Search Systems, Link Graph Physics & Information Retrieval Monographs

Most writing about search ranking is written backwards. It starts from a result that moved and reasons toward a cause, which is how an entire industry came to believe that links are counted rather than weighed. This publication starts from the other end: from the mathematics Google published, the patents it was granted, and the attribute names that surfaced in the 2024 Content Warehouse API documentation.11The leaked reference describes more than 14,000 attributes across roughly 2,500 modules. Attribute names such as homepagePagerankNs, siteFocusScore and anchorMismatchDemotion are quoted here exactly as documented; the scoring formulas that consume them are not public and are modelled, not reproduced. From those sources a consistent physics emerges. PageRank decays with distance and outdegree. Anchors are trusted only when the phrases around them agree with the document they point to. Sites have centroids, and pages far from the centroid are expensive to carry. Crawl is a budget allocated by tier, and a URL that cannot justify its serving cost is quietly demoted out of the fast index.

Each monograph below takes one of those mechanisms, states the governing equation or patent claim, and then asks what a working site operator should do differently. The instrument that follows is the fastest way into the material.

How to read the instrument

The calculator treats a source page as a reservoir of root PageRank, scaled by one thousand for legibility, and drains it through four successive filters. The first is damping: a random surfer teleports with probability 0.15, so only 85 percent of any page’s rank is ever available to its outlinks.22Page, L., Brin, S., Motwani, R. and Winograd, T. (1999), The PageRank Citation Ranking: Bringing Order to the Web. The 0.85 figure is the value used in the original paper and in nearly every later reproduction. The second is outdegree: the damped pool is divided equally across every outbound link, which is why a 200-link resource page passes almost nothing to any single target. The third is phrase alignment, the mechanism described in Anna Patterson’s phrase-based indexing patent, in which an anchor earns weight only when the phrases in the linking document’s body co-occur with the phrases the anchor predicts. The fourth is serving tier: a document that lives outside the Flash and Base tiers is rarely consulted at query time, so its outlinks are discounted accordingly.

Featured monographs

Patent and schema index

Research notes

• 21 October 2026Re-ran the outdegree decay regression on 412 collector pages after the October core update. The slope is unchanged: per-link referral traffic still falls roughly as the inverse of outbound link count once OBL exceeds twelve.
• 9 October 2026Added a pruned-tier multiplier to the calculator. Readers asked why links from indexed but rarely served pages produce no measurable lift; the tier discount is the most defensible explanation the public record supports.
• 30 September 2026Local hub-and-spoke corpus expanded to eleven national service brands. Four-fact entity grounding on every spoke remains the single strongest predictor of map-pack visibility in the sample.
• 12 September 2026Correction to Monograph II: the radius figure is a distance in embedding space, not a page count. Thanks to the reader in Porto who caught it.