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Cited by 0Adolescent and Pediatric HealthcareChild and Adolescent HealthMental Health Treatment and Access

Adequate Care Coordination is Associated with Reduced Unmet Mental Health Needs for Children

Open access
Graaf, Genevieve, Gigli, Kristin, Hughes, Phillip, Thomas, Kathleen C.·2026·Child and Adolescent Social Work Journal
DOI 10.1007/s10560-026-01101-wPMC PMC13427786

Published version of a preprint

Open this paper in CoChat — free accountOpen PDF

Abstract

Children with special healthcare needs (CSHCN), especially those with mental health needs, often receive services from multiple service sectors, including schools. Thus, care coordination may play a critical role in access to mental health care for these children. This cross-sectional study used multivariable logistic regression with pooled data from the National Survey of Children’s Health (2020–2023), focusing on a subsample of children with caregiver-reported mental health problems and a reported need for mental healthcare. We estimated the prevalence of parent-reported need for and receipt of effective care coordination and provider communication with schools. It also measures the association between parent-reported receipt of these services with unmet need for mental healthcare. Most caregivers reported need for care coordination (51.3%) and provider communication with schools (60.7%). Among those with need, 48.3% reported not having their care coordination needs met, and 57.2% of caregivers reported unmet need for provider communication with schools. The probability of reporting unmet mental health needs was 12percentage points lower when children had all needs for care coordination met and 10 points lower when providers communicated with schools. Results suggest that having care coordination needs met and provider communication with schools may play an important role in children accessing needed mental healthcare.

AI snapshot

Written from the paper’s full text.

TL;DR

Among children with caregiver-reported mental health problems and need for mental health care, unmet mental health need was 18.6%, and about half of families needing care coordination or provider-school communication did not receive it. Having all care coordination needs met and having providers communicate with schools were each associated with lower probability of unmet mental health need.

Key findings

  • In pooled 2020–2023 NSCH data, 18.6% of children with caregiver-reported mental health problems and need for mental health care had unmet mental health need.
  • 51.3% of caregivers reported need for care coordination; among those with need, 48.3% reported unmet care coordination need.
  • 60.7% reported need for provider communication with schools or childcare; among those with need, 57.2% reported that providers did not communicate with the school or childcare.
  • The probability of unmet mental health need was 12 percentage points lower when all care coordination needs were met [AME = −0.12 (−0.16, −0.08)] and 10 percentage points lower when providers communicated with schools or childcare [AME = −0.10 (−0.13, −0.07)].

Methods

  • Cross-sectional study pooling National Survey of Children’s Health data from 2020–2023, including children age 0–17 with caregiver-reported mental health problems and need for mental health care.
  • Multivariable logistic regression estimated associations between unmet mental health need and two predictors: having care coordination needs met and provider communication with schools/childcare. Average marginal effects were generated; analyses used survey weighting, stratification, and clustering in STATA v.16.1.
  • Subsamples were used: care coordination analyses included children seeing more than one type of provider in the past year; provider-school communication analyses included children whose caregivers reported need for that communication. Models controlled for child and family covariates, and sensitivity analyses using 2016–2019 data produced similar results.

Limitations

  • The paper states that NSCH excludes children in institutional settings, including justice or psychiatric institutions, where more complex mental health needs are overrepresented.
  • The paper states that measures rely on caregiver self-report, not validated clinical measures, and may be affected by recall bias; the unmet need measure may exclude children whose needs were met by primary care or who saw a mental health provider but still had unmet needs.
  • The paper states that the provider/school communication item asks about a “health care provider,” which may or may not include behavioral health professionals. The cross-sectional design also cannot establish causality (evident from the text). The text additionally contains an inconsistency: Table 2 alternative text says 8 and 11 points lower, while the Results and Table 2 report 12 and 10 points lower (evident from the text).

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1007/s10560-026-01101-w

Cites

48 of 48 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Claims the paper makes

18 of 37 cited sources checked · 14 supported · 0 flagged · accuracy not yet measured

  • Premisecitation

    Assistance in care coordination across services can play a critical role in accessing adequate care for these children.

    “can play a critical role in accessing adequate care for these children (Lindly et al., 2020).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Lindly et al., 2020 source
  • Interpretationcitation

    Cross-system collaboration can meaningfully strengthen service access and continuity for children and youth.

    “These results reinforce longstanding claims that cross-system collaboration can meaningfully strengthen service access and continuity for children and youth (Larson, et al., 2022).”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Larson, et al., 2022 source
    • Rests on an assumption: Having care coordination needs met is an adequate indicator of effective care coordination.
    • Rests on an assumption: Provider communication with schools or daycare is an adequate indicator of effective provider communication with schools.
  • Premisecitation

    Caregiver-reported provider/school communication was less common for children with mental health conditions than for children with other types of physical health or medical conditions.

    “However, caregiver-reported provider/school communication was less common for children with mental health conditions than for children with other types of physical health or medical conditions (Geffel et al., 2022).”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Geffel et al., 2022 source

      The Results report lower odds ratios for caregiver-reported provider–school communication among children with behavioral or mental health conditions (1.28) than among those with chronic physical conditions (1.37) or medical complexity (1.77). But each odds ratio compares children with a condition to children without it; the paper does not report a direct comparison showing that communication was less common for children with mental health conditions than for children with physical or medical conditions. (LLM, conf=0.82)

      Experimental — accuracy not yet measured
  • Premisecitation

    Receipt of adequate care coordination is associated with increased access to specialized medical care.

    “increased access to specialized medical care (Graaf & Gigli, 2022; Miller, 2014)”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites Graaf & Gigli, 2022 source
    • cites Miller, 2014 source
  • Premisecitation

    Over 20% of all children with caregiver-reported mental health problems and need for mental health care report unmet mental health need.

    “Over 20% of all children with caregiver-reported mental health problems and need for mental health care report unmet mental health need”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites Graaf et al., 2025 source
  • Classified as probably not a substantial claim. 23
  • May combine two claims. 12
  • The quote only partly states this claim. 1

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    The COVID-19 pandemic resulted in increased unmet mental health need for some children and increased barriers to accessing mental health care.

    “resulting in increased unmet mental health need for some children (Gigli & Graaf, 2022) and increased barriers to accessing mental health care (, Graaf, et al., Under review).”
    Quote in the paperNot a substantial claim1 of 2 sources checked
    • cites Gigli & Graaf, 2022 source
    • cites Graaf, et al., Under review

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductcitation

    Low missingness supported a complete-case approach for analysis, resulting in slightly smaller sample sizes after inclusion of covariates.

    “Low missingness supported a complete-case approach for analysis, (Langkamp et al., 2010) resulting in slightly smaller sample sizes after inclusion of covariates.”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Langkamp et al., 2010 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Caregivers of children with mental health needs frequently cite the importance of provider communication and cooperation with their children's schools.

    “Caregivers of children with mental health needs frequently cite the importance of provider communication and cooperation with their children’s schools (Graaf et al., 2024)”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Graaf et al., 2024 source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation

    The COVID-19 pandemic created changes in children's need for mental health care and practices in mental health service delivery.

    “Data used in this study spanned the COVID-19 pandemic which created changes in children’s need for mental health care and practices in mental health service delivery (Kauhanen et al., 2023; Palinkas et al., 2021; Purtle et al., 2022; Sklar et al., 2021; Zablotsky et al., 2022)”
    Quote in the paperNot a substantial claim3 of 3 sources checked
    • cites Kauhanen et al., 2023 source

      The Discussion reports increased mental health problems alongside decreased mental health service use among people aged 0–24 during the early pandemic, indicating unmet needs. This supports a change in need for care, but the paper does not describe changes in mental health service-delivery practices. Page numbers are not available in our copy. (LLM, conf=0.87)

      Experimental — accuracy not yet measured
    • cites Palinkas et al., 2021 source
    • cites Purtle et al., 2022 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    46% of families of children with caregiver-reported mental health problems and need for mental health care reported some level of difficulty in accessing mental health care.

    “46% of these families reported some level of difficulty in accessing mental health care”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Graaf et al., 2025 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Assistance in care coordination across services is highly valued by caregivers.

    “assistance in care coordination across services is highly valued by caregivers (Graaf et al., 2024)”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Graaf et al., 2024 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Variation in geographic availability of care coordination and Wraparound is an on-going concern.

    “Variation in geographic availability is also an on-going concern (Graaf et al., 2025).”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites Graaf et al., 2025 source

      The Discussion says state-based inequities in children’s mental health access merit further attention, supporting the cited sentence’s general concern about geographic variation. The passage does not address the geographic availability of care coordination or Wraparound specifically, so it does not support that narrower claim. (LLM, conf=0.86)

      Experimental — accuracy not yet measured

  • The quote only partly states this claim.

    Findingown data

    Among children with mental health problems and need for mental health care who saw 2 or more healthcare providers and had a need for care coordination, 48.3% had unmet need for care coordination.

    “| Unmet need for care coordination | 3,770 | 48.3% |”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Schools can be important in connecting children with mental health services, either by providing them directly in school settings or referring families to community-based supports.

    “schools can be important in connecting children with mental health services, either by providing them directly in the school settings or referring families to community-based supports (Hoover et al., 2020).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Hoover et al., 2020

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductown data

    Regression analyses controlled for child and family covariates, drawn from the same dataset, guided by the Behavioral Model of Health Service Use.

    “Regression analyses controlled for child and family covariates, drawn from the same dataset, guided by the Behavioral Model of Health Service Use (Andersen, 1995).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Andersen, 1995 source

  • May combine two claims.

    Premisecitation

    Caregivers of children with ASD who reported ineffective care coordination also reported more difficulty accessing mental health care and higher rates of unmet need for mental health care than counterparts reporting effective care coordination.

    “Caregivers of children with ASD who reported ineffective care coordination also reported more difficulty accessing mental health care and higher rates of unmet need for mental health care than counterparts reporting effective care coordination (Ezeh et al., 2022).”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites Ezeh et al., 2022 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    A key component of care coordination for children with complex health care needs is coordination and collaboration between school systems and health and behavioral health care providers.

    “A key component of care coordination for children with complex health care needs is coordination and collaboration between school systems and health and behavioral health care providers (Kuo et al., 2018).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Kuo et al., 2018 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Families are often unaware of where to access mental health care.

    “Families are often unaware of where to access mental health care”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Hoover et al., 2020

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Classified as probably not a substantial claim.

    Study design and conductown data

    Analyses employed survey commands to account for survey weighting, stratification, and clustering to generate nationally representative results.

    “Analyses were conducted using STATA v.16.1 (StataCorp, College Station, TX), employing the survey (‘svy’ and ‘subpop’) commands to account for survey weighting, stratification, and clustering to generate nationally representative results.”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Interpretationown data

    Among children with mental health problems, caregiver-reported need for care coordination and provider/school communication is high.

    “Among children with mental health problems, caregiver-reported need for care coordination and provider/school communication is high.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    The American Academy of Pediatrics reaffirmed the Mental Health Competencies for Pediatric Practice in 2025, which emphasizes the importance of pediatricians engaging a child's schools to appropriately address their mental health needs.

    “The American Academy of Pediatrics reaffirmed the Mental Health Competencies for Pediatric Practice in 2025, which emphasizes the importance of pediatricians engaging a child’s schools to appropriately address their mental health needs (Foy et al., 2019).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Foy et al., 2019 source

  • Probably not a substantial claim: may not pass S2 (checkable), S4 (based). May combine two claims.

    Interpretationreasoning

    Provider communication with schools or childcare can alert school personnel to the need for care, provide a pathway for schools to alert the pediatrician to mental health needs, and can support the coordination of that care to ensure that schools are fully informed about medication use or behavioral or emotional support plans.

    “Provider communication with schools or childcare can alert school personnel to the need for care, provide a pathway for schools to alert the pediatrician to mental health needs, and can support the coordination of that care to ensure that schools are fully informed about medication use or behavioral or emotional support plans.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Interpretationown data

    Most families needing care coordination or provider communication with schools did not receive an adequate amount of care coordination and experienced inadequate provider communication with schools.

    “However, most families needing these services did not receive an adequate amount of care coordination and experienced inadequate provider communication with schools.”
    Quote in the paperSubstantial claim
    • The authors state this as an assumption: Provider/school communication would likely not have taken place unless a caregiver believed it was needed and subsequently authorized it.
    • Rests on an assumption: Caregivers who failed to select the answer option “Did not need health care provider to communicate with these providers” indicated perceived need for provider communication.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductnone given

    The measure of provider/school communication asks if the child's health care provider communicated with the school, daycare or special education program.

    “Finally, the measure of provider/school communication asks if the child’s “health care provider” communicated with the school, daycare or special education program.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductreasoning

    The study's covariates were limited to individual characteristics and factors included in the National Survey of Children's Health dataset.

    “Covariates were limited to individual characteristics and factors included in the dataset”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Study design and conductreasoning

    The study's measures were based on caregiver self-report.

    “measures were based on caregiver self-report”
    Quote in the paperSubstantial claim

  • May combine two claims.

    Study design and conductnone given

    The National Survey of Children's Health excludes children in institutional settings, including justice or psychiatric institutions, among whom more complex mental health needs are overrepresented.

    “First, the NSCH excludes children in institutional settings, including justice or psychiatric institutions, among whom more complex mental health needs are overrepresented.”
    Quote in the paperNot a substantial claim

  • Classified as probably not a substantial claim.

    Study design and conductnone given

    The measure of unmet need was based on caregivers' report regarding whether their child saw a mental health provider in the last twelve months.

    “Further, the measure of unmet need was based on caregivers’ report regarding whether their child saw a mental health provider in the last twelve months.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing). May combine two claims.

    Premisecitation

    Social worker activities such as participating on child and family care teams, ensuring fidelity to family-centered planning, facilitating communication across sectors, and helping to establish and implement multi-stakeholder care plans are essential for effective cross-system collaboration and consistent care planning and implementation.

    “All of these activities are essential for effective cross-system collaboration and consistent care planning and implementation (Bruns et al., 2008; Kuo et al., 2018).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites Bruns et al., 2008 source
    • cites Kuo et al., 2018 source

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Premisecitation

    Many states provide financing for care coordination and Wraparound for children with complex behavioral health needs.

    “While many states provide financing for care coordination and Wraparound for children with complex behavioral health needs (Graaf & Snowden, 2017)”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Graaf & Snowden, 2017 source

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductreasoning

    The term health care provider in the provider/school communication measure may include behavioral health professionals, but it may also be that a child's primary care doctor or specialist communicated with the child's school while a behavioral health provider did not.

    “While the term “health care provider” may include behavioral health professionals, it may also be that a child’s primary care doctor or specialist communicated with the child’s school but a behavioral health provider did not.”
    Quote in the paperNot a substantial claim

  • May combine two claims.

    Study design and conductcitation

    Indicators of mental health problems or use of mental health services were not assessed using validated clinical measures, which, combined with recall bias, may result in inaccurate reports of unmet mental health need.

    “Thus, indicators or mental health problems or use of mental health services were not assessed using validated clinical measures which, combined with recall bias, may result in inaccurate reports of unmet mental health need (Hoagwood et al., 2000).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Hoagwood et al., 2000 source

  • Classified as probably not a substantial claim.

    Study design and conductown data

    Models controlled for child sex, race/ethnicity, age, impairments in daily activities, insurance type, gaps in insurance, family poverty level, family structure, household language, highest caregiver education level, and survey year.

    “Models controlled for child sex, race/ethnicity, age, impairments in daily activities, insurance type, gaps in insurance, family poverty level, family structure, household language, highest caregiver education level, and survey year”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim: may not pass S2 (checkable), S3 (load-bearing).

    Premisecitation

    State mental health agencies, Medicaid authorities, and insurance market governing bodies can play an important role in the extent to which care coordination services are covered for children in their state and the adequacy of reimbursement rates for these services.

    “State mental health agencies, Medicaid authorities, and insurance market governing bodies can play an important role in the extent to which these services are covered for children in their state and the adequacy of reimbursement rates for these services (Graaf & Snowden, 2021).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites Graaf & Snowden, 2021 source
29 of 29

  • The authors state this as an assumption.

    Provider/school communication would likely not have taken place unless a caregiver believed it was needed and subsequently authorized it.

    “our analysis assumed that provider/school communication would likely not have taken place unless a caregiver believed it was needed and subsequently authorized it.”

  • The paper relies on this without support.

    Caregivers who failed to select the answer option “Did not need health care provider to communicate with these providers” indicated perceived need for provider communication.

    “The rationale for this coding is that these children’s caregivers failed to select the answer option “Did not need health care provider to communicate with these providers”, indicating perceived need.”

  • The paper relies on this without support.

    No study has examined associations between receipt of care coordination, or provider/school communication, and access to mental health care for children with mental health conditions.

    “Further, no study has examined associations between the receipt of care coordination, or its important subcomponent provider/school communication, in relation to access to mental health care for children with mental health conditions.”

  • The paper relies on this without support.

    Few nationally representative estimates of caregiver need and unmet need for help in arranging care for children with mental health conditions exist.

    “there are few nationally representative estimates of caregiver need and unmet need for help in arranging care for children with mental health conditions.”

  • The paper relies on this without support.

    Little is known about the prevalence of care coordination for children with mental health conditions nationwide or the role it may play in access to mental health care.

    “Further, little is known about the prevalence of care coordination for children with mental health conditions nationwide or the role it may play in access to mental health care.”

  • The paper relies on this without support.

    Even less is known about provider/school communication for children with mental health conditions.

    “Even less is known about a subcomponent of care coordination highly valued by caregivers: provider/school communication (Graaf et al., 2024).”

  • The paper relies on this without support.

    Having care coordination needs met is an adequate indicator of effective care coordination.

    “This study demonstrates that effective care coordination and provider communication with schools are associated with reduced unmet mental health needs among children with caregiver-reported mental health concerns.”

  • The paper relies on this without support.

    Provider communication with schools or daycare is an adequate indicator of effective provider communication with schools.

    “This study demonstrates that effective care coordination and provider communication with schools are associated with reduced unmet mental health needs among children with caregiver-reported mental health concerns.”
8 of 8

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • School-communication effect differs in Table 2 alternative text

    Minor

    The alternative text says the probability was 11 percentage points lower, but Table 2 reports an average marginal effect of −0.10, or 10 percentage points.

  • Care-coordination effect differs in Table 2 alternative text

    Minor

    The alternative text says the probability was 8 percentage points lower, but Table 2 reports an average marginal effect of −0.12, or 12 percentage points.

  • Table 1 alternative text reverses the care-coordination majority

    Minor

    The alternative text says just under half had all their care-coordination needs met, while Table 1 reports no unmet need for 51.7% of those with a need.

  • Discussion calls unmet care-coordination need a majority

    Minor

    The discussion says most families needing care coordination did not receive enough of it, whereas the results report unmet need for 48.3%-less than half.

4 of 4

Cites

Flagged first, then by citations

Cited by

Still being checked.

Authors
Graaf, G., Gigli, K., Hughes, P., & Thomas, K. C.
Affiliations
  • The University of Texas at Arlington (US)
  • Binghamton University (US)
  • University of North Carolina at Chapel Hill (US)
Corresponding author
Graaf, Genevieve
ORCID
Venue
Child and Adolescent Social Work Journal
Publisher
Springer Science and Business Media LLC
Published
2026-03-24
Volume
43
Issue
4
Pages
1295-1302
ISSN
  • 0738-0151 (ISSN-L)
  • 1573-2797
DOI
10.1007/s10560-026-01101-w
PMC
PMC13427786
OpenAlex
W7140164696
Semantic Scholar
ced81e7995be53502bd5d590479c99bdd8681e66
Cited by
0
References
48
FWCI
0.00
Type
journal article
Language
en
Open access
Licence
Locations
  • Child and Adolescent Social Work Journal (publishedVersion, cc-by)
  • Research Square (acceptedVersion, cc-by)
  • PubMed (publishedVersion)
  • The Open Repository - Binghamton (Binghamton University) (submittedVersion, cc-by)
  • PubMed Central (submittedVersion, cc-by)
Funders
National Institute of Mental Health (1K01MH129991)
Topics
  • Health Sciences › Health Professions › Speech and Hearing › Adolescent and Pediatric Healthcare
  • Health Sciences › Health Professions › General Health Professions › Child and Adolescent Health
  • Social Sciences › Psychology › Social Psychology › Mental Health Treatment and Access
Keywords
care coordination, unmet mental health needs, children with special health care needs, school-based mental health services, access to mental health care, National Survey of Children's Health

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Claims read by deepseek-v4.1-flash under definition version 3 (extract-v3) on 2026-10-24.

Classified by jev-1.13-20260917 (gold-guideline-v0.2) on 2026-10-24.

Cited sources are checked by gpt-6-sol.

Statistics and arithmetic are recomputed, not judged.

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