reversal)
d: p (was p, still p)

Next with ring wrap (k=ord → k=1)

Position wraps, winding increments.

LOAD:    ?ord=7&k=7&w=5&t=0&d=p
ACTION:  Click "next →"
RESULT:  ?ord=7&k=1&w=6&t=0&d=p

k: 7 → 1 (wrap)
w: 5 → 6 (boundary crossing)
t: unchanged
d: p

Next at torus boundary

Winding wraps through the hole.

LOAD:    ?ord=1&k=1&w=8191&t=0&d=p
ACTION:  Click "next →"
RESULT:  ?ord=1&k=1&w=-8191&t=0&d=p

k: 1 → 1 (ord=1, always wraps)
w: 8191 → 8192 → wraps to -8191
t: unchanged
d: p

The hole is real.

Next after prev (direction reversal)

Turning count increments.

LOAD:    ?ord=7&k=3&w=0&t=0&d=n
ACTION:  Click "next →"
RESULT:  ?ord=7&k=4&w=0&t=1&d=p

k: 3 → 4
w: unchanged
t: 0 → 1 (direction reversal: was n, now p)
d: n → p

Prev Transitions

Normal prev (no wrap)

LOAD:    ?ord=7&k=5&w=3&t=0&d=n
ACTION:  Click "← prev"
RESULT:  ?ord=7&k=4&w=3&t=0&d=n

k: 5 → 4
w: unchanged
t: unchanged (was n, still n)
d: n

Prev with ring wrap (k=1 → k=ord)

LOAD:    ?ord=7&k=1&w=3&t=0&d=n
ACTION:  Click "← prev"
RESULT:  ?ord=7&k=7&w=2&t=0&d=n

k: 1 → 7 (wrap)
w: 3 → 2 (boundary crossing, decrement)
t: unchanged
d: n

Prev at torus boundary

LOAD:    ?ord=1&k=1&w=-8191&t=0&d=n
ACTION:  Click "← prev"
RESULT:  ?ord=1&k=1&w=8191&t=0&d=n

k: 1 → 1
w: -8191 → -8192 → wraps to 8191
t: unchanged
d: n

Through the hole, other direction.

Prev after next (direction reversal)

LOAD:    ?ord=7&k=3&w=0&t=0&d=p
ACTION:  Click "← prev"
RESULT:  ?ord=7&k=2&w=0&t=1&d=n

k: 3 → 2
w: unchanged
t: 0 → 1 (direction reversal: was p, now n)
d: p → n

Auto-Navigation

Auto-next one-shot

LOAD:    ?ord=1&k=1&w=8190&t=0&d=p&auto=next
RESULT:  Redirects to ?ord=1&k=1&w=8191&t=0&d=p

auto param stripped (one-shot mode)
w: 8190 → 8191 (boundary crossing on ord=1)

Auto-prev one-shot

LOAD:    ?ord=1&k=1&w=-8190&t=0&d=n&auto=prev
RESULT:  Redirects to ?ord=1&k=1&w=-8191&t=0&d=n

auto param stripped
w: -8190 → -8191

Auto with empty value (inherit direction)

LOAD:    ?ord=1&k=1&w=0&t=0&d=n&auto
RESULT:  Redirects to ?ord=1&k=1&w=-1&t=0&d=n

auto="" inherits d=n → fires prev
w: 0 → -1

Auto-next through torus hole

LOAD:    ?ord=1&k=1&w=8191&t=0&d=p&auto=next
RESULT:  Redirects to ?ord=1&k=1&w=-8191&t=0&d=p

w: 8191 → 8192 → wraps to -8191

Auto-prev through torus hole

LOAD:    ?ord=1&k=1&w=-8191&t=0&d=n&auto=prev
RESULT:  Redirects to ?ord=1&k=1&w=8191&t=0&d=n

w: -8191 → -8192 → wraps to 8191

Edge Cases

ord=1 (degenerate ring)

Every action is a boundary crossing.

LOAD:    ?ord=1&k=1&w=0&t=0&d=p
ACTION:  Click "next →"
RESULT:  ?ord=1&k=1&w=1&t=0&d=p

Every next increments w.
Every prev decrements w.
You are the ring.

High turning count

LOAD:    ?ord=3&k=2&w=0&t=100&d=p
ACTION:  Click "← prev"
RESULT:  ?ord=3&k=1&w=0&t=101&d=n

Oscillator pattern: high t, low w.

Compressed URL mode

With data-wwn-compress-url"true"=:

LOAD:    ?w=5&t=2&d=n&utm_source=ring
ACTION:  Click "next →"
RESULT:  ?w=5&t=3&utm_source=ring

Note: d omitted when p (default)
      ord and k not included

Wrap Function Verification

Mathematical verification of wrapW():

function wrapW(w) {
  var size = 2 * W_MAX + 1;  // 16383
  var normalized = ((w + W_MAX) % size + size) % size;
  return normalized - W_MAX;
}

Input w	w + W_MAX	% size	+ size % size	- W_MAX	Result
0	8191	8191	8191	0	0
8191	16382	16382	16382	8191	8191
8192	16383	0	0	-8191	-8191
-8191	0	0	0	-8191	-8191
-8192	-1	-1	16382	8191	8191
16383	24574	8191	8191	0	0

The double-modulo ((x % n) + n) % n handles JavaScript's negative modulo behavior.

Bot Fingerprinting Signatures

Behavior	w pattern	t	Torus class
Human browser	low, oscillating	>0	low-order, non-monotonic
Linear scraper	monotonic	0	(1, ord)-torus knot
Ping-pong bot	≈0	→∞	trivial (contractible)
auto=next loop	monotonic to boundary	0	knot until browser limit