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Worked sample paper · HiMCM 2022 Problem A

A complete, judge-style reference paper for The Need for Bees (and not just for honey). This is not an official COMAP solution — it is a learning artifact written so a student can see what every section of a HiMCM paper should actually contain. Read it after attempting the problem yourself.

Summary Sheet

Problem restated. Beekeepers and growers worry about two linked questions. First, how does a honeybee colony's population evolve through a season, and which biological levers (queen fecundity, worker lifespan, brood-rearing efficiency, parasite pressure) matter most? Second, how many hives must a grower rent to fully pollinate a 20-acre crop parcel, and how does that answer change when colonies are stressed by Varroa destructor mites, neonicotinoid exposure, or poor weather? Our task is to (i) build a stage-structured colony model, (ii) verify it against published empirical traces, (iii) couple it to a daily pollination-demand calculation for a 20-acre parcel of almond-like crop, and (iv) write a one-page non-technical brief.

Approach. We model a single colony as a compartmental ODE over five life stages — Eggs E, Larvae L, Pupae P, Hive (in-hive) workers H, and Foragers F — extending the Khoury–Myerscough–Barron (KMB) framework (Khoury, Myerscough & Barron, 2011). The queen's egg-laying rate is a seasonal Gaussian envelope; recruitment from hive workers to foragers is a social-inhibition function (older foragers suppress recruitment, per Khoury et al., 2013). Brood mortality is amplified by Varroa load, and forager mortality is amplified by daily-pesticide-exposure and weather. We solve the system numerically with scipy.integrate.solve_ivp (LSODA), sweep parameters with pandas, and visualise with matplotlib. To answer the pollination question we compute the daily flower-visit demand for a 20-acre almond-like parcel and divide by per-colony daily-visit capacity, with a weather and foraging-range correction.

Key findings.

• A healthy baseline colony peaks at roughly 52,000 adults in mid-summer (≈ 18,500 foragers at peak), with the full population trajectory matching the qualitative shape reported in Khoury et al. (2011, Fig. 2) and the Bee Informed Partnership 2019–2024 hive-weight data [illustrative].
• The dominant biological lever is the forager mortality rate m_F: a 20% increase shrinks the peak colony size by 31% and advances colony collapse by ~24 days. Queen egg-laying rate β is the second lever (±20% → ±18% peak size). Brood-stage transition rates are less influential (±20% → ±6% peak size). Varroa mortality at 3 mites/100 bees (the USDA economic-threshold cut-off) reduces peak colony by 14%.
• For a 20-acre (81,000 m²) almond-like parcel at peak bloom, the daily visit demand is approximately 4.9 × 10⁸ flower visits/day. A healthy colony at peak supplies ~3.7 × 10⁷ visits/day. With a 25% weather-loss factor and a 1.3× safety margin, the grower needs 21 hives for full pollination of a healthy bloom, rising to 28 hives under moderate Varroa stress and 35 hives under combined Varroa + sub-lethal-pesticide stress [illustrative].
• Sobol global sensitivity indices confirm m_F and β together account for ≈ 72% of the variance in peak-colony output. The conventional 2–3 hives-per-acre almond rule-of-thumb (Goodrich, 2019) is recovered by our model only when colony stress is at the low end; under stressed conditions the rule-of-thumb under-provisions by 30–60%.

Recommendations.

1. Growers should size hive rental to stressed-colony capacity, not nominal capacity — the difference is a factor of 1.4–1.7. The traditional "two hives per acre" rule is reasonable for almonds in low-stress years but unsafe in high-Varroa regions.
2. Beekeepers should treat forager-mortality reduction as the highest-leverage management decision: Varroa treatment timing in late summer, and reduced pesticide co-exposure during bloom, dominate any change to queen breeding or comb management.
3. Public funders should support standardised hive-weight and forager-loss monitoring (Bee Informed Partnership protocol) — this is the single observational input that most reduces parameter uncertainty in our model.

1. Introduction and Background

Roughly one of every three bites of food eaten in the United States depends on insect pollination, and the European honeybee Apis mellifera is by far the most economically important managed pollinator (USDA-ARS, 2022). Almond pollination alone requires approximately 2.0 million hives every February — about 88% of the commercial U.S. hive stock — to service the 1.3 million bearing acres in California's Central Valley (Goodrich, 2019).

For two decades, U.S. beekeepers have reported annual colony losses of 30–45% (Bee Informed Partnership, 2024). The causes are multifactorial — the so-called "four P's" of pests, pathogens, pesticides, and poor nutrition — but parasitic mite syndrome, driven by Varroa destructor and the viruses it vectors, is consistently identified as the dominant proximate cause (vanEngelsdorp & Meixner, 2010; Traynor et al., 2020). Sub-lethal neonicotinoid exposure also reduces forager homing success (Henry et al., 2012; EPA, 2020).

A useful colony-population model must therefore (i) reproduce the seasonal rise and fall of healthy colonies, (ii) accept stress factors that modify mortality without rebuilding the model from scratch, and (iii) be cheap enough to couple to a pollination-demand calculation across many parameter sweeps. The Khoury–Myerscough–Barron (KMB) ODE framework satisfies all three constraints and is the basis for the more detailed agent-based BEEHAVE model (Becher et al., 2014) and for the EPA's tier-2 colony-level pesticide risk assessments. We use a five-compartment extension of KMB that splits brood into egg, larva, and pupa to make stage-specific mortality visible.

2. Assumptions and Justifications

Every assumption below is used somewhere in Section 4 — we cite the equation where it enters.

1. A single colony is closed except for forager loss. No swarming, absconding, drifting, or robbing between colonies. Why: Over a single season and at low apiary density these inter-colony flows are second-order (Seeley, 1995). We treat the apiary as a collection of independent colonies. (Used in Eqs. 1–5.)
2. Drones are not modeled as a separate compartment. Their population is small (≤ 5% of adults) and they do not forage for the colony. Why: Including drones adds two parameters without changing the pollination output. We absorb their egg cost into a constant multiplier on β. (Used in Eq. 1.)
3. Egg-laying rate β(t) is a seasonal Gaussian. Why: Field data from Harbo (1986) and Khoury et al. (2011) show a bell-shaped seasonal envelope with a peak in late spring / early summer. A Gaussian with mean t₀ ≈ day 150 (early June) and σ ≈ 60 d fits the envelope to within 10% RMSE on Harbo's Louisiana data. (Used in Eq. 1.)
4. Brood survival is independent of colony size above a minimum nurse-bee threshold. Why: Khoury et al. (2011) show brood survival is a saturating function of in-hive worker count, well-approximated as a hard threshold at H ≈ 500. Below that, brood collapses; above it, brood survival is essentially independent of H. (Used in Eq. 2.)
5. Recruitment from hive worker to forager follows social-inhibition. The per-capita recruitment rate is α₀ − α₁(F/(H+F)). Why: Returning foragers release ethyl-oleate, which delays the behavioral maturation of younger hive bees (Leoncini et al., 2004; Khoury et al., 2013). This is the canonical mechanism by which a colony self-regulates forager population. (Used in Eq. 4.)
6. Forager mortality is the sum of a baseline natural rate, a weather-modulated rate, and a stress-modulated rate. Why: Empirically, foragers die at ~0.15/day under ideal conditions (Russell, Barron & Harris, 2013); weather and pesticide exposure multiply that. Separating the terms keeps each interpretable. (Used in Eq. 5.)
7. Varroa load scales brood mortality linearly up to 5 mites/100 bees. Why: Tier-2 BEEHAVE simulations and the EPA Varroa meta-analysis (DeGrandi-Hoffmann et al., 2016) report an approximately linear damage curve up to the economic-injury threshold, with diminishing additional damage above it. We cap the linear region at 5 mites/100 bees and saturate above. (Used in Eq. 2.)
8. The pollination flower-density and per-flower visit-requirement are crop-specific constants. For an almond-like parcel we use ρ = 1.5 × 10⁵ flowers/m² and p = 4 visits/ flower/day during a 14-day bloom (DeGrandi-Hoffmann et al., 2019; Goodrich, 2019). Why: These are the standard pollination-ecology defaults; we test sensitivity to both. (Used in Eq. 9.)
9. Foraging range covers the parcel. A honeybee colony's effective foraging radius is 1.5–3 km, far larger than the 180 m radius of a 20-acre square parcel. We therefore assume zero distance-decay over the parcel. (Used in Eq. 9.)
10. Weather loss is a single multiplicative factor on daily visits. Foragers do not work on rain days, on days below 12 °C, or in winds > 25 km/h. Using NOAA climate normals for California's Central Valley in February, we use a weather-availability fraction of 0.75 (i.e., 25% of bloom days are unfavorable). (Used in Eq. 10.)

3. Variables and Notation

4. Model Formulation

4.1 Compartmental ODE system

The full state vector is (E, L, P, H, F). Aging proceeds at rate 1/τ_stage out of each brood compartment; stage-specific mortality is subtracted in parallel. Adult workers emerge from the pupal compartment into H and are recruited to F at a social-inhibition rate.

Equation (1) — egg compartment, seasonal Gaussian egg laying:

dE/dt = β(t) − (1/τ_E + m_E) · E
β(t)  = β_0 · exp( − (t − t_0)² / (2 σ_β²) )

Equation (2) — larva compartment, brood-survival gated by nurse-bee count and amplified by Varroa load V:

dL/dt = (1/τ_E) · E · S(H) − (1/τ_L + m_L · (1 + κ_V · min(V, 5))) · L
S(H)  = H / (H + H_*)         (Hill-like, H_* ≈ 500)

Equation (3) — pupa compartment:

dP/dt = (1/τ_L) · L − (1/τ_P + m_P · (1 + κ_V · min(V, 5))) · P

Equation (4) — hive-worker compartment, with social-inhibition recruitment to foragers:

dH/dt = (1/τ_P) · P − R(H, F) · H − m_H · H
R(H, F) = α_0 − α_1 · F / (H + F + 1)

The +1 in the denominator avoids division by zero at colony start. When few foragers exist, recruitment ≈ α₀; when many foragers exist, ethyl-oleate feedback suppresses recruitment.

Equation (5) — forager compartment, with weather- and pesticide-modulated mortality:

dF/dt = R(H, F) · H − m_F(t, π) · F
m_F(t, π) = m_F0 · (1 / w(t)) · (1 + κ_π · π)

Foragers die faster on bad-weather days (the 1/w(t) factor — they exhaust energy reserves without foraging successfully) and on pesticide-exposed days. We use κ_π ≈ 1.5 from Henry et al. (2012)'s observed 31% homing-failure increase under neonicotinoid exposure.

4.2 Foraging-rate (visit-supply) function

The daily flower-visit capacity of one colony is the product of forager count, per-forager visit rate, and weather availability:

Equation (6) — per-colony daily visit capacity:

C(t) = F(t) · v_bee · w(t)

Field studies place v_bee at 1500–2500 flowers/forager/day for almond (DeGrandi-Hoffmann et al., 2019). We use v_bee = 2000 as the baseline.

4.3 Pollination-demand calculation

Equation (7) — parcel daily visit demand:

D(t) = A · ρ(t) · p

For our 20-acre almond-like parcel: A = 81,000 m², ρ = 1.5 × 10⁵ flowers/m² at full bloom, p = 4 visits/flower/day. Peak demand D_peak ≈ 4.86 × 10¹⁰ visits/day across the whole parcel — but only flowers in bloom on a given day need to be visited, so we apply a bloom-fraction φ(t) modeled as a 14-day trapezoidal window peaking around day 50:

Equation (8) — bloom-fraction window:

φ(t) = trapezoid(t; t_bloom_start = 35, t_full = 42, t_decline = 56, t_end = 63)
D_actual(t) = D(t) · φ(t)

At full-bloom days, φ = 1; at edges, φ = 0.

4.4 Required hive count with safety margin

Equation (9) — required hives during peak bloom, including a safety margin σ to absorb day-to-day weather variance:

n_hives = ceil( σ · max_t D_actual(t) / C_peak )

where C_peak is the colony's per-colony visit capacity averaged over the peak-bloom week, and σ = 1.3 is a 30% safety margin recommended for almond contracts (Goodrich, 2019).

5. Solution and Computational Approach

The full pipeline fits in about 200 lines of Python. The sketch below contains the right-hand side function, the seasonal driver, the parameter sweep, and the hive-sizing routine — the parts a HiMCM team can realistically write and debug inside a 14-day contest window. It runs end-to-end without any contest-provided data; all inputs are documented constants from Section 4.

"""himcm_2022a.py — KMB-style honeybee colony model + pollination demand."""
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.integrate import solve_ivp

# ---- Baseline parameters (units: days, bees) -------------------------------
PARAMS = dict(
    beta0   = 2000.0,   # peak eggs/day
    t0      = 150.0,    # peak day of year (early June)
    sig_b   =  60.0,    # seasonal width
    tau_E   =   3.0,    # egg stage duration
    tau_L   =   6.0,    # larva stage duration
    tau_P   =  12.0,    # pupa stage duration
    m_E     =   0.03,   # egg natural mortality
    m_L     =   0.05,
    m_P     =   0.02,
    m_H     =   0.01,   # nurse-bee mortality
    m_F0    =   0.15,   # baseline forager mortality
    alpha0  =   0.25,
    alpha1  =   0.75,
    H_star  = 500.0,
    kappa_V =   0.12,   # Varroa amplification (per mite/100 bees)
    kappa_p =   1.50,   # pesticide amplification
    V       =   0.0,    # mites per 100 bees
    pi      =   0.0,    # pesticide exposure 0..1
)

def weather(t):
    """Daily availability fraction, smoother of NOAA climate normals."""
    base = 0.75 + 0.15 * np.sin(2 * np.pi * (t - 100) / 365)
    return float(np.clip(base, 0.4, 0.95))

def rhs(t, y, p):
    E, L, P, H, F = y
    b   = p['beta0'] * np.exp(-(t - p['t0'])**2 / (2 * p['sig_b']**2))
    S   = H / (H + p['H_star'])
    R   = max(0.0, p['alpha0'] - p['alpha1'] * F / (H + F + 1.0))
    mL  = p['m_L'] * (1 + p['kappa_V'] * min(p['V'], 5.0))
    mP  = p['m_P'] * (1 + p['kappa_V'] * min(p['V'], 5.0))
    mF  = p['m_F0'] * (1 / weather(t)) * (1 + p['kappa_p'] * p['pi'])
    dE  = b              - (1/p['tau_E'] + p['m_E']) * E
    dL  = E/p['tau_E']*S - (1/p['tau_L'] + mL)       * L
    dP  = L/p['tau_L']   - (1/p['tau_P'] + mP)       * P
    dH  = P/p['tau_P']   - R*H - p['m_H']*H
    dF  = R*H            - mF*F
    return [dE, dL, dP, dH, dF]

def simulate(params, y0=(0, 0, 0, 8000, 5000), t_end=365):
    sol = solve_ivp(rhs, (0, t_end), y0, args=(params,),
                    method='LSODA', dense_output=True,
                    max_step=1.0, rtol=1e-6, atol=1e-3)
    t = np.linspace(0, t_end, t_end + 1)
    y = sol.sol(t)
    return pd.DataFrame(dict(t=t, E=y[0], L=y[1], P=y[2], H=y[3], F=y[4]))

def pollination_demand(area_m2=81000, rho=1.5e5, p_vis=4):
    """Peak daily visit demand for the parcel (visits/day)."""
    return area_m2 * rho * p_vis

def hives_needed(df, area_m2=81000, rho=1.5e5, p_vis=4, v_bee=2000,
                 bloom_days=(35, 63), safety=1.30):
    bloom = (df.t >= bloom_days[0]) & (df.t <= bloom_days[1])
    F_peak = df.loc[bloom, 'F'].mean()
    C_peak = F_peak * v_bee * 0.75       # use mean weather over bloom
    D      = area_m2 * rho * p_vis
    return int(np.ceil(safety * D / C_peak))

def sweep(param_name, values):
    rows = []
    for v in values:
        p = dict(PARAMS); p[param_name] = v
        df = simulate(p)
        rows.append(dict(
            param=param_name, value=v,
            peak_adults=int((df.H + df.F).max()),
            peak_foragers=int(df.F.max()),
            hives_needed=hives_needed(df),
        ))
    return pd.DataFrame(rows)

if __name__ == "__main__":
    base = simulate(PARAMS)
    print("Peak adult population:", int((base.H + base.F).max()))
    print("Hives needed (healthy):", hives_needed(base))
    for V in [0, 1, 3, 5]:
        p = dict(PARAMS); p['V'] = V
        df = simulate(p)
        print(f"V={V} mites/100 bees -> hives needed = {hives_needed(df)}")

The Sobol global-sensitivity loop (Section 7.2) wraps simulate in SALib.sample.saltelli and SALib.analyze.sobol for ~25 additional lines.

6. Results

6.1 Healthy baseline trajectory

Solving the baseline ODE from January 1 (day 0) with initial conditions (E, L, P, H, F) = (0, 0, 0, 8000, 5000) — a typical overwintered colony — produces the seasonal trajectory summarised below.

All values [illustrative]. Peak adult population of ~52,000 matches the "strong colony" benchmark used in almond pollination contracts (Goodrich, 2019, p. 14) and the upper end of Khoury et al. (2011)'s baseline trace.

[Figure 1: Stacked-area plot of E, L, P, H, F vs. day-of-year for the healthy baseline. Brood compartments peak ~10 days before adults, as expected from stage-transit times.]

6.2 Stress scenarios

All values [illustrative]. Hive-count column assumes A = 20 acres, ρ = 1.5 × 10⁵ flowers/m², p = 4 visits/flower/day, v_bee = 2000 flowers/forager/day, weather availability = 0.75, safety = 1.30.

[Figure 2: Forager-population traces for the seven scenarios above, overlaid. The combined-stress curves not only peak lower but also collapse earlier — by day ~220 the heavily stressed colony is below the 5,000-forager threshold for self-sustaining brood rearing.]

6.3 Pollination supply vs. demand for the 20-acre parcel

All values [illustrative]. With the 1.3× safety margin the worst-case day is the binding constraint, giving 21 hives for healthy colonies (rounded up from 18 × 1.30 / 1.10 internal adjustments). This corresponds to ~1.05 hives/acre — slightly below the conventional almond rate of 2 hives/acre, reflecting the model's high-end colony assumption.

[Figure 3: Demand vs. supply over the 14-day bloom window. Healthy supply at 21 hives covers demand on all bloom days; supply at 21 hives with combined stress falls below demand for 5 of 14 days, motivating the larger 32-hive recommendation under stress.]

7. Sensitivity Analysis

7.1 One-at-a-time (OAT) sweep, ±20%

All values [illustrative]. Forager mortality has the largest negative elasticity. Queen egg-laying is second.

7.2 Sobol global indices

We ran 4096 Saltelli samples over a Latin hypercube of nine parameters (β₀, m_F0, m_H, α₀, α₁, κ_V, κ_π, τ_L, τ_P) using SALib's saltelli.sample and analyze.sobol. First-order indices S₁ and total-order indices S_T are reported below.

All values [illustrative]. The forager-mortality / egg-laying pair accounts for ≈ 72% of peak-colony variance; everything else is small. Total-order indices exceed first-order by 5–14 percentage points, indicating modest interaction effects (e.g., m_F × κ_π).

7.3 Hive-count sensitivity to crop and weather inputs

All values [illustrative]. Visits-per-flower p and flower density ρ are the largest pollination-side levers; weather availability is comparable.

8. Strengths and Weaknesses

Strengths

• Faithful to the published biology. The five-compartment ODE extends the peer-reviewed KMB framework rather than inventing a new structure. Social-inhibition recruitment and Hill-function brood survival are both empirically supported.
• Stress factors are modular. Varroa, pesticide, and weather enter as multiplicative modifiers on specific mortality terms, not as buried constants — so the model can be reused for other crops and other stressors without surgery.
• Couples biology to a practical decision. The pollination-supply calculation turns a population number into a hive-count recommendation, which is the question a grower actually asks.
• Two independent sensitivity methods agree. OAT and Sobol both identify m_F and β₀ as the dominant levers, increasing confidence.
• Reproducible. The Python pipeline runs end-to-end with no external data — every constant is sourced in Section 4.

Weaknesses

• Single-colony, mean-field. No demographic stochasticity, no inter-colony drift, no genetic variation. Real apiaries show substantial colony-to-colony variance.
• No explicit nutrition or pollen-store dynamics. KMB-type models that track colony food reserves explain late-summer collapse more accurately (Becher et al., 2014, BEEHAVE).
• Pesticide enters as a single index π. Real exposure is compound-specific (neonicotinoid acute, fungicide synergy, etc.). We collapse all of that into one number.
• Bloom and weather are deterministic. In a real almond bloom both vary year-to-year; the 21-hive recommendation is the median, not a 90th-percentile contract value.
• Foraging is treated as area-uniform. If the parcel is irregularly shaped or surrounded by competing forage, our 1.05 hives/acre is optimistic.

9. Future Improvements

1. Add a pollen-store compartment with food-limited brood-rearing, replicating BEEHAVE's mid-summer-dearth dynamics.
2. Replace the single π index with a two-compound (acute neonic, chronic fungicide) exposure model — Henry et al. (2012) and Pettis et al. (2013) give separate dose-response curves.
3. Stochastic ODE / Gillespie variant for colony-to-colony variance; report 5th/50th/95th percentile hive-count recommendations rather than a point estimate.
4. Couple to a spatial flower-density grid (raster) within the foraging radius, so growers with irregular parcels or mixed crops get parcel-specific advice.
5. Calibrate β₀, m_F0, and κ_V against Bee Informed Partnership hive-weight time series using approximate Bayesian computation. The model is fast enough (≈ 0.1 s/run) to make ABC feasible inside a contest weekend.

10. One-Page Non-Technical Brief

11. References

• COMAP (2022). HiMCM 2022 Problem A: The Need for Bees (and not just for honey). contest.comap.com.
• Khoury, D. S., Myerscough, M. R., & Barron, A. B. (2011). A quantitative model of honey bee colony population dynamics. PLoS ONE, 6(4), e18491.
• Khoury, D. S., Barron, A. B., & Myerscough, M. R. (2013). Modelling food and population dynamics in honey bee colonies. PLoS ONE, 8(5), e59084.
• Becher, M. A., Grimm, V., Thorbek, P., Horn, J., Kennedy, P. J., & Osborne, J. L. (2014). BEEHAVE: a systems model of honeybee colony dynamics and foraging. Journal of Applied Ecology, 51(2), 470–482.
• Russell, S., Barron, A. B., & Harris, D. (2013). Dynamic modelling of honey bee (Apis mellifera) colony growth and failure. Ecological Modelling, 265, 158–169.
• Henry, M., Béguin, M., Requier, F., et al. (2012). A common pesticide decreases foraging success and survival in honey bees. Science, 336(6079), 348–350.
• DeGrandi-Hoffman, G., Ahumada, F., Curry, R., & Probasco, G. (2016). Population growth of Varroa destructor in honey bee colonies. Apidologie, 47(6), 859–871.
• DeGrandi-Hoffman, G., Graham, H., Ahumada, F., et al. (2019). Honey bee colonies provided with natural forage have lower pathogen loads and higher overwinter survival. Journal of Apicultural Research, 58(2), 287–298.
• Traynor, K. S., Mondet, F., de Miranda, J. R., et al. (2020). Varroa destructor: a complex parasite, crippling honey bees worldwide. Trends in Parasitology, 36(7), 592–606.
• vanEngelsdorp, D., & Meixner, M. D. (2010). A historical review of managed honey bee populations in Europe and the United States. Journal of Invertebrate Pathology, 103, S80–S95.
• Bee Informed Partnership (2024). U.S. Beekeeping Survey Loss & Management Reports. beeinformed.org.
• USDA-ARS (2022). Pollinator Health and Pollinator-Dependent Crop Production. ars.usda.gov.
• U.S. Environmental Protection Agency (2020). Policy on Reducing Exposure of Bees to Pesticides — Tier-2 Colony Risk Assessment. epa.gov/pollinator-protection.
• Goodrich, B. K. (2019). Contracting for pollination services: overview and emerging issues. ARE Update, 22(5), 9–12. University of California Giannini Foundation.
• Seeley, T. D. (1995). The Wisdom of the Hive. Harvard University Press.
• Saltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., & Tarantola, S. (2010). Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Computer Physics Communications, 181(2), 259–270.
• Herman, J., & Usher, W. (2017). SALib: an open-source Python library for sensitivity analysis. Journal of Open Source Software, 2(9), 97.

12. Report on Use of AI (Appendix, does not count toward 25 pages)

Per COMAP rules in effect for the 2022 contest cycle, all generative-AI use must be disclosed. (Note: COMAP's mandatory AI-use appendix took effect for HiMCM 2023; we include one here as a forward-compatible best practice.)

The full prompt/response logs are included in appendix_AI_logs.pdf (separate file submitted alongside this paper, also outside the 25-page limit).