# YEAH issue 02 — chemistry and manufacturing evidence

Research checked 2026-09-22. Read the supplied Markdown draft and the relevant chemistry/manufacturing passages in `digests/02-the-shape-of-softness/source/extracted/Modern_Running_Shoe_Foams.txt` as claims to investigate. This file is a research brief, not finished article copy. Manufacturer evidence describes that supplier’s products/processes; it is not an independent ranking. Numeric examples below belong to identified experiments or grades.

## Twelve claims suitable for the article

### 1. Material family, blowing method, and shaping route are separate variables

**Safe claim:** A-TPU is a subtype of TPU. “Supercritical” describes processing, while “expanded bead” describes an intermediate structure and assembly route. These are not five mutually exclusive material/process boxes.

**Evidence:** BASF’s current Infinergy portfolio explicitly lists aliphatic A790A and A1190A for both E-TPU steamchest and autoclave routes, aliphatic SP9631 for SCF injection, and aromatic SP9552 for SCF injection. A790A’s listed midsole densities differ by route: 110–140 g/L for steamchest, 80–110 g/L for autoclave. Both list >75% **pendulum rebound**, not shoe compression-loop energy return.

**Source / locator / depth:** [BASF, Infinergy portfolio](https://plastics-rubber.basf.com/emea/en/performance_polymers/products/infinergy), “What are the foam properties…” tables and “How can Infinergy be processed?”; full manufacturer page read. Its HTML places multiple product headings before tables; use the rendered brochure/table when reproducing any detailed grade table.

**Graphic:** three selectors: polymer → gas-generation method → shaping route. Use examples of supported combinations, not a claim that every grade works in every process.

### 2. EVA’s vinyl-acetate units interrupt crystallizable ethylene sequences

**Safe claim:** EVA is a statistical copolymer; vinyl-acetate content is one control over its crystallization and melting behavior. It is not a fixed molecular recipe.

**Evidence:** Shi et al. studied 14, 18, and 28 wt% VA grades. Under their shared DSC protocol, increasing VA reduced crystallization tendency and crystal perfection. The VA units were treated as randomly distributed along the chain, with noncrystallizable interruptions in ethylene sequences.

**Source / locator / depth:** [Shi et al., 2008, DOI 10.3144/expresspolymlett.2008.75](https://www.expresspolymlett.com/articles/EPL-0000692_article.pdf), §2.1; §3.1–3.2; Tables 1–3; conclusion; full-text PDF consulted at these sections. These are unfoamed resin grades, not a survey establishing a universal footwear VA range.

**Graphic:** an ethylene-rich chain with intermittent acetate side groups, plus small polyethylene-like crystalline regions. Do not draw EVA as alternating hard and soft blocks.

### 3. Chemical crosslinking and chemical blowing are different operations

**Safe claim:** A physically blown EVA foam can still have a covalently crosslinked network. “Physical foam” does not mean “no chemical crosslinks.”

**Evidence:** Li et al. compared azodicarbonamide blowing with supercritical N₂ foaming of peroxide-crosslinked EVA. The physical route used crosslinked solid sheets; the chemical route coupled blowing-agent decomposition and crosslinking. BIPB supplied the crosslinks in both. Their physical foams had reported 50–100 μm cells; their chemical samples included much larger cells and broader distributions. This is a controlled formulation/process result, not a universal law about either method.

**Source / locator / depth:** [Li et al., Materials 2024, 17, 3719, DOI 10.3390/ma17153719](https://doi.org/10.3390/ma17153719), §2.1–2.2, Table 1, Figs. 1, 7–10, §4. Full-text consultation at these sections via [open-access PDF mirror](https://pdfs.semanticscholar.org/360f/134fcbef51a7f38fa7e340bc6fa1886baa8e.pdf); publisher/PMC HTML could not be fetched directly. The paper uses slightly different processing-window summaries in abstract/body/conclusion; do not lift a single universal temperature range.

**Graphic:** separate the “build network” and “supply gas” steps. Annotate this as one EVA process example.

### 4. TPU has covalently connected chains and physically associated domains

**Safe claim:** In a conventional TPU, long soft segments and shorter hard segments belong to polymer chains. Associations between hard segments create reversible physical junctions that help restrain flow; heating permits thermoplastic processing.

**Evidence:** Covestro describes polyol + short-chain diol + diisocyanate synthesis, rigid/flexible phases, physical interactions between neighboring rigid segments, mixed phases, and reversibly melting junctions. Composition and production history both change properties. Hydrogen bonding is important, but “all hard domains are perfect crystals” is too strong.

**Source / locator / depth:** [Covestro, Chemical-physical structure](https://solutions.covestro.com/en/highlights/articles/theme/product-technology/chemical-physical-structure-tpu), “A structured network…” and “Tunable building blocks…”; full manufacturer text read through indexed result. Supplementary primary support: [chain-extender structure study, Polymer 2026](https://www.sciencedirect.com/science/article/pii/S003238612600025X), introduction, explicitly describes hard-segment association as physical crosslinks; abstract/introduction excerpts only.

**Graphic:** soft coils covalently connected to hard blocks; several chains contribute blocks to the same hard-rich domain. Label this an idealized morphology. Do not draw a covalent crosslink symbol between all neighboring hard blocks or imply perfect elastic recovery.

### 5. “Aliphatic” does not imply one universal softness, density, or crystallinity

**Safe claim:** Aliphatic and aromatic TPU differ in isocyanate chemistry. Their mechanical behavior also depends on isocyanate shape/symmetry, soft segment, chain extender, proportions, and processing.

**Evidence:** Wang et al. held PTMG/BDO chemistry while comparing five isocyanates. In that series, HDI-based PU had the strongest crystallinity and the highest hardness/modulus despite HDI’s flexible linear structure. This directly counters the draft’s blanket “no aromatic ring → disrupted crystallinity → softer and lighter” mechanism. H₁₂MDI is cycloaliphatic: it retains saturated rings, not a universally flexible linear chain.

**Source / locator / depth:** [Wang et al., Polymers 2024, 16, 3045](https://www.mdpi.com/2073-4360/16/21/3045), DOI 10.3390/polym16213045, §3 hydrogen-bond/crystallinity discussion and §4 conclusion; indexed full-text excerpts read, not successfully fetched end-to-end. Nonfoam PU experiment; do not transfer its numerical properties to shoes.

**Additional source:** [Covestro, Optical properties](https://solutions.covestro.com/en/highlights/articles/theme/product-technology/optical-properties), “Yellowing”; manufacturer text read. It supports improved resistance to aromatic-urethane UV yellowing. It does not establish immortal color stability for every finished foam/additive package.

### 6. PEBA is a tunable block family, not a frictionless spring

**Safe claim:** PEBA combines polyamide hard blocks and polyether soft blocks. Changing their makeup/ratio changes behavior; Pebax is a trade family, not a single foam recipe.

**Evidence:** Arkema identifies PA12 blocks in standard Pebax and PA11 in Pebax Rnew. A primary study of Pebax 3533/4533/5533 used PA12/PTMO grades of different hardness. Increasing hard-segment content improved compressive strength but reduced resilience in that experiment; foam expansion also changed the result.

**Sources / locators / depth:** [Arkema, Pebax family](https://hpp.arkema.com/en/product-families/pebax-elastomer-family/), “What are Pebax polymers?” and Rnew paragraph; manufacturer page read. [Li et al., 2023, DOI 10.1016/j.supflu.2023.106052](https://www.sciencedirect.com/science/article/pii/S0896844623002164), abstract, Materials, highlights; abstract and publisher preview read, not full paper.

**Graphic:** PA domains anchor a soft polyether-rich phase. The block-ratio control should communicate a tradeoff, not a quality score. Remove “frictionless,” “near-zero internal friction,” and “highest energy-to-weight in polymer engineering.”

### 7. TPEE commonly uses polyester hard blocks and polyether soft blocks

**Safe claim:** A common TPEE architecture is crystalline PBT hard segments with PTMG soft segments. “Polyester elastomer” does not mean every segment is polyester.

**Evidence:** Jiang et al. studied PBT/PTMG TPEEs with different block ratios and CO₂ solid-state foaming. Higher hard-segment content changed crystallinity, melting temperature, and the foaming window. CO₂ solubility and diffusivity were higher in the soft segments than the hard segments. These are process-relevant changes, not proof of a universal firmer or more laterally stable running feel.

**Source / locator / depth:** [Jiang et al., CIESC Journal 2020, 71(2), 871–878](https://hgxb.cip.com.cn/EN/10.11949/0438-1157.20191196), DOI 10.11949/0438-1157.20191196, English/Chinese abstracts and Figs. 3–9 captions; abstracts and captions read. English abstract says the window broadened, but its reported Chinese endpoint ranges are not consistent with a simple width claim; retain only “changed/shifted” without further full-text checking.

**Graphic:** PBT-rich domains + soft polyether connections; gas uptake differs across phases. Do not claim PBT always crystallizes “faster and cleaner” than PA or TPU.

### 8. SCF processing does not guarantee homogeneous nucleation or one cell-size band

**Safe claim:** Temperature, pressure, dissolved gas, crystallinity, rheology, nucleating interfaces, and cooling history jointly determine the cellular structure. Crystals can nucleate cells heterogeneously.

**Evidence:** Wang et al. intentionally changed PEBA crystallinity before CO₂ foaming. The same approach produced uniform or bimodal cell populations. Their reported cell-density span was 6.8 × 10⁶ to 3.58 × 10¹⁰ cells/cm³; the large-cell size decreased from 206.4 to 48.0 μm as crystallization changed. Crystals supplied heterogeneous nucleation sites. This defeats the draft’s universal 5–30 μm, 10⁹–10¹² cells/cm³, instant homogeneous-nucleation recipe.

**Source / locator / depth:** [Wang et al., 2023, DOI 10.1016/j.supflu.2023.106030](https://www.sciencedirect.com/science/article/pii/S0896844623001948), abstract/highlights and final introduction paragraph; publisher preview read, not full paper.

**Graphic:** controls affect competing nucleation, growth, coalescence, and stabilization. Any animated cell-size changes are qualitative unless reproducing one named experimental series.

### 9. Gas diffusion after foaming matters: closed cells are not hermetically sealed forever

**Safe claim:** Gas can diffuse through polymer cell walls. If blowing gas leaves faster than ambient gas enters, the foam can shrink; processing must manage expansion and subsequent dimensional stability.

**Evidence:** Yang et al. foamed one PEBA grade using CO₂/N₂ mixtures. Adding nitrogen reduced the large shrinkage/recovery excursions observed with pure CO₂ under their conditions. The paper measures gas solubility, evolving expansion, cellular morphology, and cyclic compression. It illustrates why “lighter immediately after release” is not identical to “stable final low density.”

**Source / locator / depth:** [Yang et al., Macromolecular Materials and Engineering 2024, DOI 10.1002/mame.202300437](https://onlinelibrary.wiley.com/doi/10.1002/mame.202300437), §2.1–2.3, §3.1–3.3, Figs. 2–6; full-text methods/results consultation. Some prose about cell-size trends is internally inconsistent between results/conclusion; use the robust dimensional-stability finding, not a universal nitrogen-versus-CO₂ cell-size rule.

**Graphic:** arrows for gas out and ambient gas in, linked to shrinkage then stabilization. Pressure generation, gas diffusion, polymer relaxation, and crystal/network constraints interact.

### 10. Bead expansion and bead welding are distinct; the weld is an engineered load path

**Safe claim:** Expanded beads contain cells; the shaped part also contains interbead interfaces. Steam is used to heat/soften bead surfaces for joining in the cited Infinergy route. It should not be described as the historical blowing agent.

**Evidence:** BASF describes pressure/heat expansion of granules followed by steam bonding. A recent primary study varies ETPU surface modification and RF welding time: insufficient joining produces interbead failure, stronger welding shifts fracture into beads, and excessive welding can collapse/densify the foam. Therefore bead skins are neither automatically “dead mass” nor an automatic durability guarantee.

**Sources / locators / depth:** [BASF, Small beads for long distances](https://www.basf.com/gb/en/media/science-around-us/small-beads-for-long-distances), manufacturing paragraph and “2,500 foam beads…”; manufacturer text read. [Himsel et al., 2026, DOI 10.1002/pola.70317](https://onlinelibrary.wiley.com/doi/10.1002/pola.70317), §3.2 RF-processing results and §4; full-text results/conclusion consultation, first published 2026-09-03. This controlled study does not establish a lifespan for finished shoes.

**Graphic:** zoom from part → beads/welds → cells within one bead. Show chains joining across a softened interface schematically, not beads glued only at geometric dots.

### 11. A slab/preform can be saturated and expanded without assembling beads

**Safe claim:** Gas can enter a preformed solid polymer piece in an autoclave; expansion and final part shaping need not happen in the same machine or step.

**Evidence:** Zotefoams’ documented three-stage platform extrudes a plate, saturates slabs with nitrogen in a high-pressure autoclave, and expands gas-charged slabs in a lower-pressure autoclave. Its public generic process includes crosslinking and staged cooling. This verifies a manufacturing pathway; it does not disclose every detail of a proprietary Nike/PEBA formulation.

**Source / locator / depth:** [Zotefoams, Three-stage process](https://www.zotefoams.com/who-we-are/3-stage-process/), Stage 1, Stage 2, Stage 3; manufacturer process page read. Do not universalize the generic crosslink step to every named PEBA product without a product-specific source.

**Graphic:** plate/slab → gas saturation → controlled expansion → foam stock → part conversion. Label subsequent cutting/molding as options, not proof every ZoomX midsole is CNC-machined. No source here establishes slab foam as inherently highest-return.

### 12. Direct injection introduces gas into the melt before it fills a mold

**Safe claim:** In a documented SCF injection process, a metered gas dissolves in polymer melt in the barrel, then cells develop during molding. Counterpressure and mold-opening are process variants, not requirements built into the definition.

**Evidence:** Trexel describes controlled SCF dosing, formation of a single-phase polymer/gas solution, and cell nucleation/growth as material enters the mold. Its packaging-system example explains cavity packing by cell growth. That supports the sequence, not a universal midsole cycle time or a guarantee of zero scrap.

**Sources / locators / depth:** [Trexel, MuCell technology](https://trexel.com/mucell/), technology/four-step description; manufacturer page read. [Trexel P-300 technical sheet](https://trexel.com/wp-content/uploads/2019/06/Trexel_P-300_datasheet_2019_FINAL.pdf), “Foaming technology for fast cycling applications”; manufacturer technical text read. Product context is thin-wall packaging, not validation of running-shoe performance.

**Graphic:** pellet feed → heated screw + gas dosing → pressurized polymer/gas mixture → mold → nucleation/growth/cooling. Keep this distinct from autoclave saturation of an existing solid piece.

## Required corrections and limits for both drafts

- Replace the five-rung material hierarchy with **EVA, TPU (including aliphatic TPU), PEBA, TPEE** plus process/structure choices. The consumer-facing five tabs can remain, but show A-TPU nested within TPU.
- Remove all universal energy-return, foam-density, cold-stiffening, lifespan-kilometer, and resin-price ranges unless tied to a dated grade/model, method, and conditions. The sources above do not establish those category-wide tables.
- Delete the original draft’s aromatic-ring-mass explanation for TPU foam weight. Foam mass depends on final volume and density; resin chemistry, expansion and formulation all contribute. Monomer molecular weight alone is not bulk polymer density.
- Remove “covalent network is EVA’s structural flaw” and “physical domains pull it back to its exact origin.” Covalent crosslinks help restrain chain flow and support foaming. Physical networks can also dissipate, rearrange, creep, and fail. Neither phrase is a fatigue mechanism or a mileage prediction.
- Remove the PDF’s assertion that physical foaming necessarily leaves no covalent network. Claim 3 supplies a direct counterexample.
- Change “SCF does not rewrite the polymer’s hysteresis” to: **The backbone remains the same, but gas and thermal processing can change the polymer’s organization as well as its cell structure.** Claims 7–9 support that distinction.
- Remove “frictionless thermal agitation,” universal tan δ <0.04, and “hundreds of degrees above Tg.” Even the draft’s own −65°C Tg is only 85°C below a 20°C room, and a single Tg does not imply temperature-invariant performance.
- Do not turn compression recovery, pendulum rebound, ball rebound, DMA tan δ, and compression-loop work ratios into one “energy return” scale. Likewise, a resin datasheet is not a whole-shoe test.
- Replace “steam historically” as a TPU blowing agent with separate expansion and steam-fusion stages (claim 10). The exact original industrial gas recipe is not established by the BASF explainer and should remain unspecified there.
- Avoid claims that bead skins are non-working mass, that bead hierarchy guarantees durability, or that slab continuity guarantees maximal energy return. Local load paths and welding quality matter.
- Avoid material-only sensory promises: “TPEE means lateral stability,” “EVA cannot race,” “A-TPU lasts longer than PEBA,” or “PEBA is cold-invariant.” Finished formulation, geometry and test conditions remain essential.

## Diagram guardrails

Use an explicitly schematic scale ladder: **chemical repeat units / chain architecture → nanometer-scale domains → micrometer-scale cells → millimeter-scale beads or part structure**. Do not portray every material as a bag of literal molecular springs. Distinguish a covalent bond *along* a block-copolymer chain from a covalent network bridge *between* chains. Gas space and the polymer skeleton both influence foam compression; “millions of sealed micro-pneumatic springs” alone misses the solid’s mechanics. Relative density (foam density divided by unfoamed compound density) is a useful independent label; compare like volume and account for fillers/blends when defining the solid reference.

The best quantitative inset is an identified process example, not a universal leaderboard: claim 1 provides supplier-grade route-dependent density, claim 8 provides an experimental crystallinity/cell-morphology example, and claim 10 provides a welding-quality mechanism. Clearly distinguish measured examples from illustrative animation controls.


---

# Mechanics evidence for YEAH issue 02

Verified 2026-09-22. Scope: mechanics, fatigue, test interpretation, running economy. Read both supplied drafts; neither is an authority. Primary-source findings below are restricted to the tested specimens and protocols. DOI links are the preferred public citations; accessible full-text mirrors are supplied for audit.

## Editorial decisions

- Use one original **whole-shoe compression-versus-returned-work scatterplot** from S1. Label each point by shoe model, with the material as secondary information. This is a compact demonstration of why return percentage alone is incomplete.
- Use the S2 metabolic results as **two measured endpoints**, fresh and worn. Connecting lines may guide the eye but must not imply measurements at intermediate mileage. Do not draw family-wide service-life curves.
- A conceptual hysteresis animation can explain the integral, but must be visibly labeled **illustration, not measured material data**. Give it neutral sample names. Do not assign invented curve shapes to polymer families.
- Keep four evidence levels visually separate: resin/material specimen; foam component; assembled shoe; human metabolic outcome.
- There is no verified matched A-TPU/EVA/TPU/PEBA/TPEE experiment here. Empty evidence cells are preferable to an invented ranking.

## S1 — Whole-shoe compression and metabolic cost

Hoogkamer et al., *A Comparison of the Energetic Cost of Running in Marathon Racing Shoes*, Sports Medicine 48, 1009–1019 (2018). [DOI](https://doi.org/10.1007/s40279-017-0811-2); [full article PDF](https://www.greif.de/downloads/A_Comparison_of_the_Energetic_Cost_of_Running_in_M.pdf).

**Read depth:** full methods/results/discussion; §2.2, Fig. 3, Tables 1–2. Whole shoes: rigid last, force-controlled vertical loading, approximately 2,000 N peak and 185 ms contact. Tests followed running use; every pair accumulated <50 km. Test temperature not specified in §2.2.

| Shoe | Construction | Peak deformation, mm | Return, % | Returned work, J |
|---|---|---:|---:|---:|
| Nike Zoom Streak 6 | EVA + rearfoot airbag | 6.1 | 65.5 | 3.28 |
| adidas Adios Boost 2 | TPU | 5.9 | 75.9 | 3.56 |
| Nike prototype | PEBA + carbon plate | 11.9 | 87.0 | 7.46 |

Eighteen high-caliber men ran 14/16/18 km/h; masses were matched. Prototype metabolic cost averaged 4.16% below Streak and 4.01% below Boost. Nike funded the study; two authors were Nike employees and Kram consulted for Nike.

**Limit:** model comparison confounds foam, stack, plate and geometry. Higher returned work mainly accompanied greater compliance. Mechanical percentages are not metabolic percentages. No uncertainty bars for these mechanical values are supplied here.

## S2 — Fresh versus 450 km, with an essential measurement distinction

Rodrigo-Carranza et al., *Influence of different midsole foam in advanced footwear technology use on running economy and biomechanics in trained runners*, Scandinavian Journal of Medicine & Science in Sports 34, e14526 (2024; online 2023). [Full primary article/DOI](https://onlinelibrary.wiley.com/doi/full/10.1111/sms.14526).

**Read depth:** full text; §2.2–2.3, Tables 1–2. Twenty-two men; randomized crossover; four 4-minute trials, 13 km/h, 20–23°C. One researcher accumulated 450 km on asphalt, approximately 13 km/h, 40 sessions.

| Condition | Metabolic cost, W/kg, mean ± SD | Bending return, J | Bending hysteresis, % |
|---|---:|---:|---:|
| New EVA | 15.15 ± 1.13 | 4.39 ± 0.02 | 26.0 ± 1.3 |
| Worn EVA | 15.13 ± 1.14 | 3.93 ± 0.05 | 39.5 ± 0.6 |
| New PEBA | 14.87 ± 0.99 | 4.83 ± 0.14 | 24.7 ± 0.8 |
| Worn PEBA | 15.21 ± 1.01 | 3.64 ± 0.18 | 42.4 ± 1.1 |

Mechanical test: complete-shoe **three-point bending**, 80 mm support spacing, 20 mm displacement, 4 mm/s, ten cycles. **Not compression return.** Different prototype dimensions confound materials. PEBA metabolic cost increased significantly; EVA did not. Only endpoints measured. On supplied prototypes.

## S3 — Fatigue in extracted foam samples

Aimar et al., *Compression fatigue of elastomeric foams used in midsoles of running shoes*, Footwear Science 16(2), 93–103 (2024). [DOI](https://doi.org/10.1080/19424280.2024.2317881); [author-hosted full PDF](https://laurent-orgeas.github.io/papers/aimar_et_al_2024_footsci.pdf).

**Read depth:** full methods/results/discussion; Tables 1–2; Figs. 2–5. Three samples per foam; 2 mm thickness; 22°C, 55% RH; lubricated platens; 200,000 compression cycles; 1.25 Hz; stated displacement-rate/initial-height = 4 s⁻¹; maximum compression natural-strain magnitude 1.6. Most specimens were 2 mm-diameter cylinders; TPU used 10 × 10 mm sections.

| Specimen | Polymer | Density, g/cm³ | Initial loss factor η |
|---|---|---:|---:|
| F1 | EVA | 0.17 ± 0.02 | 0.13 ± 0.01 |
| F2 | EVA | 0.13 ± 0.02 | 0.14 ± 0.01 |
| F2* | EVA insert | 0.23 ± 0.02 | 0.12 ± 0.01 |
| F3 | TPU | 0.24 ± 0.02 | 0.05 ± 0.01 |
| F4 | PEBA | 0.09 ± 0.02 | 0.06 ± 0.01 |

η = dissipated work/(π × loading work): **η is not fractional hysteresis**. Cycling produced densification and reduced stress/absorbed work. No universal mileage conversion. Formulation, density and architecture varied together. Two authors had Decathlon affiliations.

## S4 — More closely matched EVA/TPU prototypes, including individual outcomes

Worobets et al., *Softer and more resilient running shoe cushioning properties enhance running economy*, Footwear Science 6(3), 147–153 (2014). [DOI](https://doi.org/10.1080/19424280.2014.918184); [author-uploaded full text](https://www.researchgate.net/publication/265340597_Softer_and_more_resilient_running_shoe_cushioning_properties_enhance_running_economy).

**Read depth:** full text; Methods, Fig. 2, Tables 1–2. Adidas prototypes matched uppers/outsoles/geometry; mass equalized with 30 g additions. Whole-shoe compression: rigid last, 1,700 N peak, 4,250 N/s loading, three 20-cycle sessions; analysis used cycle 20. Temperature not specified.

| Experiment/shoe | Stiffness, N/mm | Hysteresis, % |
|---|---:|---:|
| Treadmill EVA | 167.0 | 31.3 |
| Treadmill TPU | 131.2 | 20.9 |
| Overground EVA | 186.1 | 32.3 |
| Overground TPU | 129.7 | 22.3 |

Each experiment involved 12 different runners. Mean oxygen consumption decreased 1.0% on treadmill (p=.044), 1.2% overground (p=.028). Treadmill individual percentage changes: −1.5, −2.3, −1.7, −0.2, −1.8, +0.9, −2.4, −1.7, 0.0, −0.5, −0.5, −0.3.

**Limit:** compliance and resilience changed together; their contributions cannot be isolated. Individual trial differences are not a validated persistent “responder” classification. Adidas supplied shoes; funding was not verified in the accessed text.

## S5 — Temperature is a test condition, not a family guarantee

Meuchelböck et al., *Influence of temperature on the compression properties of expanded thermoplastic polyurethane (ETPU)*, Journal of Materials Science: Materials in Engineering 19, 10 (2024). [Full primary article/DOI](https://link.springer.com/article/10.1186/s40712-024-00149-9).

**Read depth:** full methods/results/conclusions; Methods, Figs. 5–6, 9–10. Infinergy 32-100 U10 beads were steam-welded into plates; specimens conditioned ≥144 h at 23°C/50% RH. Quasi-static tests followed ISO 844, with ≥3 samples per density/temperature, to 75% compression. Fig. 6 specifies 4 mm/min. DMTA used 1 Hz, 4% static compression, ±1% amplitude and 1 K/min heating.

Reported example, approximately 250 kg/m³ ETPU:

| Temperature, °C | Compression modulus, MPa |
|---:|---:|
| −20 | 1.19 |
| 23 | 0.87 |
| 40 | 0.82 |

The maximum-loss-factor Tg was approximately −25°C for this grade. This supports temperature-sensitive mechanical behavior; it does not supply a PEBA/TPU ranking or a running-rate temperature curve. Treat these three points as measured examples, not a fitted universal law. Authors declared no competing interests.

## S6 — Foam/plate factorial human experiment; abstract-level access only

Perry et al., *Effects of longitudinal bending stiffness and midsole foam on running energetics*, Footwear Science 17(1), 3–9 (2025; online 2024). [Publisher abstract/DOI](https://doi.org/10.1080/19424280.2024.2431004).

**Read depth:** primary publisher abstract, key points and disclosures. Full text blocked (403); do not imply tables/methods were audited.

Four conditions crossed PEBA/EVA and plate/no plate. Eight men ran 14 km/h; six women 12 km/h; randomized mirrored order, each condition twice. Abstract reports approximately 1.0% main effects for plate and foam, no significant interaction. Relative to EVA/no plate, either individual feature improved economy 1.3%; both combined improved it 1.9%. Additional benefit from the second feature was not significant.

**Use:** qualify any claim that foam alone “explains the 4%.” Do not make a mechanistic pie chart allocating supershoe benefit to components. A nonsignificant interaction does not establish true additivity or a universal diminishing-return rule. Full geometry, mechanical protocol and condition-level uncertainty remain unaudited. Partly funded by Saucony; Perry employed by Puma; Hoogkamer disclosed company grants.

## Mechanical explanation to use

For a force–displacement test, loading work is the area under the loading branch, and recovered work is the magnitude of the area under the unloading branch. The difference is the loop loss. In a stabilized cycle returning to the same state, the lost mechanical energy is dissipated; in an initial cycle with residual deformation, avoid implying all missing energy instantly becomes measured heat.

Define the percentage explicitly:

`return fraction = recovered work / loading work`

`fractional hysteresis = (loading work − recovered work) / loading work`

Consequently `return fraction = 1 − fractional hysteresis` only when the numerator/denominator and complete cycle are the same. “Hysteresis” can also mean the loop area in joules; it is then not a number one can subtract from 1. S3’s η contains an extra π normalization and cannot be substituted.

**Compliance is not strain capacity.** Structural compliance describes deformation per force (locally dx/dF); stiffness is its reciprocal only with consistent local or secant definitions. Modulus uses stress and strain and attempts to normalize geometry. N/mm is shoe/specimen stiffness; MPa is a material-level modulus. A durometer reading is another indentation protocol, not any of these interchangeable values.

For nonlinear foams, report the force/displacement interval and whether stiffness is tangent, secant, fitted, or dynamic. For small-amplitude sinusoidal testing, storage/loss modulus and tan δ describe frequency-dependent response; this is different from integrating a large-strain running-like compression cycle.

Specify before comparing: specimen geometry and location; skin/bead interfaces; whole shoe versus extracted foam; force- versus displacement- versus energy-control; peak load/strain and waveform; rate and repetition frequency; rest/preconditioning; temperature/humidity; calculation definitions. Identical nominal peak force does not imply identical work input. Identical displacement does not imply identical force.

Step frequency and the repetition frequency experienced by one shoe are different: alternating-foot cadence counts both sides, whereas each shoe is normally loaded once per stride. Do not describe an arbitrary 2–4 Hz material test as automatically representative merely because runners take approximately that many steps per second.

Returned mechanical work is not automatically useful work for propulsion, and cannot be converted directly to oxygen savings. The runner changes movement, force generation and muscle–tendon behavior in the complete shoe. More compliance does not guarantee a lower peak ground-reaction force, less knee loading, or fewer injuries. Those need human measurements appropriate to the claim.

## Corrections to the supplied Markdown draft

1. Remove the “one mechanical objective”/“defined entirely by three properties” framing: the shoe also experiences shear/bending and spatially distributed loads, and geometry and runner interaction matter.
2. Replace universal 2.5–3.0 BW and 50–100 kN/s numbers with a specific protocol or omit. Do not generalize an impact-transient loading rate to the full stance phase.
3. Replace “compliance (strain capacity)” and “dynamic stiffness (modulus)” with the distinctions above.
4. Do not infer reduced skeletal peak force solely from a longer deceleration argument. The runner is not a passive rigid mass dropped onto a pad.
5. Remove the family-wide dynamic-return and mileage table. It has no shared test and no proven family-specific service-life endpoints. “Initial pop” is not an operational outcome.
6. Remove “PEBA avoids compaction/creep” and “does not pack down; it tears.” These are categorical failure-mode assignments that the supplied draft does not establish. Do not imply physically crosslinked foams are immune to irreversible damage.
7. Remove “A-TPU sustains its initial ride beyond 600 km,” “EVA loses 20–30% compliance by 150 km” and the drawn lifetime curves unless replaced with traceable specimen-specific measurements.
8. Remove “PEBA/A-TPU nearly identical −5 to 35°C” and universal temperature-stiffening percentages. A low Tg is not proof of temperature invariance in the complete foam.
9. Remove “PEBA frictionless thermal agitation” and “hundreds of degrees above Tg.” Room temperature minus −65°C is approximately 85°C, not hundreds. Mobility does not mean zero dissipation.
10. Remove the claim that foam resilience by itself explains 2–4% running economy via reduced calf/Achilles/plantar-fascia “torque demand.” Tendons and fascia are not independent active metabolic engines; the particular mechanism requires direct evidence.
11. Remove the conclusion that gas diffusion through micro-tears is the general cause of EVA packing-out. Separately identify cell damage, structural set, viscoelastic recovery and possible chemical change; the relative mechanisms are not established by a schematic.
12. Remove “bead skins are non-working mass” and “continuous slab gives highest return.” A mass penalty does not establish mechanical inactivity, and microstructure-dependent performance needs measurement.
13. Do not claim a soft foam that reaches densification automatically transfers the load specifically to the knee. Densification is a material response; joint loading is a human-system outcome.

## Additional corrections to `Modern_Running_Shoe_Foams.txt`

- A warning beneath a mixed-method table does not make the table quantitatively comparable. Separate ball rebound, large-strain compression and assembled-shoe percentages into different datasets or remove the numerical comparison.
- HOKA Mach-versus-Clifton numbers cannot isolate processing: shoe geometry, grade/blends, density, formulation and testing conditions may also differ. “That gap is process” overstates identification.
- “Supercritical does not rewrite hysteresis” is misleading: the base chemical identity need not change, but processing changes the cellular structure and the measured foam’s hysteresis can change.
- The 450 km observation is about two specific prototype models. Do not turn “no significant EVA metabolic change” into “EVA is nearly as good at mile 280 as mile 10” for the whole family.
- “Lost 2.3% economy” is ambiguous. Prefer the measured W/kg table, with direction: **metabolic cost rose**. Ratios of the displayed group means are derived values, not necessarily the published average paired percentage change.
- Its “worn PEBA midsoles” mechanics paragraph must say **whole-shoe bending**. It cannot be used as evidence that foam compression return fell by the table’s percentage.
- Remove “PEBA and A-TPU win cold races” and universal role recommendations based on chemistry alone. No winter race trial or matched A-TPU temperature experiment was established here.
- Higher hysteresis percentage does not alone establish higher operating temperature; total input work, cycle rate, heat capacity and thermal transport also matter. “Heat drives compression set” is not a complete single-cause explanation.
- Creases visible on the outside do not identify a microscopic failure mechanism or remaining running-economy benefit by themselves.

## Remaining uncertainty and chart restrictions

- No reliable universal A-TPU versus PEBA durability, TPEE versus PEBA stability, or foam-family temperature ranking is established by this set.
- S1 reports model-level mechanics without chart-ready uncertainty. Use dots with exact labels; do not fabricate error bars or curves.
- S1 source discrepancy identified during implementation: **Figure 3 labels the Streak at 3.28 J; discussion prose prints 3.38 J.** The table above and the implemented chart now use **3.28 J, attributed specifically to Figure 3**. Do not average the values or claim an author correction. This supersedes the earlier ledger cell that followed the discussion prose.
- S2 SD is between participants for metabolic cost; it is not the uncertainty of the paired change. Do not infer significance from overlapping SD bars. Mechanical repetitions are not independent worn-shoe replication.
- S3’s Table 2 prints the specific-energy unit as mJ/g, which appears dimensionally suspect against the reported stress scale. Avoid charting that column without checking supplementary data/authors. Density and η above are suitable specimen-specific tabular examples.
- S5 is quasi-static specimen testing; the temperature points do not predict how a particular complete shoe will feel or perform while running.
- S6 is limited to abstract-level claims until its full methods/tables can be obtained.
- Search located *Mechanical Testing of Midsole Properties at Different Impact Frequencies* (Applied Sciences 16(10), 5130; [publisher](https://www.mdpi.com/2076-3417/16/10/5130)). Search-visible abstract/method passages describe 1,500 N and 1.5–2.5 Hz, but direct full text returned 429 and PDF/XML were inaccessible. Do not include precise plotted values from it; no full table was audited.
- Search also located a very recent racing-foam preprint, [arXiv:2609.20485v1](https://arxiv.org/html/2609.20485v1), dated 17 September 2026. It should not be silently substituted for peer-reviewed fatigue evidence. It was not fully audited for this ledger and is not a chart source.


---

# Corrections to the supplied foam drafts

Recorded 22 September 2026. The supplied Markdown and PDF remain source material, not authorities. Their original bytes are preserved separately in the issue packet. This document records decisions made when adapting them; it does not silently amend their prose or the cited papers. The final scientific scope is the inspected article implementation and its optional research reading.

The three categories below distinguish an assertion unsupported at the claimed scope, a faulty causal or definitional account, and a citation that cannot establish the intended inference. A precise value without adequate support is unverified; it is not automatically false.

## Unsupported generalizations

| Supplied location or proposition | Why it exceeds the evidence | Resolution and support |
| --- | --- | --- |
| MD comparison matrix: one density, return, cold-stiffening and mileage band per family; PDF matched-SCF rebound ranking | No shared specimen selection or testing protocol establishes the five-way table. Polymer identity, subtype, process and trade name are mixed. | Remove the leaderboard and synthetic retention curves. Use named whole-shoe observations with their methods, plus qualitative architecture. Ledger foam-01, foam-18, foam-20 and foam-24. |
| MD universal 2.5–3.0 body-weight force and 50–100 kN/s loading rate | Population, speed, contact definition and measuring method are missing. An impact-transient slope is not the entire stance waveform. | Use the approximately 2,000 N, 185 ms **laboratory** protocol only beside the Hoogkamer dataset; never label it every footstrike. [Methods and Figure 3](https://www.greif.de/downloads/A_Comparison_of_the_Energetic_Cost_of_Running_in_M.pdf). |
| MD 5–30 μm cells, 10⁹–10¹² cells/cm³ and pressure-drop threshold as universal SCF output | Cell formation depends on the polymer, gas, crystals, rheology and processing history. Experiments deliberately produce different distributions. | Keep the route qualitative; identify SCF as a condition. PEBA research demonstrates uniform and bimodal structures. [Primary morphology study](https://www.sciencedirect.com/science/article/pii/S0896844623001948), abstract/highlights. |
| MD/PDF near-identical behavior across subzero-to-warm conditions, or PEBA/A-TPU winning cold races | A low transition temperature is not a complete temperature-dependent material test, much less a race trial. | State temperature as a test condition. Do not assign family-wide percentages. [ETPU temperature study](https://link.springer.com/article/10.1186/s40712-024-00149-9), Methods and Figures 5–6. |
| MD universal 200–800 km lifespans; PDF A-TPU durability advantage and EVA almost unchanged over hundreds of miles | A useful lifetime requires a defined outcome and replicated exposure. Two endpoints for two shoes do not define families. | Show fresh and 450 km observations only, attached to prototypes and protocol. Do not interpolate wear states. [Wear study](https://onlinelibrary.wiley.com/doi/full/10.1111/sms.14526), Sections 2.2–2.3 and Table 2. |
| MD PEBA as a pure spring, frictionless, or best energy-to-weight throughout polymer engineering | Absolute claims lack a defined comparison set and measurement. A soft phase is not dissipation-free. | Describe tunable blocks and distinguish return fraction from useful human outcome. [PEBA architecture](https://hpp.arkema.com/en/product-families/pebax-elastomer-family/); ledger foam-16 and foam-23. |
| PDF TPEE inherently stable/sharp, EVA unable to provide race-day response, or TPU inherently a heavy daily-trainer material | Sensation and use category are assigned from polymer names while formulation, density and geometry vary. | Replace role prescriptions with questions about the finished shoe. The current TPU portfolio itself spans several processing routes. [BASF portfolio](https://plastics-rubber.basf.com/emea/en/performance_polymers/products/infinergy). |
| MD direct injection eliminates all waste; slabs necessarily provide greatest return | Neither conclusion follows from the shaping route alone. Yield, trimming, rejects and final mechanics require process-specific data. | Explain routes without a waste-free or return-maximizing guarantee. [Trexel process example](https://trexel.com/wp-content/uploads/2019/06/Trexel_P-300_datasheet_2019_FINAL.pdf); [Zotefoams stages](https://www.zotefoams.com/who-we-are/3-stage-process/). |
| PDF resin prices and broad product-to-polymer mappings | Prices need date, geography, grade, volume and source. Trade names can cover changing model generations and blends. | Omit price rankings and undisclosed proprietary recipes. No inferred brand chemistry database is shipped. |

## Incorrect mechanisms or definitions

| Supplied proposition | Correction | Resolution and support |
| --- | --- | --- |
| PDF expanded TPU historically uses steam as its physical blowing agent | The cited Infinergy explanation describes expansion first and steam heating/fusion of expanded beads afterward. It does not establish a historical gas recipe. | Show expansion and joining as different steps. [BASF process account](https://www.basf.com/gb/en/media/science-around-us/small-beads-for-long-distances), manufacturing and 2,500-bead sections; ledger foam-13. |
| Physical foaming means no covalent network | Gas introduction and network formation are different operations. Physically foamed EVA can be crosslinked beforehand. | Explicitly retain this counterexample in article depth and the chemical-route caption. [Li et al. full text](https://pdfs.semanticscholar.org/360f/134fcbef51a7f38fa7e340bc6fa1886baa8e.pdf), Section 2.2, Table 1 and Figure 1; ledger foam-04. |
| EVA covalent crosslinks are inherently a structural flaw; TPU physical junctions guarantee exact recovery | Crosslinks can restrain flow and stabilize expansion. Physical junctions do not imply immunity to dissipation, irreversible damage or creep. | Explain connection type without assigning perfect recovery or mileage. [EVA experiment](https://pubmed.ncbi.nlm.nih.gov/39124388/); [TPU structure](https://solutions.covestro.com/en/highlights/articles/theme/product-technology/chemical-physical-structure-tpu). |
| Aliphatic chemistry automatically removes rings, disrupts crystallinity and makes a lighter, softer foam | Cycloaliphatic building blocks retain saturated rings. Packing, symmetry, composition and expansion matter; monomer mass does not determine foam density. | A-TPU appears within TPU. The material panel cites the HDI counterexample without translating nonfoam measurements into shoe performance. [Five-isocyanate experiment](https://www.mdpi.com/2073-4360/16/21/3045), results/conclusion excerpts; ledger foam-06. |
| Supercritical processing leaves hysteresis unaffected because the polymer name is unchanged | The backbone identity can remain while crystallinity, morphology and cellular structure change. Measured foam mechanics can therefore change. | Replace with a distinction between chemical identity and material organization. [PEBA crystallization/foaming study](https://www.sciencedirect.com/science/article/pii/S0896844623001948). |
| Cells are hermetically sealed micro-springs; packing-out generally requires gas escaping through micro-tears | Gas can diffuse through intact polymer. Structural set, cell damage and time-dependent recovery must not be reduced to one assumed cause. | Use a conceptual solid-network/cellular-space graphic; deeper research separates diffusion and dimensional stability. [Gas-mixture study](https://onlinelibrary.wiley.com/doi/10.1002/mame.202300437), Figures 5–6. |
| Bead skins are non-working mass, or bead hierarchy automatically supplies durability | Interfaces carry load; joining quality changes failure locations. A skin is not mechanically inactive solely because it adds mass. | Show the bead/cell hierarchy without a universal performance hierarchy. [Welding study](https://onlinelibrary.wiley.com/doi/10.1002/pola.70317), Section 3.2 and conclusion. |
| Compliance equals strain capacity; stiffness equals modulus; durometer equals either | Compliance describes deformation per load; structural stiffness and stress/strain modulus use different quantities. Indentation hardness is another protocol. | Main copy uses deformation under load; depth defines test object and work. Avoid interchangeable units or a universal stiffness scalar. [Hoogkamer methods](https://www.greif.de/downloads/A_Comparison_of_the_Energetic_Cost_of_Running_in_M.pdf), Section 2.2. |
| Return is always one minus hysteresis | Only true when hysteresis means fractional loss with the same loading-work denominator and cycle. Loop loss may instead be in joules; Aimar's η includes π. | Define the displayed ratio directly. [Aimar methods](https://laurent-orgeas.github.io/papers/aimar_et_al_2024_footsci.pdf); ledger foam-16–17. |
| A Tg near −65°C puts room-temperature operation hundreds of degrees above transition | At 20°C the difference is approximately 85°C. Mobility also does not imply zero dissipation. | Delete the arithmetic and thermal-invariance argument rather than replace it with another universal Tg band. |
| Softer foam necessarily lowers skeletal impact; densification necessarily increases knee load; return directly reduces named tissue torque and explains 2–4% economy | Material compression is not a complete human-system model. These causal or clinical outcomes need appropriate human measurements. | Keep mechanical return, whole-shoe response and metabolic outcomes distinct. No injury or joint-load benefit is inferred. Ledger foam-23. |

## Inconclusive citations and source discrepancies

| Evidence problem | What the source actually permits | Disposition |
| --- | --- | --- |
| Hoogkamer Figure 3 versus discussion: Streak returned work | Figure 3 labels **3.28 J**, while discussion prose says **3.38 J**. The present graphic is explicitly a redraw of Figure 3. | Use 3.28 J in the chart/table and disclose both entries. No invented reconciliation or claim of author correction. Source and ledger foam-18–19 preserve the discrepancy. |
| Hoogkamer shoe comparison used as proof of PEBA's isolated contribution | Three complete constructions differ in foam, plate, stack and geometry. Mechanical return and metabolic cost are measured separately. | Identify shoe models and protocol. A four-percent whole-shoe result cannot allocate a unique foam contribution. [Primary full text](https://www.greif.de/downloads/A_Comparison_of_the_Energetic_Cost_of_Running_in_M.pdf). |
| 450 km Table 1 return numbers described as foam compression | They arise from whole-shoe three-point **bending**. Human metabolic observations are in Table 2. | Chart Table 2 means/SD and label the bending distinction beside source notes. [Primary article](https://onlinelibrary.wiley.com/doi/full/10.1111/sms.14526), Section 2.2 and Tables 1–2. |
| Ratios of displayed wear-study means treated as the study's average paired percentage change | A ratio of rounded group means is a derived statistic, not necessarily the mean within-person percentage. SD bars do not give uncertainty of paired change. | Display measured W/kg means and SD. Retain the study's significance statements without deriving a replacement paired statistic. |
| PDF Mach-versus-Clifton figures used to isolate manufacturing process | Different shoes can vary in density, grade/blend, geometry and protocol, even when a brand and broad polymer label match. | Do not infer that the measured difference is entirely caused by SCF processing. No such brand comparison is used as causal evidence. |
| Supplier rebound figures blended with whole-shoe compression or human percentages | A supplier result supports its grade under its specified method; a pendulum measure is not a human economy percentage. | Keep manufacturer-reported labels and method notes. No mixed-scale leaderboard. [BASF test labels](https://plastics-rubber.basf.com/emea/en/performance_polymers/products/infinergy). |
| Abstract-only or indexed-excerpt access presented as full-paper review | It supports the inspected propositions at limited depth; unseen methods and tables remain unaudited. | Source notes and claim-ledger read_depth fields explicitly distinguish full-text consultation, abstracts/previews and manufacturer pages. |
| Retailer guide or unreviewed video treated as quantitative authority | The retailer guide was read; the video title, metadata, description and chapter markers were inspected, but no transcript or speech was obtained. | Retain them as supplied reading references only. They do not source the numerical charts. See editorial-audit.md for access history. |

The final article's molecular and cellular drawings remain labeled conceptual. Their geometry, motion and colors explain relationships; they do not add observations to the measured datasets. Service-life curves, family scores, proprietary blends and clinical implications absent from the verified evidence remain absent from the article.

## 23 September 2026 — familiar-ball teaching examples

The revised material lesson uses original sports-ball cutaways to introduce one structural idea before returning to the polymer explanation. These pairings are editorial analogies, not empirical correspondences. They do not assert that a foam practice ball is EVA, a basketball is TPU, a volleyball is A-TPU, a rubber bouncy ball is PEBA, or a baseball is TPEE. The existing chemistry/manufacturing evidence above continues to support the molecular claims.

### Primary sources recorded in `BALL_SOURCES`

The following source identities and locators are transcribed from the current `ball-content.js` registry. This documentation pass inspected the implementation and its source records; it did not independently reopen or expand the source-reading depth. Manufacturer descriptions support their stated constructions, and the experiment supports its tested balls and conditions.

| Article source ID | Primary source and locator | What the lesson may borrow | Limit on inference |
| --- | --- | --- | --- |
| `ball-foam` | [ITF, 2026 technical booklet](https://www.itftennis.com/media/15639/2026-technical-booklet.pdf), §1.1 | Foam training balls are distinct from hollow rubber-core tennis balls; a cellular ball is a useful familiar object. | This classification does not identify the polymer in every practice ball or establish EVA foam performance. The SVG's cell layout is authored, not microscopy. |
| `ball-inflated` | [Molten, 2017 basketball and volleyball catalogue](https://moltenusa.com/product_images/uploaded_images/2017-Molten-Catalogue.pdf), printed pp. 10–12 and 32 | Cover, winding and bladder contribute to an inflated ball's construction. Basketball and volleyball can illustrate the same general shell-and-air mechanism. | Macroscopic covers, winding and bladders are not TPU hard/soft molecular domains. These descriptions do not establish that the depicted basketball or volleyball uses TPU or A-TPU, or that A-TPU has a superior return. |
| `ball-recovery` | [Cross, 1999, *The bounce of a ball*](https://www.physics.usyd.edu.au/~cross/PUBLICATIONS/5.%20BallBounce.pdf), §§IV–V and Figures 2 and 5 | Primary impact/compression experiments provide grounding for discussing ball deformation and rebound as teaching examples. | The lesson does not reproduce the measured trajectories or calibrate its compression/timing to this experiment. Ball rebound cannot rank midsole polymers or directly predict running economy. |
| `ball-baseball` | [Rawlings R100-H2 product description](https://production.rawlings.com/product/R100-H2.html), construction description | The specified model has a cushioned-cork center, wool winding and leather cover: different parts perform different jobs. | This is a specified construction, not a universal description of all baseballs. TPEE's flexible segments and crystalline polyester regions are molecular organization, not literal winding/cover/core layers; no hardness or stability ranking follows. |

### Pairings and boundaries

| Material selection | Familiar example | Intended bridge back to chemistry | Interpretation to avoid |
| --- | --- | --- | --- |
| EVA | Foam practice ball with small cells | Cellular space within a connected network; many EVA foams have permanent links between chains. | Treating the drawn cell count or perfectly recovering shape as a measured EVA microstructure or durability result. |
| TPU | Basketball with an air cavity and supporting shell | Flexible segments and supporting hard-rich junctions work together. | Equating one large air chamber with a foam's many cells, or a ball casing with a molecular hard domain. |
| A-TPU | Volleyball with the same general inflated construction | Changing a TPU building block does not create a separate basic polymer architecture. | A separate family, a different physical rebound law, or an inherently softer/lighter/better TPU. |
| PEBA | Rubber bouncy ball with a continuous network | Deformation and recovery; flexible polyether bridges with polyamide-rich support in the actual polymer. | Assuming the ball is PEBA, claiming frictionless recovery, or inferring a universal high-return winner. |
| TPEE | Baseball cutaway with winding and core | Different components can have different roles; in the polymer, flexible segments coexist with crystalline polyester support. | Literal baseball layers inside the foam, or inherently greater hardness, stability or durability. |

### Illustrative mechanics and editorial treatment

All five ball illustrations use identical compression depth, timing and baseline. The sequence squeezes, recovers and then opens a cutaway; it does not compare bounce heights. The molecular sketch's small accompanying scale change is explanatory motion, not a molecular simulation. Colors, texture, cell size, shell thickness, network spacing and the baseball's winding are authored geometry without a measurement scale.

The separate energy lesson uses unnamed specimens to distinguish deformation under the same force from rebound after the same release height. Its selected deformations, heights and timing are illustrative rather than reported observations; they are not assigned to EVA, TPU, A-TPU, PEBA or TPEE. A ball-rebound example remains a different test from compression-loop return in a foam or assembled shoe, and from metabolic measurements in runners. The named-shoe charts retain their own sources, protocols and uncertainty notes.

The main material copy now consists of a short ball description, one borrowed idea and a concise chemistry bridge. Necessary analogy limits stay beside the lesson and in its disclosure; detailed chemistry and sources remain accessible. The material links in the header and the generated static cutaways change how readers reach this content, not the evidential status of the claims. This dated addition supplies no browser verification or new review sign-off.