The mathematics makes research paths visible. Following them well means keeping track of what each step establishes. This chapter uses the paper’s 2 October 2026 edition and its unchanged 1 October vector snapshot. The links are live entry points; the numbers below describe that dated audit.
Open Jeff Dean’s Anthropology profile. This is the identity and source-record starting point. The profile’s signal links include several news directions; no single one is “Jeff Dean’s eigenvector.”
Open the explicit Dean
view on news axis N24 and people pattern P2. The model selector
matters: this is the Eigen Hacks hn1 people model. Its
all-history Dean profile uses 253 qualified candidate
articles. The displayed news coordinate is approximately
+0.433 and the people coordinate
+0.371. N24’s leading terms include learn,
machin, model, and deep. The two
scores measure different projections; they are not probabilities or two
estimates of the same number.
Inspect neighbors. The audit records Sanjay Ghemawat at cosine 0.7514 with 31 candidate articles, Andrew Ng at 0.7413 with 394, and Noam Shazeer at 0.7403 with 38. These cosines use the retained 24-dimensional people space. The corresponding centered 60-dimensional comparisons are 0.7082, 0.6380, and 0.6687. Compression changes the numerical similarity. Follow the Andrew Ng selection, then Ng’s canonical profile, to inspect another person’s evidence.
Read an article. The Dean evidence includes a WIRED interview published on 14 December 2019. Its HN-derived record carries 15 December. Keep those dates distinct: the publisher and the archive record describe different observations. Then return to the map and ask which details in the source support the numerical association.
The related Eigen Hacks people view and Eigen Times people view extend the exploration into their separate corpora. Their axis numbers are local addresses, not universal concepts.
The audited current-news overlay has zero newly qualified article-person joins. It can display recent articles in the fixed news basis, but proximity to Dean’s historical profile does not establish that a recent article mentions him. This distinction is precisely where a promising research lead still needs evidence.
This query combines three tables: articles relevant to databases on a chosen date, sourced executive roles valid on that date, and qualified links between articles and people. The word “today” must resolve to an explicit date in all three.
Let be the queried date, a role’s known start date, and its known exclusive end date. Exclusive means the role is no longer valid on that endpoint. The symbol includes equality, whereas does not. Validity at the queried date can then be written . This is a useful interval convention, not permission to invent an end date. An unknown end does not by itself prove that a role continues today; retain the source’s as-of date and uncertainty.
The paper’s dated role query reaches executive records that have no supported profile in either published people model. The correct result is a visible gap, not a fabricated point on the map. Larry Ellison’s historical database coverage also cannot be substituted for a claim that he is the current CEO of a database company. A founder, a chair, and a current chief executive are distinct roles.
The research query can therefore show topic-ranked articles beside sourced roles while leaving missing joins visible. A completed current-CEO comparison would need additional profile coverage and article attribution. A larger identity catalog alone supplies neither.
Canonical identity answers which entity a record refers to. A Wikipedia/Wikidata correspondence can help confirm the node; it does not validate every article placed in a same-name bucket. Reviewed Devreal mappings reuse the existing canonical node. Name similarity alone never settles that correspondence.
A typed graph assertion answers another question: what relationship does a particular source state? “Employed by,” “reports to,” “coauthored,” and “competes with” have different meanings and sometimes different directions. Two people working for the same organization need not have overlapped or known each other. A co-mention records shared appearance in an article, leaving the relationship unspecified.
Dates and review states travel with the assertion. A source assertion, a machine classification, and a curator’s judgment are different kinds of support. A citation provides a route to inspection; it is not a measured probability of truth. Unknowns remain part of the record.
Suppose a synthetic article’s record says it names canonical person A. That establishes the recorded article-person association under its review status. A topic model gives the article a coordinate on a database-related axis. That establishes a measurement in a particular news basis. A cosine places A near B. That establishes similar coverage directions in a particular representation. None of these records states that A employs B.
To add an employment assertion, inspect a source that actually states that relationship, identify the subject and organization, and retain its dates and review status. To add a colleague assertion, evidence must support the relevant overlap or relationship rather than merely a shared organization name. One can preserve a candidate lead without promoting it to an asserted fact. This chain keeps identity, attribution, numerical similarity, source assertion, and curator judgment separate enough to correct independently.
Use a fictional announcement: “FinchDB raised $4 million; Harbor Ventures led and Cedar Capital participated.” There is one financing event, one recipient, and two explicitly named investor roles. The statement does not tell us how much either investor contributed. A partner quoted about the company is not automatically a personal investor or the deal’s lead partner.
One mathematical picture is an incidence table: rows are entities and columns are events. An entry records participation, with a separate role label such as recipient, lead, or participant. This explanatory picture lets several entities meet at one event without inventing every possible pairwise relationship. The deployed catalog stores event records and optional investor relationships; it need not materialize this matrix.
Now imagine a separate fictional regulatory notice reports $1 million sold, later amended to $3 million. These are successive cumulative observations of an offering, so adding them to claim $4 million would double-count. An offering target, proceeds sold to date, and an announced round total answer different questions. First-sale, filing, and announcement dates also remain distinct until evidence reconciles the events.
The audited catalog contains 2,893 financing events and 81 investor/partner relationship records. The totals need not agree: an event can have several known investors or none. Eight historical investor associations are excluded from the financing total. Of the financings, 2,875 come from selected SEC issuer-reported notices; publication is not SEC verification, and the selected notices are not a census of venture rounds.
Checkpoint. A financing has no named investor. Is its event record necessarily incomplete collection? Answer: No. The source may establish the financing while withholding investor identities. Preserve the event and the unknown participants.
Checkpoint. Two profiles have cosine 0.95 and share an employer. May we add “colleagues”? Answer: Those facts motivate a search. They do not establish overlapping employment or a sourced colleague relationship.
Use The Dual Geometry of People and News for the compact derivation, implementation audit, limitations, and source references behind this companion. Return to The Mathematics of Eigen Times for the foundations, especially text representation, covariance, SVD, named axes, and projection. Then explore Anthropology with three questions in view: which coordinates are being compared, what evidence supports the link, and which date does the claim describe?