# Dyatlov Pass: a physics assessment of the slab-avalanche explanation and its rivals

*Independent replication and stress test of Gaume & Puzrin (2021) and of the rival mechanisms, with reproducible code. Code and figures: `code/physics/` (see its README). Working copies of the raw sources are not included in this folder (file names given in the reference list); the paper, its supplements and its peer-review file are saved under `code/geo/raw/`, the 2022 Comment and Mellor 1975 under `data/`.*

**Scope and honesty notes.** Everything quantitative below was recomputed from the equations printed in the paper's Methods; the authors' own code (Zenodo record 4088052, ref. [Z]) could not be downloaded (Zenodo returned HTTP 504 through the proxy on three attempts). The paper's MPM (material-point-method) avalanche and thorax simulations were **not** replicated; they are cross-checked with lumped-parameter models. Two primary biomechanics sources (Kroell et al. 1974, SAE 741187; Lobdell 1973) are paywalled and were used only through the paper and secondary literature (Kimpara et al. 2003, IRCOBI, open PDF). Pigol'tsyna (2020) was read in the original Russian PDF; Popovnin's findings are known only from press interviews, not from his written report, which is not public. The 30-page Borzenkov rebuttal was read in the dyatlovpass.com English rendering. Slope measurements from a public DEM are in `geo-timeline-weather.md` and are not repeated here.

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## 0. Bottom line

1. **The analytical delayed-release model replicates exactly** (wind-snow height 0.236/0.444 m, delay 7.2/13.5 h, tension crack 4.95 m, width 8.8 m). But with the paper's own snow parameters it works **only in a 2-3 degree band around the assumed 28 degrees** (release window 24.7-29.7 degrees; the forensic 9.5-13.5 h window is hit at 26-28.5 degrees). At 22-23 degrees the slab **never releases** for any wind flux; at 25 degrees it releases only if the wind snow never sinters and then only after >150 h (or with a ~12x larger flux); at 30 degrees it fails while the cut is being made.
2. The paper's snow parameters sit on a knife edge: cohesion 300 Pa gives immediate failure, 440 Pa the published delay, 450 Pa no guaranteed release; +-0.05 m slab thickness, +-1 degree of slope or friction, +-30 kg/m3 density flip the regime or change the delay by factors 3-20. The delay itself is linear in the wind deposition flux Q, and the literature envelope for Q at 9-12 m/s spans **two orders of magnitude** (delay 0.2-20 h). The peer-review file shows the authors conceded this: the paper does not predict the delay, it back-calculates Q from it.
3. **The slope angle is the decisive physical question.** Field values at or near the tent are 16-17 degrees (Borzenkov, winter snow surface), 21 degrees (Popovnin 2019, one point, contested location), 21-22 / 25-26 degrees (Pigol'tsyna, from a 1:10,000 map), ~20 degrees average with metre-scale steps >30 degrees (Puzrin-Gaume 2022 drone DEM, 9 cm), 30 degrees (1959 case file). The model needs a **buried weak layer inclined at >=25-28 degrees over ~7 m above the cut**. Nobody has measured the geometry of buried layers at the site in winter. Everything else about release hangs on that.
4. **The impact physics is permissive, not discriminating.** A 50-200 kg block of wind slab at 1-2 m/s onto a person lying on a firm floor compresses the thorax 20-70 % in a lumped model (the paper's MPM gives 28-34 %); contact pressures are only 25-50 kPa, so rib fractures without skin wounds are exactly what such a load produces. But the same is true of a collapsing snow roof or 3-4 m of static snow on a body against a firm base. The injury physics cannot tell "slab on tent" from "ravine burial". Thibeaux-Brignolle's depressed temporal fracture needs a concentrated load (hard object or fall), not a snow face.
5. **Hypothermia is the one part that is physically overdetermined:** for 0.5-1.0 clo at -25 to -30 degrees C and 5-20 m/s, incapacitation in 0.2-0.9 h and unconsciousness in 0.6-2 h (model; true values perhaps up to 2x longer), consistent with the 1959 medical and search estimates. Wind chill was -36 to -52 degrees C.
6. Rivals scored on physics alone: hypothermia for six deaths (5/5, but it is not a trigger); slab avalanche (release 2/5 on the measured slopes, 4/5 if a 28-30 degree step lies under the site; injuries 4/5); ravine fall or snow-load crushing for the four (3/5); wind-driven tent collapse / katabatic wind (2/5 as a trigger, 0/5 for injuries; unconstrained by any measurement); infrasound (0-1/5).

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## 1. What Gaume & Puzrin (2021) actually claim, number by number

Source: Gaume J., Puzrin A.M., *Communications Earth & Environment* 2:10 (2021), https://doi.org/10.1038/s43247-020-00081-8 [GP21]; Supplementary Information (MOESM3, 20 pp., Notes 1-7) and Peer Review File (MOESM1) linked from the article page; the 2022 Comment [PG22] https://doi.org/10.1038/s43247-022-00393-x (mirrors: https://dyatlovpass.com/puzrin-gaume, https://infoscience.epfl.ch/record/293343); and the authors' Q&A on dyatlovpass.com [QA22].

### 1.1 The four "puzzles" and the claimed answers (GP21 p. 1-2, Fig. 1)
The paper states four objections to the 1959 avalanche verdict: (1) no avalanche signs found 26 days later; (2) mean slope angle below the usual ~30 degree threshold; (3) release 9.5-13.5 h after the cut was made rather than during the cutting; (4) thorax and skull injuries "not typical" for avalanche victims. Fig. 1a-c: the last photograph of the group cutting the platform; the tent 26 days later; the sketch of tent below a "small shoulder", with snow deposition above the cut. The forensic delay (SI Note 1, p. 2, after Buyanov & Slobtsov 2014) is built as follows: sunset at Burmantovo 17:02, so the cut was made "not later than at 4:00 pm"; lanterns found outside the tent imply night; the watches stopped at 05:31 (Dyatlov), 08:14/08:39 (Thibeaux) and 08:45 (Slobodin), taken as ~1 h after death, so death at 04:30-07:30; death 6-8 h after the last meal; survival outside "around 2 to 3 hours"; hence release between 01:30 and 05:30 and a delay of 9.5-13.5 h after the cut.

### 1.2 Slope angle: provenance (GP21 Fig. 2; PG22 p. 1)
* Fig. 2a is an ASTER-GDEM terrain map (30 m class), from which no 28 degree local slope can come. Fig. 2b shows the slope-angle distribution of 139 accidentally triggered avalanches (paper's ref. 11): few below ~28-30 degrees. Fig. 2c: dynamic friction angles from van Herwijnen & Heierli (2009).
* The 28 degrees is an **assumption**: PG22 p. 1: "the topography of the slope is irregular, built of 4-to-6 m-high steps: although the average slope inclination (observed when the steps are covered by snow) is indeed too low for an avalanche to release, we assumed (based on the evidence available at that time), that a locally steeper slope above the tent had an inclination of at least 28 degrees. Such a high angle makes a slab avalanche possible, because a buried weak snow layer would follow this steep terrain."
* PG22 Fig. 2 (drone photogrammetry, summer 2021, 9 cm resolution): "although the average slope angle is around 20 degrees, locally steeper steps have indeed an inclination exceeding 30 degrees".

### 1.3 Snow, weak layer and wind parameters (GP21 Methods and SI Note 6, p. 17-19)
| quantity | value | provenance in the paper |
|---|---|---|
| weak-layer inclination alpha | 28 degrees | assumed (see 1.2) |
| slab thickness at cut h0 / on the upper slope hc | 0.5 m / 0.1 m | tent-photo geometry, Fig. 1c |
| length over which the slab thins lc | 4 m | Fig. 1c/3a |
| slab modulus E', weak-layer shear modulus G, thickness d, characteristic length le0 | 8 MPa, 1 MPa, 0.2 m, 1 m | Methods; Reiweger et al. 2015 / Gaume et al. 2017 class of values |
| slab density rho / wind-snow density rho_w | 300 / 400 kg/m3 | SI Note 6 |
| lateral pressure coefficient K0 | 0.5 | Methods |
| weak-layer friction angle phi / cohesion c | 20 degrees / 440 Pa | phi from the friction distributions (Fig. 2c, Reiweger et al. 2015); c fixed so that the slope is stable before the cut and the cut alone does not fail |
| snow deposition flux Q | 0.008 kg/m/s (paper's Methods write "~0.01") | back-calculated; compared with Sturm & Stuefer (2013) (paper's ref. 15) |
| wind speed considered | 4-10 m/s | SI Note 3, p. 12: Ivdel station 2-4 m/s, Burmantovo up to 9 km/h, "expert-based" 10-15 m/s at the tent |
| slab tensile strength / wind-slab tensile strength | 6 / 10 kPa | Methods (Eq. 44-46) |
| sintering | wind snow either adds only load (no sintering) or full strength (full sintering) -> two bounds | Methods, paper's ref. 16 |

### 1.4 The delayed-release mechanism and its results (GP21 Fig. 3-4, Eq. 1-9 and Methods Eq. 33-43)
A planar weak layer under a slab that thins up-slope as h(x) = h0(1 - x/L0)^2. The cut removes the downslope support, so the shear stress in the weak layer at the cut rises to tau_0; the slab holds if tau_0 < tau_p = c + sigma_n tan(phi). Wind snow then accumulates in the lee of the cut/shoulder as a wedge of height hw0 growing linearly with time at rate Q; failure at the cut occurs when tau_0(hw0) reaches tau_p, and the delay is dt = rho_w hw0 L0 / (3Q) [1 - (1 - lc/L0)^3] (Eq. 9). The condition for a delayed (rather than immediate or never) release is tan(phi_min) < tan(phi) < tan(phi_max), Fig. 4a. Results (GP21 p. 4-5, Fig. 4b-c): hw0 between 0.24 m (no sintering) and 0.44 m (full sintering); delay between 7.2 and 13.5 h, overlapping the forensic 9.5-13.5 h.

### 1.5 Slab size and dynamics (GP21 Methods Eq. 44-46; Fig. 5; SI Note 5, p. 15-16)
Tension crack 4.95 m above the cut (lcw), slab width 8.8 m for a 6.5 m long cut; so a slab of roughly 5 x 9 m, 0.3-0.5 m thick. 2D MPM run with alpha = 28 degrees, h0 = 0.5, hc = 0.1, hw = 0.5 m, lwc = 5.0 m, bed friction angle 22 degrees, mesh 5 mm: impact velocity "up to 2 m/s", blocks "up to 0.5 m3". In the 2022 Q&A [QA22] the slab is "about 5 m x 5 m", it "hit the part of the tent further away from the entrance" (the entrance pole was found standing, with urine traces at the entrance), and "the run-out ... did not exceed 1-2 meters below the tent".

### 1.6 Impact and injury model (GP21 p. 6 and Methods "Impact simulations"; Fig. 5 inset; SI Note 5-6, Fig. SF8-SF9)
A 3D MPM thorax with restrained back, elastic modulus E_body = 0.215 MPa (nu = 0.35), calibrated so that "a 10 kg rigid block (0.15 x 0.15 x 0.06 m) moving with velocity 7 m/s" produces a maximum normalized deflection C = 0.49, "in line with the crash test laboratory experiments of Kroell et al. (1974) with restrained back". Then elastoplastic snow blocks of 0.125, 0.25 and 0.5 m3 at 400 kg/m3 and 2 m/s give C = 0.28-0.34, mapped through the Abbreviated Injury Scale (SI Note 6) to "non-fatal thoracic injuries from moderate to severe". The rigid-back argument (p. 6): "the victims were trapped between the falling slab and the tent floor, which was placed on compacted snow reinforced by skis". The paper does not model the skull fracture; it says a small slab "could have led to severe but non-lethal thorax and skull injuries" (p. 2) and, in the Discussion (p. 7), that "it is also possible that the thorax injuries were the result of a later snow impact in a very steep ravine where the bodies of the victims ... were found".

### 1.7 Stated limitations (GP21 Discussion p. 6-7)
Brittle weak layer (no process zone); no volumetric collapse; 2D geometry; simplified deposition profile; and: "An important source of uncertainty lies in the dependency of the wind deposition flux on the average wind velocity. The available research shows a very wide range of measured deposition fluxes for a relatively narrow range of the average wind velocity." The thorax result is "rather sensitive to the size of the disintegrated slab blocks ... and thus to the relative positions of the bodies".

### 1.8 What the peer review file says (MOESM1)
Reviewer Dieter Issler: the measured Q "in the wind-speed range 4-10 m/s indeed vary by about three orders of magnitude ... this uncertainty makes the agreement between the computed and forensically inferred delay times coincidental" (MOESM1, first-round review). Authors' response: "in the revised paper, we use our model to back-calculate the rate Q from forensic estimated delays. The back-calculated value of Q = 0.008 kg/m/s corresponds to a range of velocities ...". Second round (Issler): the authors "no longer claim that they have reproduced the delay established by the forensic investigation, but instead show that this delay requires a reasonable snow deposition rate in their model". Reviewer Pascal Hagenmuller (second round) objected to the word "delay" ("the triggering factor is snow accumulation and not the cut in the slope ... one may as well define a delay between the beginning of the winter season and the avalanche release") and summarised that the incident "lies in a narrow range of snow conditions (stable enough so that the avalanche does not release when cutting a pit, instable enough so that limited accumulation leads to snow failure)".

### 1.9 The 2022 follow-up expeditions (PG22)
* Expeditions: winter, March 2021 (with RSI film director Matteo Born), and summer, September 2021 (drone photogrammetry), both organised around the RSI documentary; then 28-29 January 2022 by the Ekaterinburg guides Oleg Demyanenko and Dmitriy Borisov.
* Slope: DEM 9 cm resolution; "average slope angle around 20 degrees, locally steeper steps ... exceeding 30 degrees" (PG22 Fig. 2 A-A' section, three candidate tent locations marked).
* Avalanches: Borisov photographed on 29 March 2021 "a peculiar" dark zone below a ridge ~3 km (caption: 2.8 km) from the tent, possibly a crown fracture; Born filmed it on 30 March 2021 (PG22 Fig. 3b-c; the authors write that doubts remain about this one). On 29 January 2022 Demyanenko and Borisov found "two new snow slab avalanches" on an eastern slope <3 km from the tent: the first with a crown "of about 1 m", the second, in the middle of the slope, with a smaller crown "close to the one predicted in our model", which "slid along a smooth weak interface with an older compacted snow and was very likely triggered by a local cornice fall"; it "was practically invisible after less than an hour, as it was covered by the wind-transported snow" (PG22 p. 5, Fig. 3d-e, Supplementary Movie 2). The authors concede the differences: "slab softer, slope steeper, not undercut, trigger different" [QA22].
* Experts: Popovnin (MSU) "confirmed that the assumptions on the snow properties that we used in our models are consistent with his measurements during a winter expedition to Dyatlov Pass in 2019"; Pigol'tsyna (Voeikov MGO) reported snow cover above the tent >150 cm, winter snow transport 600-1000 m3/m, and a best estimate of 9-12 m/s wind above the tent (PG22 p. 4).
* A further slab avalanche ~700 m from the tent on Kholat Syakhl was photographed by Borisov on 7 January 2023 (dyatlovpass.com "Avalanche 2023" page [DP-AV23]).

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## 2. Replication and stress tests (Part B)

All numbers here come from `code/physics/` (`gp_model.py`, `slab_release.py`, `slab_impact.py`, `hypothermia.py`; logs `*_results.txt`).

### 2.1 Exact replication (`gp_model.py`, `slab_release_results.txt` section 0)
L0 = 7.236 m, lambda0 = 52.4, r1 = 7.75; phi_min = 18.11 degrees, phi_max(lambda0) = 22.91 degrees, so the paper's phi = 20 degrees lies inside the delayed-release band; hw0 = 0.236 / 0.444 m (paper 0.24 / 0.44); delay 7.21 / 13.55 h (paper 7.2 / 13.5); tension crack 4.95 m (paper 4.95); width 8.81 m (paper 8.8); slab mass 7.2 t in 20.6 m3 (with hw0 = 0.5 m as in the MPM). **The published numbers are reproduced to the quoted precision.**

### 2.2 Slope dependence (Fig. `fig_B1_delay_vs_slope.png`, `fig_B1_regime_map.png`)
With every other parameter as published:

| weak-layer slope | regime | wind-snow height needed | delay (Q = 0.008) |
|---|---|---|---|
| 22 degrees | never releases: even an unlimited wind load cannot bring the weak layer to its peak strength | - | - |
| 23 degrees | never releases | - | - |
| 25 degrees | only if the wind snow does not sinter | >= 5.2 m (!) | >= 159 h |
| 28 degrees | delayed release | 0.24-0.44 m | 7.2-13.5 h |
| 30 degrees | fails at the cut (while digging) | 0 | 0 |

The regime map (Fig. B1 regime map, slope vs friction angle, c = 440 Pa) shows the delayed-release band is 2-3 degrees wide at any slope; for the paper's phi = 20 degrees the release window is 24.7-29.7 degrees and the 9.5-13.5 h forensic window is met at 26-28.5 degrees depending on Q (0.002-0.064 kg/m/s). At 25 degrees the forensic window can be met only with no sintering and a flux ~12x the paper's (Q ~ 0.1 kg/m/s, the upper Sturm-Stuefer envelope at ~6 m/s). **Answer:** 9-13 h release after the cut is possible at 28 degrees, marginal at 26-27, impossible at 22-23 and 30 degrees with the published snow parameters.

### 2.3 Which parameter dominates (`slab_release_results.txt` section 4, Fig. `fig_B1_sensitivity.png`)
One-at-a-time changes around the published point:
* cohesion c: 396 Pa -> delay 0.6 h; 440 -> 7.2-13.5 h; 484 -> 13.8 h to never. c = 300 Pa: failure at the cut; c = 450 Pa: no upper bound (fully sintered wind snow never fails).
* slab thickness h0: 0.45 m -> 15 h to never; 0.55 m -> immediate failure.
* slope +-1 degree: 27 -> 15.6 h to never; 29 -> 2.6-2.9 h. Friction +-1 degree: the mirror image.
* density rho +-30 kg/m3: 270 -> 13 h to never; 330 -> 1.3-1.4 h.
* le0 +-0.1 m: 4-4.7 h / 10.9 h to never. K0 +-0.05: 9.8 h to never / 4.6-6.0 h.
* Q +-10 %: 8.0-15.1 h / 6.6-12.3 h (exactly linear).

So the *regime* is controlled by the strength margin at the cut (c, h0, alpha, phi, rho enter through tau_0/tau_p, and a few per cent decide between "fails while digging", "delayed" and "never"), and, once in the delayed regime, the *time* is set linearly by Q. The model does not have a robust 9-13 h prediction; it has a tunable one.

### 2.4 Wind flux Q against measurements (`slab_release_results.txt` section 3, Fig. `fig_B1_delay_vs_Q.png`)
Sturm & Stuefer (2013) bracket measured drift fluxes by Q_upper = 1.3e-3 w^2.5 and Q_lower = 3.3e-9 w^6.5 (kg/m/s, w in m/s, w > 5). At Pigol'tsyna's 9-12 m/s the model's upper-bound delay ranges from 0.17-0.34 h (upper flux) to 3-21 h (lower flux). The paper's Q = 0.008 kg/m/s equals the lower envelope at ~9.6 m/s or the upper envelope at ~2 m/s. Borzenkov's typical winter winds of 12-15 m/s (often 20-25) would, on the lower envelope, give Q = 0.03-0.9 kg/m/s and delays of minutes to 3 h. **The delay is not constrained by any wind measurement; Issler's objection stands.** Note also that the paper's own SI Note 3 gives station winds of only 2-4 m/s (Ivdel) and "up to 9 km/h" (Burmantovo), so the 4-10 m/s range used is an expert estimate.

### 2.5 Can it still release at 22-23 degrees? (`slab_release_results.txt` section 5, Fig. `fig_B3_lowslope_window.png`)
Scanning friction angle 5-32 degrees and cohesion 0-1500 Pa at Q = 0.008 kg/m/s:
* 22 degrees: delayed release exists only for phi <= 16.8 degrees; the 9.5-13.5 h window needs phi 5-15.2 degrees with c 400-988 Pa (the two are locked: lower friction needs higher cohesion).
* 23 degrees: phi 5-16.2 degrees, c 400-1025 Pa. 25 degrees: phi <= 18 degrees, c 400-1125 Pa. 28 degrees: phi 5-20.2, c 425-1262 Pa.
Are such weak layers realistic? Reiweger, Gaume & Schweizer (2015, GRL 42:1427) fit friction angles of 12-28 degrees (mean ~20) and cohesion ~0.17 kPa to weak-layer failure data; van Herwijnen & Heierli (2009, GRL 36:L23502) measured crack-face friction of ~0.6 sigma (~30 degrees) in 34 field experiments (that is a post-collapse dynamic value, not the static one the model needs); Jamieson & Johnston (2001, Ann. Glaciol. 32) report shear-frame strengths of persistent weak layers of 0.1-2 kPa, facets and depth hoar 25-50 % weaker than the rest; Casassa, Narita & Maeno (1991, J. Glaciol. 37) found snow-on-snow *sliding* friction dropping from 0.47 at 0 degrees C to ~0.22 at -25 degrees C, but at 0.9-25 m/s, i.e. for the run-out, not for the static failure. So a release at 22-23 degrees requires a weak layer in the **low tail of measured friction (<= 15-16 degrees) combined with unusually high cohesion (0.4-1.0 kPa)**: not impossible for depth hoar under a stiff slab, but no such layer has ever been observed at the site (Borzenkov's pits 2010-2019 found none; Popovnin reported only densities). Hard to rule out, impossible to assert.

### 2.6 Propagation scale check (`slab_release_results.txt` section 6)
The anticrack critical crack length (Gaume et al. 2017, TC 11:217) for the paper's slab is 0.16-0.45 m for slopes 21-30 degrees and slab depths 0.5-1 m, far shorter than the 6.5 m cut. Once the weak layer yields over the cut, self-propagation is plausible; the delay mechanism, not propagation, is the weak link.

### 2.7 Geometry check against measured snow profiles
The model needs the slab to thin up-slope from the cut (0.5 m at the tent to 0.1 m at 4 m) with wind snow filling the lee of the cut. Borzenkov measured in February 2014 a snow depth of 80 cm at the tent site rising to 2.2-2.5 m about 20 m up-slope towards the NE spur, all hard crust [BORZ22, "Snow" section]; Pigol'tsyna's computed profile (Trudy GGO 597, Table 4) also rises from 150 cm at the tent to 250 cm 50 m above it, with the maximum-accumulation zone ~50 m above the tent. Total depth is not slab thickness above a weak layer, so this is not a refutation, but it means the only measured winter geometry at the site is the opposite of the sketched one: the site is on the *receiving* side of the drift, with the thickest snow above it, not a thin cover below a small shoulder. A stratigraphic survey (Section 5) would settle this.

### 2.8 Impact: velocity (`slab_impact_results.txt` A, Fig. `fig_B2_velocity.png`)
Energy balance v = sqrt(2 g s (sin a - tan(phi_bed) cos a)) with the MPM's bed friction of 22 degrees: at 28 degrees, 1.5 / 2.1 / 3.3 m/s after 1 / 2 / 5 m of sliding (so the paper's "<= 2 m/s" corresponds to <= 2 m of sliding); at 25 degrees 1.0-2.4 m/s; at 23 degrees 0.6-1.4 m/s; at 21 degrees the slab does not move at all with 22 degree bed friction (1.2-2.7 m/s with 17 degrees). Run-out on the flat cut platform: deceleration mu g = 3.9 m/s2, so a 2 m/s slab stops in 0.5 m and a 3.3 m/s slab in 1.4 m: the "1-2 m run-out" of [QA22] is physically consistent *provided the slab lands on the flat platform*; on the 20 degree slope below, the stopping distance would be 6-16 m.

### 2.9 Impact: thorax (`slab_impact_results.txt` B, Fig. `fig_B2_chest_deflection.png`)
A 1-DOF fixed-back thorax (spring k1, cubic stiffening, damper 300 Ns/m, bottoming stop at 60 % compression) is hit by a crushable snow block (contact force capped at crushing strength x 0.12 m2 chest area).
* Calibrated exactly as the paper (10 kg rigid at 7 m/s -> C = 0.49): k1 = 15.8 kN/m, a soft chest, in the quasi-static range measured in CPR (5-25 kN/m). **Caveat on the paper's calibration point:** Kroell's fixed-back series used 19.5-23.1 kg pendulums at 4.9-7.2 m/s (as reported by Kimpara et al. 2003 and other secondary sources; the SAE report itself was not read), 2-2.5x the impact energy of "10 kg at 7 m/s". If the paper's thorax was calibrated to a 10 kg impact that Kroell did not perform, its body modulus is too soft and its snow-block deflections are overestimated. A second calibration to Kroell's actual 23.1 kg at 7.2 m/s (k1 = 84 kN/m) is therefore carried alongside; the truth is presumably between the two.
* Results at 2 m/s, 400 kg/m3 (the paper's case): 0.125 m3 (50 kg): C = 0.41 (soft) / 0.21-0.22 (stiff); 0.25 m3: 0.57 / 0.31; 0.5 m3 (200 kg): 0.60-0.69 / 0.21-0.45. The paper's MPM values 0.28-0.34 fall inside this bracket. Threshold velocity for C >= 0.34 (50 % probability of >= 7 rib fractures in males, Kimpara et al. 2003 pooled Nahum/Kroell/Stalnaker data): 0.8 m/s (soft) to 1.6 m/s (stiff) for a 200 kg block; 1.7-3.2 m/s for a 50 kg block.
* Snow crushing strength matters only for a stiff chest: with the soft calibration even 30 kPa snow (3.6 kN cap) drives the chest to bottoming; with the stiff calibration 30 kPa snow caps C at 0.21 (rib fractures possible, flail chest unlikely) while >= 100 kPa (four-finger to pencil hardness, typical of a 400 kg/m3 wind slab) lets C reach 0.45-0.6. McElwaine's remark that the block would have to be "incredibly stiff and moving at some speed" (National Geographic, Jan 2021) is therefore half right: hardness of the order of a wind slab suffices, speed of 1-2 m/s suffices, but only if the body lies on a firm base and the block's momentum is taken by the chest.
* Contact pressure at the chest is 25-50 kPa (3-6 kN over 0.12 m2): two to three orders of magnitude below what lacerates skin. "Multiple rib fractures with no external injury" is the signature of a broad, heavy, low-velocity impactor; it does not identify the impactor.
* Comparison with the autopsies (dyatlovpass.com/death [DP-DEATH]): Dubinina, ribs 2-5 right and 2-7 left, two fracture lines each, haemorrhage into the heart, death "10-20 minutes" after injury per Vozrozhdenny; Zolotaryov, ribs 2-6 right, two lines; these bilateral/two-line patterns imply large (>= 35-40 %) compression, C values my model reaches with 100-200 kg blocks at 1-2 m/s or, quasi-statically, with 1.5-2.5 kN on the sternum. Slobodin: 6 x 0.1 cm frontal crack, compatible with a fall or a modest blow. Thibeaux-Brignolle: multi-fragment depressed fracture of the right temporal bone into the frontal and sphenoid, which the examiner attributed to a great force, not to a fall from one's own height.
* Skull (`slab_impact_results.txt` D): temporo-parietal fracture needs 2.5-10 kN (mean 5.2 kN, Allsop et al. 1991; 5.6-9.9 kN, Yoganandan et al. 2004). A snow face can transmit at most sigma_c x A: 0.06-0.3 kN at 30 kPa, 0.2-1 kN at 100 kPa, 0.6-3 kN at 300 kPa over 20-100 cm2. A snow block cannot produce Thibeaux-Brignolle's injury unless the head is pressed against a hard object (Buyanov's camera-as-pillow, a rock, a ski) or the "snow" is ice-hard. A fall of 2-3 m onto a rock edge in the ravine (6-8 m/s head-first is not needed; 1-2 m onto a rock suffices) does it easily.
* The whole block momentum was assigned to the chest; a real slab face spans chest, pelvis and legs and part of it is carried by the floor, so chest deflections for a given block are upper estimates. That reinforces, not weakens, the conclusion that any 100-300 kg of hard snow moving at 1-2 m/s is enough.

### 2.10 Quasi-static burial (`slab_impact_results.txt` C)
3-4 m of 400 kg/m3 snow is 11.8-15.7 kPa, 1.4-1.9 kN on a 0.12 m2 chest: quasi-static compression of 34-42 % on the soft calibration, 8-11 % on the stiff one. CPR compressions of 5-6 cm (25-30 %) fracture ribs in roughly a third of mostly elderly patients; young adults tolerate more. So the prosecutor's "three to four metres of snow, about half a tonne" (Kuryakov, 11 July 2020 [RIA20]) can break ribs, especially against stones or a ledge, but it is not a certain mechanism; a *collapsing* roof (a 1 m slab dropping 1 m gives ~4 m/s) is more than sufficient.

### 2.11 Hypothermia (`hypothermia_results.txt`, Fig. `fig_B4_survival.png`)
* Wind chill (Osczevski & Bluestein 2005): -36 degrees C at -25/5 m/s, -40 to -45 at -25/10-20 m/s, -42.5 at -30/5 m/s, -47 to -52 at -30/10-20 m/s: exposed skin freezes in 2-10 min. Pigol'tsyna's own computed wind chill at the tent went from -30 degrees C at 19:00 to -50.5 degrees C at 07:00 (Trudy GGO 597, Table 3).
* A single-compartment Tikuisis-type heat-balance model (resting metabolism, shivering up to 150 W/m2 with 6 h endurance, tissue insulation 0.09 m2K/W, wind penetration of clothing) gives, for 0.5-1.0 clo, dry, at -25 to -30 degrees C and 5-20 m/s: time to 34 degrees C core (incapacitation, confusion) 0.2-0.9 h; to 30 degrees C (unconsciousness) 0.6-2.0 h; to 28 degrees C 0.7-2.4 h. Walking (150 W for 1.5 h) adds 20-40 %; wet clothing removes 30 %. Against Tikuisis' (1995) published anchors the model is 25-30 % pessimistic for nude subjects and 3-4x pessimistic for clothed ones in light wind (2.7 vs 8.6 h at -30 degrees C), so treat the clothed numbers as lower bounds: the honest range for unconsciousness is roughly 1-4 h. This is consistent with the 1959 material as summarised in the paper's SI Note 1 (search-party estimate of 2-3 h survival; watches stopped 05:31-08:45, taken as ~1 h after death; death 6-8 h after the last meal) and with the finding of the three on the slope in postures of attempted return. What the model cannot capture: individual variation (Dubinina, small, 20; Zolotaryov, 38), exhaustion after exertion, frostbite of hands ending any purposeful action long before core hypothermia, huddling and shelter in the ravine den, injuries and shock, and paradoxical undressing (reported in a substantial minority of lethal hypothermia cases and irrelevant to the question of why they left the tent).

---

## 3. The strongest objections, quantitatively

### 3.1 Slope: reconciling 16-17, 21, 25-26 and 28-30 degrees (the decisive question)
* **1959 case file: 30 degrees** (the site protocol, quoted by Lenta.ru 2 Feb 2024 as "по протоколу — в 30" [LENTA24]); this was an estimate by eye, not a measurement. The 22-23 degree figure often quoted against the paper is not in the case-file pages read here; it matches the later measured/mapped values (Pigol'tsyna's 21-22 degrees on the N side; the 2019 measurement of 21 degrees).
* **Popovnin (MSU), 18 March 2019, for the prosecutor's re-investigation: 21 degrees** ("конкретно там угол склона — 21 градус"; lower limit for avalanche formation 15 degrees, most avalanches 25-35 degrees; upper snow density 0.40 g/cm3; total snow <= 160 cm; a stone ridge under the snow at the tent site probed; conclusion nevertheless "однозначно в лавиноопасном месте") [KP-POP19]. Komsomolskaya Pravda later reported that he measured at the journalists' presumed tent site, while the prosecutors' geodesists placed the tent ~100 m to the NE, and that the prosecutor's map carries three candidate sites [KP-POPCRIT]. Lenta.ru 2024 repeats "фактический уклон 21 градус" for the tent 300 m from the summit [LENTA24].
* **Pigol'tsyna (Voeikov MGO, 2020), from the 1:10,000 map: 25-26 degrees NW of the tent, 21-22 degrees on the N side** [PIG20]; her snow depths are computed from station data and a transport model (600-1000 m3/m per winter after Mikhel & Rudneva 1967), not measured.
* **Kuryakov's press conference, 11 July 2020: "25 degrees per the experts", a snow "cornice" 50 m above the tent** [KP20a], which contradicts his own expert's 21 degrees.
* **Borzenkov (six winter expeditions 2012-2019): snow-surface slope 16-17 degrees along the whole slope, ~20 degrees in the last 5 m below the shoulder, +-1-3 degrees; steps of 28-30 degrees are no more than 5-6 m long** [BORZ22].
* **Puzrin-Gaume 2022 drone DEM: ~20 degrees average with steps >30 degrees over a few metres; tent location uncertain (three candidates)** [PG22 Fig. 2].
* **Gaume-Puzrin 2021 model: 28 degrees, assumed** [PG22 p. 1].

Physically these are answers to different questions. 16-23 degrees describe the winter *snow surface* or the *average ground*, and the model itself agrees that the average is too low. 28-30 degrees describes the *ground steps*. The model needs the *buried weak layer* to be inclined at >= 25-28 degrees over the L0 ~ 7 m above the cut where the stress concentrates. A weak layer that follows a 4-6 m step at 30 degrees would work (marginally, given L0 = 7 m); one that follows the smoothed snow surface at 17-21 degrees cannot fail in this model for any wind load (Section 2.2). Whether early-February stratigraphy at the tent site follows the steps or the surface has never been measured; Borzenkov's 2014 profile (thickness rising 0.8 -> 2.5 m over 20 m up-slope, hard crust throughout) suggests the steps are buried under drift by mid-winter, which is also what Pigol'tsyna's 600-1000 m3/m transport implies and what PG22 itself says ("the steps are covered by snow"). **On the evidence available, the 21 degree measurement and the 28-30 degree assumption cannot be reconciled by argument; only a winter stratigraphic survey of the actual site can (Section 5, Q1-Q2).**

### 3.2 No avalanche debris, tent under only 15-20 cm of hard snow
Slobtsov (case file pp. 298-300): 15-20 cm of hard wind-packed snow on the tent, no footprints near the tent, tracks from 15-20 m below [DP-CF-SLOB]. Maslennikov: north-side guy lines disrupted, rear half covered, "snow was not much" [DP-CF-MASL]. The model's slab is 12-20 m3; spread over the ~5 x 9 m footprint it is 0.3-0.5 m thick, i.e. a deposit that 26 days of 10-15 m/s winds could erode to the 15-20 cm found, or that never existed. The January 2022 observation that a small slab "was practically invisible after less than an hour" [PG22] shows trace erasure is real. **Not decisive either way**; it removes the "no debris" objection without adding support.

### 3.3 Intact entrance pole and guy lines; footprints only from 15-30 m below
Karelin ("Avalanche is a myth", dyatlovpass.com [DP-KAR]): entrance pole standing with its guys intact; the rear pole only tilted; a pole can only fall after a guy fails. [QA22] answers that a ~5 x 5 m slab hit the far end; the standing entrance pole is consistent with that. Quantitatively a 4-7 t slab at 1-2 m/s carries 4-14 kN s of momentum; the canvas and the two ski-pole supports would not stop it, the bodies and the platform would, so a half-collapsed tent with the far guys torn is what either a slab or a 20-25 m/s gust (dynamic pressure 250-400 Pa on ~5 m2 of tent side, 1.3-2 kN) leaves. Footprints starting 15-30 m below are consistent with hard wind crust near the tent or with a slab deposit. **No discrimination from physics.**

### 3.4 The injuries do not match "impact at the tent" in location and timing
Two of the four injured were found 1.5 km away in the ravine; Dubinina's injuries were judged survivable for 10-20 min. Walking 1.5 km with a bilateral flail chest and then living 10-20 min is not credible; either they were carried, or the chest injuries happened in the ravine (as the paper itself allows, p. 7, and as the 2020 re-investigation concluded). The physics (Section 2.9-2.10) is compatible with both places. **This is the strongest objection to the injury half of the paper, and it is forensic, not physical.**

### 3.5 The delay is fitted, not predicted (Section 2.3-2.4)
Established in the peer-review file and by the sensitivity analysis. A 9.5-13.5 h delay is *achievable* in the model; it is not *implied* by any measured quantity.

### 3.6 Borzenkov (April 2022, https://dyatlovpass.com/borzenkov), claim by claim
| Borzenkov's claim | status after the calculations |
|---|---|
| Snow-surface slope 16-17 degrees, ~20 degrees near the shoulder, steps of 28-30 degrees only <= 5-6 m long | Survives as a description of the winter surface; agrees with the DEM average of ~20 degrees. Whether a 5-6 m step at 28-30 degrees is enough is open (the model's stress-concentration length is ~7 m). |
| Snow density at the tent site 458 kg/m3, constant across years; hard crust; loose snow <= 30 cm | Survives as a measurement (matches Popovnin's 400 kg/m3). It hurts the model: with rho = 330 instead of 300 the delay is already 1.3 h; at 400-460 kg/m3 the published parameter set fails at the cut unless c or phi are re-tuned upward. |
| Depth 0.8 m at the tent rising to 2.2-2.5 m 20 m up-slope (Feb 2014) | Survives; the only measured winter profile; opposite to the up-slope-thinning slab in Fig. 1c/3a, though not a refutation (slab thickness above a weak layer is not total depth). |
| Pits in 2010, 2014, 2015, 2019: strong bonding, no weak layer, no depth hoar; March 2019 shear test: shear force > 10x the driving force | Survives for those winters. The model requires the weak layer to be within a few per cent of failure at the cut (Section 2.3); a 10x margin is a different snowpack. But four winters do not characterise 1959, and the paper's SI Note 3 argues from the 1959 temperature swings that depth hoar formed. Unresolved. |
| Winds usually 12-15 m/s, often 20-25, up to 36 m/s | Survives (Pigol'tsyna computed 9-12; Kuryakov claimed 19-20 gusting 35 during the descent). Stronger wind shortens the model delay to minutes-hours (Section 2.4), so his wind climatology is an argument *against* a 9-13 h delay, not for a stronger avalanche. |
| Borisov's 29 March 2021 site is a 30-45 degree lee cliff 3 km away with 1 m slabs, unlike the tent slope | Survives; PG22 concedes the differences. Those observations refute "avalanches never happen here", not "no avalanche at the tent". |
| Popovnin measured one point for 1-3 h at a contested location; tent location uncertain +-50-100 m | Survives, and cuts both ways. |
| Slab, if any, would have left deposits; no runout | Does not survive as stated: a 12-20 m3 slab stopping on the flat platform (Section 2.8) leaves 0.3-0.5 m that 25 days of wind can rework; PG22's <1 h erasure is a direct observation. |
| The 28-30 degree slope of the paper is fiction | Half survives: it is an assumption, admitted in PG22; whether a step of that inclination underlies the actual tent site is unknown. |

### 3.7 The prosecutor's 2019-2020 physics
Kuryakov, 11 July 2020 [RIA20, MEDUZA20, KOMM20, KP20a, KP20b]: an avalanche ("snow board"); the group left through cuts and went 50 m to a stone ridge, "a natural avalanche limiter"; visibility 16 m (KP: 6-11 m); they could not find the tent; temperatures -40 to -45 (KP: wind chill -46 by 03:00); tent site 25 degrees "per the experts" with a cornice 50 m above; injuries to the ravine four from "three-four metres of snow, about half a tonne" pressing from all sides ("tennis-ball" analogy), with Rosreestr giving 11 degrees at the bodies and a 2 m stream-bank cliff that "in winter with the snow cover can reach 3 m and more"; wind 19-20 m/s gusting 35 during the descent. Pigol'tsyna's published tables give air -17.9 (19:00), -22.5 (23:00), -28.7 (03:00), -31.7 degrees C (07:00) with 9-12 m/s at the tent (10-15 m/s on the plateau for three days; >= 10 mm precipitation 31 Jan-1 Feb) [PIG20 Tables 2-3]. Internal inconsistencies: 21 degrees (Popovnin) vs 25 degrees (Kuryakov); 9-12 m/s (Pigol'tsyna) vs 19-20 gusting 35 (Kuryakov). The 50 m, 16 m and 6-11 m figures are assertions without a stated method; the blindfold experiment (a man and a woman walked 30 m from the tent and could not find it) is not a measurement of 1959 visibility. The "half a tonne" is a column of 3-4 m x 400 kg/m3 over ~0.35 m2, i.e. 12-16 kPa, the same pressure as in Section 2.10.

---

## 4. Rival mechanisms scored on physics alone (0 = physically impossible or unconstrained, 5 = quantitatively established)

| mechanism | what physics requires | quantitative verdict | score |
|---|---|---|---|
| **Delayed wind-slab release onto the tent** (Gaume-Puzrin 2021) | weak layer at >= 25-28 degrees over ~7 m above the cut, strength margin of a few %, Q ~ 0.01 kg/m/s; then 100-200 kg blocks at 1-2 m/s on bodies against a firm floor | release: replicates only on the assumed slope and tuned parameters; impossible on the measured 16-23 degrees with published parameters; the delay is fitted. Injuries: fully sufficient for the rib fractures, insufficient alone for the temporal skull fracture | release 2/5 (4/5 if a 28-30 degree step is shown under the tent); injuries 4/5 |
| **Small snow slide / "snow board" onto the tent end** (Maslennikov 1959; Buyanov & Volodicheva 2011-2014: 300-400 kg/m3 slab over 200-250 kg/m3 base, slope 15-20 degrees, 1-2 m snow [BUY]) | same release problem on a 15-20 degree slope, without a delay mechanism | on a 15-20 degree weak layer a hard slab does not fail in any static model unless friction is < ~15 degrees; if it does move, the injury physics is identical to the row above | 2/5 |
| **Katabatic / fall wind, sudden storm collapsing the tent** (Holmgren & Liljegren 2019 [DP-SWE]; Anaris 24 Feb 1978: -15 degrees C, 6 m/s rising to 20-25 m/s, 8 of 9 dead in a 0.8 m ditch with 4-6 m drifts 15-20 m away, rescue gear unopened because of frozen hands [IKAR18, SV-WIKI]) | 20-25 m/s at the tent: dynamic pressure 250-400 Pa, 1.3-2 kN on the tent side, enough to flatten a ski-pole tent and to make flight plausible; explains none of the fractures | not a mechanically implausible trigger, but no measurement supports 25 m/s that night (Pigol'tsyna computed 9-12; the paper's SI cites 2-4 m/s at Ivdel), and true katabatic flows need a cold plateau or glacier the Urals do not have; a synoptic gust front is the realistic version. Wind chill -45 to -65 degrees C would kill on the Anaris time scale (Section 2.11) | trigger 2/5, injuries 0/5, deaths 4/5 (through hypothermia) |
| **Infrasound / Karman vortices from the summit** (Bedard via Eichar 2013) | shedding frequency f = St U/D ~ 0.2 x 10 m/s / 100-300 m = 0.007-0.02 Hz at low amplitude; a physiological effect of such infrasound at these levels is undocumented (Snopes review [SNOPES]) | no measurement, no established effect, no injuries explained | 0-1/5 |
| **Hypothermia with paradoxical undressing** (cause of death of six; behaviour) | 0.5-1 clo at -25 to -30 degrees C, 5-20 m/s | incapacitation 0.2-0.9 h, unconsciousness 0.6-2 h (model, lower bounds), wind chill -36 to -52 degrees C; consistent with all six hypothermia autopsies and the return attempt; explains nothing about leaving the tent | 5/5 as cause of death; 0/5 as trigger |
| **Ravine: fall from the bank or snow-load crushing** (prosecutor 2020: den collapse, up to 3 m of snow) | fall of 2-3 m onto stones: 6-8 m/s, ample for both chest and depressed temporal fractures; static 3-4 m burial: 1.4-1.9 kN on the chest, 34-42 % (soft) or 8-11 % (stiff) compression; a collapsing 1 m roof: ~4 m/s, ample | fully sufficient for all four sets of injuries, and the only mechanism that naturally produces Thibeaux-Brignolle's fracture; consistent with Dubinina's 10-20 min survival at the place she was found | 3/5 (sufficient, not demonstrated) |

---

## 5. Physically decisive questions and the measurement that settles each

1. **Where exactly was the tent?** Everything else (21 vs 28 degrees, the stone ridge, the "cornice 50 m above") depends on a location known to +-50-100 m. Settle by photogrammetric matching of the 1959 search photographs (skyline and boulder field) against the 9 cm drone DEM already produced in 2021; publish the coordinates.
2. **Is there a >= 25-28 degree ground step of >= 5-7 m length directly above that location?** The 2021 DEM answers this today for each of the three candidate sites; the section in PG22 Fig. 2 should be re-cut through the matched location and the profile published with numbers.
3. **Does the early-February snowpack there have a weak layer that follows the step rather than the smoothed surface, with friction <= 16-20 degrees and cohesion 0.3-1 kPa?** Settle by a winter campaign (late January) with ground-penetrating radar or trenches on a line 30 m up-slope of the site to map layer geometry, plus shear-frame / propagation-saw tests on any persistent layer, repeated over several winters. Borzenkov's four pits (no weak layer) and Popovnin's one visit (densities) are the only data; neither is published in a checkable form.
4. **What is the drift flux Q at 9-12 m/s in the lee of the shoulder?** A season of drift-flux sensors (FlowCapt-type) and an anemometer at the site would fix Q to better than a factor 3 and turn the model's fitted delay into a prediction. Pigol'tsyna's 9-12 m/s is a downscaling from stations 60-120 km away; Borzenkov's 12-36 m/s are spot observations; no anemometer record from the pass exists for 1959.
5. **Would 0.3-0.5 m of slab deposit on the flat platform survive 26 days of 10-15 m/s wind as more than 15-20 cm of hard snow?** Settle by placing an instrumented artificial deposit on the platform in January and re-surveying it after 3-4 weeks (or by an erosion/deposition model driven by the measured wind).
6. **Where did the four sustain their injuries?** The physics allows both the tent and the ravine; only forensics can decide: re-examination of the skeletal remains (fracture morphology and healing signs, if exhumation were ever permitted), or a reconstruction of the stream-bank geometry at the flooring in winter to test the fall/burial scenario (bank height, snow depth in early February, roof thickness of a den dug there).
7. **Could Thibeaux-Brignolle's fracture come from snow at all?** It cannot from a snow face at < 300 kPa (Section 2.9); it needs a hard object or a fall. Check the 1959 inventory for what he lay on (camera, flashlight, ski) and where those objects were found.
8. **Was the wind that night 9-12 m/s or 20-35 m/s?** No measurement can be made retrospectively, but a permanent automatic weather station at the pass, correlated for a few winters with Burmantovo/Ivdel records, would show whether Pigol'tsyna's downscaling or Borzenkov's climatology describes the site, which decides between "slow delayed slab" and "storm collapse" as the physically favoured trigger.

Two things the physics has settled as far as it can: the deaths of six by hypothermia within a few hours are inevitable once they are outside in that wind with that clothing; and multiple rib fractures without skin wounds are what any 100-300 kg of hard snow at 1-2 m/s (or a few metres of static snow against a hard floor) does to a person lying on a firm base, so the injuries by themselves do not identify an avalanche.

---

## References (with archived file names)

* [GP21] Gaume J., Puzrin A.M. (2021) Mechanisms of slab avalanche release and impact in the Dyatlov Pass incident in 1959. *Commun. Earth Environ.* 2:10. https://doi.org/10.1038/s43247-020-00081-8 (open access; `gaume_puzrin_2021.pdf/.txt`). SI: MOESM3 (`gaume_puzrin_2021_MOESM3_ESM.pdf`, Notes 1-7, Fig. SF1-SF9); Peer Review File MOESM1 (`gaume_puzrin_2021_MOESM1_ESM.pdf`); movies MOESM2. Code: [Z] https://doi.org/10.5281/zenodo.4088052 (not retrievable, HTTP 504).
* [PG22] Puzrin A.M., Gaume J. (2022) Post-publication careers: follow-up expeditions reveal avalanches at Dyatlov Pass. *Commun. Earth Environ.* 3:63. https://doi.org/10.1038/s43247-022-00393-x (`puzrin_gaume_2022_followup.pdf/.txt`). Press: ETH News 2021/2022 (`eth_news_2021.md`, `eth_news_2022.md`, https://ethz.ch/en/news-and-events/eth-news/news/2022/03/the-dyatlov-pass-mystery-and-what-a-research-article-can-trigger.html), EPFL (https://actu.epfl.ch/news/intense-press-coverage-prompts-new-expeditions-to-/), EurekAlert 947564.
* [QA22] "Puzrin and Gaume answer questions", dyatlovpass.com, 2022. https://dyatlovpass.com/puzrin-gaume (`dp_puzrin_gaume.md`).
* [DP-AV23] dyatlovpass.com, "Avalanche 2023" (Borisov, 7 Jan 2023, ~700 m from the tent), https://dyatlovpass.com/avalanche-2023 (`dp_avalanche_2023.md`).
* [BORZ22] Borzenkov V. (April 2022) rebuttal of the avalanche version, 30 pp., https://dyatlovpass.com/borzenkov (`dp_borzenkov.md`, `borzenkov_body.txt`).
* [PIG20] Пигольцина Г.Б. (2020) Микроклиматические характеристики горы Холатчахль (перевал Дятлова)... *Труды ГГО* вып. 597, с. 61-82, Tables 1-4. http://voeikovmgo.ru/images/stories/publications/2020/%D0%A2%D1%80%D1%83%D0%B4%D1%8B%20%D0%93%D0%93%D0%9E%20597%20%D0%BE%D0%BA.pdf (`pigoltsina_trudy_ggo_597.pdf`, extracts `pigoltsina_extract.txt`, `pigoltsina_pp69_76.txt`, `pigoltsina_pp77_82.txt`).
* [KP-POP19] Popovnin V. interview, Komsomolskaya Pravda, 2019: https://www.kp.ru/daily/26985/4045358/ (`kp_popovnin_interview.md`). [KP-POPCRIT] KP critique of the tent location used for the 21 degree measurement: https://www.kp.ru/daily/27262/4394254/ (`kp_popovnin_critique.md`).
* [RIA20] RIA Novosti, 11 July 2020, https://ria.ru/20200711/1574208839.html; [MEDUZA20] https://meduza.io/feature/2020/07/11/v-1959-godu-na-urale-pogibla-gruppa-dyatlova-spustya-61-god-prokuratura-ob-yasnila-chto-sluchilos-sperva-lavina-zatem-plohaya-vidimost-i-45-gradusnyy-moroz; [KOMM20] Kommersant https://www.kommersant.ru/doc/4415256; [KP20a] KP https://www.kp.ru/daily/27154.5/4251446/; [KP20b] KP "main results" https://www.kp.ru/daily/27154.5/4251493/ (Rosreestr 11 degrees, 2 m bank); Interfax https://www.interfax.ru/russia/716956.
* [LENTA24] Lenta.ru, 2 Feb 2024, https://lenta.ru/articles/2024/02/02/pereval/ (`lenta_2024_pereval.md`).
* [DP-KAR] Karelin V., "Avalanche is a myth", https://dyatlovpass.com/karelin-avalanche-myth (`dp_karelin_avalanche_myth.md`). [DP-CF-SLOB] Slobtsov testimony, case file pp. 298-300, https://dyatlovpass.com/case-files-298-300 (`dp_cf_slobtsov.md`); [DP-CF-MASL] Maslennikov testimony and radiograms, case file pp. 62-75 and 295-297, https://dyatlovpass.com/case-files-62-75 and https://dyatlovpass.com/case-files-295-297 (`dp_cf_maslennikov.md`, `dp_cf_maslennikov_add.md`); [DP-DEATH] autopsy summaries, https://dyatlovpass.com/death (`dp_death.md`); prosecutor's re-investigation page, https://dyatlovpass.com/prosecutors-investigation (`dp_prosecutors_investigation.md`); investigation materials, https://dyatlovpass.com/investigation-materials; "Was there an avalanche?" (Louhi, Dmitrievskaya, Litvinova, Ankudinov), https://dyatlovpass.com/louhi-dmitrievskaya-litvinova-ankudinov (`dp_byla_li_lavina_en.md`); theories overview, https://dyatlovpass.com/theories (`dp_theories.md`).
* [DP-SWE] Holmgren R., Liljegren A., Swedish-Russian expedition 2019 and the katabatic-wind theory, https://dyatlovpass.com/swedish-russian-expedition-2019 (`dp_swedish_russian_2019.md`). [IKAR18] Anaris accident review, IKAR 2018 (`anaris_ikar_2018.pdf`); [SV-WIKI] https://sv.wikipedia.org/wiki/Anarisolyckan; https://en.wikipedia.org/wiki/Anaris_accident.
* [BUY] Buyanov E.V. (with Volodicheva N.), mountain.ru: https://www.mountain.ru/legacy-material.php?article_id=3916 and ?article_id=9235 (`buyanov_mountainru_*.md`).
* National Geographic, 28 Jan 2021 (Hendrikx, McElwaine quotes): https://www.nationalgeographic.com/premium/article/has-science-solved-history-greatest-adventure-mystery-dyatlov (`natgeo_2021.md`). Vice 2022 (`vice_2022.md`). Snopes 2017 (`snopes_dyatlov.md`, https://www.snopes.com/news/2017/12/28/dyatlov-pass-incident/).
* Snow mechanics: Reiweger I., Gaume J., Schweizer J. (2015) *GRL* 42:1427, https://doi.org/10.1002/2014GL062780; van Herwijnen A., Heierli J. (2009) *GRL* 36:L23502, https://doi.org/10.1029/2009GL040389; Gaume J. et al. (2017) *The Cryosphere* 11:217, https://doi.org/10.5194/tc-11-217-2017; Jamieson J.B., Johnston C.D. (2001) Evaluation of the shear frame test for weak snowpack layers, *Ann. Glaciol.* 32:59-69 (`jamieson2001_cambridge.md`); Schweizer J., Jamieson J.B., Schneebeli M. (2003) Snow avalanche formation, *Rev. Geophys.* 41:1016; Casassa G., Narita H., Maeno N. (1991) Shear cell experiments of snow and ice friction, *J. Glaciol.* 37:420; Sturm M., Stuefer S. (2013) Wind-blown flux rates derived from drifts at arctic snow fences, *J. Glaciol.* 59:21, https://doi.org/10.3189/2013JoG12J110; Hoeller P., Fromm R. (2010) Quantification of the hand hardness test, *Ann. Glaciol.* 51:39. Abstract files: `crossref_abstracts.txt`, `semanticscholar_abstracts.txt`.
* Biomechanics: Kroell C.K., Schneider D.C., Nahum A.M. (1974) SAE 741187, https://doi.org/10.4271/741187 (paywalled, not read); Nahum et al. (1970) SAE 700400; Kimpara H. et al. (2003) Biomechanical properties of the male and female chest subjected to frontal and lateral impacts, IRCOBI (`ircobi_2003_chest.pdf`); Allsop D.L., Perl T.R., Warner C.Y. (1991) SAE 912907; Yoganandan N., Pintar F.A. (2004) *Clin. Biomech.* 19:225.
* Cold physiology: Osczevski R., Bluestein M. (2005) *Bull. Am. Meteorol. Soc.* 86:1453, https://doi.org/10.1175/BAMS-86-10-1453; Tikuisis P. (1995) Predicting survival time for cold exposure, *Int. J. Biometeorol.* 39:94 (`tikuisis1995_pubmed.md`); Dow J. et al. (2019) WMS clinical practice guidelines for accidental hypothermia, *Wilderness Environ. Med.* 30:S47; Wedin B., Vanggaard L., Hirvonen J. (1979) "Paradoxical undressing" in fatal hypothermia, *J. Forensic Sci.* 24:543.

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**Note on section 2.9 and question 7.** The categorical statements in section 2.9 ("a snow block cannot produce Thibeaux-Brignolle's injury unless...") and in question 7 ("it cannot from a snow face at < 300 kPa") are withdrawn. The computed range 0.06-3 kN overlaps the 2.5-10 kN threshold, and the 300 kPa ceiling was an assumption: Gaume and Puzrin's own MPM gives the wind slab a yield pressure of 100 kPa hardening with compaction, while Mellor's 1975 compilation (Fig. 17, `data/mellor-1975-snow-mechanics.pdf`) puts rapid-loading compressive strength of laboratory snow at 300-700 kPa at 0.40 g/cm3 and 500-950 kPa at 0.46. Over the 63 cm2 of the depression the 2.5 kN floor needs ~400 kPa, over the 10.5 cm2 bone piece 2.4 MPa. The argument is now a constraint (soft or medium slab excluded as sole loader; hard slab or crust with the head backed, or a hard object under the snow, not excluded) and it does not discriminate the tent from the ravine. Arithmetic: `code/physics/skull_constraint.py`.