The hand that beat the machine — until the machine measured rounder: an Avogadro-sphere craft legend that thinned as its sources were chased, over a metrology that stayed Tier 1

metrologycraftsmanshiptactile-cognitionmeasurement-historyavogadro-constantverification-methodsourcing-tierssiliconsi-units

The recurring argument in this cluster is not "Achim Leistner was a great optician" (the most-mentioned figure) and not "the Avogadro spheres are round" (the most-mentioned object). It is that one object carried two claims of very different sourcing weight, and only one of them survived being chased to primary sources. The measurement — enriched silicon-28 spheres built to count atoms and pin the Avogadro constant for the 2019 SI kilogram redefinition — is Tier 1 from NIST and from the International Avogadro Coordination's own papers, and it holds. The legend stacked on top of it — that a craftsman's unaided fingertips, the "atomic feeling," achieved a roundness "found to be superior to any purely machine-based method" — is Tier-3 magazine-and-museum prose, and every step toward a primary either fails to find one or turns up a document pointing the other way.

Titled for the argument's arc — a superiority claim and its Tier-1 reversal — not for Leistner or the spheres, per the 2026-07-25 lesson. What makes this a map rather than a list is a load-bearing bridge: the single Tier-1 document that speaks to hand-versus-machine (claim-ptb-repolish-out-rounded-leistners-original-avogadro-spheres) revises the exact roundness figures the legend decorates (claim-avogadro-silicon-spheres-among-roundest-objects-ever-made). The metrology sub-theme and the craft-legend sub-theme are not two themes circling — they are one story about the same two spheres, which is what distinguishes this from a held-open two-sub-theme case like moc-musical-instruments.

The bedrock — a measurement that redefined the kilogram

Tier 1, uncontested, load-bearing for everything else. This is the part that does not thin.

• claim-avogadro-silicon-28-spheres-realized-2019-kilogram-redefinition — the metrology. The 2019 SI kilogram redefinition moved mass off the platinum-iridium artifact and onto a fixed Planck constant, realized by two independent routes; the silicon route counted atoms in spheres of "99.9995 percent silicon-28," each "about a 94-mm diameter sphere" with "a mass of 1 kg," to determine the Avogadro constant. Tier 1 (NIST), re-fetched and cross-corroborated at arXiv.
• claim-avogadro-silicon-spheres-among-roundest-objects-ever-made — the roundness, and why it was load-bearing rather than decorative: to back out the Avogadro constant the sphere's volume had to be known to matching precision, so its diameter had to be uniform to nanometer tolerances. NIST's own scale analogy: blown up to Earth's size, the surface would deviate only "3–5 meters." Tier 1, verified_verbatim. This is the note the reversal below revises.

The legend — a craft-superiority story that will not source

The vivid part, and the exposed part. Each note here is honest about its own tier and is held seedling and flagged pending corroboration it has not received.

• claim-leistner-atomic-feeling-hand-polished-avogadro-spheres — the anecdote. Per the Powerhouse Museum's object record, Leistner (Zeiss-Jena-trained, emigrated to Australia 1957) did the final figuring by hand, using "his hands to feel for any imperfections," a technique the team nicknamed "atomic feeling," which the museum states "proved superior to purely machine-based methods." Tier 3, flagged [unverified-historical]: a surprising, load-bearing craft-superiority claim resting on a single museum caption. [Corrected 2026-08-16, cross-model audit — the record was re-fetched this session and three things in the sentence above are not in it, which also put this bullet at odds with the map's own open-threads section. (a) The Zeiss-Jena training and the 1957 emigration do not appear in the object record; their source is elsewhere and unlocated. (b) The nickname "atomic feeling" does not appear in the object record either — the map says so four sections down, and should not have attributed it here. (c) The museum's actual sentence is "Leistner's fabrication method has been found to be superior to any purely machine-based method," not "proved superior to purely machine-based methods"; the map's own opening paragraph already quotes it correctly. What the record does carry, and what this bullet is entitled to: the hand-figuring, and "his hands to feel for any imperfections." The member note carried the same three defects, flagged by the 2026-08-14 audit as a carried finding and fixed there this session.]
• claim-leistner-atomic-feeling-corroborated-beyond-powerhouse-museum — the careful half-win, and the half-loss. Two independent named journalists (Keats, Wired 2011; Powell, New Scientist 2008) corroborate the hand-polishing practice without paraphrasing the museum — so the anecdote is not one caption dressed as fact. But a 2026-08-14 cross-model audit found the nickname "atomic feeling" appears in neither new source and not even in the Powerhouse record itself; its only traceable home is a Tier-4 Wikipedia article citing a BBC Four documentary no vault note has read. The practice corroborates; the nickname does not.
• claim-leistner-hand-beats-machines-claim-lacks-tier1-primary — the superiority claim, twice sourced and still short. Keats (Wired) writes that "the most advanced computer imaging has confirmed … no machine can match his touch"; the museum makes the same claim. Two Tier-3 venues independently asserting superiority establish the claim is real (someone at CSIRO said it, more than once) — but a specific technical-mechanism claim needs Tier 1–2, and neither venue cites the "advanced computer imaging" study. flagged [unverified-mechanism — needs primary].

The reversal — the one Tier-1 test cuts the other way

The bridge that makes this an argument. The strongest primary found while investigating the "beats machines" claim measures against it.

• claim-ptb-repolish-out-rounded-leistners-original-avogadro-spheres — Tier 1, the load-bearing reversal. Azuma et al., Metrologia 52 (2015), reports that spheres AVO28-S5 and AVO28-S8 — the actual spheres Leistner hand-finished — were later etched and repolished at PTB in 2013–2014, and the peak-to-valley roundness deviation dropped (S5: 98 nm → 69 nm; S8: 90 nm → 38 nm) below "the initial spherical state produced by the Australian polishing." A later process made these specific spheres rounder than Leistner's hand-finish. The note is scrupulous about what it does not claim: the method paper for the PTB rework was unread, so whether that later process was machine-automated or still hand-guided is not established. It claims only the measured outcome — which is enough to unmake "hand beat machine, permanently."

Why the pieces belong together

The legend is a claim about the metrology — it asserts that hands achieved the roundness the Tier-1 notes measure. So the sourcing gap is not incidental: the map's whole point is that the measurement and the story about how it was achieved sit at different tiers, and the one document that can adjudicate the story is itself a metrology paper reporting on the same two spheres. Read the cluster for that gap, not for the romance.

The method's home, cross-linked not folded

Touch standing in for — or exceeding — instrumented precision is a thread with its own lineage; kept as a cross-link so the join is visible rather than silently merged into the sphere story. The member note itself draws the distinction: those cases substitute touch for absent sight, while Leistner's hands reportedly beat available machines.

• claim-saunderson-palpable-arithmetic-tactile-calculating-device and claim-blind-mathematicians-independently-reinvented-private-notation / moc-blind-mathematicians-working-methods — the tactile-cognition thread this episode bridges into, at a different constraint.
• moc-the-number-that-outran-its-evidence and moc-too-clean-to-be-real — methodological cousins: a vivid claim deflated by reading the record rather than re-running an experiment. This cluster is a metrology instance of the same shape, cross-linked, not claimed as those maps' spine.

Open threads (honest caveats, not hidden)

• The superiority claim has no primary and its one Tier-1 test fails it. "Found to be superior" is double-Tier-3; the only Tier-1 document on hand-vs-machine roundness for these spheres reports a later repolish beating the hand-finish. The claim is real but unproven, and the record leans against it. Tracked at question-verify-leistner-atomic-feeling-superior-to-machines.
• The nickname is unsourced at both ends. "Atomic feeling" is in neither corroborating source nor the museum record; its home is a Tier-4 Wikipedia citation of an unread BBC documentary.
• The reversal's method is unestablished. Whether PTB's rounder result came from a machine or from other opticians' hands is not known — the note refuses to say, and so does this map.
• Australia's NMIA/CSIRO — where the spheres were polished — is the one collaborator NOT on the Tier-1 NIST roster (it rests on Tier-3 reporting), which is precisely the corner of the story the craft legend occupies.
• Every member note is still seedling. A live cluster; this map records its current sourcing footing, not a frozen verdict.