Studies 48 and 49: the atom already has an address, and the phase code never needs pi
Founder, 2026-09-16: add 1 nm atomic lithography and holographic SLM field generation
as shear studies. Both are sealed here, with the surfaces they need.
Study 48 - hydrogen depassivation lithography on Si(100)-2x1:H. The write target is an
integer address, not a length: which dimer row, which dimer, which atom of the dimer.
Carrying the tip as a length in single precision mis-addresses its first hydrogen site
at step 8,783 and 4,183,204 of 4,194,304 sites; carrying it as a count mis-addresses 0,
and cannot. Seal 4b299340, seven arms, one of which must NOT hold.
Study 49 - phase-only wavefront synthesis. The device holds one of 256 codes per pixel,
and for a blazed grating and a Fresnel lens the code is a ratio of integers, so pi
cancels. Seal ec768ab3, thirteen arms, two of which must NOT hold.
Both compile to wasm32-wasip1 and print their sealed native transcripts byte for byte
under wasmtime. The in-browser Studio run is ABSENT: the Studio is pinned at 25a8a0c5,
which carries neither program, and the pages say so rather than implying otherwise.
A six-agent adversarial review before publication returned 42 findings. The ones that
changed the science:
Study 48 had the surface physics backwards. 2n+b put the dimer bond ALONG the row; on
Si(100)-2x1 the bond is PERPENDICULAR to it. The bracket is now b-free on dimer
centres, dn^2 + 4dm^2 in units of (dimer pitch)^2, and the intra-dimer Si-Si distance
is REPORTED and held ABSENT from every integer compared, with an arm proving the
b-freedom. The thesis was untouched: the graded section never called sqSeparation.
Study 49's A4 compared a formula against a copy of its own body. Dropping the factor
of 2 from 2*lambda*f mis-coded 2,064,821 pixels and every arm still held. It now
carries the power of pi as a symbol and checks that the division by 2pi drives it to
zero, paired with an arm that must NOT hold when the 2 is dropped.
Study 49 attributed four float counts to pi; only three are pi. Cancelling pi out
takes grating float64 47->0, grating float32 45->0, lens float64 16->0, but lens
float32 only 1,974->970. Half the single-precision lens disagreement is precision
alone. Reported, with the arm that measures it.
Study 48's stall figure was a doubling-grid point published as "tested directly".
The threshold, bisected out of the bit pattern, is 7.81 mm, not 12.9 mm.
Study 49's "84 pixels change code with the direction of the sum" was mostly the
reverse arm's multiplied seed. Summing the same step gives 4, and pi removed still
gives 4: order dependence is float accumulation, not pi.
Surfaces: index rows, sidebar entries, White Paper v5.1, Readers' Guide, and Home.md,
which gains one bullet in the measured list and a passage on what these two add. The
scale claim on every surface is the board's span, not the gap between the two studies:
counting the scale each page states it works at, twenty-four orders of magnitude from
Study 27's nuclear matter radius to Study 05's L1 point. "Quanta to galaxies" is not
claimed - no page here states a quantum length and none grades a galactic one.
Also repaired while in these files: three pages named paths inside the private repo;
the sidebar linked a page that exists nowhere; the index numbering note and the White
Paper conclusion counted forty-six on a forty-eight-study board; the White Paper gave
three different OPEN sets and carried two board rows with three cells in a four-column
table; and one duplicated sentence was the only divergence between the two clones.
22 check_figure pins, every one printed by its program and present on its page.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>