clearK Rank: A Kindness-Weighted Citation Ranking for a Curated Web
The Studio · Clear.lol
PageRank orders the open web by treating a link as a vote: a page is important if important pages link to it. The model is elegant, but it is neutral about why a page earned its links, and on the open web links can be bought, farmed, or provoked by outrage. This paper describes K Rank, a citation ranking adapted to a small, curated, human-vetted web. K Rank keeps PageRank's recursive link analysis and adds one mechanism the open web cannot support: every vote is weighted by the voter's standing in a vouching system. A link from a trusted, vouched-for page counts at full weight. A link from a page whose standing has fallen counts for less, everywhere, automatically. We give the algorithm, a worked example, its resistance to manipulation, and its (deliberately trivial) computational cost at corpus scale 2,053 pages. K Rank is PageRank reapplied to a web where admission itself is an editorial act.
The whole paper, in words a 13-year-old would use.
Every page on our websites can point at other pages, like saying "hey, this one is good, go look." A link is a recommendation.
Google's famous trick, PageRank, says: a page matters if pages that matter recommend it. If the front page of a big site points at you, that counts way more than some random page nobody has heard of.
K Rank uses the same trick, with one extra rule: who is doing the recommending counts. If a kind, trusted person, somebody the whole community vouched for, recommends a page, that recommendation counts at full power. If the recommendation comes from someone brand new and untested, it counts for less. And if it comes from someone who got removed for being cruel, it counts for basically zero.
That kills the main cheat. You cannot make a hundred fake pages that all recommend your page, because nobody vouched for the fake pages, so their recommendations are worth nothing.
It works like picking teams at school. You trust the picks of the kid with a great reputation more than the picks of a stranger who just showed up. K Rank is that idea, written as math. It runs every night over all of our pages and takes less than a second.
Want the friendlier full tour? Kindness Rank explains it with all 109 of our tags.
1. Introduction
In 1998, Brin and Page observed that the link structure of the web resembles the citation structure of academic literature, and that a paper cited by important papers is probably important [1]. PageRank turns that observation into a number. The ranking helped Google organize a web of billions of pages with no editors, and it remains the canonical example of extracting quality from structure alone.
But structure alone is silent about intent. A link may be an endorsement, an advertisement, a provocation, or a trap. PageRank's successors spent decades fighting the manipulation this neutrality invites: link farms, paid link networks, and content engineered to be linked in anger. The ranking assumes an adversarial corpus because, at web scale, the corpus is adversarial.
Our corpus is different in kind, not just in size. The Clear network is a curated web of roughly two thousand pages, published by one small team and a vetted community. Admission is an editorial decision. Social surfaces are gated by application and vouching. In such a corpus, trust is not something the ranking must infer from structure under attack. It is something the community already maintains, explicitly, in its vouching records. K Rank connects those records to the ranking: kindness and standing become inputs to the mathematics of importance.
2. The K Rank Algorithm
2.1 Preliminaries: PageRank
Let A be a page, let T1 ... Tn be the pages that link to A, and let C(T) be the number of outgoing links on page T. With damping factor d, conventionally 0.85, PageRank is defined as [2]:
The value is computed iteratively until convergence. Intuitively, A inherits a share of the rank of every page that cites it, and a citation from a highly ranked page is worth more. The (1−d)/N term models our little climber, who follows links from peak to peak and occasionally stops climbing and starts over on a uniformly random page.
The formula without the math costume. Every page has a score, and the score is built out of recommendations. When a page links to you, it is vouching for you, and it hands you a slice of its own score.
How much that slice is worth depends on who is vouching. Think about real life. If a friend who has built three successful businesses tells you, "Use this accountant, she is the real deal," you listen. He is picky, he is proven, and he does not recommend people often, so his word carries serious weight. Now picture someone who recommends everything to everybody, every single day. Their recommendation is worth almost nothing.
Reviews work the same way. If a person who has written 5,000 careful Google reviews says a little restaurant is great, you book the table. Their taste is on record, so their praise means something. A page that is trusted, and that links out rarely, passes real trust when it links to you. A page nobody trusts, linking to everything in sight, passes almost none.
The last piece is the 15 percent. Picture our little climber, climbing the web like a mountain range, peak to peak, link to link. About 85 percent of the time he follows the trail in front of him. The other 15 percent, he stops, looks out over the range, and picks a mountain nobody pointed him to, a campsite nobody has tried yet. That exploring keeps every page reachable, even brand new ones nobody links to yet, and it lets all the scores settle into one final number per page.
2.2 The kindness coefficient
Each page T carries a kindness coefficient k(T) in [0, 1], computed from the community's vouching graph: who vouched for the page's author, whether those vouchers remain in good standing, and the author's moderation record. A tenured, vouched-for member's pages hold k(T) near 1. A new member on probation begins lower and earns standing over time. A member removed for cruelty takes their coefficient to 0, and it stays there.
K Rank redefines the vote. A page's endorsement of A is worth k(T) times its structural value:
The K Rank equation. When every k(T) = 1, it reduces exactly to PageRank.
The consequence is the point of the design. Rank in this system is partly reputation, and reputation lost is endorsement power lost, on every page the fallen member ever pointed at. Nobody has to patrol the links. The mathematics devalues them.
2.3 The considerate climber
PageRank imagines a random surfer. K Rank's figure is a considerate climber: he follows links from pages he trusts, and when he starts over, he does not teleport uniformly. His restart distribution is weighted by vouch standing, concentrated on the front door and on pages the community has vouched for most strongly. Formally, the (1−d)/N term is replaced by (1−d)·v(A), where v is a personalization vector derived from the vouching graph, in the family of TrustRank [3]. Trusted pages are not just worth more when they vote; they are where climbs begin.
2.4 TagRank: rank for topics
Every page in the corpus is tagged (in this project, tagging is a hard house rule, not a nicety). K Rank therefore runs on a bipartite graph of pages and tags: pages pass a fraction of their rank to their tags, and tags return it to the pages that carry them. A tag such as kindness or python accrues the pooled authority of everything honestly filed under it, which lets search rank topics, not only pages, and lets a well-kept tag outrank a louder one.
3. A Worked Example
Consider a four-page corpus: a front door (D), a recipe (R), a course (C), and a story (S). Links: D→R, D→C, R→S, C→R, S→D. Starting from uniform rank 0.25 with d = 0.85 and all k = 1, one iteration gives:
| Page | Inherited from | KR after 1 iteration |
|---|---|---|
| Front door (D) | S | 0.2500 |
| Recipe (R) | D and C | 0.3563 |
| Course (C) | D | 0.1438 |
| Story (S) | R | 0.2500 |
The recipe leads because two pages, including the well-cited course, point at it. Now suppose the course author's standing falls, k(C) = 0.2. The recipe's inheritance from C is discounted by that factor, and KR(R) drops to 0.1863 in a single iteration. No editor intervened. The recommendation of a member in poor standing simply weighs less, which is what standing means.
4. Differences from PageRank
| PageRank (1998) | K Rank (2026) | |
|---|---|---|
| Corpus | The open web, billions of pages | A curated web, thousands of pages |
| Admission | None; the climber takes all | Editorial; social members vetted and vouched |
| A vote is | Any link | A link, weighted by the voter's standing |
| Teleport | Uniform over all pages | Weighted by vouch standing (seeded trust) |
| Manipulation | Link farms, paid links, outrage bait | Requires admission and a reputation; both revocable |
| Topics | Not modeled | Tags hold rank in a bipartite graph (TagRank) |
| Compute | Clusters, days | One small machine, seconds, nightly |
| Objective | Importance | Importance, as judged by people the community trusts |
5. Computation at Our Scale
The corpus is small: 2,053 pages and the links between them. A laptop runs the whole ranking in under a second, so we recompute it from scratch every night. The inputs are published on our dev page, and the corpus is small enough that anyone can check the numbers by hand. We consider that a feature.
6. Discussion
Three honest limitations. First, K Rank inherits PageRank's indifference to content quality: a charming, empty page linked by trusted pages will rank. Tagging discipline and editorial admission mitigate this; they do not solve it. Second, the kindness coefficient is only as good as the vouching community maintaining it, which is a social process with mathematical consequences, and must be governed like one: published rules, human moderators, an appeals path. Third, at small scale the ranking is legible enough to game socially, by courting the trusted. We accept this. A ranking that can be influenced by becoming genuinely trusted by kind people is failing in the right direction.
7. Conclusions
PageRank ranked the web by asking who points at you. K Rank keeps the question and adds the one a curated community can answer and the open web cannot: how much is the pointer's word worth? On a small, vetted, honestly counted web, that addition turns a relevance signal into a reputation system, and makes kindness, mechanically, a form of authority.
The plain-English version of this paper, with the interactive tag explorer, lives at Kindness Rank. Live corpus numbers live at /dev/.
References
- S. Brin and L. Page. "The Anatomy of a Large-Scale Hypertextual Web Search Engine." Computer Networks and ISDN Systems, 1998.
- L. Page, S. Brin, R. Motwani, and T. Winograd. "The PageRank Citation Ranking: Bringing Order to the Web." Stanford InfoLab Technical Report, 1999.
- Z. Gyöngyi, H. Garcia-Molina, and J. Pedersen. "Combating Web Spam with TrustRank." Proceedings of VLDB, 2004.
- The Clear Project. "Kindness." clr.fm/kindness/, 2026. The value this ranking operationalizes.