WWN Auto-Navigation Parameter

1. Auto-Navigation Parameter

1. Auto-Navigation Parameter

1.1. Motivation

A webring member may want to send a visitor directly to the next member rather than landing them at their own site. The auto parameter triggers a state transition on arrival, converting a coordinate snapshot into an imperative navigation.

1.2. Parameter Specification

Parameter	Domain	Description
auto	`\{next, prev, "", nil\}`	Trigger transition on load (default: nil)

When auto is present, the client executes the corresponding transition function before rendering, then redirects to the resulting state URL. An empty value (bare &auto) inherits direction from d: if d=p, fires next; if d=n, fires prev.

1.3. Fiber Collapse (Opaque Fibers)

auto implies opaque fibers. The transition operates on $\pi(\mathcal{C})$, discarding $\sigma$. The visitor always lands at $v_0$.

Auto-navigation always redirects to the root of the target member, regardless of the current DAG position. Every auto collapses the fiber:

\begin{equation} (\sigma, k, w) \xrightarrow{\text{auto}} (/, k', w') \end{equation}

This is the opaque fiber model — ring navigation only occurs at roots. If you're deep in a site's DAG and trigger auto, you get ejected to the next member's root. The path $\sigma$ is forgotten.

1.3.1. Interior case

  /research/wwn/testing/?w=5&d=p&auto

  σ collapses: /research/wwn/testing/ → /
  w updates:   5 → 6 (if boundary crossing)

  → /?w=6&d=p

You were spelunking; now you're at root.

1.3.2. Boundary case

At a torus boundary, both collapses happen simultaneously:

  /research/wwn/?w=-8191&d=n&auto

  1. σ collapses: /research/wwn/ → /    (fiber projection)
  2. w wraps:     -8191 → 8191          (through the hole)

  → /?w=8191&d=n

Maximum topological violence: traverse the torus boundary and collapse the fiber in one click.

Transition on auto=next:

\begin{equation} \mathcal{C} = \langle \text{ord}, k, w, t, d \rangle \xrightarrow{\text{auto=next}} \mathcal{C}' = \langle \text{ord}, k', w', t', + \rangle \end{equation}

Where $k' = (k \mod \text{ord}) + 1$, $w' = w + \mathbf{1}_{k=\text{ord}}$.

1.4. Behavioral Modes

1.4.1. One-Shot (Safe)

The auto parameter is stripped from the resulting URL after firing. The visitor lands at the next member's site with a clean state URL. Navigation stops.

  Sender → auto=next → Member₂ (clean URL, no auto param)
                         ↓
                        stop

1.4.2. Self-Preserving (Dangerous)

The auto parameter is retained in the resulting URL. The next member's page loads with auto=next still present, triggering another transition. Navigation continues autonomously.

  Sender → auto=next → Member₂ (auto=next) → Member₃ (auto=next) → ...

This is a self-propagating traversal. The visitor's browser becomes a crawler.

1.5. Implications by Ring Order

1.5.1. ord > 1: Distributed Relay

Each member site receives one hit per revolution. The request propagates around the ring, incrementing $w$ at each $k = \text{ord} \to k = 1$ boundary. Every member becomes an unwitting redirect relay.

  site₁ → site₂ → site₃ → ... → site_ord → site₁ (w+1) → site₂ → ...

Effect: Distributes load across members. Still infinite, but slow enough per-member that it may go unnoticed until $w$ reaches the clamp boundary.

Detection signature: $t = 0$, $w$ monotonically increasing, $d = +$ constant. Textbook linear torus knot — the exact crawler fingerprint the winding number was designed to identify.

1.5.2. ord = 1: Self-Inflicted DDoS

Every hop returns to the sole member. The redirect loop has zero network fan-out. All requests hit the same origin.

  you → you (w+1) → you (w+2) → you (w+3) → ...

Effect: A tight loop bounded only by redirect latency and the browser's redirect limit (Chrome: 20, Firefox: 20, RFC 2068 suggestion: 5). Each browser that opens the link becomes an independent attack vector — against yourself.

Time to boundary (assuming 100ms per redirect, $w_{\max} = 8191$):

\begin{equation} T = \frac{(8191 - w_0)}{1} \times 0.1\text{s} \approx 13.7 \text{ minutes} \end{equation}

At which point $w$ wraps to $-8191$ and the loop continues in the other direction. The period of the full oscillation across $\mathbb{Z}_{16383}$ is approximately 27 minutes per browser tab.

Summary: You invented a way to DDoS yourself by being the only member of your own webring.

1.6. Pathological Scenarios

1.6.1. Chain Letter Propagation

A user shares a URL with auto=next intact. Each recipient's browser fires the transition, generating a new URL with incremented state, which may itself be shared. The winding number becomes a proxy for social propagation depth.

\begin{equation} w_n = w_0 + \sum_{i=1}^{n} \mathbf{1}_{k_i = \text{ord}} \end{equation}

1.6.2. Amplification via Sharing

On ord=1, sharing a self-preserving auto=next link to $N$ people opens $N$ concurrent redirect loops against your own site. This is unintentional reflection amplification where the attacker, reflector, and victim are all the same person.

1.6.3. Race Condition at Clamp Boundary

If $w = w_{\max}$ and two auto-navigations fire concurrently, behavior at the clamp boundary depends on whether wrapping is atomic. URL-encoded state avoids server-side races (state is in the client), but the semantic discontinuity ($w: 8191 \to -8191$) may confuse analytics.

1.7. Recommended Design

  function handleAutoNavigation(params) {
    const auto = params.get('auto');
    if (!auto) return null;

    // One-shot: strip auto param before redirect
    const nextState = transition(currentState, auto);
    const nextUrl = stateToUrl(nextState);

    // CRITICAL: do not preserve auto param
    // Preserving creates self-propagating traversal
    nextUrl.searchParams.delete('auto');

    return nextUrl;
  }

1.7.1. Safeguards (if self-preserving mode is ever desired)

TTL parameter: auto_ttl=N decrements on each hop. Navigation halts at $N = 0$.
Rate limiting: Server-side tracking of redirect frequency per session.
Winding budget: Halt auto-navigation when $|w - w_0| > \Delta w_{\max}$.
Browser redirect limits: Browsers cap redirects at ~20. This is not a safeguard; it's a symptom that something has gone wrong.

1.8. State Diagram

stateDiagram-v2
    [*] --> Landing: URL with auto=next

    state "One-Shot Mode" as OneShot {
        Landing --> Transition: fire transition
        Transition --> StripAuto: remove auto param
        StripAuto --> Redirect: clean URL
        Redirect --> [*]: visitor lands, navigation stops
    }

    state "Self-Preserving Mode (DANGEROUS)" as Danger {
        Landing --> Transition2: fire transition
        Transition2 --> KeepAuto: retain auto param
        KeepAuto --> Redirect2: URL with auto=next

        state "ord > 1" as Multi {
            Redirect2 --> NextMember: hit next member
            NextMember --> Transition2: auto fires again
        }

        state "ord = 1 (SELF-DDOS)" as Solo {
            Redirect2 --> Self: hit yourself
            Self --> Transition2: auto fires again
        }
    }

    note right of Danger
        Self-propagating traversal.
        Each redirect triggers the next.
        Terminates only at browser
        redirect limit (~20 hops)
        or clamp boundary wrap.
    end note

1.9. Classification via Torus Signature

The auto-navigation parameter, ironically, produces the exact winding signature the WWN system was designed to detect and classify:

Behavior	$w$ pattern	$t$	Torus class
Human browsing	low, oscillating	>0	low-order, non-monotonic
`auto=next` one-shot	$w_0$ or $w_0 + 1$	0	point or single step
`auto=next` preserved	monotonic increasing	0	$(1, \text{ord})$-torus knot
`auto=prev` preserved	monotonic decreasing	0	$(1, -\text{ord})$-torus knot
Confused bot	chaotic	>>0	dense, high-genus approximation

The feature designed to assist navigation is indistinguishable, by the system's own classification metrics, from a malicious crawler.

1.10. References

WWN Overview
Winding Ring Spec
Sheaf Model — fiber collapse context
Test Procedures — auto transition verification