DNA — geometry and the layered error budget
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An engraved plate in seven panels. The B-form duplex (I) is drawn to scale at 7 px per ångström from two sourced constants only — the rise, 3.4 Å (0.34 nm) per bp (CN05-01), and the 20 Å (2 nm) envelope diameter (CN05-07). Base pairs per turn (II) is drawn at 10.5 because a drawing must choose a number; 10.5 is NOT a measurement this corpus can trace (NOT-SOURCED, CN05-06), and the two solution primaries it sits between — 10.4 ± 0.1 (Wang 1979, topoisomer ladder) and 10.6 ± 0.1 (Rhodes & Klug 1980, DNase I periodicity) — are two assays of the same quantity under the same nominal condition and are UNRECONCILED (CN05-05). Groove widths are marked NOT-SOURCED, not NOT-MEASURED: both circulating pairs (~12/~6 Å and 22/12 Å) and the ~5.8 Å convention offset are untraceable in this corpus, and CN-05 records a fabricated citation for the 12/6 pair as its own most instructive failure. The groove brackets in panel I mark 0.4 / 0.6 turn axial spans that follow from the drawn 0.4-turn backbone offset — a construction, not a measurement. Panel III carries the A/B/Z families; panel IV the persistence length (~50 nm ≈ 150 bp) and its temperature and sub-100 bp fences. The layered error budget (V) is drawn as three successive filters — polymerase base selection, 3′→5′ proofreading, mismatch repair — with the error rate after each layer (≈10⁻⁵ → ≈10⁻⁷ → ≈10⁻¹⁰) and the errors per diploid copy (≈61,000 → ≈610 → ≈0.6). Every rung is MODELED: the decades are a review's round estimate (Fijalkowska, Schaaper & Jonczyk 2012) that composes exactly because it was chosen to, and does NOT reproduce from Schaaper 1993's measured fold-discriminations, which on a 10⁻⁵ rung span ~10⁻⁷·⁹ to ~10⁻⁹·⁹ (CN05-32); the first rung is contested three ways. The packing hierarchy (VI) derives 2.08 m of diploid DNA into a 113 µm³ nucleus at ~5.8 % of nuclear volume — the nucleus is 94 % not-DNA, so packing is a topology and access problem, not a space problem — and marks the 30 nm fibre CONTESTED in vivo, drawn as a ghost, with the disordered 5–24 nm curvilinear chain (Ou et al. 2017) drawn solid as what was actually observed. Loops/TADs/chromosome are drawn as an empty box: NOT-SOURCED in this pass. The plate's evidence marks are NATURA classes and carry no UNI claim of any kind.
Claims
| ref | symbol | value | units | scope |
|---|---|---|---|---|
| rise | ~3.4 (0.34) | Å (nm) /bp | B-DNA | |
| bp/turn (fibre) | 10.0 | bp | B-form fibre diffraction | |
| bp/turn (solution) | 10.4 ± 0.1 | bp | B-DNA free in solution, physiological; topoisomer gel | |
| bp/turn (Rhodes & Klug) | 10.6 ± 0.1 | bases | DNase I cutting periodicity on DNA immobilised on three surfaces; the authors identify the value with the repeat in solution | |
| bp/turn 10.4 vs 10.6 | unreconciled — two primaries, same nominal condition (solution), two assays | bp | topoisomer ladder (Wang) vs DNase I periodicity (Rhodes & Klug) | |
| bp/turn '10.5' | 10.5 | bp | quoted everywhere; printed by Potaman & Sinden Table 1 as B-DNA residues/turn; sits between two unreconciled primaries | |
| diameter | 23 (A) / ~20 (B) / 18 (Z) | Å | A-, B-, Z-DNA | |
| groove widths (12/6) | major ~12, minor ~6 | Å | B-DNA, convention not sourced here | |
| groove widths (22/12) | 22 / 12 | Å | widely repeated textbook pair — different convention | |
| groove convention offset | ~5.8 | Å | claimed offset between P–P and vdW-corrected conventions | |
| A-DNA | 11 bp/turn; rise 2.55 Å; C3′-endo; 9 Å axial hole; tilt ~20° | — | A-form | |
| Z-DNA | left-handed; 12 bp/turn; rise 3.7 Å; 18 Å; 30°/bp | — | Z-form, atomic-resolution crystal | |
| ℓ_p | ~50 (~150) | nm (bp) | dsDNA, ~0.1 M NaCl, ~20–25 °C; tweezers + AFM consensus | |
| ℓ_p vs temperature | 53.2 nm (5 °C) → 42.5 nm (42 °C) | nm | TBE + 10 mM MgCl₂ — a different ionic condition from the row above; j-factor + linking-number methods. A condition on the 50 nm consensus, not support for it: at ≥37 °C it sits at or below that row's own falsifier band | |
| ℓ_p sub-100 bp | short DNA more bendable than WLC predicts | — | <100 bp cyclisation | |
| G_human | 3,054,815,472 (+16,569 mtDNA) | bp | T2T-CHM13, gapless, chr1–22 + X | |
| ε_selection | ~10⁻⁴–10⁻⁵ (in vitro); ~10⁻⁵ (in vivo E. coli, a review's round estimate) | per bp | polymerase base selection alone | |
| Schaaper's measured factors | base selection 200,000–2,000,000×; proofreading 40–200×; MMR 20–400× | fold discrimination | E. coli, 866 sequenced lacI mutations in correction-deficient strains | |
| ε_selection in vivo vs in vitro | in vivo base selectivity >100× higher than in vitro | — | yeast Pol ε / Pol δ, proofreading- and MMR-deficient background | |
| ε_proof | ~10⁻⁷ as a ladder rung (= 10⁻⁵ × the review's ~10⁻² factor) | per bp | + 3′→5′ exonucleolytic proofreading | |
| ε_MMR | ~10⁻¹⁰ overall as the ladder rung (× the review's ~10⁻³ factor); measured overall band 10⁻⁹–10⁻¹¹ | per bp | + mismatch repair; overall | |
| ladder vs measured factors | Schaaper's measured factors on a 10⁻⁵ rung span ~10⁻⁷·⁹ to ~10⁻⁹·⁹ — reaching 10⁻¹⁰ only at the most generous edge | per bp | the decades do not reproduce from the measurement | |
| proofreading asymmetry | strand-asymmetric (Pol ε leading vs Pol δ lagging); proofreading > MMR on average, but varies per mismatch | — | yeast, in vivo | |
| errors/replication | ~6.1e4 → ~610 → ~0.6 | errors per diploid genome copy | 6.11 Gbp at 10⁻⁵ / 10⁻⁷ / 10⁻¹⁰ (in-vivo ladder); ~6.1e5 at the in-vitro 10⁻⁴ rung | |
| μ_germline | 1.20e-8 | per nt per generation (mean paternal age 29.7; +~2 mutations/yr; paternal doubling ~16.5 yr) | human trios — different denominator from ε | |
| L_DNA | 1.04 (2.08) | m, haploid (diploid) | 3.055e9 bp × 0.34 nm | |
| V_nucleus | ~113 | µm³ | sphere, d = 6 µm | |
| f_DNA,vol | ~5.8 | % of nuclear volume | DNA as r = 1 nm cylinder, 2.08 m, in 113 µm³ | |
| packing ratio | ~3.5e5 | dimensionless (linear) | 2.08 m / 6 µm | |
| nucleosome | 146 bp @ 2.8 Å; 147 bp @ 1.9 Å; 1.65 superhelical turns; histone octamer | bp | crystal structures — different crystals, both real | |
| 30 nm fibre in vivo | contested — not observed in cryo-EM of vitrified cells nor in ChromEMT | nm | in vivo interphase/mitotic chromatin | |
| chromatin chain in vivo | disordered 5- to 24-nanometer-diameter curvilinear chain | nm | ChromEMT, interphase + mitosis | |
| loops / TADs / chromosome | — | — | levels above the chain |
What this plate does NOT claim
- Not claimed: any groove width. Both circulating pairs (~12/~6 Å and 22/12 Å) and the ~5.8 Å convention offset that supposedly reconciles them are NOT-SOURCED in this corpus. The offset accounts for the minor pair (12 − 5.8 = 6.2 ≈ 6) but fails on the major (22 − 5.8 = 16.2, not 12 — a 10 Å gap), so 'different convention' is not a sufficient explanation. A groove width quoted without its convention is underspecified.
- Not claimed: that the 0.4 / 0.6 turn groove spans bracketed in panel I are a measurement. They follow from the drawn 0.4-turn backbone offset, which is a construction choice. The plate asserts the grooves' alternation and the 20 Å envelope, nothing more.
- Not claimed: that 10.5 bp/turn is a measurement, that it is a midpoint, or that it reconciles 10.4 and 10.6. It is the number the drawing had to choose in order to exist. Its provenance — independent determination, rounding, or midpoint — is NOT-SOURCED.
- Not claimed: that the fidelity ladder's rungs are settled. They are assay-dependent, assembled from different systems against different denominators, and the first rung is contested three ways (~10⁻⁴ in vitro; ~10⁻⁵ a review's in vivo estimate; >100× better than in vitro measured in vivo in yeast, which would push it below 10⁻⁶). The stacking principle survives the discrepancy; the specific rungs do not travel without their assay.
- Not claimed: that 10⁻¹⁰ is the polymerase's error rate. It is the rate after three layers. This is the single most common error in the material and is drawn on the plate as a recorded trap.
- Not claimed: that the per-generation germline rate (1.20×10⁻⁸, Kong et al. 2012) belongs beside the per-replication rates. Different denominators; a generation contains many germline divisions. It is deliberately absent from panel V.
- Not claimed: that the 30 nm fibre does not exist. It exists in vitro. Only its status as an in vivo structural level is contested, and it is carried as contested.
- Not claimed: that the stipple density in panel V is proportional. It is schematic — 61,000 : 610 : 0.6 cannot be drawn to scale on one plate.
- Not claimed: that the packing arithmetic is a measurement of a real nucleus. It is MODELED on a spherical nucleus of d = 6 µm and DNA as a 1 nm-radius cylinder. The assumptions are the fence; nuclei are not spheres.
- Not claimed: that this plate's geometry is DNA's only geometry. A-, B- and Z-forms are all real; which is occupied depends on sequence and environment.
- Not claimed: that DNA is a program, source code, blueprint, or specification. CN-05 records that reading as INADMISSIBLE as stated — a metaphor doing argumentative work with no falsifier attached. This plate draws a physical polymer with measured dimensions.
- Not claimed: that anything on this plate raises any UNI rung. A NATURE CITATION IS NEVER A UNI GATE. The plate contains ZERO UNI claims. The honest program position is unchanged by it: ~2 of 11+ developmental rungs earned, a developmental active-inference simulation, a toy world, never a person. 'Full human' and 'beyond human' appear nowhere as targets — they are permanent open questions.
Design fence — {"static":"No script elements, no on-event handlers, no external references (no xlink to a URL, no @import, no webfont, no
Source chapters
cookbook/recipes-natura/CN-05-dna.mdencyclopedia/NATURE-LEDGER.md (rows CN05-01…CN05-44 — the authority for every value)encyclopedia/wing-NATURA/NA-00-how-to-read-this-wing.md (evidence vocabulary; amended 2026-07-15)
sha256 01633f39b3a52226 — of the original file, so what was ingested stays checkable.