book21/Spiral.lean, a true identity about a 2×2 spiral matrix. They were added because the word “discriminant” appears in the prose (tools/proved_labels.py matches words); the theorem supports nothing on this page. They are generated, so they stay until the generator is changed. Still UNCHECKED, no source in the repository: the ISS exercise minutes and 45-day recovery, the xEMU 1-in-2500 figure, the regolith reactivity numbers carrying a [VERIFIED] tag (50% in 3.5 hours; ten times quartz), and the 13.4× depth-and-subdivision figure, which cannot be reproduced because the page gives no failure probability, k-of-n rule or cave definition. Checked and holding: every Risk Approach Plan identifier, date and quote against the retained PDF, the micrometeoroid compounding table, n* = 2/p, and the n1/3 surface rule. Script: book6/wp71-verify.py.§1 · The Wrong Variable
A measurement can fail in two ways. It can be imprecise — the right quantity, badly estimated. Or it can be uninformative — the wrong quantity, estimated perfectly. The second failure is worse, because collecting more data does not fix it, and because a well-run programme producing clean numbers looks exactly like a successful one.
Two of the largest hazards facing a sustained lunar presence are currently monitored in the second way. Bone loss is tracked against activity volume; dust exposure is regulated against mass concentration. In both cases the underlying process is not an accumulation, and the metric therefore cannot distinguish two crewmembers at very different risk. This paper sets out why, what the right variables are, and — more usefully — a discriminant that says which of four categories any given risk falls into, including the category where the honest answer is that no amount of measurement will help.
§2 · Bone — Threshold-Governed
A 2021 NASA Ames conference paper (Jones, ICES 2021) concludes that partial gravity below 0.4 g will be insufficient to maintain musculoskeletal and cardiopulmonary conditioning in the long term; the paper itself says direct evidence is not yet available and the conclusion rests on indirect evidence. Lunar gravity is 0.167 g — under half that floor. Mars, at 0.38 g, sits essentially on the boundary; the Moon is nowhere near it.
A bone mineral density loss of 0.39% per week in lunar gravity (0.22% per week on Mars) is assumed below. These two rates are model predictions of bone mineral content loss, not measurements: Keller and Strauss (1992), Bone loss and human adaptation to lunar gravity, Table 2, from a power-law fit to lumbar data from power-lifters (Moon −0.39%/week, Mars −0.22%/week; the same paper's running text gives slightly different values, 0.41% and about 0.4%). Measured spaceflight loss in that paper runs 0.4 to 0.7%/week, so the table is conditional on a model rate. Checked 2026-10-15 against the paper's text as returned by a fetch tool; the PDF itself should still be read. Compounded, absent countermeasures:
| BMD loss | Lunar (0.39%/wk) | Mars (0.22%/wk) |
|---|---|---|
| 5% | 3.0 months | 5.4 months |
| 10% (osteopenic range) | 6.2 months | 11.0 months |
| 20% | 13.1 months | 23.3 months |
| 30% (osteoporotic range) | 21.0 months | 37.3 months |
Months, not years — clinically meaningful loss inside a single long-duration stay. The rate is modelled, and unvalidated in humans, because total human exposure to lunar gravity amounts to roughly two weeks, all of it Apollo. That absence is itself the finding.
But the interesting part is not the rate. Bone responds to dynamic loading above a strain threshold, and the osteogenic response saturates after a few tens of cycles: magnitude buys adaptation, cycle count buys very little once magnitude suffices, and nothing at all when it does not. At one-sixth g, peak ground reaction force in ambulation is roughly one-sixth of terrestrial — plausibly below threshold however far one walks.
What the measured record adds
Rates in weightlessness. NASA reports that weight-bearing bones lose on average 1% to 1.5% of mineral density per month during spaceflight (The Human Body in Space); a second NASA article gives roughly 1% a month for crew who take no precautions. Compounded monthly:
| BMD loss | At 1%/month | At 1.5%/month |
|---|---|---|
| 5% | 5.1 months | 3.4 months |
| 10% | 10.5 months | 7.0 months |
| 20% | 22.2 months | 14.8 months |
| 30% | 35.5 months | 23.6 months |
Outcomes with exercise. In a 2023 npj Microgravity study of 46 ISS astronauts on missions of 178 ± 48 days, with about 600 minutes of exercise per week (range about 450 to 720), mean bone density fell 2.1% to 3.7% depending on site and trabecular bone content fell 5.3% to 8.5%. Divided by the mean mission length, the density loss is about 0.36% to 0.63% per month, below NASA’s 1% to 1.5%. The authors project that 15% of astronauts on future missions could lose 20% or more of femoral-neck trabecular content. Exercise was mandatory, so the study has no non-exercise group, and it cannot say whether minutes or peak load did the work. NASA also reports bisphosphonates as effective in preventing bone loss in its studies. For myostatin inhibitors, the flight evidence NASA cites is in mice (Lee et al., PNAS 2020).
Recovery. NASA says bone loss might not be completely corrected by rehabilitation after return, while reporting that fracture risk is not higher. Gabel et al. (2022) followed 17 astronauts: at one year, median tibia strength, density and trabecular microarchitecture were still 0.9% to 2.1% below preflight, and nine of the 17 had not fully recovered total density. Longer missions recovered less. More on recovery is in Book 3 · Bones in Orbit.
Partial gravity. The nearest flight data are for muscle and not bone. Mice held on the ISS centrifuge at 0.33 g kept soleus cross-sectional area, with a partial shift in fibre type, and 0.67 g preserved muscle performance and fibre type (Tsuji et al., Science Advances 2026; the abstract as listed by a co-author’s institution was read, not the paper). The lowest level tested was about twice lunar gravity.
Low-equipment options. Treadmill and ARED hardware are too large for long-duration vehicles, and Zero T2 tests removing the treadmill. Its three arms are all equipment, ARED plus the CEVIS cycle only, and the compact E4D device only, so every arm keeps a machine. No results were found in the search of 2026-11-08. Arms two and three remove treadmill foot loading, which makes the study a possible partial test of §6.
Muscle-against-muscle training, the mail-order “Dynamic Tension” of the 1920s, needs no hardware at all, and has been studied as maximal voluntary co-contraction. In a 12-week trial with nine men in the training group, elbow flexor strength rose 15%, extensor strength rose 46% and muscle thickness rose 4%. A 2021 University of São Paulo dissertation found no significant changes in participants who paused conventional strength training for it. The abstracts report no bone measurement, so whether muscle-generated force reaches a skeletal threshold is unknown. Jumping and hopping are reported to promote muscle and bone adaptation in ground research.
§3 · Dust — Kinetics-Governed
Here the absent atmosphere matters, and not in the way the phrase "no ozone layer" usually suggests. For a suited crewmember, ultraviolet does not reach tissue; the suit stops it. What UV reaches is the regolith.
Lunar soil is activated by three mechanisms: solar ultraviolet, solar wind, and micrometeorite comminution. With no atmosphere and therefore no ozone column, the surface receives UVC and vacuum ultraviolet that never touch any terrestrial surface. Grain-surface activation in sunlit terrain is not a one-off event; it is continuously renewed.
Activated soil is chemically aggressive. Ground lunar material generates hydroxyl radicals at roughly ten times the rate of quartz, driven by nanophase metallic iron — a species with no terrestrial analogue, which is why simulants cannot substitute for the measurement. And the reactivity decays: NASA's measurements give a fall to 50% of initial reactivity in approximately 3.5 hours in a habitable environment, with no sample returning fully to baseline within a week [UNCHECKED: NASA decks found show a half-life near 3 h for ground simulant in aqueous suspension and a return toward baseline by about 24 h; the 3.5 h and one-week wording was not found].
One consequence appears not to have been raised. At the lunar south pole, regolith in permanently shadowed regions has never received direct sunlight, while adjacent sunlit regolith is irradiated continuously. (Shadowed regions are not wholly dark in the ultraviolet: interplanetary Lyman-alpha is reported to reach them, per the 2012 SwRI release on the LRO LAMP instrument, so a difference in reactivity is a hypothesis, not a known contrast.) A single Artemis traverse can cross both. If reactivity differs by terrain illumination history, then dust hazard is route-dependent, and traverse planning becomes a health countermeasure.
§4 · Galactic Cosmic Rays — Accumulation-Governed
This section exists to keep the paper honest. A framework that classifies every hazard as threshold-governed predicts nothing and excludes nothing; its value lies entirely in the cases where the standard metric is already correct.
Stochastic radiation risk is modelled linear-no-threshold. Cancer probability is taken proportional to the integrated dose, with no threshold below which risk vanishes. Here cumulative dose in millisieverts is exactly the right variable, dosimeters integrating over a mission are doing precisely the correct thing, and nothing in this paper suggests otherwise.
§5 · Micrometeoroids — Stochastic-Catastrophic
The fourth category is the one intuition finds hardest and expected-value reasoning handles worst. NASA's xEMU micrometeoroid and orbital debris assessment (NTRS 20230015411) states a requirement of 1-in-2500 failure odds per eight-hour, two-person EVA; its computed results were about 1 in 4,550 for ISS and about 1 in 8,256 for the lunar surface (2021 design), so both meet it. The 1-in-2500 figure used below is the requirement, hence a conservative bound. That is a tolerance, not an elimination, and it compounds:
| EVAs | P(at least one penetration) |
|---|---|
| 52 (≈ 6-month rotation, twice weekly) | 2.1% |
| 100 | 3.9% |
| 500 (sustained presence) | 18% |
Two details deserve more attention than the headline number. First, 99% of lunar-surface MMOD risk sits in softgoods — arms, legs, gloves — which is precisely the surface that cannot be armoured without destroying the dexterity the EVA exists for. Second, the lunar assessment still runs on the Apollo-era NASA SP-8013 ejecta model, with reassessment pending a new engineering model. The number underwriting the risk posture rests on 1960s secondary-ejecta physics.
§6 · The Discriminant
| Category | Governing quantity | Instance | Instrument | Lever |
|---|---|---|---|---|
| Accumulation | exposure integral | GCR cancer risk | integrator | reduce total dose |
| Threshold | supra-threshold event count | bone under loading | event counter | raise peak magnitude |
| Kinetics | exposure × decaying state | dust reactivity | time-resolved sampler | delay contact |
| Stochastic-catastrophic | tail probability | micrometeoroids | none helps | subdivide and shelter |
Each cell is falsifiable in its own terms. If skeletal outcome correlates better with total ambulation time than with supra-threshold event count, bone is not category 2. If dust toxicity tracks inhaled mass irrespective of time since disturbance, dust is not category 3. Both are testable with instrumentation that requires no dedicated crew time.
§7 · Read Against the Risk Approach Plans
Source, retained. Every row in this section is verified against the
NASA Human Research Program Risk Approach Plans (twelve risks, June 2026), a copy
of which is held in this repository at book6/sources/hrp-rap-for-web-62026.pdf,
retrieved 2026-08-20, sha256 d4e77d646fa6e485… (full digest in
book6/sources/README.md). A claim verified against a document nobody retained
is a claim resting on a reading; retaining it makes each row below checkable by anyone.
A discriminant is only useful if it points somewhere. In June 2026 the Human Research Program published Risk Approach Plans for twelve risks — Behavioural Health, Bone, Carcinogenesis, Earth-Independent Human-System Operations, EVA, Food and Nutrition, Immune, Injury Due to Dynamic Loads, SANS, Sensorimotor, Team, and Venous Thrombosis — each with knowledge gaps, countermeasure lines, dated deliverables and a named receiving organisation. Read individually they are workplans. Read as a set they show where the agency believes its uncertainty lies, and the distribution is uneven in a way that is itself informative.
Bone is the thinnest plan in the collection
Behavioural Health carries nine numbered deliverables. Earth-Independent Operations carries eight, Team eight, Carcinogenesis eight. Bone carries one — “Bone Standards and Recommendations: OCHMO by 2028; MRI Informing Pharmaceutical Use TTO 2027” — and that single deliverable is printed identically in both the characterisation column and the countermeasure column. Its timeline bar carries one marker.
The four gaps are BONE-101 (characterise changes in density and structure), BONE-102 (characterise turnover and biochemical markers), BONE-201 (tools to estimate bone strength and the probability of overloading bones, and fracture assessment), and BONE-301 (post-flight monitoring tools), with BONE-401 covering countermeasures undifferentiated.
Note where BONE-201 points. It concerns strength, overload probability and fracture — the mechanics of failure under too much load. Nothing in the plan asks what pattern of loading maintains a skeleton. The plan asks how much load breaks a bone; it does not ask what load keeps one. That is precisely the gap §2 describes, and it is not on the list.
The partial-gravity split exists — in other plans
The strongest evidence that this is an oversight rather than a considered judgement is that the same document makes the distinction elsewhere. Venous Thrombosis carries CV-108, “determine the contribution of flow abnormalities to venous thrombosis risk in 0G and partial-G,” and splits its deliverables accordingly: likelihood and consequences in 0-G by 2031, and in partial-G by 2033. Two regimes, two dates, two products. EVA-102 does the same, characterising surface EVA performance specifically in partial-gravity environments, with Lunar Hi-Tempo Capabilities due 2028 and the Martian equivalent in 2029.
Why partial gravity is worse than none for this purpose
NASA reports ISS crew averaging about two hours of exercise per day (NASA, Astronaut Exercise); its exercise technical brief (OCHMO-TB-031) prescribes roughly 30 minutes of aerobic work and 30 to 60 minutes of resistive training, with crew VO2peak back at preflight baseline about 30 days after return and a 45-day postflight reconditioning program that can be extended. The budget is denominated in minutes. Those three devices are not doing the same kind of work. Aerobic capacity is genuinely accumulation-governed, so minutes is the correct variable for the ergometer. If bone is threshold-governed, minutes is the wrong variable for the resistive device, and a single time budget measured with a single clock is bundling two categories.
On ISS this is a bookkeeping problem. On the Moon it becomes a hazard, because of an inversion. In orbit, ambient loading is zero, so every osteogenic event comes from the device by construction — the countermeasure and the loading are the same object, and nobody can mistake floating for exercise. On the lunar surface, ambient loading is 0.167 g: continuous, felt all day, and by the threshold argument contributing nothing.
Two absences worth recording
Lunar dust has no Risk Approach Plan in this set of twelve, though the risk of adverse health effects from lunar dust exposure is a named HRP concern with its own evidence report. Whether that reflects prioritisation or simply a publication subset cannot be determined from the document, and should not be asserted either way. What can be said is that §3’s kinetics claim — that the health-relevant variable is reactivity at the moment of exposure, not inhaled mass — has no plan to be tested against.
Second, offered as bookkeeping rather than criticism: the deliverable “Days post-landing prior to initial EVA” appears twice under different owners, once under EVA-101 with OCHMO by 2027 and once under Sensorimotor SM-106 with OCHMO by 2033. Same title, two plans, six years apart.
Where a contribution would attach
The near-term door is EVA-102’s Lunar Hi-Tempo Capabilities line, due 2028 — the one deliverable in the set explicitly about what surface crews can sustain in partial gravity, and therefore the natural home for a crew-time argument. The longer-term attachment is BONE-401, where a countermeasure specified in supra-threshold event count rather than exercise minutes would be a different object from the one currently implied.
§8 · Architecture as the Only Countermeasure for Category 4
If monitoring cannot touch a tail risk, something else must. For micrometeoroids the answer is geometric, and it has two independent parts that turn out not to be substitutes.
Subdivision
Splitting a habitat into n pods reduces the consequence of a penetration by a factor n while increasing total exposed skin as $n^{1/3}$ — eight pods have exactly twice the surface of one pod of equal volume. Against this runs the chance that an isolation interface fails to contain. Balancing the two:
Depth
Radar re-analysis of Lunar Reconnaissance Orbiter data confirmed in 2024 an accessible cave conduit beneath the Mare Tranquillitatis pit — not inferred from a skylight, but detected. Under a few metres of rock, galactic cosmic rays, solar particle events, micrometeoroids and 300 K thermal cycling are all strongly attenuated, with no biological intervention whatsoever. (How strongly is not computed here. A published lander-dose study recommends at least 50 cm of regolith for a base and notes that neutron flux rises with regolith depth: Zhang et al., Sci. Adv. 6(39), 2020.)
They compound
Scored on tail probability — P(mission-ending volume loss over ten years) — rather than expected loss:
| monolithic | 8 pods | |
|---|---|---|
| surface | baseline | 3× better |
| in the cave | 3× better | 13.4× better |
Three times three is nine; the result is 13.4. Depth and subdivision are super-multiplicative, because the binomial tail is convex in per-pod failure probability: requiring k-of-n failures becomes disproportionately protective as each individual failure grows rarer. Subdivision works better inside the cave than outside it. Pods in a lava tube are not two good ideas stacked; each makes the other more effective than it is alone.
The isolation exists only if the hatches are shut. That makes this a countermeasure whose efficacy depends on crew compliance under fatigue and habituation — a human-factors dependency sitting inside an architectural solution, and the most likely mode of silent failure.
The parity effect is real: with a "lose half or more" abort criterion, even pod counts are penalised (three beats four), because losing exactly half counts against you; with a strict "more than half" criterion the order reverses and four beats three (recomputed in wp71-verify.py). Where that criterion is set changes the answer.
All figures in this section are [MODEL]; an internal-failure rate was assumed. The ratios are the content. The absolutes require real habitat-shell ballistic limits and real seal reliability data, neither of which is in hand.
§9 · The Control We Destroy by Arriving
One further consequence follows from the same habit of asking what a measurement can and cannot see, and it is the one with the longest reach.
Suppose a subsurface habitat succeeds. Liquid water, a thermal gradient, organics, a pressurised volume, centuries of operation. Suppose that in some crevice at the margin of it, something begins to replicate. The discovery would be the most consequential in the history of biology — and it would be uninterpretable, because we would have no way to establish that we had not brought it, seeded it, or created the conditions that produced it. Our presence is what makes the observation possible and what makes it worthless as evidence.
This is forward contamination stated as an epistemic rather than a custodial problem. Planetary protection is usually argued on stewardship grounds: do not spoil the sample. The sharper argument is that arrival destroys the control, permanently and unrecoverably, and no subsequent care restores it. The measurement and the intervention are the same act.
This is the same structure recorded twice already in the corpus. In quantum chemistry, molecular geometry is inserted by clamping the nuclei under Born–Oppenheimer and then recovered and reported as found — Lombardi's objection. In the anyon experiments, the braid is built by applying gates chosen by the experimenter, so "the order of operations is physically recorded" holds by construction and tests nothing; the fractional quantum Hall system is the control precisely because nobody imposed the braiding.
Lunar biogenesis after human arrival is the third instance, and the most severe, because unlike the other two there is no control case available anywhere. Sterile Moon is a state that exists once. The asymmetry — two impositions and one control — was already noted as a paper in the Chapter 7 revision; this is its third leg, and it argues for measuring the pristine state before the habitat, not because the sample is precious but because the baseline is the only thing that cannot be recovered later.
§10 · Honest Inventory
| Claim | Status | Basis |
|---|---|---|
| 0.4 g maintenance floor; 0.39%/wk lunar BMD loss | [MODEL] rate (prediction, not measurement) | Keller and Strauss 1992, Table 2 |
| Bone responds above a strain threshold; response saturates in cycle number | [VERIFIED] | mechanostat literature |
| Activity volume cannot predict skeletal outcome | [MODEL] | follows from the two above; untested in partial gravity |
| Weight-bearing bone loses 1% to 1.5% of density per month in spaceflight | [VERIFIED] as NASA’s statement | NASA, The Human Body in Space |
| Modelled lunar loss (about 1.7%/month) exceeds that weightless average | [OPEN] tension; sites and measures differ | wp71-verify.py block 8 |
| 46 ISS astronauts, about 600 min/week: density down 2.1% to 3.7% | [VERIFIED] as read through a fetch tool | npj Microgravity 2023; no non-exercise group |
| Bone strength incomplete at one year (17 astronauts) | [VERIFIED] abstract | Gabel et al. 2022 |
| 0.33 g preserves area and 0.67 g preserves performance in mouse muscle | [VERIFIED] abstract listing; muscle only, mice | Tsuji et al. 2026 |
| Co-contraction training builds strength | [VERIFIED] abstract, one trial; a 2021 dissertation found no change | elbow only |
| Co-contraction or jumping protects bone at 0.167 g | [OPEN] | no data found |
| Dust reactivity half-life ≈ 3.5 h; incomplete passivation at one week | [UNCHECKED] sources found give about 3 h for ground simulant in suspension and near-baseline by about 24 h; neither 3.5 h nor one week was found | NASA dust reactivity measurements |
| UV as a continuous re-activation mechanism at the surface | [VERIFIED] | three named activation mechanisms |
| Route-dependent dust hazard (PSR vs sunlit) | [OPEN] | inference; not measured |
| xEMU 1-in-2500 per EVA; 99% of risk in softgoods | [VERIFIED] | xEMU MMOD risk assessment |
| $n^{*} = 2/p_{\text{iface}}$ | [MODEL] | analytic + numeric; assumed failure model |
| Depth × subdivision super-multiplicative | [MODEL] | binomial tail convexity; assumed internal rate |
| Accessible cave conduit below Mare Tranquillitatis | [VERIFIED] | LRO Mini-RF radar re-analysis, 2024 |
| Bone is the thinnest of the twelve June 2026 Risk Approach Plans (one deliverable, printed in both columns) | [VERIFIED] | HRP Risk Approach Plans, June 2026 |
| BONE-201 concerns overloading and fracture, not maintenance loading | [VERIFIED] | ibid., Bone plan |
| Venous Thrombosis and EVA split 0-G from partial-G; Bone does not | [VERIFIED] | ibid., CV-108 / EVA-102 / Bone plan |
| Cancer risk is rate-dependent as well as dose-dependent | [VERIFIED] | ibid., Cancer-104 |
| No dust Risk Approach Plan in the June 2026 set of twelve | [VERIFIED] absence · [OPEN] cause | ibid.; subset vs prioritisation undetermined |
| Partial-gravity ambient loading is a deceptive signal to crew and to time-based monitoring | [MODEL] | follows from §2 threshold law; untested |
| Direct Earth–Moon transfers take several days; few stable lunar orbits; L2-region orbits considered for relays | [VERIFIED] as statements in the primer | AFRL cislunar primer, 2021 (read from the PDF) |
| That relays give a south-pole surface crew continuous contact, or enough for remote medical support | [OPEN] | not in the primer; not searched |
| Real habitat-shell ballistic limits and seal reliabilities | [OPEN] | not in hand; absolutes unusable without them |
What the cislunar primer adds to this paper, and what it does not
The Air Force Research Laboratory’s “A Primer on Cislunar Space” (Holzinger, Chow and Garretson, 3 May 2021) is about orbits and observation, not surface hazards, and it barely discusses radiation. It therefore gives no support to the dust, cosmic-ray or micrometeoroid claims above, and nothing in §§2 to 5 changes. It bears on this paper in two narrow ways. First, it says direct Earth–Moon transfers take several days; that is the order of magnitude for how fast a crew could be reached or returned, which matters for any abort criterion like the one in §8. Second, it says that the Moon’s uneven gravity leaves only a few stable lunar orbits, and that orbits around the L2 point, including the one planned for NASA’s Gateway, are being considered for communications relays with views of Earth and the Moon’s far side. A surface crew’s link to Earth, and so any remote medical or monitoring support the §9 control question depends on, would depend on such relays. The primer does not say how many relays, how much capacity, or what coverage a south-pole base would get, and I have not looked for that. The geometry and arithmetic behind its figures are worked in the cislunar space chapter. Figures are the primer’s, checked against the PDF on 2026-11-01; the interpretation is mine.
§11 · Where This Sits
The G6 Crystal treated lunar architecture as structure. This paper argues it is something else as well: the only available countermeasure for the one hazard class that no drug and no monitoring programme can reach. That reframing is the contribution — not architecture as engineering, but architecture as the answer to category four.
The methodological sibling is Book 4 · Chapter 20 · The Defect Lattice, which runs the same discipline on a mathematical rather than a physiological question: fix the falsification criterion first, report the negative result, and record which half of a problem was closed and which was not. Readers coming from WP54 · Quantum Weave Topology will recognise §9's structure from the engineered-versus-emergent distinction developed there.
Nothing in this paper depends on the operator chain, and nothing in it should be cited as extending the chain. The four categories are ordinary risk analysis; their only novelty is being applied together, and being made to exclude as well as include.