---
slug: ask-a-random-friend
passed: 2026-10-14
by: the assay line (research/assay-line/queue-1014c/), Codex fixer directed by claude-assaying-boyle-1014; source record by Codex, checked by Codex and a Claude agent
checked: 160
confirmed: 108
wrong: 52
unverifiable: 0
observed: 0
stale: 0
---

This pass addresses the 53 directed triage items for ask-a-random-friend at 11cce0dab7, using the supplied Codex source record and independent Codex and Claude checker records. The fixer re-read the evidence for every triage item before editing, independently recomputed the arithmetic from the unchanged edge list, and exercised the page script. Unaffected CONFIRMED claims below consolidate the supplied checker rereads; repeated descriptions changed by these fixes are explicitly scoped to their revised wording. The by line credits those existing checkers, not a new checker delegation. All 15 MINOR lines count toward wrong and have individual findings; no MINOR correction line was added to the page. The one rejected finding is CONFIRMED. This is a directed correction pass, not a new blind audit of every claim. The Codex repair review confirmed two copied-error groups in there-here, leaving six linked WRONG findings open with note IDs PENDING and 46 findings fixed. The review also narrowed dated corrections 9 and 11; see research/assay-line/queue-1014c/ask-a-random-friend/repair-report.md.

Feld's web PDF fetch timed out; the fixer read the existing full PDF text at /home/liam/.assay-line/queue-1014c/ask-a-random-friend/N1/external/feld.txt, pp. 1464-1466 and 1469-1475. Other triage sources were opened directly, including the UCINET dataset documentation, the MIT slides, the two arXiv abstracts, the PLOS study and the Nature paper. Source and arithmetic details, exact dated lines, before/after edits and command results are in research/friendship-paradox/fix-report-2026-10-14.md. Literal \u2014 represents pre-existing punctuation in quoted checker wording.

## Claims

- WRONG | X1 "almost certainly bigger" | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1465-1466; research/friendship-paradox/assay-2026-10-14.py | Feld reports 80 of 146 below their friends, about 55%, and describes a tendency. The endpoint identity supplies no near-certainty for an individual.
- WRONG | X2 "why it can't be otherwise." | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1474, Fig. 5; research/friendship-paradox/assay-2026-10-14.py | The connected six-node counterexample has degrees 2,2,3,3,3,3, with two below and four above their own friends. The club itself has 29 below and five above.
- WRONG | X3 "most people." | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1474, Fig. 5; research/friendship-paradox/assay-2026-10-14.py | The connected six-node counterexample has degrees 2,2,3,3,3,3, with two below and four above their own friends. The club itself has 29 below and five above.
- WRONG | X4 "\"most children are below the average height of children\" would be a contradiction." | research/friendship-paradox/assay-2026-10-14.py; https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1469-1470 fn. 3 | Heights 100,100,130 average 110; two of three are below that arithmetic mean.
- MINOR | X5 "the most-studied small network there is" | https://ocw.mit.edu/courses/esd-342-advanced-system-architecture-spring-2006/0e254650c1bf8cea51fcad92e1e3cb03_lec10.pdf slide 16 | The slide limits its superlative to community-finding researchers, with no ranking of all small networks.
- WRONG | X6 "The exact limits, computed from the network, are shown above" | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs; research/friendship-paradox/verify.mjs | The unchanged 78-edge list gives person mean 78/17, person-then-friend mean 799877/83232 = 9.6102100154 and gap 417989/83232 = 5.0219747213. Endpoint mean remains 101/13 = 7.7692307692.
- WRONG | X7 "What's true is that a clear majority are below" | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1474, Fig. 5; research/friendship-paradox/assay-2026-10-14.py | The connected six-node counterexample has degrees 2,2,3,3,3,3, with two below and four above their own friends. The club itself has 29 below and five above.
- WRONG | X8 "Here, the spread of those same degrees decides who feels outnumbered." | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1471-1472; research/friendship-paradox/assay-2026-10-14.py | K4 plus two disjoint edges and a four-cycle with one leaf per vertex share degrees 3,3,3,3,1,1,1,1 and endpoint mean 2.5. Their person-friend means are 2 and 8/3, with zero and four below their friends.
- MINOR | X9 "every number recomputed here is re-derived offline." | research/friendship-paradox/verify.mjs; public/strata/ask-a-random-friend/index.html | Offline sensor uses 1000 nodes and mean infection times; browser sensor uses 250 nodes and the 50% crossing. Star and preferential-attachment example sizes also differ.
- WRONG | X10 "always exceeds the mean number of friends" | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1470; research/friendship-paradox/assay-2026-10-14.py | On the four-cycle every degree is 2 and both means equal 2. For positive mean degree, endpoint excess is variance/mean, strictly positive only with positive variance.
- WRONG | X11 "rust to μ+σ²/μ = 7.77, gap +3.18" | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs; research/friendship-paradox/verify.mjs | The unchanged 78-edge list gives person mean 78/17, person-then-friend mean 799877/83232 = 9.6102100154 and gap 417989/83232 = 5.0219747213. Endpoint mean remains 101/13 = 7.7692307692.
- WRONG | X12 "43/43 in research/friendship-paradox/verify.mjs" | research/friendship-paradox/verify.mjs | The full repository run passes 50/50. Seven HTML drift checks are skipped when the page is absent, leaving 43/43. The baseline run already had 50 checks.
- WRONG | X13 "the variance σ² is the whole paradox." | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1471-1472; research/friendship-paradox/assay-2026-10-14.py | K4 plus two disjoint edges and a four-cycle with one leaf per vertex share degrees 3,3,3,3,1,1,1,1 and endpoint mean 2.5. Their person-friend means are 2 and 8/3, with zero and four below their friends.
- WRONG | X14 "the rust one to\n  `μ + σ²/μ` (`7.77`), the gap to `σ²/μ` (`+3.18`)." | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs; research/friendship-paradox/verify.mjs | The unchanged 78-edge list gives person mean 78/17, person-then-friend mean 799877/83232 = 9.6102100154 and gap 417989/83232 = 5.0219747213. Endpoint mean remains 101/13 = 7.7692307692.
- MINOR | X15 "Everything\nrecomputed in the browser is re-derived offline" | research/friendship-paradox/verify.mjs; public/strata/ask-a-random-friend/index.html | Offline sensor uses 1000 nodes and mean infection times; browser sensor uses 250 nodes and the 50% crossing. Star and preferential-attachment example sizes also differ.
- MINOR | X16 "whose every load-bearing number is\nchecked." | research/friendship-paradox/verify.mjs; research/friendship-paradox/assay-2026-10-14.mjs | The original seven HTML checks use substring presence, and did not test Instrument I targets. Code does not justify checking every displayed number.
- WRONG | X17 "→ μ + σ²/μ = 7.77" | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs; research/friendship-paradox/verify.mjs | The unchanged 78-edge list gives person mean 78/17, person-then-friend mean 799877/83232 = 9.6102100154 and gap 417989/83232 = 5.0219747213. Endpoint mean remains 101/13 = 7.7692307692.
- WRONG | X18 "The shape most real networks take." | https://arxiv.org/abs/1801.03400; public/strata/ask-a-random-friend/index.html | Broido and Clauset tested nearly 1000 networks and found diverse structures rather than universal scale-free form. The page constructs a preferential-attachment example.
- WRONG | X19 "predicted +3.18" | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs; research/friendship-paradox/verify.mjs | The unchanged 78-edge list gives person mean 78/17, person-then-friend mean 799877/83232 = 9.6102100154 and gap 417989/83232 = 5.0219747213. Endpoint mean remains 101/13 = 7.7692307692.
- MINOR | X20 "\"dateModified\":\"2026-06-19\"" | git show 6c62eb137a4:public/strata/ask-a-random-friend/index.html; git show 0a4a5bcd9d3:public/strata/ask-a-random-friend/index.html | The June 22 title change predates JSON-LD still claiming June 19 in the July 12 copy. This correction pass uses the task date 2026-10-14.
- MINOR | X21 "The page earns the result and shows the check at each step" | research/friendship-paradox/verify.mjs; public/strata/ask-a-random-friend/index.html | The original endpoint algebra did not establish Instrument I targets for the different draw. The blanket checking promise was too broad.
- WRONG | X22 "with the exact size of the gap (mean + variance/mean)." | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1470; research/friendship-paradox/assay-2026-10-14.py | The endpoint mean is mean + variance/mean; its excess above the person mean is variance/mean. Club values are 101/13 and gap 703/221.
- WRONG | X23 (added) "and acquaintance immunization (Cohen et al. 2003) turn the same sampling bias into epidemic early-warning." | https://arxiv.org/abs/cond-mat/0207387; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | The immunization paper studies reduced immunization thresholds and spread prevention; the sensor study tests earlier detection.
- WRONG | X24 (added) "A5 instructor (node 34) has degree 17" | https://sites.google.com/site/ucinetsoftware/datasets/zachary-karate-club; research/friendship-paradox/data.mjs | UCINET maps node 34 to the president and node 1 to the instructor. The edge list still gives degrees 17 and 16 respectively.
- WRONG | K1 [#3 intro-almost-certain] The unsettling theorem on this page says that second number is almost certainly bigger | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1465-1466; research/friendship-paradox/assay-2026-10-14.py | Feld reports 80 of 146 below their friends, about 55%, and describes a tendency. The endpoint identity supplies no near-certainty for an individual.
- WRONG | K2 [#4 intro-most-forced] and that this is true for most people at once, which sounds impossible until you see exactly why it can't be otherwise. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1474, Fig. 5; research/friendship-paradox/assay-2026-10-14.py | The connected six-node counterexample has degrees 2,2,3,3,3,3, with two below and four above their own friends. The club itself has 29 below and five above.
- WRONG | K3 [#6 height-contradiction] "most children are below the average height of children" would be a contradiction. | research/friendship-paradox/assay-2026-10-14.py; https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1469-1470 fn. 3 | Heights 100,100,130 average 110; two of three are below that arithmetic mean.
- WRONG | K4 [#9 feld-named-proof] The phenomenon was named and proved by the sociologist Scott Feld in 1991, in a paper with exactly this title. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1464 | The paper title is Why Your Friends Have More Friends than You Do; neither Ask a Random Friend nor the nearby declarative wording is exactly that title. This does not establish who coined a later term.
- WRONG | K5 [#10 karate-history] the 34 members of a 1970s university karate club, with the 78 friendships an anthropologist recorded before the club split in two | https://sites.google.com/site/ucinetsoftware/datasets/zachary-karate-club | The Background reports 50 to 100 members during the study. The network represents 34 members rather than a complete 34-person club.
- MINOR | K6 [#11 karate-ties] 78 friendships an anthropologist recorded before the club split in two | https://networkrepository.com/ucidata-zachary.php; https://ocw.mit.edu/courses/esd-342-advanced-system-architecture-spring-2006/0e254650c1bf8cea51fcad92e1e3cb03_lec10.pdf slide 15 | The standard dataset has 34 vertices and 78 edges; the MIT slide disputes the 23-34 tie. This supports identifying the version, not deleting an edge.
- MINOR | K7 [#12 most-studied] the most-studied small network there is | https://ocw.mit.edu/courses/esd-342-advanced-system-architecture-spring-2006/0e254650c1bf8cea51fcad92e1e3cb03_lec10.pdf slide 16 | The slide limits its superlative to community-finding researchers, with no ranking of all small networks.
- WRONG | K8 [#15 sampler-limits] The blue average converges to the true mean degree; the rust average converges higher. The exact limits, computed from the network, are shown above -- and proved below. | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs; research/friendship-paradox/verify.mjs | The unchanged 78-edge list gives person mean 78/17, person-then-friend mean 799877/83232 = 9.6102100154 and gap 417989/83232 = 5.0219747213. Endpoint mean remains 101/13 = 7.7692307692.
- WRONG | K9 [#22 majority-unqualified] What's true is that a clear majority are below, and the network decides exactly how many. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1474, Fig. 5; research/friendship-paradox/assay-2026-10-14.py | The connected six-node counterexample has degrees 2,2,3,3,3,3, with two below and four above their own friends. The club itself has 29 below and five above.
- CONFIRMED | K10 [#27 feld-deprived-quote] the often-quoted figure that 74% "feel relatively deprived" is conditional on assuming each person's friends are a representative sample | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1465, 1469, 1475 | REJECTED with evidence: the short phrase feel relatively deprived occurs on pp. 1465 and 1475. Page 1469 gives the conditional 74% calculation, and the page preserves its sampling condition. Absence from one secondary retelling does not refute often-quoted.
- MINOR | K11 [#43 immunize-friend] If you can only reach a fraction of a population and you don't know who the hubs are, immunize a random friend of a random person instead of a random person -- the friend is probably a hub, and hubs are where an epidemic lives. | https://arxiv.org/abs/cond-mat/0207387 | The source supports acquaintance selection as a bias toward high connectivity; it gives no universal probability above one half of selecting an undefined hub.
- WRONG | K12 [#62 spread-outnumbered] Here, the spread of those same degrees decides who feels outnumbered. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1471-1472; research/friendship-paradox/assay-2026-10-14.py | K4 plus two disjoint edges and a four-cycle with one leaf per vertex share degrees 3,3,3,3,1,1,1,1 and endpoint mean 2.5. Their person-friend means are 2 and 8/3, with zero and four below their friends.
- MINOR | K13 [#64 citation-eom-cite] Eom, Y.-H. & Jo, H.-H. (2014). Generalized friendship paradox in complex networks. Scientific Reports 4: 4603. | https://www.nature.com/articles/srep04603; research/friendship-paradox/data.mjs | The source title includes the subtitle The case of scientific collaboration; the original author, journal and article number identified the correct paper.
- MINOR | K14 [#74 footer-offline] every number recomputed here is re-derived offline. | research/friendship-paradox/verify.mjs; public/strata/ask-a-random-friend/index.html | Offline sensor uses 1000 nodes and mean infection times; browser sensor uses 250 nodes and the 50% crossing. Star and preferential-attachment example sizes also differ.
- MINOR | K15 [#78 twitter-card-two-weeks] And that sampling quirk gives epidemiologists a two-week head start. | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 Abstract and Results | The 13.9-day lead is the clinical-diagnosis comparison in the 2009 Harvard study. Lead time varies with the outbreak and network.
- WRONG | K16 [#79 dek-always-exceeds] the mean number of friends of friends always exceeds the mean number of friends, by exactly variance/mean. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1470; research/friendship-paradox/assay-2026-10-14.py | On the four-cycle every degree is 2 and both means equal 2. For positive mean degree, endpoint excess is variance/mean, strictly positive only with positive variance.
- WRONG | K17 [#82 dek-sampler] pick a random person then ask them for a random friend and watch two running averages pull apart (blue converges to mean 4.59, rust to μ+σ²/μ = 7.77, gap +3.18) | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs; research/friendship-paradox/verify.mjs | The unchanged 78-edge list gives person mean 78/17, person-then-friend mean 799877/83232 = 9.6102100154 and gap 417989/83232 = 5.0219747213. Endpoint mean remains 101/13 = 7.7692307692.
- WRONG | K18 [#91 dek-pass-43] 43/43 in research/friendship-paradox/verify.mjs | research/friendship-paradox/verify.mjs | The full repository run passes 50/50. Seven HTML drift checks are skipped when the page is absent, leaving 43/43. The baseline run already had 50 checks.
- WRONG | K19 [#94 related-variance] Here the same per-node counts, read for their spread rather than their parity, decide how badly a typical member is outnumbered by their friends -- the variance σ² is the whole paradox. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1471-1472; research/friendship-paradox/assay-2026-10-14.py | K4 plus two disjoint edges and a four-cycle with one leaf per vertex share degrees 3,3,3,3,1,1,1,1 and endpoint mean 2.5. Their person-friend means are 2 and 8/3, with zero and four below their friends.
- WRONG | K20 [#100 md-sampling-limits] blue running mean converges to the true mean degree (`4.59`), the rust one to `μ + σ²/μ` (`7.77`), the gap to `σ²/μ` (`+3.18`). | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs; research/friendship-paradox/verify.mjs | The unchanged 78-edge list gives person mean 78/17, person-then-friend mean 799877/83232 = 9.6102100154 and gap 417989/83232 = 5.0219747213. Endpoint mean remains 101/13 = 7.7692307692.
- WRONG | K21 [#102 md-everything-offline] Everything recomputed in the browser is re-derived offline: `research/friendship-paradox/verify.mjs`, **43/43** (Feld's identity exact on four networks, the sensor and immunization sims seeded and reproducible, plus a pencil-and-paper anchor and a page drift guard). | research/friendship-paradox/verify.mjs | The full repository run passes 50/50. Seven HTML drift checks are skipped when the page is absent, leaving 43/43. The baseline run already had 50 checks.
- MINOR | K22 [#103 md-all-numbers] whose every load-bearing number is checked. | research/friendship-paradox/verify.mjs; research/friendship-paradox/assay-2026-10-14.mjs | The original seven HTML checks use substring presence, and did not test Instrument I targets. Code does not justify checking every displayed number.
- WRONG | K23 [#105 panel-aReads] draws 0 random person running mean degree 0.00 → true mean 4.59 random friend running mean degree 0.00 → μ + σ²/μ = 7.77 gap so far +0.00 (predicted +3.18) | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs; research/friendship-paradox/verify.mjs | The unchanged 78-edge list gives person mean 78/17, person-then-friend mean 799877/83232 = 9.6102100154 and gap 417989/83232 = 5.0219747213. Endpoint mean remains 101/13 = 7.7692307692.
- WRONG | K24 [#116 panel-scale-most] The shape most real networks take. | https://arxiv.org/abs/1801.03400; public/strata/ask-a-random-friend/index.html | Broido and Clauset tested nearly 1000 networks and found diverse structures rather than universal scale-free form. The page constructs a preferential-attachment example.
- WRONG | K25 [#121 panel-after500] draws 500 random person running mean degree 4.58 → true mean 4.59 random friend running mean degree 9.96 → μ + σ²/μ = 7.77 gap so far +5.38 (predicted +3.18) | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs; research/friendship-paradox/verify.mjs | The unchanged 78-edge list gives person mean 78/17, person-then-friend mean 799877/83232 = 9.6102100154 and gap 417989/83232 = 5.0219747213. Endpoint mean remains 101/13 = 7.7692307692.
- MINOR | K26 [#126 schema-dateModified] "dateModified":"2026-06-19" | git show 6c62eb137a4:public/strata/ask-a-random-friend/index.html; git show 0a4a5bcd9d3:public/strata/ask-a-random-friend/index.html | The June 22 title change predates JSON-LD still claiming June 19 in the July 12 copy. This correction pass uses the task date 2026-10-14.
- WRONG | K27 [#136 metadata-gap] with the exact size of the gap (mean + variance/mean). | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1470; research/friendship-paradox/assay-2026-10-14.py | The endpoint mean is mean + variance/mean; its excess above the person mean is variance/mean. Club values are 101/13 and gap 703/221.
- WRONG | K28 (added) Then the social-network sensor (Christakis & Fowler 2010) and acquaintance immunization (Cohen et al. 2003) turn the same sampling bias into epidemic early-warning. | https://arxiv.org/abs/cond-mat/0207387; https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | The immunization paper studies reduced immunization thresholds and spread prevention; the sensor study tests earlier detection.
- MINOR | K29 (added) You can check the whole thing by hand on the smallest interesting case: a star, one centre joined to four leaves. | research/friendship-paradox/assay-2026-10-14.py; https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1473 fn. 6 | The smaller three-node path has mean 4/3 and endpoint mean 3/2, with positive gap 1/6. The five-node star arithmetic is correct.
- CONFIRMED | N1 #1 headline-average: on average, your friends have more friends than you do | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1470 gives the endpoint mean as mean plus variance/mean and says "at least as great". Equality is the regular case; the displayed networks have positive mean.
- CONFIRMED | N1 #2 headline-town: the same quirk lets a town watch its epidemic from the future | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | Checker source reread: The study proposes "simply monitoring the friends of randomly selected individuals" and explains their earlier infection on average. The page describes this method, not a measured town trial.
- CONFIRMED | N1 #7 popularity-weighting: When you list the friends of friends, popular people get listed over and over \u2014 once for every friend they have \u2014 and unpopular people barely get listed at all. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1465 explains that a person with 40 friends appears in 40 friendship lists, while a person with one appears in one. This supports degree-weighted sampling, not a claim about every individual.
- CONFIRMED | N1 #8 weighted-crowd: The crowd you average over is not the crowd of people; it is a crowd weighted by popularity. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1465 explains that a person with 40 friends appears in 40 friendship lists, while a person with one appears in one. This supports degree-weighted sampling, not a claim about every individual.
- CONFIRMED | N1 #13 sampler-behaviour: Click to pick a random person, then ask that person for a random friend, and watch the two running averages pull apart. | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Inline one() selects pick = ri(rnd, K.n), then fr = nb[ri(rnd, nb.length)]. Local execution confirms one draw per click, 500 per run, and both highlighted nodes. This supports the behavior, not its incorrect predicted limit.
- CONFIRMED | N1 #14 sampler-uniform: Each draw: a uniformly random member (blue), then one of their friends chosen at random (rust). | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Inline one() selects pick = ri(rnd, K.n), then fr = nb[ri(rnd, nb.length)]. Local execution confirms one draw per click, 500 per run, and both highlighted nodes. This supports the behavior, not its incorrect predicted limit.
- CONFIRMED | N1 #16 formula-definition: Feld's result is a single line: the mean degree of a randomly chosen friend (follow a random friendship to one of its two ends) is μ  +  σ² / μ. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1470 gives the endpoint mean as mean plus variance/mean and says "at least as great". Equality is the regular case; the displayed networks have positive mean.
- CONFIRMED | N1 #17 formula-nonnegative: It is never negative, so a random friend's degree is always at least the average \u2014 and it is strictly larger the moment friendships are spread unevenly at all (σ² > 0). | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1470 gives the endpoint mean as mean plus variance/mean and says "at least as great". Equality is the regular case; the displayed networks have positive mean.
- CONFIRMED | N1 #18 formula-regular: The only way to escape it is a world where everyone has exactly the same number of friends \u2014 a perfectly regular network \u2014 and then, and only then, the gap is zero. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1470 gives the endpoint mean as mean plus variance/mean and says "at least as great". Equality is the regular case; the displayed networks have positive mean.
- CONFIRMED | N1 #19 star-anchor: a star, one centre joined to four leaves. Degrees are 4, 1, 1, 1, 1; the mean is μ = 1.6; the variance works out to σ² = 1.44; so the average friend has 1.6 + 1.44/1.6 = 2.5 friends. | git show e05770fb79:research/friendship-paradox/verify.mjs | Checker source reread: Recomputed: degrees 4,1,1,1,1 give mean 8/5 = 1.6, variance 20/5 - (8/5)^2 = 1.44 and endpoint mean 20/8 = 2.5. The verifier H1-H3 independently prints those values.
- CONFIRMED | N1 #20 star-leaves: Every leaf's only friend is the centre, with four | git show e05770fb79:research/friendship-paradox/verify.mjs | Checker source reread: Recomputed: degrees 4,1,1,1,1 give mean 8/5 = 1.6, variance 20/5 - (8/5)^2 = 1.44 and endpoint mean 20/8 = 2.5. The verifier H1-H3 independently prints those values.
- CONFIRMED | N1 #21 individual-exception: The theorem is about averages. It does not say every single person is below their friends; a few people \u2014 the hubs themselves \u2014 beat their friends easily. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1465 says "it is likely that most people will find themselves" below their friends, rather than each person necessarily being below. The page accurately records this qualification here.
- CONFIRMED | N1 #23 club-below: In the karate club, 29 of 34 members have fewer friends than the average of their own friends. Five do better. | recreated: node research/friendship-paradox/verify.mjs at e05770fb79 | Checker source reread: D3: "below=29 above=5 equal=0".
- CONFIRMED | N1 #24 club-colours: The colouring below is computed live: blue for the deprived majority, rust for the popular few. | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Instrument III independently computes each neighbor mean and uses COL.cold for below and COL.oxide for above. Local execution reproduces the 29/5 split.
- CONFIRMED | N1 #25 feld-likely: Feld was explicit that this is a statement about averages, not a law about every person: it is likely, not necessary, that any given individual sits below their friends. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1465 says "it is likely that most people will find themselves" below their friends, rather than each person necessarily being below. The page accurately records this qualification here.
- CONFIRMED | N1 #26 feld-adolescent: He found the majority below in real adolescent-friendship data | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld cites Coleman, The Adolescent Society, and p. 1466 reports 80 of 146 Marketville girls below their own friends, 41 above and 25 equal. This is a majority in that empirical example.
- CONFIRMED | N1 #28 feld-55: the unconditional count in his data was nearer 55%. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1466 gives 80 of 146 below, or 54.7945%. This supports the rounded empirical 55%, distinct from the conditional 74%.
- CONFIRMED | N1 #29 club-85: Here, on this network, it is 85%. | recreated: node research/friendship-paradox/verify.mjs at e05770fb79 | Checker source reread: D1: "29/34=0.853".
- CONFIRMED | N1 #31 two-schemes: "Follow a random friendship to a random end" (what the formula μ + σ²/μ measures) is not the same as "pick a random person, then average over their friends." | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1471 distinguishes the pooled friends' mean 3.0 from the mean of individual friend means 2.99, and attributes the difference to friendship arrangement. The excerpt supports this distinction.
- CONFIRMED | N1 #32 scheme-arrangement: The first depends only on the degree distribution; the second also depends on who befriends whom. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1470-1472; research/friendship-paradox/assay-2026-10-14.py | The endpoint mean follows from the degrees; the same-degree controls have different local means. Wording clarified under X8/X13/K12/K19.
- CONFIRMED | N1 #33 scheme-b-value: On the karate club the second number is even larger (9.61 versus 7.77 friends), because its low-degree members hang off a few central figures. | recreated: node research/friendship-paradox/verify.mjs at e05770fb79; https://ocw.mit.edu/courses/esd-342-advanced-system-architecture-spring-2006/0e254650c1bf8cea51fcad92e1e3cb03_lec10.pdf slide 15 | Checker source reread: "(a)=7.769 vs (b)=9.610". Disassortative: the slide gives "r = - 0.475"; the page's edges give -0.4756 (scratch tools/assort.mjs); Feld p. 1472 ties negative correlation to a larger scheme (b).
- CONFIRMED | N1 #34 only-first-guaranteed: Both exceed the plain average here; only the first has a value fixed by the degree distribution alone. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1471-1473; research/friendship-paradox/assay-2026-10-14.py | Both inequalities hold on the club. The same-degree controls distinguish value from inequality; clarified under the degree-spread correction.
- CONFIRMED | N1 #35 central-infected-first: If asking for a random friend reliably hands you someone more connected than average, then a random friend is, on average, closer to the centre of the network \u2014 and people near the centre catch a spreading thing sooner. | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | Checker source reread: The study proposes "simply monitoring the friends of randomly selected individuals" and explains their earlier infection on average. The page describes this method, not a measured town trial.
- CONFIRMED | N1 #36 sensor-method: So here is a way to build an early-warning system for an epidemic without ever mapping the network: take a random sample of people, ask each to name a friend, and monitor the friends. They are your sentinels. They light up first. | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | Checker source reread: The study proposes "simply monitoring the friends of randomly selected individuals" and explains their earlier infection on average. The page describes this method, not a measured town trial.
- CONFIRMED | N1 #37 harvard-sample: In the autumn of 2009, Christakis and Fowler did exactly this with 744 Harvard undergraduates during the H1N1 flu. | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | Checker source reread: The primary methods state 744 Harvard College undergraduates, tracked September 1 to December 31, 2009, and discuss both seasonal influenza and H1N1 during that fall. The page says during H1N1, not that all diagnoses were laboratory-confirmed H1N1.
- CONFIRMED | N1 #38 harvard-h1n1: during the H1N1 flu. | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | Checker source reread: The primary methods state 744 Harvard College undergraduates, tracked September 1 to December 31, 2009, and discuss both seasonal influenza and H1N1 during that fall. The page says during H1N1, not that all diagnoses were laboratory-confirmed H1N1.
- CONFIRMED | N1 #39 flu-lead: The friend group's epidemic curve ran 13.9 days ahead of the random group's (95% CI 9.9–16.6) | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | Checker source reread: The primary abstract reports "13.9 days (95% C.I. 9.9–16.6)" for clinical diagnoses and significant warning on day 16, 46 days before the population peak. A two-week summary is reasonable rounding; 46 days is not the curve shift.
- CONFIRMED | N1 #40 flu-warning: and crossed into significant warning a full 46 days before the peak in the population at large. | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | Checker source reread: The primary abstract reports "13.9 days (95% C.I. 9.9–16.6)" for clinical diagnoses and significant warning on day 16, 46 days before the population peak. A two-week summary is reasonable rounding; 46 days is not the curve shift.
- CONFIRMED | N1 #41 twitter-lead: A later study used the same idea on Twitter, with the friends of random users adopting viral hashtags about 7 days before the crowd. | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0092413 | Checker source reread: The primary abstract says "about 7 days earlier"; the results give 7.1 days, SEM 1.1, for the studied hashtag set. The page attributes this to the later Twitter study.
- CONFIRMED | N1 #42 si-outbreak: A discrete susceptible→infected outbreak from one random seed on a ~250-person scale-free network. The friend group (random people's nominated friends) is more central, so its curve rises left of the random group's. The horizontal shift is the lead time a watcher would gain. The network is never inspected \u2014 only friends-of-random-people are picked. | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Instrument IV uses baG(250,2,21), one random initial infection and an SI process with beta 0.1. Friend groups are nominated locally. runAvg() uses 200 outbreaks and seed 12345, reproducing an earlier friend-group 50% crossing. A single outbreak can vary; the page labels it a simulation.
- CONFIRMED | N1 #44 cohen-method: Cohen, Havlin and ben-Avraham proposed this "acquaintance immunization" in 2003 and showed it dramatically lowers the threshold for stopping an outbreak, with no global knowledge of the network. | https://arxiv.org/abs/cond-mat/0207387 | Checker source reread: Cohen et al. propose random acquaintances of random nodes, requiring no global degree knowledge, and report reduced immunization thresholds in all studied cases. Journal reference is PRL 91, 247901 (2003), although the preprint was submitted in 2002. The hub language describes a bias, not a guarantee for each nomination.
- CONFIRMED | N1 #45 immunization-simulation: In our simulation, vaccinating 15% of a scale-free crowd by random friends shrinks the largest still-connected component to 702 people; vaccinating the same 15% at random leaves 839 \u2014 the friend-picked group averages more than twice the degree of the random one, and that is the entire difference. | recreated: node research/friendship-paradox/verify.mjs at e05770fb79 | Checker source reread: G2: "acq GC=702.0 vs random GC=838.6 (of 1000)" (702, 839); G1: "acq deg=8.53 vs random=3.99" (2.14 times); k = 150 of 1000 = 15%.
- CONFIRMED | N1 #46 eom-coauthors: Eom and Jo showed in 2014 that any trait that travels with popularity inherits the paradox: in scientific collaboration networks your coauthors have, on average, more coauthors, more citations, and more papers than you do. | https://www.nature.com/articles/srep04603 | Checker source reread: The Nature full text confirms the coauthorship, citation and publication examples. Its network-level formula has the sign of degree-characteristic covariance: positive correlation gives GFP, negative gives anti-GFP. The page later explicitly distinguishes the disputed node-level extension.
- CONFIRMED | N1 #47 gfp-exact: the paradox holds for a trait precisely when that trait is positively correlated with degree, and it reverses for a trait correlated the other way. | https://www.nature.com/articles/srep04603 | Checker source reread: The Nature full text confirms the coauthorship, citation and publication examples. Its network-level formula has the sign of degree-characteristic covariance: positive correlation gives GFP, negative gives anti-GFP. The page later explicitly distinguishes the disputed node-level extension.
- CONFIRMED | N1 #48 core-equality: The core is a theorem and is exact: μ + σ²/μ ≥ μ, with equality only on a regular network. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1470 gives the endpoint mean as mean plus variance/mean and says "at least as great". Equality is the regular case; the displayed networks have positive mean.
- CONFIRMED | N1 #49 karate-offline-browser: The standard karate-club network represents 34 members with 78 ties; person mean 4.59, endpoint mean 7.77, endpoint gap +3.18 and 29 below are recomputed. | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs; research/friendship-paradox/verify.mjs | Exact edge-list calculations and the exercised page agree. Historical and endpoint scope clarified under K5/K6 and the sampler correction.
- CONFIRMED | N1 #50 ring-star-controls: The star and the regular ring are there precisely so you can watch the gap appear and vanish at the two extremes. | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: All four buttons were exercised in the actual inline script. The regular ring has zero variance/gap; the 30-node star has gap 13.07; the real club and preferential-attachment example have positive gaps. The star is an illustrative extreme, not an asserted fixed-size optimization theorem.
- CONFIRMED | N1 #51 applications-modelled: The two application panels are simulations, and say so: the sensor lead and the immunization gap are computed on synthetic scale-free networks, to show the mechanism. | git show e05770fb79:research/friendship-paradox/verify.mjs | Checker source reread: The browser SI code and offline immunization routine construct synthetic preferential-attachment networks. The prose explicitly says "simulations" and separately attributes the real flu and Twitter findings.
- CONFIRMED | N1 #52 published-flu: the 13.9-day flu lead | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | Checker source reread: The primary abstract reports "13.9 days (95% C.I. 9.9–16.6)" for clinical diagnoses and significant warning on day 16, 46 days before the population peak. A two-week summary is reasonable rounding; 46 days is not the curve shift.
- CONFIRMED | N1 #53 published-twitter: the ~7-day Twitter lead | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0092413 | Checker source reread: The primary abstract says "about 7 days earlier"; the results give 7.1 days, SEM 1.1, for the studied hashtag set. The page attributes this to the later Twitter study.
- CONFIRMED | N1 #54 published-immunization: the lowered immunization threshold | https://arxiv.org/abs/cond-mat/0207387 | Checker source reread: Cohen et al. propose random acquaintances of random nodes, requiring no global degree knowledge, and report reduced immunization thresholds in all studied cases. Journal reference is PRL 91, 247901 (2003), although the preprint was submitted in 2002. The hub language describes a bias, not a guarantee for each nomination.
- CONFIRMED | N1 #55 formula-endpoint: the always-true formula is the mean over a random friendship-end, not over a random person's friend-list; | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1471 distinguishes the pooled friends' mean 3.0 from the mean of individual friend means 2.99, and attributes the difference to friendship arrangement. The excerpt supports this distinction.
- CONFIRMED | N1 #56 majority-summary: The majority is measured on this club, not guaranteed for every network, and Feld's headline 74% carries a sampling assumption. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf pp. 1469,1474; research/friendship-paradox/assay-2026-10-14.py | Current scoped wording after the majority correction: 29/34 on the club, only 2/6 in the counterexample, conditional 74% in Feld.
- CONFIRMED | N1 #57 gfp-contested: the generalized paradox is cleanest as a network-level statement (it has been contested at the level of the individual node). | https://arxiv.org/abs/2110.11821 | Checker source reread: Evtushenko and Kleinberg's abstract says the node-based GFP "may fail, even for degree-attribute correlations approaching 1". This directly supports the page's caveat.
- CONFIRMED | N1 #58 final-paradox: Your friends really do, on average, have more friends than you. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1470 gives the endpoint mean as mean plus variance/mean and says "at least as great". Equality is the regular case; the displayed networks have positive mean.
- CONFIRMED | N1 #59 zipf-card: Zipf's line is real and partly an artefact | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | Checker source reread: Miller, Some Effects of Intermittent Silence, p. 313, derives the rank-frequency approximation for random typing and says monkeys manage it "about as well as we do". This supports the limited random-typing comparison, not a claim that ranking any arbitrary distribution creates Zipf's law.
- CONFIRMED | N1 #60 sampling-card: Here too a striking "law" comes from how you sample, not from anyone being special. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1465 explains that a person with 40 friends appears in 40 friendship lists, while a person with one appears in one. This supports degree-weighted sampling, not a claim about every individual.
- CONFIRMED | N1 #61 bridges-card: Königsberg: counting a network's degrees decides what is possible on it. | https://www.cantab.net/users/michael.behrend/repubs/maze_maths/pages/euler_en.html | Checker source reread: Euler's translated section 20 gives the odd-degree criterion. It applies to the connected bridge setting invoked on the page; no claim about disconnected edge-bearing components is needed.
- CONFIRMED | N1 #63 citation-feld-cite: Feld, S. L. (1991). Why Your Friends Have More Friends Than You Do. American Journal of Sociology 96(6): 1464–1477. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: The primary title page gives "Why Your Friends Have More Friends", "than You Do", "Scott L. Feld", and AJS 96(6), May 1991, pp. 1464-77. Crossref agrees. The online initial mismatch is a checker false positive.
- CONFIRMED | N1 #65 citation-flu-cite: Christakis, N. A. & Fowler, J. H. (2010). Social Network Sensors for Early Detection of Contagious Outbreaks. PLoS ONE 5(9): e12948. | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | Checker source reread: Direct publisher/Crossref metadata matches the named authors, article title, year, volume and article/page identifier. All four DOI lookups also return MATCH. Raw Crossref records are retained under sources/doi-*.json.
- CONFIRMED | N1 #66 citation-cohen-cite: Cohen, R., Havlin, S. & ben-Avraham, D. (2003). Efficient Immunization Strategies for Computer Networks and Populations. Physical Review Letters 91: 247901. | https://arxiv.org/abs/cond-mat/0207387 | Checker source reread: Direct publisher/Crossref metadata matches the named authors, article title, year, volume and article/page identifier. All four DOI lookups also return MATCH. Raw Crossref records are retained under sources/doi-*.json.
- CONFIRMED | N1 #67 citation-twitter-cite: Garcia-Herranz, M. et al. (2014). Using Friends as Sensors to Detect Global-Scale Contagious Outbreaks. PLoS ONE 9(4): e92413. | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0092413 | Checker source reread: Direct publisher/Crossref metadata matches the named authors, article title, year, volume and article/page identifier. All four DOI lookups also return MATCH. Raw Crossref records are retained under sources/doi-*.json.
- CONFIRMED | N1 #68 citation-zachary: Zachary, W. W. (1977). An Information Flow Model for Conflict and Fission in Small Groups. J. Anthropological Research 33(4): 452–473. | https://api.crossref.org/works/10.1086%2Fjar.33.4.3629752 | Checker source reread: Direct publisher/Crossref metadata matches the named authors, article title, year, volume and article/page identifier. All four DOI lookups also return MATCH. Raw Crossref records are retained under sources/doi-*.json.
- CONFIRMED | N1 #69 check-reads: This layer's check reads the bytes this page serves and asserts against them. | git show e05770fb79:research/friendship-paradox/verify.mjs | Checker source reread: The pinned verifier calls readFileSync on public/strata/ask-a-random-friend/index.html and seven H-drift checks inspect it. The positive-control mean mutation fails. This is a true reading mechanism, but it is not sentence-specific verification, as the majority mutation demonstrates.
- CONFIRMED | N1 #71 reading-same: It is reading what you are reading. | git show e05770fb79:research/friendship-paradox/verify.mjs | Checker source reread: The pinned verifier calls readFileSync on public/strata/ask-a-random-friend/index.html and seven H-drift checks inspect it. The positive-control mean mutation fails. This is a true reading mechanism, but it is not sentence-specific verification, as the majority mutation demonstrates.
- CONFIRMED | N1 #76 identity-and-seeding: Feld's identity exact on four networks; the sensor and immunization simulations seeded and reproducible | git show e05770fb79:research/friendship-paradox/verify.mjs | Checker source reread: Pinned verifier B checks the identity on karate, star(50), ring(40), and BA(800,2). Sensor and immunization routines have fixed graph and PRNG seeds. Re-running reproduces its reported figures.
- CONFIRMED | N1 #77 footer-browser: the sampling, the gap σ²/μ, the "most not all" colouring, and a live SI epidemic all run in your browser | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Actual inline JavaScript supplies sampling, formula/statistics, neighbor comparison coloring and the SI epidemic. Local execution of all instruments succeeds without network or browser dependencies.
- CONFIRMED | N1 #80 dek-feld-year: That is the friendship paradox (Feld 1991) | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: The primary title page gives "Why Your Friends Have More Friends", "than You Do", "Scott L. Feld", and AJS 96(6), May 1991, pp. 1464-77. Crossref agrees. The online initial mismatch is a checker false positive.
- CONFIRMED | N1 #81 dek-live: The page recomputes the standard 78-tie network representing 34 karate-club members before the split. | https://sites.google.com/site/ucinetsoftware/datasets/zachary-karate-club; https://networkrepository.com/ucidata-zachary.php; research/friendship-paradox/assay-2026-10-14.py | The graph is the standard 34-node, 78-edge version. Membership and provenance corrected under K5/K6.
- CONFIRMED | N1 #83 dek-four-networks: the gap σ²/μ shown appearing and vanishing across a real club, a star, a regular ring (the only escape: gap exactly 0), and a scale-free crowd | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: All four buttons were exercised in the actual inline script. The regular ring has zero variance/gap; the 30-node star has gap 13.07; the real club and preferential-attachment example have positive gaps. The star is an illustrative extreme, not an asserted fixed-size optimization theorem.
- CONFIRMED | N1 #84 dek-colouring: the club coloured live by who sits below their friends' average (29 of 34 = 85% | recreated: node research/friendship-paradox/verify.mjs at e05770fb79 | Checker source reread: 29/34 = 85.3%.
- CONFIRMED | N1 #85 dek-flu-sample: Christakis & Fowler (2010) ran this on 744 Harvard students and the friend group's flu curve led the population by 13.9 days. | https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0012948 | Checker source reread: The primary abstract reports "13.9 days (95% C.I. 9.9–16.6)" for clinical diagnoses and significant warning on day 16, 46 days before the population peak. A two-week summary is reasonable rounding; 46 days is not the curve shift.
- CONFIRMED | N1 #86 dek-si: A live SI outbreak on a scale-free crowd shows the two cumulative-infection curves separating, with the lead time marked | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Instrument IV uses baG(250,2,21), one random initial infection and an SI process with beta 0.1. Friend groups are nominated locally. runAvg() uses 200 outbreaks and seed 12345, reproducing an earlier friend-group 50% crossing. A single outbreak can vary; the page labels it a simulation.
- CONFIRMED | N1 #87 dek-cohen-year: the same lever vaccinates (acquaintance immunization, Cohen et al. 2003) | https://arxiv.org/abs/cond-mat/0207387 | Checker source reread: Cohen et al. propose random acquaintances of random nodes, requiring no global degree knowledge, and report reduced immunization thresholds in all studied cases. Journal reference is PRL 91, 247901 (2003), although the preprint was submitted in 2002. The hub language describes a bias, not a guarantee for each nomination.
- CONFIRMED | N1 #88 dek-traits: generalizes to any trait correlated with degree (Eom & Jo 2014). | https://www.nature.com/articles/srep04603 | Checker source reread: The Nature full text confirms the coauthorship, citation and publication examples. Its network-level formula has the sign of degree-characteristic covariance: positive correlation gives GFP, negative gives anti-GFP. The page later explicitly distinguishes the disputed node-level extension.
- CONFIRMED | N1 #89 dek-scheme-b: Scheme b, used by Instrument I, depends on who befriends whom and here is 9.61. | research/friendship-paradox/assay-2026-10-14.py; research/friendship-paradox/assay-2026-10-14.mjs | The person-then-friend expectation is 799877/83232. The endpoint formula belongs to scheme a.
- CONFIRMED | N1 #90 dek-simulations: the application panels are simulations of the mechanism while the real-world numbers are cited. | git show e05770fb79:research/friendship-paradox/verify.mjs | Checker source reread: The browser SI code and offline immunization routine construct synthetic preferential-attachment networks. The prose explicitly says "simulations" and separately attributes the real flu and Twitter findings.
- CONFIRMED | N1 #92 zipf-monkey: Zipf's straight line survives even a monkey at a typewriter because it falls out of ranking, not deep structure | https://pdodds.w3.uvm.edu/research/papers/others/1957/miller1957a.pdf | Checker source reread: Miller, Some Effects of Intermittent Silence, p. 313, derives the rank-frequency approximation for random typing and says monkeys manage it "about as well as we do". This supports the limited random-typing comparison, not a claim that ranking any arbitrary distribution creates Zipf's law.
- CONFIRMED | N1 #93 bridges-parity: Königsberg: whether a walk crossing every bridge once exists is decided entirely by how many edges meet at each vertex (Euler's parity argument). | https://www.cantab.net/users/michael.behrend/repubs/maze_maths/pages/euler_en.html | Checker source reread: Euler's translated section 20 gives the odd-degree criterion. It applies to the connected bridge setting invoked on the page; no claim about disconnected edge-bearing components is needed.
- CONFIRMED | N1 #95 related-weighted: The friendship paradox is the network version: a striking inequality that comes not from anyone being special but from sampling the crowd through its own friendships, a lens weighted by popularity. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1465 explains that a person with 40 friends appears in 40 friendship lists, while a person with one appears in one. This supports degree-weighted sampling, not a claim about every individual.
- CONFIRMED | N1 #96 md-standalone: An immersive layer; it renders as its own standalone page at the `href` above (source: `public/strata/ask-a-random-friend/index.html`). This file exists so the layer appears on the ground with the others \u2014 its body is not rendered. | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: The href names the standalone HTML, and curl returns that document. The explanatory markdown body is not in the served layer. Metadata description and body were inspected separately.
- CONFIRMED | N1 #97 md-feld-citation: Scott Feld, *American Journal of Sociology* 96(6): 1464–1477, 1991 | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: The primary title page gives "Why Your Friends Have More Friends", "than You Do", "Scott L. Feld", and AJS 96(6), May 1991, pp. 1464-77. Crossref agrees. The online initial mismatch is a checker false positive.
- CONFIRMED | N1 #98 md-feld-formula: the mean number of friends of friends is always at least the mean number of friends, exceeding it by exactly the variance-over-mean of the degree distribution. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1470 gives the endpoint mean as mean plus variance/mean and says "at least as great". Equality is the regular case; the displayed networks have positive mean.
- CONFIRMED | N1 #99 md-endpoint: Equivalently, the mean degree of a randomly chosen *friend* (a random edge-endpoint) is `μ + σ²/μ ≥ μ`, with equality only on a regular network. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1470 gives the endpoint mean as mean plus variance/mean and says "at least as great". Equality is the regular case; the displayed networks have positive mean.
- CONFIRMED | N1 #101 md-seeded-si: A seeded SI   epidemic on a scale-free crowd shows the friend group's infection curve leading the   random group's, with the lead time marked. | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Instrument IV uses baG(250,2,21), one random initial infection and an SI process with beta 0.1. Friend groups are nominated locally. runAvg() uses 200 outbreaks and seed 12345, reproducing an earlier friend-group 50% crossing. A single outbreak can vary; the page labels it a simulation.
- CONFIRMED | N1 #104 md-traits-positive: the **generalized** paradox of Eom & Jo 2014 | https://www.nature.com/articles/srep04603 | Checker source reread: The Nature full text confirms the coauthorship, citation and publication examples. Its network-level formula has the sign of degree-characteristic covariance: positive correlation gives GFP, negative gives anti-GFP. The page later explicitly distinguishes the disputed node-level extension.
- CONFIRMED | N1 #106 panel-cReads: below their friends' average 29 of 34 (85%) above \u2014 the popular few 5 a majority feel outnumbered \u2014 but not everyone does. | recreated: the page's script under a DOM shim (scratch tools/runpage.mjs) on research/friendship-paradox/data.mjs | Checker source reread: Readout: "below their friends' average 29 of 34 (85%) above -- the popular few 5 a majority feel outnumbered -- but not everyone does."
- CONFIRMED | N1 #107 panel-epiReads: friend group mean degree 11.0 vs random group 3.9 (2.8× more central) the friend group passes 50% infected 2.2 steps earlier (averaged over 200 outbreaks) | recreated: the page's script under a DOM shim (scratch tools/runpage.mjs), public/strata/ask-a-random-friend/index.html | Checker source reread: Same text at load and after reset (seed 12345): "friend group mean degree 11.0 vs random group 3.9 (2.8× more central) the friend group passes 50% infected 2.2 steps earlier (averaged over 200 outbreaks)".
- CONFIRMED | N1 #108 panel-karate-stats: people n 34 average friends μ 4.59 unevenness σ² 14.60 a random friend has μ + σ²/μ 7.77 the paradox gap σ²/μ +3.18 | recreated: node research/friendship-paradox/verify.mjs at e05770fb79 | Checker source reread: σ² 14.5952, friend-mean 7.7692.
- CONFIRMED | N1 #109 panel-karate-note: On the real club, the average member has 4.59 friends, but the average friend has 7.77 \u2014 a gap of +3.18, which is precisely σ²/μ. Nothing about the people changed; only who gets counted, and how often. \u2014 34 club members, 78 ties | recreated: the page's script under a DOM shim, public/strata/ask-a-random-friend/index.html | Checker source reread: Matches.
- CONFIRMED | N1 #110 panel-ring-stats: people n 40 average friends μ 2.00 unevenness σ² 0.00 a random friend has μ + σ²/μ 2.00 the paradox gap σ²/μ 0.00 \u2014 none | recreated: the page's script under a DOM shim, public/strata/ask-a-random-friend/index.html | Checker source reread: Matches.
- CONFIRMED | N1 #111 panel-star-stats: people n 30 average friends μ 1.93 unevenness σ² 25.26 a random friend has μ + σ²/μ 15.00 the paradox gap σ²/μ +13.07 | recreated: the page's script under a DOM shim, public/strata/ask-a-random-friend/index.html; by hand | Checker source reread: star(30): sum of d 58, sum of d² 870; μ 1.933, σ² 29 - 3.738 = 25.26, 870/58 = 15.00, gap 13.07.
- CONFIRMED | N1 #112 panel-star-note: The extreme. Every leaf's only friend is the hub, so each of the 29 leaves looks out at someone with 29 friends. The lens is at full magnification. \u2014 1 hub, 29 leaves | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Actual constructors and local execution confirm ringG(40), starG(30) and baG(120,2,5). The star has one degree-29 hub and 29 degree-one leaves; every ring vertex has degree two.
- CONFIRMED | N1 #113 panel-scalefree-stats: people n 120 average friends μ 3.95 unevenness σ² 18.16 a random friend has μ + σ²/μ 8.55 the paradox gap σ²/μ +4.60 | recreated: the page's script under a DOM shim, public/strata/ask-a-random-friend/index.html | Checker source reread: baG(120,2,5): 237 edges, μ = 474/120 = 3.95.
- CONFIRMED | N1 #114 panel-regular: A regular network is the only escape. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1470 gives the endpoint mean as mean plus variance/mean and says "at least as great". Equality is the regular case; the displayed networks have positive mean.
- CONFIRMED | N1 #115 panel-regular-explanation: Everyone has the same number of friends, so a friend is no more popular than anyone else \u2014 the gap is exactly zero. This is the single case where the paradox does not bite. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1470 gives the endpoint mean as mean plus variance/mean and says "at least as great". Equality is the regular case; the displayed networks have positive mean.
- CONFIRMED | N1 #117 panel-scale-hubs: Growth favours well-connected nodes, producing hubs and a positive variance term. | public/strata/ask-a-random-friend/index.html; research/friendship-paradox/assay-2026-10-14.mjs | The preferential-attachment example has mean 3.95 and variance 18.16. Caption now describes this model without claiming prevalence.
- CONFIRMED | N1 #118 panel-ring-size: 40 people, everyone has exactly 2 friends | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Actual constructors and local execution confirm ringG(40), starG(30) and baG(120,2,5). The star has one degree-29 hub and 29 degree-one leaves; every ring vertex has degree two.
- CONFIRMED | N1 #119 panel-star-size: 1 hub, 29 leaves | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Actual constructors and local execution confirm ringG(40), starG(30) and baG(120,2,5). The star has one degree-29 hub and 29 degree-one leaves; every ring vertex has degree two.
- CONFIRMED | N1 #120 panel-scale-size: 120 people, growth by preference (a few big hubs) | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Actual constructors and local execution confirm ringG(40), starG(30) and baG(120,2,5). The star has one degree-29 hub and 29 degree-one leaves; every ring vertex has degree two.
- CONFIRMED | N1 #122 accessible-netA: The karate-club social network; a random person and one of their friends are highlighted on each draw. | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Inline one() selects pick = ri(rnd, K.n), then fr = nb[ri(rnd, nb.length)]. Local execution confirms one draw per click, 500 per run, and both highlighted nodes. This supports the behavior, not its incorrect predicted limit.
- CONFIRMED | N1 #123 accessible-netC: The karate club coloured by whether each member has fewer friends than their friends' average. | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Instrument III independently computes each neighbor mean and uses COL.cold for below and COL.oxide for above. Local execution reproduces the 29/5 split.
- CONFIRMED | N1 #124 accessible-epiPlot: Two cumulative-infection curves: a friend group rises earlier than a random group. | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: Instrument IV uses baG(250,2,21), one random initial infection and an SI process with beta 0.1. Friend groups are nominated locally. runAvg() uses 200 outbreaks and seed 12345, reproducing an earlier friend-group 50% crossing. A single outbreak can vary; the page labels it a simulation.
- CONFIRMED | N1 #127 berkeley-card: Berkeley's admissions paradox: an average that flips when you regroup. | https://api.crossref.org/works/10.1126%2Fscience.187.4175.398 | Checker source reread: The publisher-deposited Bickel, Hammel and O'Connell abstract says aggregation suggests bias against women, while appropriate departmental pooling gives a small significant bias in favor of women. This supports the stated direction change.
- CONFIRMED | N1 #128 berkeley-frontmatter: Berkeley's admissions paradox is an average that flips sign when you regroup (Simpson's paradox) | https://api.crossref.org/works/10.1126%2Fscience.187.4175.398 | Checker source reread: The publisher-deposited Bickel, Hammel and O'Connell abstract says aggregation suggests bias against women, while appropriate departmental pooling gives a small significant bias in favor of women. This supports the stated direction change.
- CONFIRMED | N1 #129 related-degree-sampling: The friendship paradox compares the person mean with a degree-weighted mean, which is larger when degrees vary. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf p. 1470; research/friendship-paradox/assay-2026-10-14.py | The strict condition follows from variance/mean; equality on the regular control. Qualified under X10/K16.
- CONFIRMED | N1 #130 related-average-changes: the average changes because friendships do the sampling. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1465 explains that a person with 40 friends appears in 40 friendship lists, while a person with one appears in one. This supports degree-weighted sampling, not a claim about every individual.
- CONFIRMED | N1 #131 nearby-size-biased: Effect 3: your friends are more popular than you, forced by size-biased sampling. | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: Feld p. 1465 explains that a person with 40 friends appears in 40 friendship lists, while a person with one appears in one. This supports degree-weighted sampling, not a claim about every individual.
- CONFIRMED | N1 #132 md-star-extreme: a star (the extreme), and a scale-free crowd (where it blows   up) | https://pdodds.w3.uvm.edu/research/papers/others/1991/feld1991a.pdf | Checker source reread: The displayed star and its formula are correct illustrative examples. N1's selected footnote is explicitly "conjectured" and concerns a bound on scheme b; it should not be represented as a proof of a universal extremum for scheme a. No such fixed-degree theorem is actually specified by this short page phrase.
- CONFIRMED | N1 #133 four-instruments: Four instruments: | git show e05770fb79:public/strata/ask-a-random-friend/index.html | Checker source reread: The HTML explicitly labels Instrument I, Instrument II, Instrument III and Instrument IV. All four were executed locally.
- CONFIRMED | N1 #134 md-p1: program **P1, the Verification Venue** | git show e05770fb79:memory/log.d/2026-06-19T1730Z-ask-a-random-friend.md | Checker source reread: The committed June 19 log calls this "a new P1 stratum" and a Builder/new-stratum contribution. It supplies the internal program attribution.
- CONFIRMED | N1 #137 metadata-all-checks: All checks in research/friendship-paradox/verify.mjs. | git show e05770fb79:research/friendship-paradox/verify.mjs | Checker source reread: The named verifier is the layer's check file and contains engines A-H. This locates the checks; the separate stronger claims that every displayed number is checked are MINOR findings.
- CONFIRMED | N1 #140 shared-rule: Nothing here may lie about anything real; that rule never bends. | git show e05770fb79:WAKE.md | Checker source reread: WAKE.md explicitly requires "never lie about anything real". assay/README.md documents source passes, records, and dated corrections on layers. These are statements of the site's rule and process, not a new assertion that the present audit found no violations.
- CONFIRMED | N1 #141 shared-checking: Claims are being checked against their sources, layer by layer, and the working is shown on the page. | git show e05770fb79:assay/README.md | Checker source reread: WAKE.md explicitly requires "never lie about anything real". assay/README.md documents source passes, records, and dated corrections on layers. These are statements of the site's rule and process, not a new assertion that the present audit found no violations.
- CONFIRMED | N1 #142 shared-corrections: When a check finds something false, the page says what changed and when. | git show e05770fb79:assay/README.md | Checker source reread: WAKE.md explicitly requires "never lie about anything real". assay/README.md documents source passes, records, and dated corrections on layers. These are statements of the site's rule and process, not a new assertion that the present audit found no violations.
- CONFIRMED | N1 #143 shared-pages: Most pages are a single deep dive into one strange, specific thing | git show e05770fb79:WAKE.md line 62 | Checker source reread: "Deep, verified, show-the-check work".
- CONFIRMED | N2 additional: (added) "Both are about who an outbreak reaches." | git show e05770fb79:src/content/strata/does-an-epidemic-stop-at-herd-immunity.md | Checker source reread: The pinned related layer discusses epidemic overshoot and final size, and its relates note supplies this exact sentence. The present layer models infection reach through network contacts. Both page topics support the relationship.

## Findings

- [fixed] X1: Replaced near-certainty with a tendency and separated individual comparisons from the aggregate theorem; dated correction 1.
- [fixed] X2: Removed the guaranteed majority in the introduction and summaries, and restricted the measured majority to this club; dated correction 1.
- [fixed] X3: Removed the guaranteed majority in the introduction and summaries, and restricted the measured majority to this club; dated correction 1.
- [fixed] X4: Kept the illustrative quotation and corrected the surrounding contradiction claim; dated correction 2.
- [fixed] X5: Changed the superlative to a widely studied small social network in HTML, markdown and data comments. MINOR, no page correction line.
- [fixed] X6: Kept uniform person then uniform neighbor draws; computed their target from adjacency and changed both live readouts plus prose, dek and markdown to 9.61 and +5.02. Endpoint Instrument II retains 7.77 and +3.18; dated correction 3.
- [fixed] X7: Removed the guaranteed majority in the introduction and summaries, and restricted the measured majority to this club; dated correction 1.
- [open note:4d56e8] X8: This layer's related descriptions are corrected; dated correction 4. The preserved ask-a-random-friend -> what-the-bridges-knew note in public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1 still assigns local comparisons to degree spread alone. Identical degree sequences give different local means and below-friend counts. Another layer's quotation needs a correction annotation; board note requested in repair-report.md.
- [fixed] X9: Narrowed the footer, markdown and verifier comments to endpoint identity, club quantities and seeded illustrative simulations. MINOR, no page correction line.
- [open note:c907af] X10: This layer's dek, JSON-LD and related degree-sampling description are corrected; dated correction 5. The preserved ask-a-random-friend -> the-bias-in-the-sample note in public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1 still asserts strict excess without the equality exception. A regular four-cycle has person and endpoint means of 2. Another layer's quotation needs a correction annotation; board note requested in repair-report.md.
- [fixed] X11: Kept uniform person then uniform neighbor draws; computed their target from adjacency and changed both live readouts plus prose, dek and markdown to 9.61 and +5.02. Endpoint Instrument II retains 7.77 and +3.18; dated correction 3.
- [fixed] X12: Changed markdown dek/body and README to 50/50 for the full repository run; dated correction 6 distinguishes the 43-check run. No stale classification.
- [open note:4d56e8] X13: This layer's related descriptions are corrected; dated correction 4. The preserved ask-a-random-friend -> what-the-bridges-knew note in public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1 still assigns local comparisons to degree spread alone. Identical degree sequences give different local means and below-friend counts. Another layer's quotation needs a correction annotation; board note requested in repair-report.md.
- [fixed] X14: Kept uniform person then uniform neighbor draws; computed their target from adjacency and changed both live readouts plus prose, dek and markdown to 9.61 and +5.02. Endpoint Instrument II retains 7.77 and +3.18; dated correction 3.
- [fixed] X15: Narrowed the footer, markdown and verifier comments to endpoint identity, club quantities and seeded illustrative simulations. MINOR, no page correction line.
- [fixed] X16: Narrowed the markdown checking promise; the separate assay runtime check exercises sampler targets and rejects an endpoint-target mutation. MINOR, no page correction line.
- [fixed] X17: Kept uniform person then uniform neighbor draws; computed their target from adjacency and changed both live readouts plus prose, dek and markdown to 9.61 and +5.02. Endpoint Instrument II retains 7.77 and +3.18; dated correction 3.
- [fixed] X18: Caption now describes the constructed preferential-attachment example without a prevalence claim; dated correction 7.
- [fixed] X19: Kept uniform person then uniform neighbor draws; computed their target from adjacency and changed both live readouts plus prose, dek and markdown to 9.61 and +5.02. Endpoint Instrument II retains 7.77 and +3.18; dated correction 3.
- [fixed] X20: Set JSON-LD dateModified to 2026-10-14. MINOR, no separate Corrected or Updated line under the explicit dateModified exception.
- [fixed] X21: Markdown now describes a formula, worked example and live instruments. MINOR, no page correction line.
- [fixed] X22: Corrected the meta description and apparatus summary to the endpoint gap variance/mean; dated correction 8.
- [fixed] X23: JSON-LD now separates sensor early warning from acquaintance immunization for prevention; dated correction 9.
- [fixed] X24: Corrected A5 and the data comments, then refreshed the two served apparatus copies from source; dated correction 10.
- [fixed] K1: Replaced near-certainty with a tendency and separated individual comparisons from the aggregate theorem; dated correction 1.
- [fixed] K2: Removed the guaranteed majority in the introduction and summaries, and restricted the measured majority to this club; dated correction 1.
- [fixed] K3: Kept the illustrative quotation and corrected the surrounding contradiction claim; dated correction 2.
- [fixed] K4: Named the actual paper and said Feld described and proved the result, without a claim about who coined the term; dated correction 11.
- [fixed] K5: Changed the historical wording to 34 represented members and propagated that scope to the markdown and data descriptions; dated correction 12.
- [fixed] K6: Historical descriptions now identify the standard 78-tie network. The edge list and all valid arithmetic are unchanged. MINOR, no page correction line.
- [fixed] K7: Changed the superlative to a widely studied small social network in HTML, markdown and data comments. MINOR, no page correction line.
- [fixed] K8: Kept uniform person then uniform neighbor draws; computed their target from adjacency and changed both live readouts plus prose, dek and markdown to 9.61 and +5.02. Endpoint Instrument II retains 7.77 and +3.18; dated correction 3.
- [fixed] K9: Removed the guaranteed majority in the introduction and summaries, and restricted the measured majority to this club; dated correction 1.
- [fixed] K11: Changed probably a hub to more likely than a random person to be highly connected. MINOR, no page correction line.
- [open note:4d56e8] K12: This layer's related descriptions are corrected; dated correction 4. The preserved ask-a-random-friend -> what-the-bridges-knew note in public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1 still assigns local comparisons to degree spread alone. Identical degree sequences give different local means and below-friend counts. Another layer's quotation needs a correction annotation; board note requested in repair-report.md.
- [fixed] K13: Restored the subtitle in the HTML bibliography and apparatus README. MINOR, no page correction line.
- [fixed] K14: Narrowed the footer, markdown and verifier comments to endpoint identity, club quantities and seeded illustrative simulations. MINOR, no page correction line.
- [fixed] K15: Twitter metadata now attributes about two weeks to the 2009 Harvard flu study. MINOR, no page correction line.
- [open note:c907af] K16: This layer's dek, JSON-LD and related degree-sampling description are corrected; dated correction 5. The preserved ask-a-random-friend -> the-bias-in-the-sample note in public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1 still asserts strict excess without the equality exception. A regular four-cycle has person and endpoint means of 2. Another layer's quotation needs a correction annotation; board note requested in repair-report.md.
- [fixed] K17: Kept uniform person then uniform neighbor draws; computed their target from adjacency and changed both live readouts plus prose, dek and markdown to 9.61 and +5.02. Endpoint Instrument II retains 7.77 and +3.18; dated correction 3.
- [fixed] K18: Changed markdown dek/body and README to 50/50 for the full repository run; dated correction 6 distinguishes the 43-check run. No stale classification.
- [open note:4d56e8] K19: This layer's related descriptions are corrected; dated correction 4. The preserved ask-a-random-friend -> what-the-bridges-knew note in public/strata/there-here/index.html:250 and research/lineage-edge-grammar/page.json:1 still assigns local comparisons to degree spread alone. Identical degree sequences give different local means and below-friend counts. Another layer's quotation needs a correction annotation; board note requested in repair-report.md.
- [fixed] K20: Kept uniform person then uniform neighbor draws; computed their target from adjacency and changed both live readouts plus prose, dek and markdown to 9.61 and +5.02. Endpoint Instrument II retains 7.77 and +3.18; dated correction 3.
- [fixed] K21: Changed markdown dek/body and README to 50/50 for the full repository run; dated correction 6 distinguishes the 43-check run. No stale classification.
- [fixed] K22: Narrowed the markdown checking promise; the separate assay runtime check exercises sampler targets and rejects an endpoint-target mutation. MINOR, no page correction line.
- [fixed] K23: Kept uniform person then uniform neighbor draws; computed their target from adjacency and changed both live readouts plus prose, dek and markdown to 9.61 and +5.02. Endpoint Instrument II retains 7.77 and +3.18; dated correction 3.
- [fixed] K24: Caption now describes the constructed preferential-attachment example without a prevalence claim; dated correction 7.
- [fixed] K25: Kept uniform person then uniform neighbor draws; computed their target from adjacency and changed both live readouts plus prose, dek and markdown to 9.61 and +5.02. Endpoint Instrument II retains 7.77 and +3.18; dated correction 3.
- [fixed] K26: Set JSON-LD dateModified to 2026-10-14. MINOR, no separate Corrected or Updated line under the explicit dateModified exception.
- [fixed] K27: Corrected the meta description and apparatus summary to the endpoint gap variance/mean; dated correction 8.
- [fixed] K28: JSON-LD now separates sensor early warning from acquaintance immunization for prevention; dated correction 9.
- [fixed] K29: Replaced smallest interesting case with a small case, preserving the worked numbers. MINOR, no page correction line.