The 1.35 waste-and-inequality multiplier is unsourced and fuses two terms that must be separated (its VALUE is defensible; the flat 46 g floor is the real error)

[eduaguilera]

What is wrong

whep::nourishment_thresholds lifts the raw protein floor and target
(46 and 63 g/cap/day) to the shipped supply-side thresholds (62.1 and 85.05)
by a factor of 1.35:

# data-raw/sjos_n_coefficients.R:65,69,81
"protein", "floor",  46 * 1.35, "g/cap/day",
"protein", "target", 63 * 1.35, "g/cap/day",
"waste_inequality", "factor", 1.35, "ratio",

Those thresholds decide the Under / Adequate / Over classification on the
SJOS-N "just" axis, so 1.35 moves published classifications directly.

The factor has no source

• Its origin is an inline assumption in the upstream Global code, flagged as
  unchecked by its own author:
  Global/R/sjos_n.r:66 — Low_World = 46 * 1.35, # Minimum protein intake (check AdT) assuming 35% (unavoidable) waste and inequality-driven risk.
  "AdT" appears nowhere else in that repository.
• Global's own manuscript restates the thresholds
  (documentation/sjos_n/SJOS_N_Paper.qmd:187-188) citing only FAOSTAT for the
  data, never for the numbers, and references_sjos_n.bib has no protein entry.
• git log -S "46 * 1.35" in Global returns a single commit ("Reorganizing
  repo"), so there is no earlier history to mine.
• Targeted literature searching across the nitrogen, food-system and
  safe-and-just boundary literature found no published 1.35 waste-and-inequality
  factor.

whep's own @source (R/datasets_sjos_n.R:80-86) is honest about this — it
cites Springmann et al. 2018 for the framing and states the values are
transcribed from the Global analysis pending verification. This issue is about
closing that gap, not about a mis-citation.

Two substantive problems beyond the missing citation

1. It double-counts variability. The 46 g/cap/day floor is the WHO/FAO/UNU
(2007) TRS 935 safe level of protein intake for a 55 kg adult
(0.83 g/kg/day, PDCAAS 1.0; Table 46, report p.243,
https://iris.who.int/handle/10665/43411). That safe level is defined as a
97.5th-percentile individual requirement — exp(4.654 + 1.96 x 0.12) =
133 mg N/kg/day — not a population mean, which is 0.66 g/kg/day. Using it as a
population floor already embeds an inequality allowance; multiplying by a
further inequality factor counts the same variability twice. Only the waste
component of 1.35 is conceptually free of that double count.

2. A single scalar is not how this conversion is done. FAO's own
undernourishment method takes dietary energy supply straight from the FBS and
handles waste and inequality through a lognormal distribution with a
survey-derived coefficient of variation against a minimum requirement — no
scalar at all. The closest published analogue that does use a scalar-like
uplift is O'Neill et al. 2018 (doi 10.1038/s41893-018-0021-4, SI section 3.3),
which lifts an individual minimum of 2500 kcal to a population-wide floor of
2700 "to allow for some inequality in distribution" — roughly 1.08, and with
no waste term, because FBS supply already includes retail and consumer
waste (FAO, New Food Balances, section II, p.4).

Options

1. Decompose into a sourced household/retail waste factor and a sourced
   inequality uplift, each with its own sensitivity — but note both risks above.
2. Replace with a distribution-based treatment on FAO's PoU pattern,
   classifying on prevalence of inadequacy rather than a mean crossing a scalar.
   Different estimand; needs a CV input the package does not carry
   (calculate_food_gini() is between-country and cannot substitute).
3. Keep 1.35 as an explicitly labelled unsourced assumption with a
   sensitivity band, and report classification transitions under alternatives.

Related: the 63 g/cap/day target is also unsourced (TRS 935 Table 46 gives 62
at 75 kg and 66 at 80 kg, and section 14.2 explicitly declines to set an upper
limit, so no requirement table can supply a ceiling). Split out here because
the multiplier and the target need different resolutions.

[eduaguilera]

Correction: the double-counting claim in this issue is wrong

I filed this. Two of its three charges stand, and the headline one does not.
Retitling from "…is unsourced and double-counts TRS 935 variability" to
reflect what the evidence actually supports. The original body is left intact
above rather than rewritten, so the record of the mistake stays visible.

Withdrawn: "it double-counts variability"

The argument was that 46 g/cap/day is already a 97.5th-percentile individual
value, so multiplying it again by an inequality factor counts the same
variability twice.

That is wrong, and TRS 935 says so directly. Table 2 (p.45) shows a population
whose mean intake equals the 0.83 safe level still has 7.9% below
requirement at S_I = 0.12 and 18.2% at S_I = 0.24. The report requires a
population margin on top of the individual safe level. A multiplier there is
not double-counting; something of that kind is mandatory.

The report's objection to the current construction runs the other way from what
this issue assumed:

p.41 §3.3.2: "reference intake or safe intake levels defined as above for
individuals have been incorrectly applied to populations."
p.241 §14.1.1: "For a population, a safe population intake cannot be defined
as a simple function of the mean requirement."

The safe level fails as a population threshold because it is too low, not
because a margin on top of it would be redundant.

Withdrawn: the implication that 1.35 is the main defect

Back-solving 1.35 as a supply multiplier under TRS 935 Box 1 (log-normal
requirement, S_R = 0.12, deficit SD √(S_I² + S_R²), zero correlation as the
report assumes), the CV it implies is:

tolerated prevalence p*	implied CV
2.5%	0.2333
5%	0.2826
10%	0.3609

FAO publishes the corresponding quantity: FAOSTAT Suite of Food Security
Indicators item 21058, "coefficient of variation of habitual caloric
consumption distribution" — 4,014 country-years, 169 areas, 2001–2024, CC BY
4.0, 2010 median 0.250, range 0.17–0.37.

So 1.35 sits between the 2.5% and 5% values and straddles the published median.
It is unsourced in provenance but close to the middle of the defensible band.

The larger error is the one this issue treated as background: the flat 46 g
floor, an adult value applied to whole populations including children.
Quantified — holding the floor at 62.1 and asking what prevalence it tolerates
at CV 0.25:

• against the flat 46 g anchor: 3.26%, close to FAO's stated 2.5% floor
• against a demographically weighted anchor (median country 40.7 on the safe
  basis): 1.10%

i.e. the flat adult floor silently tightens the implied risk target from ~3.3%
to ~1.1%, and it does so hardest in the youngest populations.

Stands: no source, and a scalar is not the method

Both original charges survive untouched. Global/R/sjos_n.r:66 still reads
# Minimum protein intake (check AdT) …, "AdT" appears nowhere else, and no
publication states a 1.35 waste-and-inequality factor. And a single global
scalar is still not how the conversion is done — FAO parameterises a
distribution.

Stands, and is sharper than filed: waste and inequality are fused

The name claims two things and the value can only carry one. FAO puts waste on
the supply side and inequality in the CV; 1.35 fuses them, so neither
can be sourced or varied independently. Note also that FBS "food availability"
already includes retail and consumer waste (FAO, New Food Balances, section
II, p.4), and FAO's published retail-loss wedge (FS item 21059) is only
1.5–7.0%, median 2.83% — nowhere near the ~26% that 1.35 would imply if read as
a waste factor.

What replaces it

Not a better scalar. Four separately sourced and separately reportable terms:
demographic requirement weighting, an inequality term from the published CV,
protein quality (PDCAAS — TRS 935 issues 0.83 g/kg/day only "for proteins with a
protein digestibility-corrected amino acid score value of 1.0"), and a
supply→intake loss wedge.

One arithmetic point that matters for whoever implements it: the margin must be
applied once, over the convolution. Anchoring on the safe level (which
already contains 1.96·S_R) and applying an intake margin again computes
exp(1.96(S_R + S_I)) where the correct quantity is exp(1.96√(S_R² + S_I²)).
Standard deviations do not add. At CV 0.25 that is 2.050 against 1.711 — 19.8%
too high.

Related: #500 (the axis's residual), #762 (areas classified on an incomplete
food basket). The 63 g/cap/day target remains unsourced, as originally filed.

[eduaguilera]

Provenance resolved by the author: there is no source

@eduaguilera confirms 1.35 was a preliminary number produced for a
presentation, never sourced.

That closes the question this issue opened. It also resolves the (check AdT)
marker at Global/R/sjos_n.r:66 that two separate literature passes tried to
trace: it was the author's own note-to-self on a provisional figure, not a
pointer to a reference. Nobody should search for a source for 1.35 again.

Consequence for the work: the factor is not defended, not decomposed and not
carried forward. It is replaced in full by four separately sourced and
separately reportable terms — demographic requirement weighting, an inequality
term from FAOSTAT's published CV, protein quality (PDCAAS), and a supply-to-
intake loss wedge.

One thing from the correction above survives and is worth keeping straight,
because it is easy to misread now: the observation that 1.35 sits inside the
band implied by FAO's published CV (0.233 at p*=2.5% to 0.283 at 5%, against a
published median of 0.250) is a coincidence, not a justification. Its only
use is diagnostic — it means the currently published SJOS-N numbers are not
wildly displaced, so the replacement is a correctness and provenance fix rather
than an emergency. A provisional number landing in a defensible range is still
not a source.

The remaining substantive defect named here is unchanged and is the one that
actually moves results: the flat 46 g/cap/day floor, an adult value applied to
whole populations, which tightens the implied risk target from ~3.3% to ~1.1%
once the requirement is demographically weighted.

[eduaguilera]

This issue is the active work item for the nourishment floor

Recording that here so the issue is the record rather than a filed-and-parked
note. Everything below is evidence gathered against this issue; the remaining
decisions are listed at the end and are with @eduaguilera.

Scope has grown beyond the multiplier

1.35 cannot be fixed on its own. It is one of four conflated corrections,
and replacing it requires all four to be named separately:

term	status
demographic requirement weighting	measured (see below)
within-country inequality	sourced, country-year, with a documented estimand gap
protein quality (PDCAAS)	identified, not yet built
supply → intake loss wedge	not sourced; currently 0, so every floor is a lower bound

What is now established

The flat 46 g/cap/day floor is the dominant error, not the multiplier.
46 g is TRS 935's safe intake for a 55 kg adult, applied to whole populations
including children. Weighting TRS 935 Tables 46/47 requirements by UN WPP 2024
age/sex structure gives country floors of 34.8 (Niger) to 44.8, median 40.7
— every country below 46, and the bias is largest in the youngest, poorest
populations. Recomputed on single-age WPP data the 5-year-band approximation
moves it by at most 0.105 g/cap/day, so the result is not an artifact of the
age mapping.

On WHEP's 2010 build this moves 18 of 33 countries out of "Under", none the
other way — though that count is contaminated by #762 and must be re-measured
once a coverage guard exists.

The requirement anchor must be the median, not the safe level. TRS 935 p.41:
"reference intake or safe intake levels defined as above for individuals have
been incorrectly applied to populations"; p.241: a safe population intake
"cannot be defined as a simple function of the mean requirement". This does
not lower the threshold — the population threshold comes out above the
individual safe level (median country 56.7 against 40.7). It matters because the
margin must be applied once, over the convolution: anchoring on the safe level
and re-applying an intake margin computes exp(z(S_R + S_I)) where the correct
quantity is exp(z√(S_R² + S_I²)) — 19.8% too high at CV 0.25.

A per-country inequality term is sourceable. FAOSTAT Suite of Food Security
Indicators item 21058, 4,014 country-years, 169 areas, 2001–2024, CC BY 4.0,
2010 median 0.250 (0.17–0.37).

Where 1.35 actually sits. Replacing it with FAO's own lognormal inversion
f = exp(σ²/2 − z_p·σ), σ = √(ln(1+CV²)), at a 5% shortfall target: 2010
median 1.545, range 1.339–1.922. The USA — the least unequal country in
the panel — gives 1.3389. So the shipped 1.35 is the global minimum
inequality factor while its label also claims a waste component. There is no
room in it for waste.

Calibrating 21058 to survey dispersion is the wrong operation. 21058 is
√(CV|y² + CV|r²) where CV|y is the CV of fitted values from a regression of
calories on log income; FAO calls the discarded remainder "excess variability".
FAO's own Table 4 puts its correlation with the empirical household CV at
0.29–0.34, and it sits at a median 0.574 of the empirical HCES CV from the same
surveys. It is a shrinkage estimator, not a measurement — so the gap should be
documented, not removed with a multiplier.

Multi-country calibration was nonetheless run (owner's request), 8 countries on
verified deconvolved usual-intake basis (USA, JPN, CAN, NZL, NLD, AUS, BRA,
KOR): k protein median 1.477, range 1.432–1.953. The US value of 1.845 is
the top of the range, not the centre. Note all 8 sit at CV 0.17–0.27 while
FAOSTAT runs to 0.37 — more than half the countries this applies to are above
the highest observation, and Africa returned a documented null.

Temporal coverage. 21058 starts in 2001; the axis must run from 1961. An
anchored covariate hindcast was specified and tested against hold-constant over
1,332 country-years: it wins RMSE by 2.7% and loses MAE, coefficient
stability fails, and no test has power over ~two-thirds of the extrapolation.
Hold-constant is also FAO's own documented rule. Pre-1961 is held constant by
owner decision.

The protein/energy log-SD ratio replicates at 1.006–1.146, mean 1.062 across
all 8 countries — so using the energy CV for a protein floor errs low by ~6%,
quantified.

One correction to an earlier comment on this issue

The claim that FAO builds 21058 with CV|r ≈ 0.0975 does not hold. Combining
FAO's published CV|y with CV|r = 0.20 reproduces the published totals across
40 matched country-years to median error +0.008.

Pending decisions

Estimand (keep 21058 vs adopt the individual estimand); shortfall target p;
country-year varying vs global scalar; whether the replacement carries a waste
term at all; protein vs energy as the dispersion driver.

Related: #500 (axis residual), #762 (areas classified on an incomplete basket),
#751 / PR #755 (rice mass basis, moves the axis's largest item).