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Constants — the measured numbers
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Every load-bearing constant with its units, scope, evidence class, source and falsifier.
307 rows.
| name | symbol | value | units | scope | class | source | falsifier |
|---|---|---|---|---|---|---|---|
| A4 | A4 | 440 ± 0.5 | Hz | Western concert pitch, by convention, at ~20 °C | OBSERVED-REPLICATED (as a standard, not a natural constant) | ISO 16:1975, Acoustics — Standard tuning frequency | It is a convention; only the claim that it is natural is falsifiable, and that claim is inadmissible. |
| T_ant | T_ant | ≈3.5 | K (excess antenna temperature at 4080 Mc/s) | Holmdel horn antenna, 1964–65; survived removal of every known instrumental/atmospheric term, incl. the pigeons | OBSERVED-REPLICATED | Penzias & Wilson (1965), ApJ 142:419–421 | An instrumental or local source reproducing the excess. |
| T_CMB | T_CMB | 2.72548 ± 0.00057 | K | Present-day CMB monopole temperature | OBSERVED-REPLICATED | Fixsen (2009), ApJ 707:916 | A measurement outside the stated interval by a calibrated instrument. |
| SI defining constants | SI defining constants | Δν_Cs = 9 192 631 770 Hz; c = 299 792 458 m/s; h = 6.626 070 15 × 10⁻³⁴ J·s; e = 1.602 176 634 × 10⁻¹⁹ C; k = 1.380 649 × 10⁻²³ J/K; N_A = 6.022 140 76 × 10²³ mol⁻¹ | Hz, m/s, J·s, C, J/K, mol⁻¹ | exact by convention, effective 20 May 2019 | (NO evidence class — chapter states: 'Definitional values, deliberately carrying NO evidence class … They are not observations of nature and this wing's evidence classes do not apply to them.') | BIPM, SI Brochure, 9th ed., 2019 | Not falsifiable — conventions, not observations. The chapter's instruction is: know which of your numbers are conventions. |
| N_rod | N_rod | 92 × 10⁶ (range 77.9–107.3 × 10⁶) | cells | human retina; 8 wholemounts, 7 donors, ages 27–44 | OBSERVED-REPLICATED | Curcio, Sloan, Kalina & Hendrickson (1990), J Comp Neurol 292:497–523, DOI 10.1002/cne.902920402 | Recount in a comparable cohort; a mean outside the stated range refutes. |
| N_cone | N_cone | 4.6 × 10⁶ (range 4.08–5.29 × 10⁶) | cells | as above | OBSERVED-REPLICATED | Curcio et al. (1990) | As above. |
| D_cone,fovea | D_cone,fovea | 199,000 (range 100,000–324,000) | cones/mm² | human foveal peak; same cohort | OBSERVED-REPLICATED | Curcio et al. (1990) | As above. |
| N_optic | N_optic | 1,159,000 ± 196,000 (range 816,000–1,502,000) | axons | human optic nerve; 22 nerves, 19 subjects, ages 20–75 | OBSERVED-REPLICATED | Jonas, Müller-Bergh, Schlötzer-Schrehardt & Naumann (1990), Invest Ophthalmol Vis Sci 31(4):736–744 | Recount; a mean outside the stated range refutes. |
| r_retina | r_retina | ≈ 83 : 1 | dimensionless | human visual blanket, order-of-magnitude only | MODELED — assumptions: (N_rod + N_cone)/N_optic across different cohorts, unpaired, no per-eye matching, ignores non-uniform convergence (foveal ≈ 1:1 vs peripheral ≫ 100:1) | arithmetic on Curcio et al. (1990) + Jonas et al. (1990) | Measure both counts in the same eyes. A paired ratio outside ~50–150:1 refutes this estimate. |
| f_aff (rat) | f_aff (rat) | ~80% afferent / 20% efferent | % of fibers | rat, abdominal vagus | OBSERVED-CONTESTED — the widely-quoted '80% of the vagus is afferent', routinely cited outside this scope | Prechtl & Powley (1990), Anat Embryol 181:101–115, DOI 10.1007/BF00198950 | Measure the human cervical vagus and obtain 80% ± small. Kronsteiner et al. (2024) did, and did not. |
| f_aff (human) | f_aff (human) | sensory 73.9 ± 7.5% (R), 72.4 ± 5.6% (L); parasympathetic 13.2 ± 1.8% / 13.3 ± 3.0%; sympathetic 13 ± 5.9% / 14.3 ± 4.0% | % of fibers | human, cervical vagus; 8 cadavers, immunofluorescence | OBSERVED-CONTESTED — carry with the row above; both positions stand | Kronsteiner et al. (2024), Brain Stimulation 17(3):510–524, DOI 10.1016/j.brs.2024.04.016 | Independent replication in a larger cohort; a sensory fraction outside ~65–82% refutes. |
| N_vagus | N_vagus | ~100,000 (light microscopy, 1961) vs 25,489 ± 2,781 (R) / 23,286 ± 3,164 (L) (modern, 2024) | axons | human cervical vagus | OBSERVED-CONTESTED — a ~4× disagreement between methods. The dispute is the finding; the modern claim is that light microscopy cannot resolve unmyelinated fibers | Hoffman & Schnitzlein (1961), Anat Rec 139(3), DOI 10.1002/ar.1091390312; Kronsteiner et al. (2024) | Blinded EM recount across labs on shared specimens. Convergence on either value resolves it. |
| ν (water) | ν (water) | ~10⁻² | cm² s⁻¹ | liquid water, room temp | OBSERVED-REPLICATED | Purcell (1977) | Standard viscometry. |
| Capillary length ℓ_c | Capillary length ℓ_c | ≈2.6 | mm | air–water, σ ≈ 0.07 N m⁻¹ | OBSERVED-REPLICATED | Bush & Hu (2006) | Direct meniscus measurement. |
| Min. capillary wave speed c_m | Min. capillary wave speed c_m | 23 | cm s⁻¹ | air–water interface | OBSERVED-REPLICATED | Lighthill (1979), via Bush & Hu (2006) | Waves radiated by steady motion below 23 cm s⁻¹. |
| λ (air) | λ (air) | ≈68 | nm | 1 atm, 25 °C | OBSERVED-REPLICATED | standard kinetic theory | Direct mean-free-path measurement. |
| Earth mantle viscosity | Earth mantle viscosity | 10²¹ | poise | mantle flow | MODELED (geophysical inference) | quoted in Purcell (1977) | Independent rheological determination. |
| Pr | Pr | 7 (water) / 0.71 (air) / 0.025 (mercury) | — | near room temperature | OBSERVED-REPLICATED | standard property tables | Property measurement. |
| D_GFP,ec | D_GFP,ec | 7.7 ± 2.5 | µm²/s | GFP (27 kDa), E. coli cytoplasm, FRAP/photoactivation | OBSERVED-REPLICATED | BNID 100193; Elowitz et al. 1999, J Bacteriol 181(1):197–203 | Repeat FRAP; a value outside 3–14 µm²/s under stated conditions refutes. |
| D_GFP,euk | D_GFP,euk | 27 | µm²/s | GFP-S65T, CHO cytoplasm | OBSERVED-REPLICATED | BNID 101997; Swaminathan et al. 1997, Biophys J 72(4):1900–7 | Independent FRAP in eukaryotic cytoplasm disagreeing >2×. |
| L_Thio | L_Thio | 100–300 (max 750) | µm | Thiomargarita namibiensis, cell width | OBSERVED-REPLICATED | Schulz et al. 1999, Science 284:493–495 | Larger true-cytoplasm cell found. |
| f_vac | f_vac | 80–98 | % of cell volume | Thiomargarita nitrate vacuole; cytoplasm shell ~1–2 µm | OBSERVED-REPLICATED | Schulz et al. 1999 | Show cytoplasm fills the cell. |
| ATP_ec | ATP_ec | ~10⁷ | ATP/s/cell | E. coli, growing | OBSERVED-REPLICATED | BNID 111461, 110656, 110628 | Independent measurement >10× off. |
| ATP_mam | ATP_mam | ~10⁹ | ATP/s/cell | human fibroblast, ~3,000 µm³ | OBSERVED-REPLICATED | BNID 111476 | As above. |
| P_ec | P_ec | ~10⁻¹² (1,000 W/kg) | W/cell | E. coli, glucose minimal media | OBSERVED-REPLICATED | BNID 109687 | As above. |
| c_pep | c_pep | 4 | ATP per peptide bond | 2 (PPi, aa-tRNA charging) + 1 GTP × 2 elongation factors | OBSERVED-REPLICATED | Milo & Phillips 2015, Cell Biology by the Numbers | Show a bond formed for <4. |
| ΔG_ATP | ΔG_ATP | −47 to −50 (≈20 k_BT ≈ 80–90 pN·nm) | kJ/mol | in vivo; E. coli on glucose −47 | OBSERVED-REPLICATED | BioNumbers (How much energy is released in ATP hydrolysis?) | Measured phosphorylation potential outside −40 to −65. |
| ΔG°'_ATP | ΔG°'_ATP | −28 to −34 (≈12 k_BT) | kJ/mol | standard conditions (1 M) — NOT the cell | OBSERVED-REPLICATED | as above | — |
| τ_F1 | τ_F1 | ~40 | pN·nm | F₁-ATPase torque, constant across load/speed | OBSERVED-REPLICATED | Yasuda et al. 1998, Cell 93:1117–1124 | Load-dependent torque under same assay. |
| W_F1 | W_F1 | ~80 (vs ~90 available) | pN·nm per 120° step | F₁, single-molecule, in vitro | OBSERVED-REPLICATED | Yasuda et al. 1998; Noji et al. 1997, Nature 386:299–302 | Work/step measured well below 80. |
| d_kin | d_kin | 8 | nm/step | kinesin-1 on microtubule, optical trap | OBSERVED-REPLICATED | Svoboda et al. 1993, Nature 365:721–727 | A different step periodicity. |
| n_ATP,kin | n_ATP,kin | 1 | ATP per 8-nm step | kinesin-1 | OBSERVED-REPLICATED | Schnitzer & Block 1997, Nature 388:386–390 | Measured coupling ≠ 1:1. |
| F_stall,kin | F_stall,kin | 5–6 or 7–8 | pN | 5–6: Svoboda & Block 1994. 7–8: force clamp, Visscher 1999 | OBSERVED-CONTESTED | Svoboda & Block 1994, Cell 77:773–784; Visscher et al. 1999, Nature 400:184–189 | Resolve by assay; do not average. A study reconciling both under one method. |
| v_kin | v_kin | ~0.5–1 (commonly ~0.8) | µm/s | saturating ATP, near-zero load, in vitro | OBSERVED-REPLICATED | Svoboda & Block 1994 (force–velocity) | Outside range under stated conditions. |
| d_myoV | d_myoV | ~36 | nm/step | myosin-V on actin; stall ~2–3 pN | OBSERVED-REPLICATED | single-molecule optical trap literature | Different step periodicity. |
| d_dyn | d_dyn | 8 (or 8→32, load-dependent) | nm/step | cytoplasmic dynein — unresolved | OBSERVED-CONTESTED | Optical-tweezer reports disagree | A method resolving load-dependence. |
| ε_rib | ε_rib | 10⁻⁴–10⁻³ | per codon | missense/misreading | OBSERVED-REPLICATED | Kramer & Farabaugh 2007, RNA 13:87–96 | Measured rate outside range. |
| ε_pol | ε_pol | ~10⁻⁴–10⁻⁵ | per nt | polymerase base selectivity ALONE | OBSERVED-REPLICATED | Kunkel & Bebenek 2000, Annu Rev Biochem; Kunkel 2004, JBC | Exonuclease-deficient rate outside range. |
| ε_proof | ε_proof | ~10⁻⁶–10⁻⁷ (×10²–10³ gain) | per nt | + exonucleolytic proofreading | OBSERVED-REPLICATED | as above | MMR-deficient rate outside range. |
| ε_final | ε_final | 10⁻⁸–10⁻¹⁰ | per nt | + mismatch repair; pro- and eukaryotes | OBSERVED-REPLICATED | as above | Whole-genome mutation accumulation outside range. |
| d_bilayer | d_bilayer | 4–5 | nm | lipid bilayer thickness | OBSERVED-REPLICATED | standard membrane biophysics; Milo & Phillips 2015 | Structural measurement outside range. |
| V_m | V_m | ~−70 | mV | resting neuron | OBSERVED-REPLICATED | standard electrophysiology | — |
| E_m | E_m | 1.4–1.8 × 10⁷ | V/m | V/d, 70 mV over 4–5 nm | MODELED | Computed in-chapter from V_m and d_bilayer | Arithmetic error, or d/V refuted. |
| E_air | E_air | ≈3 × 10⁶ | V/m | dry air, 1 atm — dielectric strength | OBSERVED-REPLICATED (not primary-sourced in this pass) | standard physical reference | Fetch a primary reference. |
| C_m | C_m | ~1 (0.01) | µF/cm² (F/m²) | specific membrane capacitance, near-invariant across cell types | OBSERVED-REPLICATED | standard membrane biophysics (Cole; Hodgkin & Huxley 1952) | A cell type deviating >2× with intact bilayer. |
| κ_MT | κ_MT | 2.2 × 10⁻²³ (±6.4%); 2.1 × 10⁻²³ (±4.7%, rhodamine) | N·m² | taxol-stabilised microtubule, flexural rigidity | OBSERVED-REPLICATED | Gittes et al. 1993, J Cell Biol 120(4):923–934 | Independent measurement >2× off. |
| ℓ_p,MT | ℓ_p,MT | ~5,200 (5.2 mm) | µm | microtubule persistence length, ℓ_p = κ/k_BT | OBSERVED-REPLICATED | Gittes et al. 1993 | see contested row below. |
| ℓ_p,actin | ℓ_p,actin | ~17.7 | µm | actin filament, rhodamine-phalloidin | OBSERVED-REPLICATED | Gittes et al. 1993 | Independent measurement >2× off. |
| n_Na/ATP | n_Na/ATP | 3 Na⁺ per 1 ATP | ions/ATP | Na⁺/K⁺-ATPase stoichiometry | OBSERVED-REPLICATED | Attwell & Laughlin 2001 and standard references | Measured stoichiometry ≠ 3:2:1. |
| E_Schumann@membrane | E_Schumann@membrane | — | V/m | field amplitude at a cell membrane | NOT-MEASURED | not sourced in this pass | Measure amplitude; compare to k_BT and membrane noise. |
| λ_Bcd | λ_Bcd | ≈ 100 | μm | D. melanogaster early embryo, L ≈ 490 μm | OBSERVED-REPLICATED | Gregor et al. (2007a), Cell 130(1):141–152 | Independent Bcd-GFP profiling giving a decay constant far outside ~80–120 μm at standard temperature. |
| L | L | ≈ 490 | μm | same embryo, AP axis | OBSERVED-REPLICATED | Gregor et al. (2007a) | Direct imaging outside ~450–550 μm. |
| D_Bcd | D_Bcd | 0.30 ± 0.09 (FRAP); 0.37 ± 0.05 (indirect) | μm²/s | cortical cytoplasm, cycles 10–14 | OBSERVED-CONTESTED — incompatible with λ ≈ 100 μm under SDD | Gregor et al. (2007a); dispute printed in Grimm et al. (2010), Development 137(14):2253–2264 | A method giving D large enough that √(Dτ) reproduces λ within the ~1 h formation window would dissolve the tension. |
| Δc/c | Δc/c | ≈ 10 | % | adjacent nuclei (~8 μm apart) at the hb boundary, cycle 14 | OBSERVED-REPLICATED | Gregor et al. (2007b), Cell 130(1):153–164 | Measured inter-nuclear Bcd difference at the boundary ≫ or ≪ 10%. |
| σ_x (hb domain) | σ_x (hb domain) | 2–3 | % egg length | hb transcription domain position, embryo-to-embryo | OBSERVED-REPLICATED | Gregor et al. (2007b) | Reproducibility measured far worse (≫3% EL) in a clean prep. |
| σ_x (4 gap genes) | σ_x (4 gap genes) | ≈ 1 | % egg length | joint gap-gene readout, AP axis, near-constant along axis | OBSERVED-REPLICATED | Dubuis et al. (2013), PNAS 110(41):16301–16308 | Decoding a fresh dataset yielding error ≫1% EL. |
| σ (limb bud mesoderm) | σ (limb bud mesoderm) | 20.1 | dyn/cm | chick embryonic tissue aggregate, parallel-plate compression | OBSERVED-REPLICATED | Foty et al. (1996), Development 122(5):1611–1620 | Remeasurement inverting the envelopment hierarchy. |
| σ (pigmented epithelium / heart / liver / neural retina) | σ (pigmented epithelium / heart / liver / neural retina) | 12.6 / 8.5 / 4.6 / 1.6 | dyn/cm | as above | OBSERVED-REPLICATED | Foty et al. (1996) | A tissue enveloping one of higher measured σ. |
| r_p | r_p | 8.4075(64) × 10⁻¹⁶ | m | proton rms charge radius | OBSERVED-REPLICATED | CODATA 2022 (NIST) | Next CODATA adjustment moves it beyond stated u. |
| α_s(m_Z) | α_s(m_Z) | 0.1180 ± 0.0009 | dimensionless | strong coupling at the Z mass; runs to O(1) at ~1 GeV | OBSERVED-REPLICATED | PDG world average (recent editions give 0.1179–0.1180 ± 0.0009) | A PDG edition outside 0.117–0.119. |
| a₀ | a₀ | 5.291 772 105 44(82) × 10⁻¹¹ | m | Bohr radius | OBSERVED-REPLICATED | CODATA 2022 (NIST) | Next CODATA adjustment beyond stated u. |
| α⁻¹ | α⁻¹ | 137.035 999 177(21) | dimensionless | fine-structure constant; α = 7.297 352 5643(11) × 10⁻³ | OBSERVED-REPLICATED | CODATA 2022 (NIST) | As above. |
| E_ion,H | E_ion,H | 13.6 | eV | hydrogen ionization | OBSERVED-REPLICATED (standard reference; primary not read in this pass) | standard atomic physics (NIST ASD) | Fetch NIST ASD; a value outside 13.59–13.60. |
| E_C–C | E_C–C | ~348 | kJ/mol | C–C bond dissociation enthalpy | OBSERVED-REPLICATED (standard reference; primary not read in this pass) | standard thermochemical tables | Fetch a primary table; value outside ~330–360. |
| ΔG_fold | ΔG_fold | ~20–63 (5–15 kcal/mol) | kJ/mol | net protein folding stability, typical globular | OBSERVED-REPLICATED (standard range; primary not sourced in this pass) | standard protein biophysics | Locate a primary survey; range refuted. |
| ν_water | ν_water | ~1.0 × 10⁻⁶ | m²/s | kinematic viscosity, 20 °C | OBSERVED-REPLICATED (standard reference) | standard fluid-property tables | Measurement outside ~0.9–1.1 × 10⁻⁶ at 20 °C. |
| R⊙ | R⊙ | 6.957 × 10⁸ | m | IAU nominal solar radius (exact by adoption, not a CBE) | OBSERVED-REPLICATED (adopted constant) | IAU 2015 Res. B3; Prša et al. 2016, AJ 152:41 | IAU re-adoption. |
| L⊙ | L⊙ | 3.828 × 10²⁶ | W | IAU nominal solar luminosity | OBSERVED-REPLICATED (adopted constant) | IAU 2015 Res. B3; Prša et al. 2016 | As above. |
| S⊙ | S⊙ | 1361 | W/m² | IAU nominal total solar irradiance | OBSERVED-REPLICATED (adopted constant) | IAU 2015 Res. B3; Prša et al. 2016 | As above. |
| T_eff,⊙ | T_eff,⊙ | 5772 | K | IAU nominal solar effective temperature | OBSERVED-REPLICATED (adopted constant) | IAU 2015 Res. B3; Prša et al. 2016 | As above. |
| (GM)⊙ | (GM)⊙ | 1.3271244 × 10²⁰ | m³/s² | IAU nominal solar mass parameter | OBSERVED-REPLICATED (adopted constant) | IAU 2015 Res. B3; Prša et al. 2016 | As above. |
| R_eE | R_eE | 6.3781 × 10⁶ | m | IAU nominal terrestrial equatorial radius (polar: 6.3568 × 10⁶) | OBSERVED-REPLICATED (adopted constant) | IAU 2015 Res. B3; Prša et al. 2016 | As above. |
| AU | AU | 1.495 978 707 × 10¹¹ | m | astronomical unit, exact by IAU definition | OBSERVED-REPLICATED (defined) | IAU 2012 Res. B2 (definition; primary not read in this pass) | Fetch IAU 2012 Res. B2. |
| D25_MW | D25_MW | 26.8 ± 1.1 (≈8.3 × 10²⁰ m) | kpc | Milky Way isophotal diameter | OBSERVED-CONTESTED (secondary summary; primary not read in this pass) | attributed to Goodwin et al. 1997/98, The Observatory 118:201–208 | Read the primary; an independent estimate outside 25.7–27.9 kpc. |
| R₀ | R₀ | 8178 ± 13(stat) ± 22(sys) (≈ 8.178 kpc; 0.16% stat, 0.27% total) | pc | Sun → Galactic Centre; direct geometric measurement — S2's orbit via VLTI/GRAVITY interferometry + 27 yr astrometry/spectroscopy | OBSERVED-REPLICATED (current standard reference) | GRAVITY Collab. (Abuter et al.) 2019, A&A 625:L10, DOI 10.1051/0004-6361/201935656 (primary read in this pass) | An independent geometric measurement outside ~8.13–8.23 kpc. |
| P/m E. coli | P/m E. coli | ~10³ (order-of-magnitude; wet-mass basis — see falsifier) | W/kg | E. coli strain C-3000, glucose minimal medium; a conversion, not a W/kg measurement | MODELED | Computed from BNID 109687 — an O₂ uptake rate, 30 mmol O₂/gDW/h — via the enthalpy of O₂ consumption (~478 kJ/mol O₂) ÷ a cell mass; chain via NA-08 | Recomputed: 30 mmol/gDW/h × 478 kJ/mol ÷ 3600 s = ~4 × 10³ W/kg dry ≈ ~1.2 × 10³ W/kg wet at dry/wet ≈ 0.3 — the stated ~10³ closes on a wet basis only. NA-08's mass basis is NOT-CONFIRMED in this pass. Also: an independent measurement >10× off. |
| L⊙/M⊙ | L⊙/M⊙ | 1.9 × 10⁻⁴ | W/kg | Sun; 3.828 × 10²⁶ W ÷ 1.988 × 10³⁰ kg | MODELED | Computed in-chapter from IAU 2015 nominal L⊙ and (GM)⊙/G (CODATA 2022) | Arithmetic error. |
| n_IMA | n_IMA | 6,200 | valid species | IMA-CNMNC list, January 2026 — a dated snapshot, not a constant | OBSERVED-REPLICATED | IMA-CNMNC, The New IMA List of Minerals (2026-01) | Consult current CNMNC master list; a different count. This row is built to go stale — see r_IMA. |
| d_Si–O | d_Si–O | ~1.62 (range 1.55–1.72) | Å | Si–O, tetrahedral coordination, silicate structures | OBSERVED-REPLICATED (primary not read this pass) | Si–O bond-length literature (Brown & Gibbs, Am Mineral; Cruickshank's rule ~1.63 Å) | Refine a silicate structure; mean Si–O outside 1.55–1.72. |
| θ_O–Si–O | θ_O–Si–O | 109.47 | degrees | ideal regular tetrahedron; real angles distort | MODELED | Geometry; Hückel-energy minimum at ideal angle (Am Mineral 57:1614) | A regular-tetrahedron silicate at a different angle. |
| N_sg | N_sg | 230 (32 point groups, 14 Bravais lattices, 7 systems) | space groups | periodic order in 3-D Euclidean space — a closed formal result about the space, not a survey of rocks | MODELED (closed formal result; deliberately not an empirical class — no mineral could refute it) | Fedorov (1891); Schoenflies (1891); list corrected to 230 by 1892 | Formal, not empirical: re-derive the enumeration — exhibit a 231st periodic group, or a duplicate among the 230. |
| Al₂SiO₅ triple pt | Al₂SiO₅ triple pt | both carried: ~501 °C, ~3.8 kbar (1971) and 504 ± 20 °C, 3.75 ± 0.25 kbar (1993) | °C, kbar | kyanite–andalusite–sillimanite invariant point; scoped to the Holdaway line of work — the wider aluminosilicate triple-point literature is not carried in this row | OBSERVED-CONTESTED | Holdaway (1971), Am J Sci 271:97–131; reevaluated Holdaway & Mukhopadhyay (1993), Am Mineral 78:298–315 | Re-run the brackets; coordinates outside 504 ± 20 °C, 3.75 ± 0.25 kbar. Do not average the two — the 1971 point falls inside the 1993 brackets, which is agreement, not licence to merge. |
| H_qtz | H_qtz | 12.1 ± 1.1 (micro) / 14.5 ± 0.4 (DSI) | GPa | quartz (0001) | OBSERVED-REPLICATED | Whitney, Broz & Cook (2007), Am Mineral 92:281–288, Table 1 | Independent indentation on (0001) outside range. |
| E*_qtz | E*_qtz | 117 ± 3 | GPa | quartz (0001), indentation modulus | OBSERVED-REPLICATED | Whitney et al. (2007), Table 1 | As above. |
| K_IC,qtz | K_IC,qtz | 1.5 ± 0.3 | MPa·m^½ | quartz (0001) | OBSERVED-REPLICATED | Whitney et al. (2007) | As above. |
| H_orth | H_orth | 6.9 ± 0.7 (micro) / 9.1 ± 0.6 (DSI) | GPa | orthoclase (101), Mohs 6 | OBSERVED-REPLICATED | Whitney et al. (2007), Table 1 | As above. |
| H_per | H_per | 5.3 ± 1.0 (micro) / 9.4 ± 1.4 (DSI) | GPa | periclase MgO, Mohs 6–6.5 — polycrystalline synthetic reference material, not a single crystal. Softer than orthoclase by microhardness only; the DSI column preserves Mohs order for the pair (9.4 ± 1.4 vs 9.1 ± 0.6, overlapping) | OBSERVED-REPLICATED (the values) / scope-mismatched for any rank-inversion claim — Mohs is a single-crystal scratch test | Whitney et al. (2007), Table 1 | Re-indent single-crystal MgO; the microhardness inversion disappears. |
| K_IC,per | K_IC,per | 3.9 ± 0.8 | MPa·m^½ | periclase — toughest of that set, and among the softest; polycrystalline synthetic | OBSERVED-REPLICATED | Whitney et al. (2007) | As above. |
| H_ky | H_ky | Mohs 5–5.5 on (001) vs Mohs 7 on (100)/(010); DSI 14.8 ± 1.4 on (001); E* 186 ± 8 → 253 ± 19 | GPa | kyanite — one crystal, two Mohs numbers, face-dependent; and (001), the table's lowest Mohs entry, is harder by DSI than orthoclase (9.1) and periclase (9.4) — the clean rank inversion: single-crystal, no reference-sample caveat | OBSERVED-REPLICATED | Whitney et al. (2007), Table 1 | Indent both faces and find isotropy; or find (001) softer than orthoclase by DSI. |
| t½ ²³⁸U | t½ ²³⁸U | (4.4683 ± 0.0024) × 10⁹ | yr | — | OBSERVED-REPLICATED | Jaffey et al. (1971), Phys Rev C 4:1889–1906 | Re-measure specific activity; outside stated uncertainty. |
| t½ ²³⁵U | t½ ²³⁵U | (7.0381 ± 0.0048) × 10⁸ | yr | ratio to ²³⁸U = 6.35× — the concordia's leverage | OBSERVED-REPLICATED | Jaffey et al. (1971) | As above. |
| t½ ⁴⁰K | t½ ⁴⁰K | (1.2522 ± 0.0027) × 10⁹ | yr | ⁴⁰K half-life (coverage factor not read this pass — fetch the primary) | OBSERVED-REPLICATED | DDEP 2025 evaluation; Mougeot et al., Metrologia 63(1) (2026), doi:10.1088/1681-7575/ae3733 | Supersedes 1.248 ± 0.003 × 10⁹ — re-evaluate. |
| ⁴⁰K branches | ⁴⁰K branches | β⁻→⁴⁰Ca 89.56(7)%; EC→⁴⁰Ar total ≈10.44% = EC* 10.34(7)% (excited state, 1460.8 keV γ) + EC₀ 0.098% (ground state, no γ). 89.56 + 10.44 = 100.00 | % | K–Ar uses EC₀ + EC*, i.e. all radiogenic ⁴⁰Ar — not EC* alone. Quoting 10.34% as 'the EC branch' drops a channel and loses 0.10% of the decay | OBSERVED-REPLICATED | DDEP 2025 evaluation (Mougeot et al. 2026); EC₀ first observed by the KDK collaboration, Phys Rev Lett 131:052503 (2023): I(EC₀) = 0.098% ± 0.023 (stat) ± 0.010 (sys) | Branches that fail to sum to 100%; or an EC₀ re-measurement outside the KDK uncertainty. |
| t½ ⁸⁷Rb | t½ ⁸⁷Rb | 49.61 ± 0.16 | Ga | λ₈₇ = (1.3972 ± 0.0045) × 10⁻¹¹ a⁻¹ | OBSERVED-REPLICATED | Villa, De Bièvre, Holden & Renne (2015), GCA 164:382–385 | Independent determination outside stated uncertainty. |
| t½ ¹⁴⁷Sm | t½ ¹⁴⁷Sm | 106.25 ± 0.38 | Ga | λ₁₄₇ = (6.524 ± 0.024) × 10⁻¹² a⁻¹, k = 2 | OBSERVED-REPLICATED | Villa et al. (2020), GCA (IUPAC-IUGS recommendation) | As above. |
| t½ ¹⁴⁶Sm | t½ ¹⁴⁶Sm | 92.0 ± 2.6 (k = 1) — the current determination | Ma | direct re-determination by mass spectrometry + α-counting; agrees with neither legacy value | OBSERVED-REPLICATED (one dedicated determination; not yet independently repeated) | Chiera, Sprung, Amelin, Dressler, Schumann & Talip (2024), Sci Rep, doi:10.1038/s41598-024-64104-6 | Independent re-determination outside 92.0 ± 2.6. |
| t_CAI | t_CAI | 4567.30 ± 0.16 | Ma | oldest solar-system solids; U-corrected Pb-Pb | OBSERVED-REPLICATED | Connelly et al. (2012), Science 338:651–655 | Independent Pb-Pb outside uncertainty. |
| t_zircon | t_zircon | 4404 ± 8 | Ma | Jack Hills detrital zircon; δ¹⁸O 7.4→5.0‰ | OBSERVED-REPLICATED | Wilde, Valley, Peck & Graham (2001), Nature 409:175–178 | An older confirmed terrestrial grain; or refute the δ¹⁸O inference. |
| d_borehole | d_borehole | 12,262 | m | Kola SG-3 — deepest direct sample of the Earth by true vertical depth (longer directional wells exist by measured length); ~0.19% of the way to the centre | OBSERVED-REPLICATED | Popov, Pevzner, Pimenov & Romushkevich (1999), Tectonophysics 306(3–4):345–366 | A deeper true-vertical borehole; or a re-survey of SG-3 outside 12,262 m. |
| K_qtz, G_qtz, ρ_qtz | K_qtz, G_qtz, ρ_qtz | — | GPa, g/cm³ | single-crystal adiabatic bulk/shear moduli, quartz & olivine | NOT-MEASURED (not sourced this pass) | — | Fetch Bass (1995), AGU Ref. Shelf 2:45–63. |
| T_ρmax | T_ρmax | 3.983 | °C | liquid H₂O, 1 atm | OBSERVED-REPLICATED | Wikipedia Properties of water (compiling standard reference data) | Densimetry finding max outside 3.9–4.1 °C at 1 atm. |
| ρ(3.983 °C) | ρ(3.983 °C) | 0.99997495(84) | g/mL | as above | OBSERVED-REPLICATED | as above | Value outside stated uncertainty. |
| ρ(0 °C) | ρ(0 °C) | 0.99984283(84) | g/mL | liquid, 1 atm | OBSERVED-REPLICATED | as above | As above. |
| ρ(25 °C) | ρ(25 °C) | 0.99704702(83) | g/mL | liquid, 1 atm | OBSERVED-REPLICATED | as above | As above. |
| ρ_ice | ρ_ice | 0.9167 | g/mL | ice Ih, 0 °C | OBSERVED-REPLICATED | Wikipedia Properties of water | Structural/densimetric measurement outside ±0.001. |
| k_ice | k_ice | ~2.2 (~2.2–2.3; rises as T falls) | W/(m·K) | ice Ih, 0 °C, 1 atm — higher than liquid water | OBSERVED-REPLICATED (secondary compilation) | Wikipedia List of thermal conductivities (CRC-sourced row, ~273 K); closure: fetch a primary | Measurement at 0 °C, 1 atm outside ~2.1–2.4. |
| k_water | k_water | ~0.561 | W/(m·K) | liquid water, 0 °C, 1 atm — cf. ~0.607 at 25 °C; the 0 °C value is the one used in the lake argument, and the two must not be mixed | OBSERVED-REPLICATED (secondary) | as above (compilations print 0.6065 with no temperature stated; the T is supplied in-chapter) | Measurement at 0 °C, 1 atm outside ~0.55–0.57. |
| k_snow | k_snow | ~0.074 (range ~0.05–0.25) | W/(m·K) | seasonal snow, density-dependent | OBSERVED-REPLICATED | J Glaciology, 'The thermal conductivity of seasonal snow' | Measurement outside range at stated density. |
| cₚ | cₚ | 4.181 (4.184 at 20 °C) | J/(g·K) | liquid water, 25 °C | OBSERVED-REPLICATED | Wikipedia Table of specific heat capacities (secondary compilation; cites Ashby et al., Young & Geller) | Calorimetry outside ±1 %. |
| cₚ ammonia | cₚ ammonia | 4.700 — exceeds water | J/(g·K) | liquid NH₃, 25 °C, saturation pressure ~10 bar (1003 kPa; liquid at 25 °C only under pressure — normal bp −33.34 °C) | OBSERVED-REPLICATED (secondary; T and P are not stated in the cited compilation — condition supplied in-chapter. Whether ammonia leads water across the whole liquid range is NOT-VERIFIED) | as above | Calorimetry at stated T and P showing ammonia < water. |
| cₚ ethanol / methanol / mercury | cₚ ethanol / methanol / mercury | 2.440 / 2.140 / 0.1395 | J/(g·K) | 25 °C | OBSERVED-REPLICATED (secondary) | as above | As above. |
| ΔH_vap | ΔH_vap | 2257 (40.65 kJ/mol) | kJ/kg | 100 °C, normal boiling point | OBSERVED-REPLICATED | Wikipedia Properties of water; corroborated by steam-table sources in this pass | Calorimetry outside ±1 %. |
| ΔH_vap ethanol | ΔH_vap ethanol | 38.56 kJ/mol = 837 J/g — near-equal per mole | kJ/mol | ethanol, normal bp | OBSERVED-REPLICATED (tertiary compilation; primary not fetched) | surfaced in this pass; falsifier/closure: fetch CRC or NIST | Primary value outside ±2 %. |
| λ_sweat | λ_sweat | ~2430 | J/g | the theoretical value at skin temperature — not a measured physiological constant; Havenith measured λ_eff to approach it for evaporation from the skin | OBSERVED-REPLICATED (as the value λ_eff approaches at the skin) | Havenith et al. 2013, J Appl Physiol 114(6):778–785 | A measured λ_eff for skin evaporation outside 2400–2450. |
| γ | γ | 71.97 | mN/m | water–vapour, 25 °C | OBSERVED-REPLICATED | IAPWS R1-76(2014), recomputed in-chapter from its own correlation → 71.972. The widely-copied 71.99 is Wikipedia Properties of water — a different source | Tensiometry outside IAPWS's ±0.5 % below 100 °C. |
| κ⁻¹ | κ⁻¹ | 2.71 | mm | capillary length, √(γ/ρg), 25 °C | MODELED | Computed in-chapter from γ, ρ(25 °C), g = 9.80665 | Arithmetic error. |
| h_tree,max | h_tree,max | 112.7 measured; 122–130 predicted | m | Sequoia sempervirens; ceiling set by leaf water potential, not the meniscus | OBSERVED-REPLICATED (measured) / MODELED (ceiling) | Koch et al. 2004, Nature 428:851–854 | A taller undamaged tree; or a mechanism refuting the water-potential limit. |
| μ_gas | μ_gas | 1.8546 | D | H₂O, gas phase, equilibrium | OBSERVED-REPLICATED (secondary compilation; primary not fetched) | Wikipedia Properties of water — which states no uncertainty; closure: fetch Clough et al. 1973, J Chem Phys 59:2254, or the NIST/CRC dipole-moment table | Primary measurement outside 1.8546 ± 0.001 D. |
| μ_liquid | μ_liquid | ~2.6–2.9 (ice Ih ~3.09 ± 0.04) | D | convention-dependent — no partitioning-free measurement exists | OBSERVED-CONTESTED / MODELED | reports surfaced in this pass span 2.6–2.9 ± 0.6 | A partitioning-independent determination. |
| ε_r | ε_r | ≈78.4 | dimensionless | static dielectric constant, pure water, 25 °C | OBSERVED-REPLICATED | BNID 115815; formulation: IAPWS R8-97 (Fernández et al., doi 10.1063/1.555997) | Value outside ±0.5 at 25 °C. |
| ΔH_soln(NaCl) | ΔH_soln(NaCl) | +3.9 — endothermic | kJ/mol | NaCl in excess water | OBSERVED-REPLICATED (secondary/tertiary; primary not fetched) | surfaced in this pass; closure: fetch CRC/NIST | Calorimetry showing exothermic dissolution. |
| ΔH_sub(ice Ih) | ΔH_sub(ice Ih) | 51.059 | kJ/mol | ice Ih, 0 °C | OBSERVED-REPLICATED (tertiary compilation) | LSBU Water Structure and Science (Chaplin); primary in Geochim Cosmochim Acta — not fetched in this pass | Fetch the primary; value outside ±0.1. |
| H-bond energy | H-bond energy | ≤25.5 (bound); ~23.3 (estimate) | kJ/mol | no standard definition exists | OBSERVED-CONTESTED | bound computed in-chapter (51.059/2); estimate: Chaplin, 'Water's Hydrogen Bond Strength', arXiv:0706.1355 | An agreed operational definition separating the H-bond from dispersion. |
| τ_HB,osc | τ_HB,osc | 170 | fs | underdamped H-bond oscillation period; OH of HOD in D₂O | OBSERVED-REPLICATED | Fecko et al. 2003, Science 301(5640):1698–1702 | Femtosecond IR outside 150–200 fs. |
| τ_HB,decay | τ_HB,decay | 1.2 | ps | decay of vibrational correlations (collective reorganisation) | OBSERVED-REPLICATED | Fecko et al. 2003 | Femtosecond IR outside ~1–1.5 ps. |
| L_crossover | L_crossover | ~1 | nm | hydrophobic small→large regime crossover | MODELED (theory + simulation) | Huang & Chandler 2000, PNAS 97(15):8324–8327; Lum, Chandler & Weeks 1999, J Phys Chem B 103:4570–4577 | A measurement placing the crossover an order of magnitude away. |
| θ_HOH | θ_HOH | 104.48 | degrees | H–O–H bond angle | OBSERVED-REPLICATED | Wikipedia Properties of water | Structural measurement outside ±0.1°. |
| f_N2 | f_N2 | 78.084 | % by volume | dry air, sea level | OBSERVED-REPLICATED | NASA NSSDC Earth Fact Sheet (Colorado mirror) | Independent composition measurement outside ±0.01%. |
| f_O2 | f_O2 | 20.946 | % by volume | dry air, sea level | OBSERVED-REPLICATED | as above | As above. |
| f_Ar | f_Ar | 9,340 (0.934%) | ppm by volume | dry air | OBSERVED-REPLICATED | as above | As above. |
| P_O2 | P_O2 | 212 | hPa | O₂ partial pressure at 1013.25 hPa | MODELED | Computed in-chapter: 0.20946 × 1013.25 | Arithmetic. |
| [CO₂] | [CO₂] | 431.44 | ppm | Mauna Loa monthly mean, June 2026 | OBSERVED-REPLICATED | NOAA GML Trends in CO₂, updated 05 Jul 2026 | Re-read the record; a different published monthly mean for June 2026. |
| Δ[CO₂]/yr | Δ[CO₂]/yr | 1.83 | ppm/yr | June 2025 → June 2026, single-site | OBSERVED-REPLICATED | NOAA GML, as above | As above. |
| H | H | 8.43 | km | RT/(Mg); T=288 K, M=0.028964 kg/mol, g=9.807 | MODELED | Computed in-chapter | Arithmetic; or refute an input. |
| H (published) | H (published) | 8.5 | km | Earth scale height as listed | OBSERVED-REPLICATED | NASA NSSDC Earth Fact Sheet (mirror) | Independent value outside 8–9 km. |
| M_atm | M_atm | 5.27 × 10¹⁸ (vs ≈5.15 × 10¹⁸ accepted) | kg | P₀A/g; gap = mean surface elevation | MODELED | Computed in-chapter; accepted value not primary-sourced in this pass | Fetch a primary M_atm; check the 990 hPa reconciliation. |
| ρ_air | ρ_air | 1.204 | kg/m³ | 20 °C, 101.325 kPa; PM/RT | MODELED | Computed in-chapter | Arithmetic. |
| μ_air | μ_air | 1.81 × 10⁻⁵ | Pa·s | 20 °C, 1 atm | OBSERVED-REPLICATED (not primary-sourced in this pass) | standard reference; cross-checks against Sutherland's formula → 1.813 × 10⁻⁵ | Fetch NIST/CRC; a value outside 1.79–1.84 × 10⁻⁵ refutes. |
| μ_water | μ_water | 1.002 × 10⁻³ | Pa·s | 20 °C, 1 atm | OBSERVED-REPLICATED (not primary-sourced in this pass) | standard reference (IAPWS-class value) | Fetch IAPWS; outside 0.99–1.01 × 10⁻³ refutes. |
| ρ_water | ρ_water | 998.2 | kg/m³ | 20 °C | OBSERVED-REPLICATED (not primary-sourced in this pass) | standard reference | Fetch a primary table. |
| ν_air | ν_air | 1.50 × 10⁻⁵ | m²/s | 20 °C, 1 atm; μ/ρ | MODELED | Computed in-chapter from the two rows above: 1.81 × 10⁻⁵ / 1.204 = 1.503 × 10⁻⁵ | Either input refuted. |
| ν_water | ν_water | 1.00 × 10⁻⁶ | m²/s | 20 °C; μ/ρ | MODELED | Computed in-chapter; cross-checks vs. published 1.0038 mm²/s at 20.2 °C | Either input refuted. |
| c_air | c_air | 343.2 | m/s | 20 °C; √(γRT/M), γ=1.400 | MODELED | Computed in-chapter | Measured c outside 342–344 m/s at 20 °C. |
| c_water | c_water | ~1,482 | m/s | 20 °C | OBSERVED-REPLICATED (not primary-sourced in this pass) | standard reference | Fetch a primary value. |
| Ω | Ω | 7.2921 × 10⁻⁵ | rad/s | Earth sidereal rotation | OBSERVED-REPLICATED (not primary-sourced in this pass) | standard geodetic constant | Fetch IERS conventions. |
| T_s | T_s | 288 | K | mean surface temperature | OBSERVED-REPLICATED | NASA NSSDC Earth Fact Sheet (mirror) | Independent value >2 K off. |
| T_e | T_e | 254.6 | K | [S(1−α)/4σ]^¼; S=1361 W/m², α=0.30 | MODELED | Computed in-chapter; S and albedo not primary-sourced in this pass — and the NASA sheet cited elsewhere in this chapter disagrees | Fetch CERES/TSI primaries; the cited fact sheet's own 0.385 / 1367.6 / 247.3 K disagree with this row and are believed superseded. |
| greenhouse ΔT | greenhouse ΔT | 33.4 | K | T_s − T_e | MODELED | Computed in-chapter | Either input refuted. |
| O₂ Permian peak | O₂ Permian peak | ~30 | % | Phanerozoic maximum, late Palaeozoic | MODELED | Berner 2006, GCA 70(23):5653–5664; rev. Berner 2009, Am. J. Sci. 309(7):603–606 | Recompute the mass balance; a proxy measurement contradicting. |
| Wingspan M. permiana | Wingspan M. permiana | ~71 | cm | Early Permian griffinfly; largest known insect | OBSERVED-REPLICATED | Guinness World Records (wing impressions, Elmo, Kansas, 1937); widely reported | A larger insect wing fossil. |
| Quetzalcoatlus mass | Quetzalcoatlus mass | 70 / 200–250 / 544 — a ~8× spread | kg | 10–11 m wingspan; same fossils, three answers | OBSERVED-CONTESTED | Chatterjee & Templin 2004 (~70); Paul 2002 / Witton 2008 / Witton & Habib 2010 / Martin & Palmer 2014 (~200–250, the consensus cluster); Henderson 2010 (~544) — via secondary reports | A method reconciling the three; do not quote one as 'the' mass — and do not round the ends inward, which shrinks the finding. |
| Pelagornis wingspan | Pelagornis wingspan | 6.06–7.38 | m | depends on feather-reconstruction method | OBSERVED-REPLICATED | Ksepka 2014, PNAS, doi:10.1073/pnas.1320297111 | Re-measure; a span outside the range. |
| Pelagornis mass | Pelagornis mass | ~22–40 | kg | regression-dependent; exceeds the flapping ceiling — it soared | OBSERVED-REPLICATED | Ksepka 2014 | As above. |
| T_c,☉ | T_c,☉ | 1.54 × 10⁷ | K | standard solar model, current epoch | MODELED | arXiv:2501.09971 Table 1; cf. Salmon et al. 2021, A&A 651, A106 | An SSM variant outside 1.4–1.7 × 10⁷ K reproducing helioseismology + neutrinos. |
| ρ_c,☉ | ρ_c,☉ | 149 | g/cm³ | standard solar model, current epoch | MODELED | arXiv:2501.09971 Table 1 | As above. |
| P_c,☉ (SSM) | P_c,☉ (SSM) | 2.3 × 10¹⁶ | Pa | standard solar model, current epoch | MODELED | arXiv:2501.09971 Table 1 | An SSM variant outside this range reproducing helioseismology + neutrinos. |
| t_☉,formation | t_☉,formation | 4.567 × 10⁹ | yr | Pb–Pb dating of CAIs | OBSERVED-REPLICATED | Connelly et al. 2012, Science 338:651–655 | Independent radiometric dating >1% off. |
| Φ(CNO) final | Φ(CNO) final | 6.7 (+1.2 / −0.8) × 10⁸ | cm⁻² s⁻¹ | solar CNO neutrinos; CID over the complete 2007–2021 dataset + an improved Phase-III spectral fit | OBSERVED-REPLICATED | Borexino Collaboration 2023, Phys Rev D 108:102005, arXiv:2307.14636 | An independent detector outside the interval. |
| t½(⁸Be) | t½(⁸Be) | ~10⁻¹⁶ | s | ⁸Be ground state, unbound | OBSERVED-REPLICATED (standard nuclear data; not primary-sourced in this pass) | standard nuclear data tables | Measured lifetime >10× off. |
| E_x(Hoyle) modern | E_x(Hoyle) modern | 7,654.07 ± 0.19 | keV | ¹²C second excited state, 0⁺ | OBSERVED-REPLICATED | NNDC, via Freer & Fynbo 2014, Prog Part Nucl Phys 78:1–23 | A measurement outside ±0.19 keV. |
| BE/A(⁶²Ni) | BE/A(⁶²Ni) | 8.7945 | MeV/nucleon | highest known binding energy per nucleon | OBSERVED-REPLICATED | standard nuclear mass tables | A nuclide measured higher. |
| BE/A(⁵⁸Fe) | BE/A(⁵⁸Fe) | 8.7922 | MeV/nucleon | second | OBSERVED-REPLICATED | as above | As above. |
| BE/A(⁵⁶Fe) | BE/A(⁵⁶Fe) | 8.7903 | MeV/nucleon | third — but lowest mass per nucleon (a different quantity) | OBSERVED-REPLICATED | as above | Show ⁵⁶Fe has the highest BE/A, or that mass/nucleon and BE/A are the same quantity. |
| ΔBE/A (⁶²Ni − ⁵⁶Fe) | ΔBE/A (⁶²Ni − ⁵⁶Fe) | 4.2 (0.048%) | keV/nucleon | the whole 'iron peak' spread | MODELED | Computed in-chapter from the rows above | Arithmetic error. |
| t½(⁵⁶Ni → ⁵⁶Co) | t½(⁵⁶Ni → ⁵⁶Co) | ~6 | d | powers the early Type Ia light curve | OBSERVED-REPLICATED (standard nuclear data; not primary-sourced in this pass) | standard nuclear data tables | Measured half-life >10% off. |
| t½(⁵⁶Co → ⁵⁶Fe) | t½(⁵⁶Co → ⁵⁶Fe) | ~77 | d | powers the Type Ia light-curve tail | OBSERVED-REPLICATED (standard nuclear data; not primary-sourced in this pass) | standard nuclear data tables | As above. |
| L_Edd | L_Edd | 1.26 × 10³¹ (M/M☉) ≈ 3.3 × 10⁴ (M/M☉) L☉ | W | 4πGMm_p c/σ_T; spherical, steady, ionised H, Thomson opacity only | MODELED | Eddington 1926, The Internal Constitution of the Stars; arithmetic computed in-chapter | Arithmetic error; or a steady spherical source persistently above it. |
| Y_p | Y_p | ~0.245 | mass fraction | primordial helium, BBN/CMB concordance | OBSERVED-REPLICATED (standard reference; not primary-sourced in this pass) | BBN/CMB literature | An independent determination outside ~0.24–0.25. |
| Δc_s/c_s | Δc_s/c_s | 0.10 | % (rms fractional) | SSM vs helioseismic inversion, 0.05–0.95 R☉ | OBSERVED-REPLICATED (inversion) / MODELED (the model side) | Bahcall, Pinsonneault & Basu 2001, ApJ 555:990 | An independent inversion disagreeing at >0.5%. |
| Ṗ_b,obs/Ṗ_b,GR | Ṗ_b,obs/Ṗ_b,GR | 0.9983 ± 0.0016 | dimensionless | PSR B1913+16; 9,257 TOAs over 35 yr | OBSERVED-REPLICATED | Weisberg & Huang 2016, ApJ 829:55, doi:10.3847/0004-637X/829/1/55 | A ratio outside the interval on longer baselines. |
| M_psr / M_comp | M_psr / M_comp | 1.438 ± 0.001 / 1.390 ± 0.001 | M☉ | PSR B1913+16 | OBSERVED-REPLICATED | Weisberg & Huang 2016 | As above. |
| Au in AT2017gfo | Au in AT2017gfo | NOT DETECTED; M_Au ≲ 10⁻², M_Pt ≲ few × 10⁻³ | M☉ (upper limits) | 'no platinum or gold signatures are prominent in the ejecta' | NOT-MEASURED (upper limits only) | Gillanders et al. 2021, MNRAS 506(3):3560–3577, doi:10.1093/mnras/stab1861 | A spectroscopic identification of Au or Pt in a kilonova. |
| rise | rise | ~3.4 (0.34) | Å (nm) /bp | B-DNA | OBSERVED-REPLICATED | Potaman & Sinden, NCBI Bookshelf NBK6545; Watson & Crick 1953, Nature 171:737–738 | Structural measurement outside 3.3–3.5 Å under B-form conditions. |
| bp/turn (fibre) | bp/turn (fibre) | 10.0 | bp | B-form fibre diffraction | OBSERVED-REPLICATED | Watson & Crick 1953; as compared in Wang 1979 | Re-analysis of fibre data giving ≠10. |
| bp/turn (solution) | bp/turn (solution) | 10.4 ± 0.1 | bp | B-DNA free in solution, physiological; topoisomer gel | OBSERVED-REPLICATED | Wang 1979, PNAS 76(1):200–203, doi:10.1073/pnas.76.1.200 | Repeat topoisomer ladder; value outside 10.3–10.5. |
| bp/turn (Rhodes & Klug) | 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 | OBSERVED-REPLICATED | Rhodes & Klug 1980, Nature 286(5773):573–578, PMID 7402337 | Repeat digestion periodicity outside 10.5–10.7. |
| bp/turn '10.5' | 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 | NOT-SOURCED in this pass (value printed in source; provenance not traced) | Potaman & Sinden, NBK6545 Table 1 | Establish whether 10.5 is an independent determination, a rounding, or a midpoint of 10.4 and 10.6. |
| diameter | diameter | 23 (A) / ~20 (B) / 18 (Z) | Å | A-, B-, Z-DNA | OBSERVED-REPLICATED | Potaman & Sinden, NBK6545 Table 1 | Structural measurement outside range. |
| groove widths (12/6) | groove widths (12/6) | major ~12, minor ~6 | Å | B-DNA, convention not sourced here | NOT-SOURCED in this pass | not confirmed here — NBK6545 Table 1 has no groove-width row; the prior attribution to it was fabricated (recorded in-chapter) | Fetch a primary printing these values and naming the measurement convention. |
| groove widths (22/12) | groove widths (22/12) | 22 / 12 | Å | widely repeated textbook pair — different convention | NOT-SOURCED in this pass | not confirmed here | Fetch a primary source and name the measurement convention. |
| ℓ_p | ℓ_p | ~50 (~150) | nm (bp) | dsDNA, ~0.1 M NaCl, ~20–25 °C; tweezers + AFM consensus | OBSERVED-REPLICATED | Peters & Maher 2010, Q Rev Biophys 43(1):23–63, PMID 20478077 | Independent single-molecule measurement outside 45–55 nm at the stated temperature and ionic strength. |
| ℓ_p vs temperature | 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 | OBSERVED-REPLICATED | Geggier, Kotlyar & Vologodskii 2011, NAR 39(4):1419–1426, PMID 20952402 | A measurement showing ℓ_p temperature-independent across 5–42 °C. |
| I/bp | I/bp | 2 | bits/bp | log₂(4); upper bound, assumes no correlation | MODELED | Computed in-chapter | Arithmetic error (the bound itself is definitional). |
| G_human | G_human | 3,054,815,472 (+16,569 mtDNA) | bp | T2T-CHM13, gapless, chr1–22 + X | OBSERVED-REPLICATED | Nurk et al. 2022, Science 376:44–53, doi:10.1126/science.abj6987 | Independent T2T assembly differing >0.1%. |
| f_coding | f_coding | 1–2 (exome ~1.5) | % of genome | human | OBSERVED-REPLICATED | Piovesan et al. 2019, BMC Res Notes, doi:10.1186/s13104-019-4343-8 | Annotation revision moving coding fraction outside 1–2%. |
| pg→bp | pg→bp | 1 pg = 0.978e9 | bp | flow-cytometry conversion | OBSERVED-REPLICATED | Doležel et al. 2003, Cytometry A, doi:10.1002/cyto.a.10013 | Re-derivation of nucleotide-pair molecular weight. |
| G_onion | G_onion | 16.75 pg ≈ 16.4 (≥95% repetitive) | Gbp | Allium cepa 1C | OBSERVED-REPLICATED | onion assembly literature (PMC8496297; PMC11865573) + Doležel conversion | Flow-cytometry re-measurement outside 15–18 Gbp. |
| G_lungfish | G_lungfish | 91 (~90% repeat) | Gbp | Lepidosiren paradoxa — largest sequenced animal genome | OBSERVED-REPLICATED | Schartl et al. 2024, Nature 634:96–103, doi:10.1038/s41586-024-07830-1 | Independent assembly differing >10%. |
| G_fern | G_fern | 160.45 | Gbp/1C | Tmesipteris oblanceolata — current eukaryotic record | OBSERVED-REPLICATED | Fernández et al. 2024, iScience, doi:10.1016/j.isci.2024.109889 | Independent flow cytometry differing >10%. |
| G_Paris | G_Paris | 152.23 pg ≈ 149 | Gbp | Paris japonica 1C | OBSERVED-REPLICATED | Pellicer et al. 2010, Bot J Linn Soc 164(1):10, doi:10.1111/j.1095-8339.2010.01072.x | Re-measurement outside range. |
| nucleosome | nucleosome | 146 bp @ 2.8 Å; 147 bp @ 1.9 Å; 1.65 superhelical turns; histone octamer | bp | crystal structures — different crystals, both real | OBSERVED-REPLICATED | Luger et al. 1997, Nature 389:251–260, doi:10.1038/38444; Richmond & Davey 2003, Nature 423:145, doi:10.1038/nature01595 | A re-refinement changing the wrap length. |
| μ_germline | 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 | OBSERVED-REPLICATED | Kong et al. 2012, Nature 488(7412):471–475, doi:10.1038/nature11396 | Independent trio study outside range at matched paternal age. |
| v_fork,ec | v_fork,ec | ~600 (classic ~1,000) | bp/s | E. coli, in vivo average | OBSERVED-REPLICATED | BNID 109251; Milo & Phillips | In vivo measurement outside 400–1,000 bp/s. |
| v_fork,euk | v_fork,euk | 4–40 (~1 kb/min) | bp/s | eukaryotic replisome | OBSERVED-REPLICATED | BNID 104930, 104935, 104936, 104937 | Outside range. |
| T_S | T_S | ~10 | hours | human S phase | OBSERVED-REPLICATED | BNID 103742, 103741, 102204 | Cell type outside range. |
| N_origins (measured) | N_origins (measured) | 1,000–100,000 (Drosophila ~10,000) | origins | human | OBSERVED-REPLICATED | BNID 107654, 109283 | A measurement excluding the predicted band. |
| u | u | 62 (low visc) / 65 (high visc) | µm/s | migrating human sperm, 37 °C, n = 16 / 19 | OBSERVED-REPLICATED | Smith et al. 2009, Cell Motil Cytoskeleton 66(4):220–236, DOI 10.1002/cm.20345 | Repeat high-frame-rate imaging of the migrating cohort; a mean outside 40–90 µm/s refutes. |
| λ | λ | 39 (low visc) / 18 (high visc) | µm | human sperm flagellar wavelength, 37 °C | OBSERVED-REPLICATED | Smith et al. 2009 | Outside range at stated viscosity. |
| c_wave | c_wave | 890 (low visc) / 200 (high visc) | µm/s | wavespeed = f × λ | OBSERVED-REPLICATED | Smith et al. 2009 | Recompute; c ≠ fλ under stated conditions. |
| L_flag | L_flag | ~41 | µm | human flagellum, tethered-cell imaging | OBSERVED-REPLICATED | Saggiorato et al. 2017 | Independent measurement >1.5× off. |
| µ_buffer | µ_buffer | 0.7 (0.73 ± 0.01 for HTF) | mPa·s | aqueous buffer, 37 °C | OBSERVED-REPLICATED | Saggiorato et al. 2017 | Rheometry outside range at 37 °C. |
| µ_mucus | µ_mucus | ~0.14 (analogue) / ~0.2 (midcycle, Day 0) / ~0.68 (Day 5) | Pa·s | Maxwell fit to measured G′/G″ at ~5 Hz, 37 °C | MODELED | Smith et al. 2009 (rheometry + fit); mucus moduli from Wolf et al. 1977, Fertil Steril 28:47–52 | A direct steady-shear viscosity of periovulatory mucus outside 0.1–1 Pa·s. |
| d_coast | d_coast | ~0.45 Å (4.5 × 10⁻¹¹ m), τ ≈ 0.7 µs | m | Stokes coasting, τ=m/(6πµa); V≈17 µm³, ρ_cell≈1.1×10³, a≈2 µm | MODELED | Computed in-chapter (inputs order-of-magnitude) | Recompute; a measured coasting distance >1 nm refutes. |
| n_dynein | n_dynein | ~67,500 total; ~15,000 active/beat | motors | sea-urchin sperm flagellum; active count is a hypothesis (67,500 × 2/9) | OBSERVED-REPLICATED (total, cryo-ET) / HYPOTHESIZED (active fraction) | Chen et al. 2015, Biophys J 109:2562–2573 | Count in situ; an active fraction ≠ ~2/9. |
| d_dynein | d_dynein | ~8 | nm/power stroke | axonemal dynein, single-molecule | OBSERVED-REPLICATED | Chen et al. 2015 and refs therein | Different step periodicity. |
| n_ATP/beat | n_ATP/beat | (2.3 ± 0.2) × 10⁵ (low visc) → (3.2 ± 0.5) × 10⁵ (0.5 % MC) | ATP/beat | demembranated sea-urchin sperm axoneme, single-cell, [ATP] = 20 µM, viscosity as stated — this quantity is not viscosity-independent | OBSERVED-SINGLE (single study) | Chen et al. 2015 | Bulk S. purpuratus gives ~1 × 10⁵/beat — already a 2.3× discrepancy; carry it. |
| r_ATP | r_ATP | (2.4 ± 0.3) × 10⁶ active; (9.2 ± 0.2) × 10⁵ inactive | ATP/s | demembranated Lytechinus sperm axoneme | OBSERVED-SINGLE (single study) | Chen et al. 2015 | Independent single-cell measurement >2× off. |
| ε_hydro | ε_hydro | 0.004 (low visc) → 0.013 (high visc) | dimensionless | demembranated sea-urchin axoneme, 20 µM ATP, buffer vs 0.5 % MC | OBSERVED-SINGLE (single study — not replicated) | Chen et al. 2015, Table S1 | Independent replication >3× off; not transferable to intact human sperm. |
| ε_chemo | ε_chemo | 0.34 → 0.6 | dimensionless | as above | OBSERVED-SINGLE (single study — not replicated) | Chen et al. 2015 | As above. |
| ε_swim | ε_swim | 0.001 → 0.008 | dimensionless | as above; ε_swim = ε_chemo · ε_hydro | OBSERVED-SINGLE (single study — not replicated) | Chen et al. 2015 | As above. |
| n_mito | n_mito | ~50–75 (~1 mtDNA each) | per cell | human sperm midpiece | OBSERVED-SINGLE (via review; primary count not retrieved in this pass) | Hirata et al. 2002, Reprod Med Biol 1(2):41–47 | Direct EM/qPCR count outside range. |
| toroid | toroid | ~50 (up to ~60) | kb DNA per toroid | protamine–DNA toroid | OBSERVED-REPLICATED | Hud et al. 1995, as reviewed in Balhorn 2007; single-molecule receipt for the toroid mechanism (λ-phage DNA in an optical trap — not sperm chromatin, not a compaction ratio): Brewer, Corzett & Balhorn 1999, Science 286(5437):120–123 | Structural measurement outside range. |
| min. gradient | min. gradient | 0.8 | fM/µm | A. punctulata, resact | OBSERVED-SINGLE (single group — not independently replicated) | Kashikar et al. 2012, J Cell Biol 198(6):1075–1091 | Independent measurement >10× off. |
| N_ejac | N_ejac | median ~255 × 10⁶; 5th-centile 39 × 10⁶ | sperm/ejaculate | WHO reference population (TTP ≤ 12 months) | OBSERVED-REPLICATED | Cooper et al. 2010, Hum Reprod Update 16(3):231–245; WHO 2021, 6th ed. | Re-derive from the reference cohort. |
| N_tube | N_tube | median 251 (range 79–1,386) | sperm in both Fallopian tubes | 10 parous women, ~18 h post-insemination, tubes ligated + flushed | OBSERVED-SINGLE (single study, n = 10 — not replicated) | Williams et al. 1993, Hum Reprod 8(12):2019–2026 | An independent flush study giving a median outside ~50–2,000. |
| T_colony | T_colony | ~25 | years | Pogonomyrmex barbatus, single-queen founding | OBSERVED-REPLICATED | Gordon et al. 2011, Behav Ecol 22(2):429–435, quoting Gordon 1991 | Long-term census showing mean colony persistence outside ~15–30 yr. |
| T_worker,ext | T_worker,ext | ≤ 33 (the paper's summary sentence, covering both spp.: 'about 30') | days after marking | P. barbatus exterior workers, field, 3,521 marked across 38 mature colonies, Rodeo NM, Jul–Aug 1987, checked once daily; max 33 d = a nest-maintenance worker | OBSERVED-REPLICATED | Gordon & Hölldobler 1987, Psyche 94:341–346 | Authors name two biases (paint wear-off; marked ants alive inside) that would underestimate — a mark–recapture design controlling both, finding >>33 d, moves this row. |
| t½_forager | t½_forager | 4.2 | days (half-life, marked foragers) | Cataglyphis bicolor, Southern Tunisia; constant 16.4%/day loss; single study, not independently replicated | OBSERVED-SINGLE — primary read directly in this pass. The widely-cited secondary is wrong: Gordon & Hölldobler 1987 print a '6 day half-life', which is the mean life expectancy wearing a half-life label | Schmid-Hempel & Schmid-Hempel 1984, Ins Soc 31:345–360, DOI 10.1007/BF02223652 | An independent marked-forager census in C. bicolor returning a half-life >2× off. |
| E[life]_forager | E[life]_forager | 6.1 | days (mean life expectancy) | C. bicolor, Southern Tunisia, same study and same 16.4%/day loss; single study, not independently replicated | OBSERVED-SINGLE — primary read directly. This is the number the secondary literature misprints as a 6-day 'half-life' | Schmid-Hempel & Schmid-Hempel 1984 | As above. |
| N_colony | N_colony | 10,000–12,000 (young: 2,000–10,000) | workers | P. barbatus at reproductive age (5 yr) | OBSERVED-REPLICATED | Gordon et al. 2011 | Census outside range for mature colonies. |
| N_brain (IF) | N_brain (IF) | 7.02 × 10⁴ ± 2.4 × 10⁴ (s) | brain nuclei | Novomessor spp. (desert ant), isotropic fractionator — the method of the 32 spp. / 7 superfamilies survey. The SD is ~⅓ of the mean and travels with the value | OBSERVED-REPLICATED | Godfrey, Swartzlander & Gronenberg 2021, Proc R Soc B 288:20210199 | Independent count >2× off under the same method. Not a Pogonomyrmex number — do not transfer across genera. |
| N_brain (sectioned) | N_brain (sectioned) | ≈ 9 × 10⁴ | brain nuclei | Novomessor spp., sectioned brains — the paper's method-validation cross-check on the IF adaptation, not an IF count; agrees with the IF value within ~1 SD | OBSERVED-REPLICATED | Godfrey et al. 2021 | As above. Never print this figure under the IF label. |
| release rate | release rate | 0.25 ± 0.10 | pg·cm⁻¹·s⁻¹ | (Z)-9-hexadecenal from filter-paper trails, I. humilis | OBSERVED-REPLICATED | Van Vorhis Key & Baker 1982 | Independent measurement >2× off. |
| t_decay,attract | t_decay,attract | 33 | min (95% CI of fitted curve reaching no-effect) | Monomorium pharaonis, ECF paper, 10 colonies (~1,500 workers) | OBSERVED-REPLICATED | Robinson et al. 2008, Insectes Sociaux 55:246–251 | Replication on the same substrate outside CI. |
| t_decay,repel | t_decay,repel | 78 | min (same criterion) | M. pharaonis, repellent 'no entry' pheromone, 11 qualifying trials | OBSERVED-REPLICATED | Robinson et al. 2008 | As above. |
| colony mass range | colony mass range | 0.0017 → 3,850 | g | Solenopsis morphospecies → Macrotermes bellicosus | OBSERVED-REPLICATED | Hou et al. 2010 | — |
| M_adult,Trex,published | M_adult,Trex,published | 6,000–8,000; 'Sue' perhaps ~9,500 | kg | adult T. rex — the authors' own stated conclusion | OBSERVED-CONTESTED | Hutchinson et al. 2011, PLoS ONE 6(10):e26037, abstract | An independent volumetric study concluding outside this band. |
| M(PR2081)_min | M(PR2081)_min | 9,502 | kg | T. rex 'Sue', volumetric minimal model — authors' preferred region | OBSERVED-CONTESTED | Hutchinson et al. 2011, Table 6 | Independent volumetric reconstruction outside ~8,000–11,000 kg. |
| M(PR2081)_max | M(PR2081)_max | 18,489 | kg | T. rex 'Sue', volumetric maximal model — authors judge 'less plausible' | OBSERVED-CONTESTED | Hutchinson et al. 2011, Table 6 | As above. |
| ASP | ASP | ~50–60%, up to 79% (Sauroposeidon) | % vertebral volume as air | adult neosauropod cervicals | OBSERVED-REPLICATED | Wedel 2005, as reported by Schwarz-Wings et al. 2009, Proc R Soc B 277(1678):11–17 (they cite it to Wedel; they measured no Sauroposeidon and generated no ASP data — do not name the quoter as the source) | Re-measure Wedel's CT dataset; ASP outside range. |
| ASP (2nd) | ASP (2nd) | 0.50–0.70; specific gravity to 0.2 (vs compact bone 1.8–2.0) | dimensionless | sauropod cervicals | OBSERVED-REPLICATED | Taylor & Wedel 2013, PeerJ 1:e36, DOI 10.7717/peerj.36 | As above. |
| T_body,sauropod | T_body,sauropod | 36–38 | °C | large Jurassic sauropod teeth, clumped-isotope (¹³C–¹⁸O) | OBSERVED-REPLICATED | Eagle et al. 2011, Science 333(6041):443–445, DOI 10.1126/science.1206196 | Independent thermometry outside range. |
| L_neck,max | L_neck,max | ~15.1 | m | Mamenchisaurus sinocanadorum; >6× giraffe | OBSERVED-CONTESTED | Moore et al. 2023, J Syst Palaeontol 21(1), DOI 10.1080/14772019.2023.2171818 | New cervical material; note 2013 estimate was ~12 m. |
| L_neck,giraffe | L_neck,giraffe | 2.4 | m | world-record bull giraffe | OBSERVED-REPLICATED | Taylor & Wedel 2013 | A longer measured giraffe neck. |
| n_cervical | n_cervical | sauropods 13–17 (19 in M. hochuanensis); mammals exactly 7 (sloths/sirenians excepted) | count | — | OBSERVED-REPLICATED | Taylor & Wedel 2013 | A mammal outside the exceptions with ≠7. |
| dP/dz | dP/dz | 77.3 (78.0 at ρ=1060) | mmHg per metre | ρg, ρ_blood ≈ 1050 kg·m⁻³, g = 9.81 — a definition (hydrostatics), not a measurement | MODELED | Computed in-chapter. The ~77 mmHg/m quoted in the giraffe literature is this same ρg, not an independent measurement of it — no cross-check is claimed | Arithmetic error, or ρ_blood refuted. |
| MAP_sauropod | MAP_sauropod | 750 (= 700 static column + ~50 perfusion) | mmHg | ~9 m raised head | MODELED | Seymour 2009, Biol Lett 5(3):317–319 — the in-chapter arithmetic REPRODUCES his construction using his own +50 term: a consistency check on transcription, NOT an independent landing | Re-derive; a different ρ or geometry. |
| MAP_giraffe,heart | MAP_giraffe,heart | 185 ± 41.6 | mmHg | giraffe, at heart level | OBSERVED-REPLICATED | Mitchell et al. 2006, J Exp Biol 209(13):2515 | Independent catheterisation outside range. |
| MAP_giraffe,head | MAP_giraffe,head | 100.3 ± 20.9 | mmHg | giraffe, at head | OBSERVED-REPLICATED | Mitchell & Skinner 1993, via Mitchell et al. 2006 | As above. |
| M_blue,measured | M_blue,measured | — | t | mass of the largest blue whale | NOT-MEASURED | Motani & Pyenson 2024, PeerJ 12:e16978 | Weigh one intact. |
| M_blue,piece | M_blue,piece | ≥136.4 | t | 27.1 m female, weighed in parts (fluid lost) | OBSERVED-SINGLE | Winston 1950, via Motani & Pyenson 2024 | Re-weigh under controlled loss accounting. |
| M_blue,regr | M_blue,regr | 234 (95% CI 187–294); fluid-corrected 252 (CI 201–306) @ 7% blood loss, 272 (CI 217–342) @ 14% | t | 33 m blue whale, length→mass regression. The two fluid-corrected values are separate estimates under separate blood-loss assumptions — never merge them into one interval; 'CI 201–342' is a hull of two intervals, not an interval | MODELED | Motani & Pyenson 2024 | New regression on a larger measured sample; an independent fluid-loss accounting outside 7–14%. |
| M_blue,vol | M_blue,vol | 266–279 | t | 3D volumetric model | MODELED | Motani & Pyenson 2024 | Independent volumetric model outside range. |
| L_blue,max | L_blue,max | 33.26 | m | longest reliably measured blue whale | OBSERVED-SINGLE | Risting 1928, via Motani & Pyenson 2024 | A longer verifiable measurement. |
| TE_trophic | TE_trophic | 10 | % per trophic level | 48 trophic models, 6 aquatic ecosystem types; re-estimated, not assumed | OBSERVED-REPLICATED | Pauly & Christensen 1995, Nature 374:255–257 | Re-estimate from independent models outside ~5–15%. |
| TL_range | TL_range | 1.0 (edible algae) – 4.2 (tunas) | fractional trophic level | 39 commodity groups, global catch 94.3 Mt/yr 1988–91 | OBSERVED-REPLICATED | Pauly & Christensen 1995 | Re-assign trophic levels. |
| [Mb]_cetacean | [Mb]_cetacean | 1.81–5.78 | g Mb / 100 g wet muscle | cetaceans, body mass 70–80,000 kg | OBSERVED-REPLICATED | Noren & Williams 2000, Comp Biochem Physiol A 126(2):181–191 | Measurement outside range under stated method. |
| [Mb]_dolphin,max | [Mb]_dolphin,max | ~6.3 | g Mb / 100 g | striped dolphin, epaxial middle | OBSERVED-SINGLE | Arregui et al. 2021, Animals 11(2):451 | Independent assay >2× off. |
| [Mb]_terrestrial | [Mb]_terrestrial | <~0.5 (ratio 10–30× divers:non-divers) | g Mb / 100 g | non-diving mammals — Kooyman 1989 primary not read here | OBSERVED-REPLICATED (secondary attribution) | Kooyman 1989, cited in the comparative literature | Fetch Kooyman 1989; measure human muscle Mb. |
| [Mb]_human | [Mb]_human | — | g Mb / 100 g | human skeletal muscle | NOT-MEASURED | not sourced in this pass | Fetch a primary value. |
| d_collapse,N₂ | d_collapse,N₂ | ~70 | m | Tursiops truncatus, live, inferred from N₂ washout | OBSERVED-SINGLE | Ridgway & Howard 1979, Science 206(4423):1182–1183 | Repeat washout; a different inferred depth. |
| d_collapse,CT | d_collapse,CT | range 58 (grey seal, 50% TLC) – 133 (harbour porpoise, 100% TLC); per-specimen common-dolphin values NOT-CONFIRMED | m | post-mortem hyperbaric CT, extrapolated to zero gas volume — vessel rated only to 170 m depth-equivalent, so these are extrapolations, not readings. Every value carries a TLC condition. Do not average with the row above | OBSERVED-CONTESTED | Moore et al. 2011, J Exp Biol 214:2390–2397 (abstract only — Table 2 not read in this pass) | In-vivo imaging under pressure reconciling both; fetch Table 2 for per-specimen values. |
| d_dive,max | d_dive,max | 2,992 | m | Ziphius cavirostris, mammalian depth record | OBSERVED-SINGLE | Schorr et al. 2014, PLOS ONE 9(3):e92633 | A deeper tagged mammalian dive. |
| ΔdB_air/water | ΔdB_air/water | 61.58 | dB | 10·log₁₀(20² × 3600): reference-pressure ratio × impedance ratio | MODELED (arithmetic) | Computed in-chapter; cross-checked against Møhl et al. 2003's own 235→173 conversion | Arithmetic error; a different impedance ratio. |
| c_sound | c_sound | 1477 (surface) → 1468 (500 m) | m/s | Norwegian coastal water, measured profile | OBSERVED-SINGLE | Møhl et al. 2003 | Independent CTD profile. |
| z_SOFAR | z_SOFAR | ~750–1,200 (midlat); near-surface polar | m | deep sound channel axis | OBSERVED-REPLICATED (secondary source in this pass) | Ewing & Worzel 1948, GSA Memoir 27; depth via secondary | Fetch a primary sound-speed climatology. |
| r_SOFAR,demo | r_SOFAR,demo | up to 900 nmi (~1,700 km) | km | 1944 R/V Saluda explosive-charge demonstration | OBSERVED-SINGLE | Ewing & Worzel 1948 | Read the primary; a different demonstrated range. |
| c | c | ≈343 | m/s | air, 20 °C, 1 atm; c ≈ 331.3·sqrt(1+T/273.15) | OBSERVED-REPLICATED (standard reference; not primary-sourced in this pass) | standard acoustics | Fetch a primary reference; a measured c outside 330–350 at stated conditions. |
| alpha_atm (25→50 kHz) | alpha_atm (25→50 kHz) | 0.7 → 1.7 | dB/m | 25 → 50 kHz, 20 °C, 50% RH | OBSERVED-REPLICATED | Jakobsen, Brinkløv & Surlykke 2013, Front Physiol 4:89, from Lawrence & Simmons 1982; ANSI 1995 | Re-measure at stated T/RH; values >2× off. |
| alpha_atm (45→90 kHz) | alpha_atm (45→90 kHz) | 1.4 → 4 | dB/m | 45 → 90 kHz, 25 °C, 80% RH | OBSERVED-REPLICATED | as above | As above. |
| A_MEM | A_MEM | 17–25 | dB attenuation of self-generated signal | middle-ear muscle contraction during emission | OBSERVED-REPLICATED (spread real; some sources report ~20–30) | Suga & Jen 1975; Henson 1965 (cited by, not read here) | Measure with stapedius intact vs ablated. |
| AGC | AGC | ~6 | dB sensitivity drop per halving of target distance | approach phase, attributed to middle-ear muscles | OBSERVED-REPLICATED | Jakobsen et al. 2013, citing Suga & Jen 1975 | Measure receiver gain vs range and find no schedule. |
| p@140dB | p@140dB | 200 | Pa (≈0.2% of 1 atm) | p = 20e-6 × 10^(SL/20) at 0.1 m | MODELED | Computed in-chapter | Arithmetic error. |
| miss_distance | miss_distance | ~15–20 | cm | jammed bats; matches ranging-interference prediction | OBSERVED-REPLICATED | Corcoran, Barber, Hristov & Conner 2011, J Exp Biol 214:2416–25 | A method discriminating the three hypotheses and favouring phantom echo or masking. |
| d_detect,moth | d_detect,moth | 20–25 (E. fuscus) vs <1 (E. maculatum) | m | average noctuoid moth's detection distance | OBSERVED-REPLICATED | Fullard & Dawson 1997 | Neurophysiology giving a different threshold; a moth detecting E. maculatum at >5 m. |
| N_cells,Bianconi | N_cells,Bianconi | 3.72 × 10¹³ | cells | standard adult; organ-by-organ bibliographic sum | MODELED | Bianconi et al. 2013, Ann Hum Biol 40(6):463–471 | Independent systematic count outside 2–6 × 10¹³. |
| N_cells,Sender | N_cells,Sender | 3.0 × 10¹³ (2% est. unc.; 14% CV) | cells | 70 kg reference male | MODELED | Sender, Fuchs & Milo 2016, PLoS Biol 14(8):e1002533 | Recount outside stated uncertainty. |
| N_bacteria | N_bacteria | 3.8 × 10¹³ (25% est. unc.; 52% SD) | cells | 70 kg male, mostly colon | MODELED | Sender et al. 2016 | Independent estimate outside stated band. |
| R_B/H | R_B/H | 1.3 (25% unc.; 53% variation) | dimensionless | all human cells as denominator | MODELED | Sender et al. 2016 | Recount outside band. |
| R_B/H,nucleated | R_B/H,nucleated | ~8:1 | dimensionless | nucleated human cells as denominator | MODELED | Computed in-chapter from Sender et al. 2016 | Arithmetic error. |
| m_microbiota | m_microbiota | ~0.2 (0.3% of body mass) | kg wet weight | 70 kg male | MODELED | Sender et al. 2016 | Direct measurement >2× off. |
| V̇O₂,basal | V̇O₂,basal | 250 | mL O₂/min | 70 kg man, basal state | OBSERVED-REPLICATED | Clarke & Sokoloff, Basic Neurochem, 6th ed. 1999 | Indirect calorimetry >20% off. |
| k_O₂ | k_O₂ | 4.82 (≈20.1 kJ/L) | kcal/L O₂ | mixed diet, RQ ≈ 0.82 (fat 4.68, CHO 5.03) | OBSERVED-REPLICATED | standard indirect calorimetry | Bomb-calorimetry value outside 4.6–5.1. |
| P_BMR | P_BMR | ~84 (≈1,735 kcal/day) | W | 70 kg man; from V̇O₂ × k_O₂ | MODELED | Computed in-chapter from Clarke & Sokoloff | Arithmetic error, or V̇O₂ refuted. |
| p_body | p_body | ~1.2 | W/kg | 84 W / 70 kg | MODELED | Computed in-chapter | Arithmetic error. |
| N_neurons | N_neurons | 86.1 ± 8.1 × 10⁹ | neurons | adult male human brain, isotropic fractionator | OBSERVED-REPLICATED | Azevedo et al. 2009, J Comp Neurol 513:532–541 | Independent count outside ±2 SD. |
| N_nonneuronal | N_nonneuronal | 84.6 ± 9.8 × 10⁹ | cells | same | OBSERVED-REPLICATED | Azevedo et al. 2009 | As above. |
| R_glia:neuron | R_glia:neuron | ~1:1 | dimensionless | whole human brain | OBSERVED-REPLICATED | Azevedo et al. 2009 | A count returning ≥3:1 by an unbiased method. |
| f_cortex | f_cortex | 19 | % of all brain neurons | adult male human, isotropic fractionator — the human-specific unbiased count | OBSERVED-REPLICATED | Azevedo et al. 2009 (abstract: 'With only 19% of all neurons located in the cerebral cortex') | Unbiased count outside 17–21%. |
| N_synapses | N_synapses | 1.64 × 10¹⁴ (164 × 10¹², CV = 0.17; textbook summaries span 0.6–2.4 × 10¹⁴) | synapses | human neocortex, n = 5 young male autopsy brains, unbiased stereology | OBSERVED-SINGLE (single study, n = 5; no independent replication located) | Tang et al. 2001, Synapse 41(3):258–273 — primary abstract read this pass | An independent stereological count outside 0.6–2.4 × 10¹⁴; any replication at n > 5. |
| f_brain,mass | f_brain,mass | ~2 | % of body mass | ~1.4–1.5 kg / 70 kg | OBSERVED-REPLICATED | standard anatomy; Herculano-Houzel 2012 | Measurement outside 1.5–2.5%. |
| f_brain,O₂ | f_brain,O₂ | ~20 | % of resting O₂ consumption | 70 kg man, basal | OBSERVED-REPLICATED | Clarke & Sokoloff 1999 | CMRO₂ measurement outside 15–25%. |
| P_brain,CMRO₂ | P_brain,CMRO₂ | ~17 (≈347 kcal/day) | W | from 20% × 250 mL O₂/min | MODELED | Computed in-chapter from Clarke & Sokoloff | Arithmetic error. |
| P_brain,perneuron | P_brain,perneuron | ~25 (516 kcal/day; 25% of TDEE) | W | 86 × 10⁹ × 6 kcal/d per 10⁹ neurons | MODELED | Herculano-Houzel 2012 | Direct human measurement settling the 1.5× gap. |
| N_beats,mammal | N_beats,mammal | 7.3 ± 5.6 × 10⁸ (CV ≈ 77%) | beats/lifetime | 15 mammal species, excluding humans. Provenance, per Levine's own Fig. 1 caption — 'Most coordinates represent average values (4–6)': refs 4–6 are Spector, Handbook of Biological Data (1956); Encyclopaedia Britannica (1971); and White et al. (1938). Species lifespan/HR coordinates not independently traced | OBSERVED-CONTESTED (a loose 'invariant', on averaged and untraced coordinates) | Levine 1997, J Am Coll Cardiol 30:1104–1106 | Expand the species set; a tighter or looser CV; trace the coordinates to primary measurements. |
| N_beats,human | N_beats,human | ~2.9 × 10⁹ (2.945 × 10⁹; ~4× mean, ~4 SD out) | beats/lifetime | 70 bpm × 80 yr | MODELED | Levine 1997 states ~3 × 10⁹ himself at these inputs — recomputed in-chapter as 2.945 × 10⁹ | Arithmetic error; Levine's own stated figure moving. |
| E_threshold | E_threshold | 2.1–5.7 × 10⁻¹⁰ ergs = 54–148 quanta | at the cornea | blue-green, optimal conditions | OBSERVED-REPLICATED | Hecht, Shlaer & Pirenne 1942, J Gen Physiol 25(6):819–840 | Replication outside range. |
| Ṡ_routine | Ṡ_routine | 1 | L/h | working in hot environments | OBSERVED-REPLICATED | Nutritional Needs in Hot Environments (NCBI NBK236240) | Field measurement outside 0.5–2 L/h. |
| Ṡ_max | Ṡ_max | 3.7 | L/h | n = 1 — Alberto Salazar, 1984 Olympic Marathon. A single reported record maximum: one runner, one race, uncorroborated | OBSERVED-SINGLE (single report) | primary: Armstrong, Hubbard, Jones & Daniels 1986, Physician Sportsmed 14(3):73–81; secondary route: NBK236240 | A higher documented rate; any replication at n > 1. |
| E_L(300) | E_L(300) | 2.87 × 10⁻²¹ | J per bit erased | k_B T ln2, T = 300 K | MODELED (computed) | Landauer 1961, IBM J Res Dev 5(3):183–191; k_B exact per SI 2019 | Arithmetic error. |
| E_L(310) | E_L(310) | 2.97 × 10⁻²¹ | J per bit erased | k_B T ln2, T = 310 K (body) | MODELED (computed) | as above | Arithmetic error. |
| P_brain | P_brain | ~20 | W | human brain, ~2% body mass, ~20% of resting metabolism | OBSERVED-REPLICATED (not primary-sourced in this pass) | standard cerebral-metabolism references (Clarke & Sokoloff, Basic Neurochemistry) | Fetch a primary calorimetric/CMR source; a value outside ~15–25 W. |
| E_bit,syn | E_bit,syn | ~10⁴ | ATP per bit | chemical synapse, blowfly retina | OBSERVED-REPLICATED | Laughlin, de Ruyter van Steveninck & Anderson 1998, Nat Neurosci 1(1):36–41 | Independent measurement >10× off under stated conditions. |
| E_bit,graded | E_bit,graded | 10⁶–10⁷ | ATP per bit | graded signals in photoreceptor/interneuron, or spike coding | OBSERVED-REPLICATED | as above | As above. |
| c²/h | c²/h | 1.36 × 10⁵⁰ | bits·s⁻¹·kg⁻¹ | Bremermann's limit | MODELED (computed) | Bremermann 1962, Self-Organizing Systems; c, h exact per SI 2019 | Arithmetic error. |
| m_brain | m_brain | ~1.4 | kg | adult human brain mass, as used for the Bremermann figure | OBSERVED-REPLICATED (standard reference; not primary-sourced in this pass) | standard anatomical references | Fetch a primary source; a value outside ~1.2–1.5 kg. |
| v_myel | v_myel | up to 150 | m/s | myelinated axons | OBSERVED-REPLICATED | Purves et al. 2001, Neuroscience 2nd ed., Sinauer | Measurement outside stated range. |
| v_unmyel | v_unmyel | 0.5–10 | m/s | unmyelinated axons | OBSERVED-REPLICATED | as above | As above. |
| τ_callosal | τ_callosal | 3–9 | ms | fastest cross-brain time, 95th-percentile axons, 14 anthropoid primates over a 97-fold brain-mass range | OBSERVED-REPLICATED | Phillips et al. 2015, Proc R Soc B 282:20151535 (corr. 282:20152620) | An anthropoid with 95th-percentile cross-brain time outside 3–9 ms. |
| τ_callosal,median | τ_callosal,median | 11–38 | ms | cross-brain conduction time for median axon diameters, same 14 anthropoid primates — the bulk of interhemispheric traffic | OBSERVED-REPLICATED | Phillips et al. 2015 | An anthropoid with median cross-brain time outside 11–38 ms. |
| d_callosal | d_callosal | majority < 1 | µm | callosal myelinated axons, all 14 species | OBSERVED-REPLICATED | Phillips et al. 2015 | A species with majority > 1 µm. |
| N_neur,human | N_neur,human | 86 × 10⁹ (cortex ~16 × 10⁹) | neurons | human brain, isotropic fractionator | OBSERVED-REPLICATED | Azevedo et al. 2009, J Comp Neurol 513(5):532–541 | Independent count >2× off. |
| N_neur,elephant | N_neur,elephant | 257 × 10⁹ total; 251 × 10⁹ (97.5%) in cerebellum; cortex 5.6 × 10⁹ | neurons | African elephant | OBSERVED-REPLICATED | Herculano-Houzel et al. 2014, Front Neuroanat 8:46 | Independent count >2× off. |
| N_neocort,pilot whale | N_neocort,pilot whale | ~37.2 × 10⁹ | neocortical neurons | long-finned pilot whale — ~2× the human figure | OBSERVED-REPLICATED | Mortensen et al. 2014, Front Neuroanat 8:132 | Independent count >2× off. |
| N_FlyWire | N_FlyWire | 139,255 neurons; >50 × 10⁶ synapses | — | complete adult Drosophila connectome, proofread | OBSERVED-REPLICATED | Dorkenwald et al. 2024, Nature | Independent reconstruction differing materially. |
| B_sensory | B_sensory | ~10⁹ | bits/s | human sensory data-gathering | MODELED | Zheng & Meister 2025, Neuron 113(2) | Recompute from receptor counts and rates. |
| B_behaviour | B_behaviour | ~10 | bits/s | human behavioural throughput — a literature synthesis, not a new experiment: same paper and same method as B_sensory | MODELED-CONTESTED | Zheng & Meister 2025, Neuron 113(2) (Perspective); contested by Sauerbrei & Pruszynski 2025, Nat Neurosci ('The brain works at more than 10 bits per second') | Carry both. A measure reconciling cognitive throughput and motor control under one accounting. |
sha256 e443dca15319ea0b — of the original file, so what was ingested stays checkable.