Methodology

01 · declarations and arithmetic

What the registry declares and what we compute

A declaration of 100 mg elemental magnesium corresponds to 165.78 mg magnesium oxide, using its 60.32% magnesium fraction in the calculation contract dated 2026-09-13; the element and its carrier are different masses.

The NIH Dietary Supplement Label Database is our source of label declarations. The primary magnesium row supplies the amount; a separate name identifies the chemical carrier. Taking the nutrient amount as the compound amount would reduce it a second time and produce the wrong elemental total. The conversion on this site runs in the other direction: from the declared element to the mass of the named salt required to carry it. See the NIH DSLD registry and the mineral declaration rules in 21 CFR 101.36.

The retained primary serving is the lowest serving-order magnesium entry after rows for other nutrients supplied by magnesium salts have been excluded. Repeated equal amounts collapse to one elemental value. Where distinct amounts remain, the explicit magnesium or elemental wording can resolve the primary amount; otherwise the amount is ambiguous. A magnesium salt named under vitamin C, for example, does not make the vitamin C quantity an elemental magnesium measurement.

Container arithmetic requires a positive numeric serving count. We keep a filed serving count even when dividing net contents by serving size would yield a slightly different number: rounded grams and rounded portions can disagree. The package block shows both filed inputs so the difference remains inspectable. For powders and liquids, a serving expressed in mg or mL is a measure of mass or volume, not a count of capsules.

We retain a label identifier throughout the calculation chain. Brand and product names are for human identification; the integer DSLD identifier is the stable join key within this release. A new version of a brand’s label is not automatically the same package as an older version, even when the front-facing name is unchanged.

02 · explicit chemical inputs

Elemental fractions by salt

The salt model contains 15 reference compounds as of 2026-09-13, with elemental fractions from 5.86% for gluconate to 60.32% for oxide; every configured hydrate ambiguity is carried through as a range.

The reference fraction is the mass of magnesium atoms in a formula unit divided by the molar mass of that formula unit. Magnesium’s atomic mass is taken as 24.305 g/mol. A formula with three magnesium atoms uses three times that atomic mass in its numerator. The displayed molar mass belongs to the stated reference formula; it is not a claim that every commercial material with that salt name has exactly that hydration state.

The code stores rounded fractions rather than recalculating them from the displayed rounded molar masses. Published arithmetic uses those stored fractions consistently, so a reader dividing two rounded display values can see a small rounding difference. We expose the fraction as well as the formula to make that distinction reproducible. Salt fractions characterize compounds; they do not measure a product’s absorption or establish a product ranking.

When the magnesium fraction ranges from f_low to f_high, the compound mass ranges from elemental mg ÷ f_high to elemental mg ÷ f_low. The inversion matters: the larger magnesium fraction gives the smaller required compound mass. We preserve both endpoints in the label CSV and JSON, the card’s mass table and its per-unit metadata. Taking the midpoint would conceal a physical ambiguity that the label has not resolved.

The “Range basis” column reproduces each salt’s configured ambiguity. For chloride and sulfate, water of crystallization changes the mass without adding magnesium. Citrate also covers differences in the named citrate composition. A single reference value elsewhere in the table means that the current model contains one composition, not that all possible commercial hydrates have been ruled out. The model’s chemical coverage is narrower than the vocabulary found in supplement marketing.

“Bisglycinate” and recognized spelling variants resolve to the glycinate key. “Amino acid chelate” does not identify a formula and receives no invented elemental fraction. A mixture needs constituent proportions before its total compound mass can be determined. A name match is therefore a declared-source interpretation, not a chemical assay of the bottle.

03 · a physical constraint with stated assumptions

Mass budget and capsule capacities

The capsule model compares the smallest required compound mass against 3 capacities—545, 730 and 1,100 mg—at powder density 0.6–0.8 g/mL, using the calculation contract dated 2026-09-13.

Compound mg per serving = declared elemental mg ÷ elemental fraction
Compound mg per unit = compound mg per serving ÷ units per serving

The test takes the most favourable supported interpretation for the product: the highest elemental fraction and therefore the smallest compound mass. For a hydration interval, this is the low endpoint of the compound-mass interval. The capacity comparison does not take the midpoint and does not use the largest required mass to manufacture an exceedance.

The conclusion on an exceeding product page is conditional: “If the declared salt were the sole source of magnesium here,” the minimum powder mass would exceed the standard capsule capacity. The resulting statement is: “So the label does not establish” the named salt “as the only source.” The fixed boundary of that conclusion is: “This is a statement about the label's arithmetic, not about what is in the bottle.” These are the same distinctions used in the product mass-budget component.

The mass budget is not a fill-weight measurement. Powder packing, particle size and density affect the weight a capsule can hold. The model uses the project’s deliberately generous approximate capacities; it does not infer an actual capsule dimension from a product photo. A denser blend, a non-standard capsule or a different physical interpretation of the label can change the result. The label would need additional information to distinguish those cases.

The mass of other ingredients and the capsule shell is excluded. Their quantities are usually not given in the retained record, and adding assumed amounts would make the model less favourable without adding evidence. A passing result therefore means that the salt mass clears this particular bound. It does not prove that every ingredient and the shell have been physically reconciled.

The downloadable audit is exactly the union of exceeds-all and needs-000 records. Both groups are computed from the same budget object as the product cards. The counts and product lists for the whole corpus live in the label audit. A product card carries its own result and the constants needed to interpret it.

04 · provenance travels with the value

Evidence tiers

Every new product measurement uses 1 of 5 evidence tiers as of 2026-09-13, separating a source observation, a calculation, a physical model, a proxy and a same-salt benchmark.

These tiers are kinds of evidence, not a ladder of numerical confidence scores. A computed value can be exact conditional on a doubtful input. An observed value can be a faithful transcription of an inaccurate label. A benchmark can be correctly calculated without being a plausible current retail quote. The label attached to the result says how it was obtained, while the accompanying sentence identifies the source and date.

On product cards, the evidence tier appears beside each structured measurement in the visible table. The Product JSON-LD repeats the same value and puts the tier in valueReference. Compound mass per unit is computed; the fill verdict and required capsule size are modelled. The first product sentence is also used verbatim as the Product description. That keeps the machine-readable claim attached to the same subject, unit and date as the visible claim.

Missing evidence is a dated statement. “No confirmed retail price as of 2026-09-13” differs from a zero-dollar price. “No standard size fits” differs from an unrecorded capsule size. The exports retain those distinctions in text instead of empty cells. Analysts can select numeric observations by type in JSON or by excluding the documented missing-data statements in CSV.

The daily-value calculation uses the declared elemental amount and a reference for the filed group. The package-duration calculation uses the label’s own frequency. Neither is personalized to a visitor. The arithmetic can be reproduced from its inputs without interpreting a target-group declaration as a finding about that group.

05 · identify the product before dividing its price

Price matching

The last logged price-matching run processed 283 eligible labels, examined 13,842 search candidates and recorded 0 new priced matches on 2026-09-13, according to the final entry in the retained price-match log.

The query is brand + “magnesium” + resolved salt. Amazon search results are retrieved through DataForSEO’s Merchant API; a product request supplies the price observation. The retained run identifies its search source as dataforseo_merchant_amazon_products_live_advanced and its price source as dataforseo_merchant_amazon_asin_live_advanced. A search title is candidate evidence, not a purchase link or a price guarantee.

Brand and salt are hard gates. A matching milligram number cannot rescue the wrong brand or the wrong salt. After those gates, milligrams determine confidence: a title amount within ±6% of the elemental serving amount, or within ±15% of the reference compound amount, is marked confirmed. A title with no milligram amount, or with an amount outside both tolerances, remains a candidate. The current compound gate uses the high-fraction reference endpoint; it is not a complete hydrate-identity test.

Confirmed is a result of this automated identity gate; it is not a synonym for manual review. The stored match_review_needed flag describes a separate review process. In particular, a title can match brand, salt and milligrams while naming a different pack size. The published EC100 divides the observed item price by the DSLD package amount, so a pack-size mismatch remains a material limitation until the package identity is checked.

Barcode search was tested on 2026-09-11 and did not provide a usable identity gate: Google Shopping returned jeans and a garden chair for barcode queries. That observation explains why the matcher uses brand and salt. It does not establish that barcodes never work or that those unrelated search results are supplement offers. The source barcode remains visible for independent checking; a failed search is recorded as our missing match, not as evidence of market absence.

A published observation uses the one-time item price in USD. Coupons, subscription offers, member-only discounts, shipping and tax are outside the price contract. The observed date stays attached to the amount. We do not change it to the build date, infer inventory from a stored price, or treat a retained search result as a live offer.

EC100 is compared only within one salt. The percentile is the percentage of eligible observations at or below the product’s own EC100, including itself; equal values receive equal percentiles. Fewer than three eligible observations produces an explicit small-group statement. For an unpriced label, a benchmark requires a resolved salt, a computed elemental package total and at least three eligible prices in that salt. The same median and cohort feed the benchmark table and sentence.

06 · check the label’s own arithmetic

Percent daily value

The magnesium reference for adults and children aged 4 years and older is 420 mg under 21 CFR 101.9(c)(8)(iv); the 4 group references below are used by the calculation contract dated 2026-09-13.

Percent daily value = elemental magnesium per serving ÷ the applicable group reference × 100. The table reports the original declared percentage, the reference amount, the recomputed whole percentage and the absolute difference in percentage points. It checks a declaration against an explicit reference; it does not turn that reference into an instruction to a reader. Sources: 21 CFR 101.9 and the FDA daily-value table.

The group name must identify a supported reference. A filed “children less than 4 years” category does not distinguish infants from children aged one through three; the page therefore shows an unresolved reference instead of silently using the adult value. A historical label can also use an earlier daily-value convention. Its difference from the current reference is an arithmetic comparison, not a conclusion that the historical filing violated its contemporary rules.

The enrichment record can contain entries from several serving sizes. The card states that its recomputation uses the primary serving. Repeated group entries remain visible as filed, rather than being averaged into a percentage with no corresponding label line. A serving-level comparison requires the original serving-order association; an unresolved association limits the interpretation of a difference.

07 · published measurements with named endpoints

Published absorption studies

The literature set contains 16 studies with PMID, title, journal and year checked against PubMed on 2026-09-11, retained in the release dated 2026-09-13 with each study’s design and limits.

Selection starts with work comparing magnesium preparations or measuring a relevant endpoint for a named magnesium compound. A record must have a traceable PubMed identifier and a readable design and endpoint. The retained set is a curated bibliography, not a claim that every eligible paper has been systematically retrieved. A paper’s presence establishes a published measurement in its stated setting; it does not validate a retail label that uses the same salt name.

We report what a study measured, in whom or in which animals, under what conditions. Urinary excretion, serum magnesium, intracellular magnesium, solubility and isotope tracing are different endpoints. A beaker solubility result remains a beaker result. A rat study remains a rat study. A specific clinical population is named instead of being silently generalized to all readers.

The bibliography and export retain study titles exactly, including the authors’ comparative wording where it forms part of the title. Our own summaries describe the experimental design and observations. We do not turn them into a salt ranking, a product claim, a symptom claim or a personal intake instruction. Where a trial names a broad class such as an amino-acid chelate, the class does not acquire a unique molecular formula through its appearance in a paper.

No absorption percentage is multiplied into EC100. That would combine label chemistry with an endpoint obtained in another setting and produce an apparent precision the inputs do not support. The absorption page and study CSV offer the underlying references; the product’s mass and price arithmetic stay tied to its own declaration.

08 · actual publication boundaries

What we do not publish and why

This release applies 2 source-backed boundaries to reused content as of 2026-09-13: Amazon Associates price-display conditions within that programme, and copyright in expressive material such as photographs and copied descriptions.

Amazon’s policy says a site “may only show prices and availability if” its stated display conditions are met. Those conditions concern Amazon-served links or pricing obtained through the specified programme APIs and used under their licence. This is an Associates programme condition, not a general ban on reporting historical prices. Our retained observations are dated analytical inputs; the cards do not present affiliate links or current purchase offers. Amazon Associates Program Policies.

The U.S. Copyright Office states: “Copyright does not protect facts, ideas, systems, or methods of operation”. Its guidance distinguishes those facts from protected expression, including photographs. We publish our calculations and source facts, and link to the NIH scan rather than treating a retailer’s photograph or sales copy as an openly licensed asset. U.S. Copyright Office: What Does Copyright Protect?

These grounds are not extended into invented prohibitions. The package’s filed serving count, arithmetic days, cost per label-day, same-salt benchmark and linked study findings are published where their inputs exist. Each is identified by its evidence tier and basis. A missing datum is handled as a missing datum, not as a legal restriction.

The DSLD API guide states that its data are in the public domain and requests source acknowledgement. Our attribution identifies NIH Office of Dietary Supplements, Dietary Supplement Label Database, the label identifier and the retained snapshot date. Our own derivative selection, calculations and explanatory text are released under CC BY 4.0; that licence does not relicense unrelated third-party photographs or journal articles.

09 · where the inputs stop

Known limitations

The retained dataset has 297 labels without a resolved single salt and 74 stored price records across 716 labels as of 2026-09-13; only 74 stored prices explicitly pass the current confirmed publication gate.

Resolution failure is not the same as a manufacturer failing to name a salt. Our parser can miss a name, a record can lack the relevant text, or the label can list several carriers without proportions. The dated statement on a card concerns the retained data and model. It does not claim that an external record inspected on another date must have the same gap.

The current salt resolver first uses recognized salts in the selected magnesium rows and then falls back to the full record when that first route yields none. This is the existing dataset’s resolution rule. It can resolve a single recognized salt alongside unrecognized words; it can also miss mixture information elsewhere in the record. We expose salt_source and the complete other-ingredient text so that the interpretation can be reviewed.

Values over 1,000 mg per serving are retained as filed and excluded from the existing form-level amount medians. A conspicuous number is not silently repaired. The label download retains it for inspection. For capsule budgets, the selected serving’s unit count is the divisor; variable serving sizes deserve particular attention because the legacy budget uses the minimum count while the per-unit display preserves the hydration interval at that same count.

A benchmark is available only where the same-salt observation group is large enough for the stated threshold. It does not fill missing prices in the exported observed-price columns. The absence remains visible even when a benchmark is useful. Likewise, neighbours are linked outside the product article, so their prices and mass verdicts do not become facts about the current label.

The rest of the site still includes older comparison views whose review-status vocabulary predates the explicit confidence field. This methodology describes the current product and download contract and identifies that legacy boundary instead of claiming that all stored price records have been re-reviewed. Aggregate mass-budget findings remain on the audit page.

10 · dated changes to the measurement contract

Changelog

This methodology records 4 dated stages from the initial 2026-08-10 snapshot through the 2026-09-13 release, distinguishing changes to publication rules from new source observations.

The current release adds a separate confirmed-price publication view without rewriting source JSON or the original product summaries. Download rows and product cards share the same arithmetic and confidence gate. The snapshot identifier stays fixed until the underlying registry snapshot changes; the methodology date marks this documented calculation contract.

For reproduction, start with the label CSV or JSON, retain the snapshot and derivation dates, and join back to NIH DSLD using dsld_id. Use the low and high compound-mass columns as a pair. Filter prices on match_confidence before calculating within-salt statistics. The audit CSV applies only the two published fill-verdict filters; the studies CSV preserves the bibliographic identifiers needed to revisit the original work.