The Uncertainty the Record Cannot Identify

Calibration · native field first

Make the gauge block come back

Before the JCGM procedure touches an archive, it has to reproduce the core outputs of its published end-gauge example. Press once. The page evaluates the model, checks analytic sensitivities against finite differences, then sends 1,260,000 seeded trials through all nine input distributions.

A precision wrinkle: the four one-decimal contributions shown in Annex H.1 are 25, 9.7, 2.9, and 16.6 nm, whose squares sum to 1003.06 nm². Reconstructing from the source equations gives 1002.25 nm², 16.7 effective degrees of freedom, and 6.3 × 10^-7 relative standard uncertainty. The source prints 1002 nm² and 6.4 × 10^-7. The core 32 nm result is unchanged, so the page labels rather than hides the remaining display mismatch. The 93 nm expanded value uses a stated conservative ceiling to a whole nanometre.

Layer one · ten-second archival audit

Close every envelope, or stop

The ordinary spread of repeated values is one envelope. Cavendish also judged a difference of 1/14 of the whole very unlikely. That is numerical information, but it does not uniquely say whether 0.38 is a 95 percent expanded uncertainty, a bound, or a component separate from variability already in the table. This page therefore applies a deliberately conservative adapter rule: stop unless the component-wise distribution and dependence treatment are explicit. JCGM 100 permits scientific judgment and does not require this exact rule.

Rival baselines · different measurands made explicit

The smaller question still has an answer

The primary historical rival follows Cavendish's own judgment: 5.48 ± 1/14 of the whole, approximately 5.48 ± 0.38 or [5.10, 5.86]. Merkatas and colleagues interpreted 0.38 as an approximate 95 percent expanded uncertainty. That interpretation is informative but not forced by Cavendish's prose. The other intervals below answer narrower process or sampling questions and do not include an unknown common apparatus effect.

The baseline runs when the archive audit is unlocked.

These are distinct outputs, not interchangeable estimates of the same thing. The finite printed mean is exact for those 23 numbers. Iid and cluster intervals concern a repeatable process. A partially identified statement is mu_physical = mu_process + b_common, with the sampling part numerical and the common correction left symbolic. Cavendish's 1/14 judgment concerns the physical result. The conservative completeness gate asks whether a modern component-wise physical-result model is uniquely specified.

Layer two · source against adapter

Look at what the reduction discarded

reveal the first six density rows below

row	cohort	density

Adapter audit · loss first

Four mappings enter the collision

Source-to-formal-object mappings and their losses

source	formal object	what is lost
Printed final density	Repeated output Di	Upstream covariance and the input responsible for each residual.
Rows 7 to 29 after the wire change	Primary wire_2 cohort	Conditioning, creep, ageing, and gaps inside the cohort.
Two-decimal printing	Optional independent rectangular rounding inputs	Truncation, recomputation, and editorial intervention cannot be recovered.
Air-current warning	Possible common Type B effect or model discrepancy	The 1/14 judgment survives, but its component-wise distribution, coverage meaning, and overlap with observed scatter do not.

Dropped on purpose

• the first six first-wire densities from the primary estimate
• the unresolved 4.88 to 5.88 hypothesis
• today's accepted density as a tuning target
• qualitative weather notes as invented numbers
• weight motion, arm motion, corrected arm, vibration time, and corrected vibration time

Conventions supplied here

• the physical result, finite printed table, and later-wire process are kept as different measurands
• blank means missing, never zero
• target coverage is 95 percent and intervals are shortest unless labeled otherwise
• rounding is one independent rectangular input per printed value only when its switch is on
• absent covariance is not renamed zero covariance
• the stop rule is this page's conservative adapter choice, not a command quoted from JCGM

Disable each mapping

Each button clones the current adapter data, disables one mapping, and reruns the same auditTarget, propagation, and endpoint-validation path. An ablation survives only if the verdict stays the same and the mean, trimmed, and Huber centers each move by less than 0.01 density unit. The rounding ablation explicitly starts from the enabled rounding branch. If a mapping removal makes the calculation undefined, the row says so.

Secondary reproduction · sealed until reader-state freeze

Reproduce Lauginie's narrower calculation

Lauginie's 2007 reanalysis helped motivate the later-wire cohort, so it is not independent validation of that choice. After freezing the reader's current options, this panel deliberately recomputes the immutable later-wire comparison: mean 5.48 and twice the standard error about 1.50 percent. It is a reproduction of a secondary calculation, not evidence that the adapter was untuned.

Fault bench · one catch, one miss

Break what the instrument can see

The nonlinear branch is explicitly synthetic. It doctors the model input consumed by the production audit to use a positive denominator-like quantity with 50 percent relative uncertainty. The same unmodified completeness, propagation, and endpoint-validation path then checks a first-order interval against 200,000 Monte Carlo draws. The frozen target record is untouched.

Agreement between two propagation methods is not truth. A common bias can move every result together while leaving scatter, interval width, and method agreement intact.

The check

What is fixed, free, and still missing

We searched the general web, Crossref Works, and OpenAlex Works on 10 September 2026 for an application of JCGM 100 and JCGM 101 to Cavendish's 1798 published observation tables, and did not find a source that constructs a source-audited Type A and Type B budget and validates its linear propagation against Monte Carlo. This reports the search, not universal priority.

The check that stands behind this page recomputes the page's numerical results, imports the browser engine, compares the independent frozen transcription, checks the manifest ledger, reads every static displayed figure back out of this HTML, validates the share surface, and carries mutation controls that must turn those assertions red.

Sources

The documents, not substitutes for them

1. Henry Cavendish, Experiments to Determine the Density of the Earth, Philosophical Transactions 88 (1798), 469 to 526. Conclusion table at original page 520.
2. JCGM, JCGM 100:2008 and JCGM 101:2008. The 50 mm end-gauge example is Annex H.1 and Supplement 1 section 9.5.
3. Pierre Lauginie, Weighing the Earth, weighing the Worlds (2007), reproduced as a secondary rounded calculation.
4. Merkatas, Toman, Possolo, and Schlamminger, Shades of dark uncertainty and consensus value for the Newtonian constant of gravitation, Metrologia 56 (2019) 054001. They interpret Cavendish's 0.38 as an approximate 95 percent expanded uncertainty.
5. JCGM, JCGM GUM-6:2020. Its hierarchical-model guidance motivates the experiment-cluster sensitivity without asserting that within-experiment correlation is proven.
6. Stephen M. Stigler, Do Robust Estimators Work with Real Data?, Annals of Statistics 5(6), 1977, 1055 to 1098. Huber and trimmed centers are retained as secondary robustness diagnostics, not privileged as the strongest rival.
7. Michael Friendly, HistData Cavendish documentation, machine-readable comparison path for the density column.