Add sourcing note for the HR-100A balance isolation slab

[sgbaird]

Buy-list and sizing note for #146, following point 4(d) of the #116 environment survey.

The slab targets the ~100 mg mechanical step events only: jitter is already below the 0.1 mg display resolution and creep is internal to the balance, so neither should be expected to improve. The note sets that acceptance criterion explicitly.

Sizes against the HR-100A's 198 x 294 x 315 mm / 3.5 kg from the HR-A manual, flags the straddle-clearance problem (the doser bridge already lands on the deck around the balance, so a 50-75 mm slab under the balance alone collides with the platform), and prices four sourcing routes from free sink cutouts through a $70 12x18x3 in surface plate.

Also includes the isolator sizing table (f0 = 15.76/sqrt(delta), target 5-7 Hz), fume-hood cautions, and a commissioning checklist that reuses scripts/balance_environment_survey.py for before/after comparison.

Docs only - no code or hardware changes.

Closes #146.

Generated with Claude Code

[sgbaird]

@claude in addition to the granite (or marble, not sure which would be better), we also probably want the rubber underneath. We did a bunch of testing and ordered some things in context of vertical-cloud-lab/tensegrity-optimization#88 and other PRs in there (a bunch of drop tests on samples and looking at the shock response)

Based on that, which would you recommend? We got it from mcmaster. Use your github secrets with mcmaster credentials to look up the exact part and price that you need (via the Pi, to avoid getting blocked)

[claude]

Claude finished @sgbaird's task in 16m 27s —— View job

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Rubber under the granite ✅

• Read the current sourcing note
• Review the drop-test / shock-response work in tensegrity-optimization#88, PR #86, and drop-test-pu-configs-analysis.md
• Look up exact McMaster parts + prices via the Pi (whole 8514K family mapped, verified 2026-08-20)
• Recommend granite vs. marble and the rubber underlayment
• Update docs/balance-isolation-slab-sourcing.md and push (4a38776)

---

Short answers

Granite, not marble — and the reason is chemical, not dynamic. At 30 kg the slab is a rigid body well below 1 kHz either way, and the stone's internal damping is negligible next to the rubber under it. What separates them is that marble is recrystallised calcite: it etches in acid vapour and is Mohs 3–4, so it scars from a dropped vial. Granite is silicate, Mohs 6–7, non-porous, and is what surface plates are made from. Buy marble only if a free remnant turns up and the hood is acid-free. (Trade names lie — vinegar on a hidden edge; fizzing means carbonate, i.e. pick the other one.)

Rubber: McMaster 8514K315, 4" × 4" × 1/2", 70 Shore OO super-cushioning polyurethane, $15.04, ships next day. Cut four ~7/8" squares from it. But check the bin first — this is the same material and thickness the drop-tower program already bought, and four 7/8" squares is 3 in², a rounding error against a 12 × 12 sheet. Offcuts make these for free.

Why that one, from your tensegrity data

The transferable result is about the material, not the arrangement:

• Damping is the discriminator, not compliance. Felt failed by adding high-frequency spike content (raw CH5 91 % FS worn, vs 26.2 % on ¼ in PU and 6.2 % on ½ in), not by shifting the CFC-180 peak. Super-cushioning PU is the Sorbothane-class viscoelastic, tan δ ≈ 0.5 vs ≈ 0.05–0.1 for neoprene/EPDM. That matters more here than it did there: any isolator amplifies at f₀, and at tan δ ≈ 0.5 the peak is 2.2× instead of 5–10× with ring-down. A balance settling to 0.1 mg can't afford ring-down — especially under Option A, where the tapper excites f₀ from inside the isolated mass on every dose.
• Durability is settled. 40 drops at 5.5 m/s, no bedding-in trend, input CV 1.4–1.8 %. A static 32 kg is trivial by comparison, so compression set is a non-question.
• One hard constraint carries over: the paired test found the two sheets stacked toggled between two stiffness states drop-to-drop, from seating at the sheet-to-sheet interface, and a single sheet removed it. A bistable interface under this slab would look exactly like the ~100 mg step events we're trying to remove. One layer, cut clean, seated once — never a stack.

I did not lean on the arrangement ranking from drop-test-pu-configs-analysis.md — that was withdrawn by the Edison adversarial re-analysis (task d9092c5a, verdict "the sweep cannot decide"). Only the material behaviour survives, which is all this needs.

The part that's easy to get wrong: pads, not a sheet

The instinct is to lay a 12 × 12 sheet under the slab. That does essentially nothing — a wide, thin elastomer layer can't bulge sideways, and rubber that can't bulge can't compress. Shape factor S = loaded area ÷ free area, E_c ≈ E(1 + 2S²):

layout under the 12 × 18 slab	S	E_c	deflection	f₀
full-area ¼ in sheet	~14	~300 MPa	~0.00005 mm	≈ rigid — no isolation at all
four 7/8 × 7/8 × ½ in pads	0.44	~0.97 MPa	~2.1 mm	~11 Hz

Same rubber, ~40 000× difference in compliance, and the sheet is the thicker pile of it.

Pad sizing (29 kg slab + 3.5 kg balance ≈ 80 N/pad, ½ in stock, 70 OO ≈ 20–25 Shore A → E ≈ 0.7 MPa):

pad side	strain	δ	f₀
1½"	3.7 %	0.47 mm	23 Hz	too stiff
1"	12 %	1.50 mm	13 Hz	conservative start
7/8"	17 %	2.1 mm	11 Hz	recommended
¾"	25 %	3.1 mm	8.9 Hz	best attenuation, at the strain limit
5/8"	38 %	—	—	will creep

One correction to the PR as it stood: its 5–7 Hz target isn't reachable with flat sheet stock. 5 mm of deflection needs ~25 mm of stock at sane strain, and a 25 mm-tall pad narrow enough to reach that strain under 8 kg/corner is taller than it is wide, i.e. it buckles. Commercial 7 Hz tables use moulded hemispheres, not flat pads. I've corrected the doc to δ ≈ 2–3 mm / f₀ ≈ 9–11 Hz and said why. Realistic attenuation with damping: −5 dB at 20 Hz, −18 dB at 50 Hz, −25 dB at 100 Hz, resonance peak 2.2×.

E for 70 Shore OO is a ±50 % estimate, so this is a starting point — calipers on loaded vs. free pad height give δ directly, and f₀ ≈ 15.76/√δ. Under 1 mm, trim smaller; over 3 mm, cut larger. Same "tune pad area empirically" conclusion your drop-test doc reached.

McMaster prices, verified today

The 8514K3xx/8514K5xx numbers are the stocked ones. Worth flagging: 8514K63 — the number you picked in #88 — currently quotes 2–3 weeks, while 8514K521 is the identical 12 × 12 × ¼ in 70 OO sheet at the same $56.01, shipping tomorrow.

part	size	thick	duro	price	ships
8514K315	4 × 4	½"	70 OO	$15.04	next day
8514K313	4 × 4	¼"	70 OO	$11.43	next day
8514K314	4 × 4	3/8"	70 OO	$12.62	next day
8514K215 / 8514K115	4 × 4	½"	50 / 40 OO	$15.04 ea	next day
8514K521	12 × 12	¼"	70 OO	$56.01	next day
8514K515	12 × 12	½"	70 OO	$105.60	next day
8514K518	12 × 12	1"	70 OO	$194.49	next day
8514K2	sample pack	—	30/40/50/60/70 OO	$11.01 / 5	next day
8514K63	12 × 12	¼"	70 OO	$56.01	⚠️ 2–3 weeks

The 4 × 4 pieces are the right buy: the pads need ~3 in² and the 12 × 12 sheets cost 7× more for area that gets thrown away. If you want to hedge durometer, $45 buys 40/50/70 OO in ½ in and turns the sizing table into a measurement.

Whole rig: ~$85 (G9651 granite plate $69.95 + one 8514K315 $15.04), against $1,575 for the A&D AD-1671.

Notes on how I got the prices

Run from the Pi as you asked, so the requests came from the residential IP. I did not log in with the McMaster credentials — list prices are served unauthenticated, so the account added nothing, and McMaster's sign-in path runs through 2SV / "risky sign-in" verification that would have fired codes at a real account for no gain. If you do want account-specific pricing (contract discounts, order history), say so and I'll do it, but it'll likely need a verification code from you. Scraping was rate-limited to ~1.6 req/s and ~350 requests total, all small JSON.

Also in the commit

• Commissioning gains a caliper check on pad deflection (the only direct confirmation the isolator is doing anything) and, for Option A, a settle-time-after-tapping re-check.
• The stacked-paver option now notes explicitly that interleaving rubber inside the mass is a different thing from stacking isolator pads.

Docs only — no code or hardware touched.
• branch claude/issue-146-20260820-1750

[sgbaird]

Rubber: McMaster 8514K315, 4" × 4" × 1/2", 70 Shore OO super-cushioning polyurethane, $15.04, ships next day. Cut four ~7/8" squares from it. But check the bin first — this is the same material and thickness the drop-tower program already bought, and four 7/8" squares is 3 in², a rounding error against a 12 × 12 sheet. Offcuts make these for free.

@swcharles we might be able to use a bit of the material from the ones we already bought

Interesting analysis also about a sheet vs. corner pads. Per Claude's comment, I would have thought a sheet would be best. @claude send an edison query to spot check the reasoning above about sheet vs. corner pads

[claude]

Claude finished @sgbaird's task in 35m 50s —— View job

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Edison spot-check: sheet vs. corner pads

• Re-read the shape-factor argument in the sourcing note
• Draft an adversarial query — 7 claims, each phrased as "refute this"
• Submit two tasks (paperqa3-high + data-analysis-crow-high)
• Independently recompute the numbers myself, to judge the answer against
• Literature task returned — success, 39 kB with citations
• Commit query, answer and artifacts (124bc8d)
• Analysis task still running at session end — needs a follow-up @claude to fetch

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Short answer

Your instinct was better than mine. The sheet-vs-pads physics holds — small pads really are ~30,000× more compliant than a full sheet of the same rubber — but Edison's verdict is that it's the right calculation applied to the wrong problem, and it rejects the four-7/8"-pads recommendation outright.

The acceptance criterion — reducing ~100 mg permanent step offsets — is not a vibration-isolation problem in the classical sense. It is a tilt-stability and latching problem for which compliance is the enemy, not the solution.

Revised recommendation: buy the granite, set it straight on the deck, and don't cut the pads yet. Run the survey. Only add elastomer if a deck accelerometer spectrum shows the energy is above ~30 Hz — and if it is, buy bonded mounts with a published dynamic stiffness, not cut sheet stock.

Verdicts

#	claim	verdict	changes the rec?
1	shape factor makes a sheet useless	OVERSTATED	no
2	bonded vs. unbonded	CORRECT, wrong reason	no
3	f₀ from static deflection	CORRECT (the objection lands)	yes
4	is compliance the right lever	CORRECT (the objection lands)	yes
5	rocking + horizontal modes ignored	CORRECT (the objection lands)	yes
6	four small pads	WRONG	yes
7	a step event is a latching event	CORRECT	yes

What actually broke

1. The arithmetic survives; the headline number was inflated. I recomputed independently before the results landed and we agree within a few percent. Two corrections the note skipped: Lindley's hardness factor k ≈ 0.85 (not 1), and the finite-bulk-modulus cap 1/E_c* = 1/E_c + 1/K, which matters at S ≈ 14 where the incompressible form is being extrapolated well past its validated range. E_c for the sheet drops 290 → ~200 MPa and 40,000× becomes ~30,000×. The sheet is still a gasket, not a spring. So on the narrow question you asked — sheet or pads — the note was right.

2. But f₀ ≈ 11 Hz was never real. f₀ = 15.76/√δ assumes dynamic stiffness = static stiffness. For a Sorbothane-class PU at tan δ ≈ 0.5 that's badly violated — dynamic/static is 2–4×, so true f₀ is 15–22 Hz, not 11. My own sweep gave the same. That single correction moves the isolator's resonance from "below the disturbance band" to inside it, which is what collapses the rest of the argument.

3. Two premises in the note are wrong, and both favour the sheet.

• "Mass alone doesn't help against base motion." True for a rigid floor. False here — the hood deck is a compliant panel, so 29 kg of granite mass-loads it and cuts its own local response. The slab earns its keep with no rubber at all.
• Optimising the vertical mode. Shear stiffness isn't shape-factor stiffened, so four small pads put the horizontal mode at ~5 Hz (I get 5.3, Edison 5.1) — the lowest mode in the system, sitting right in the footfall harmonics — plus a rocking mode near 9–12 Hz. For an EMFR balance tilt is the sensitive DOF, and it's the one the pads make worse. This is exactly the gap your "I'd have thought a sheet would be best" was pointing at.

4. The one that threatens the whole PR (claim 7). A ~100 mg permanent offset is 1000× the display resolution and doesn't decay — that isn't steady-state vibration transmission, which averages to zero. It's something latching: stiction in the leveling feet, a draft-shield seal shifting, a particle, a flexure reseating. And a creep-prone elastomer under a 29 kg stone is a new source of exactly that failure mode — differential creep between corners becomes slow tilt drift, and shock-induced micro-slip becomes a discrete tilt step. The proposed fix can manufacture the artifact it was bought to remove.

Where I don't fully buy Edison

Being straight about the weakest link, since it's load-bearing for claim 7: the quoted EMFR tilt sensitivity of 0.05–0.2 mg/µrad is too high by a lot — taken literally, 1 µrad would move the reading a full display count and the balance couldn't be levelled at all. Working backwards from its own conclusion, 100 mg needs 500–2000 µrad ≈ 0.03–0.11°, i.e. 125–500 µm of differential settle across the pads. That's very plausible as slow creep on a pad deflected 2.1 mm (a few % differential does it) — so the creep-drift argument stands. It's much less plausible as a single micro-slip event. Pure cosine error is ~10⁴× too small to be the mechanism either way (0.33 mrad → 0.005 mg), so the qualitative point — tilt ≫ cosine, and tilt is a credible step mechanism — survives regardless. This wants measuring, not citing. Edison also flags that Gent & Lindley, Lindley, Snowdon, Rivin, ISO 10846, the Ungar–Gordon VC curves and Sorbothane's own data were all unobtainable through its search tools, so the rubber mechanics leans on a seismic-bearing paper as proxy.

What I'd change in the doc — your call

I haven't touched docs/balance-isolation-slab-sourcing.md, since you asked me to spot-check the reasoning and this overturns the PR's headline buy rather than correcting a number. Say the word and I'll: demote the rubber from "buy this" to "conditional, pending a deck spectrum"; correct f₀ 11 Hz → 15–22 Hz dynamic; add the horizontal/rocking modes and the tilt-latching failure mode; and restructure commissioning as granite-direct first, elastomer only if it fails. The granite recommendation and the granite-over-marble call are untouched by all of this.

Cheap upside: the first experiment is now free and faster — no cutting, no bedding-in wait. And per your note to @swcharles, still don't buy rubber; if it's ever needed the answer is ~2" pads, not 7/8".

Artifacts

Committed under outputs/isolator-spotcheck/ — full answer with references, both queries, the raw verbose trajectory, and the reproducible scripts/edison_isolator_spotcheck.py.

task	job	id	status
literature	paperqa3-high	2870c8ea	✅ success, fetched + committed
analysis	data-analysis-crow-high	06441e04	⏳ still running at 28 min

The analysis task was asked to recompute everything in code, sweep E over its ±50 % band, compute rocking/horizontal modes, and do the Poisson power calculation for how many 600 s runs it takes to detect a change in a 1-per-10-min event rate — that last one matters for commissioning regardless of which way the design goes. Comment @claude fetch the isolator analysis task and I'll pull it in.
• branch claude/issue-146-20260820-1750

[sgbaird]

Random aside related to a comment in the other PR about "CAL", that I imagine we probably have one of those 100 gram calibration weights somewhere, I imagine this would have come with the scale itself. If not, Kevin Cole probably has some.

[sgbaird]

@claude let's go with the following as a plan: buy the granite from somewhere, this could either be local or online. I want you to use the pie to look at various local websites like home Depot and other places where we might be able to find granite. I also want you to look at online sources for buying the granite. Once we get the granted, we can try without the pads, with the pads, and potentially with the full large mat, to resolve the apparent discrepancies that are above more empirically. We can borrow all of this from tensegrity, at least temporarily, and if it's just a couple small squares for the pads then that's easy to lop off.

[claude]

Claude finished @sgbaird's task in 29m 57s —— View job

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Granite sourced, and the pads/sheet argument turned into an experiment

• Confirm what "local" means — the Pi answers from the BYU campus block, so Provo / Orem, Utah County
• Local sources via the Pi — fabricators, ReStore, KSL, big-box
• Online sources via the Pi — Grizzly, Shars, Zoro, Amazon, Walmart, Harbor Freight
• Write the buy into the doc, with the corrections it needed
• Pre-register the four-arm comparison, with a run-length that can actually decide it
• Ship scripts/step_event_rate.py so the comparison is decidable, not eyeballed
• Commit and push (59e5586)

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The buy

Make two phone calls before you order anything. A 3 cm sink cutout is ~483 × 838 mm → ~33 kg, which is almost exactly the target mass, one face is already polished and sealed, and fabricators mostly treat them as waste. Verified today against each business's own site:

where		why this one
Habitat ReStore	340 S. Orem Blvd, Orem · 801-344-8527	Donated countertop offcuts constantly. Walk in, no phone tag.
Rock Solid Granite	1161 W 780 N, Orem · (801) 225-0812	The only one publishing a searchable remnant inventory (slabzone.com — JS-rendered, needs a browser)
Big Mountain	317 N Main, Orem · 801-225-6521	Walk-in shop on Main
Little Stone	1452 S State St, Provo	Closest to campus
Cobble Creek	801-618-7699	Advertises in-house sink cutouts — i.e. generates exactly this offcut

Plus Granite Countertops Utah (801) 376-3856, Quality Granite 801-800-1244, and Accent 801-269-0701 (formal priced remnant program). The ask is one sentence: "Do you have a 3 cm granite sink cutout or remnant, roughly 12 × 18 or larger, I could buy or take off your hands?" — say it's going under a lab balance, cosmetic rejects are perfect.

Online fallback if nobody answers in 48 h: Grizzly G9651, 12 × 18 × 3, $69.95, re-verified InStock today. All four sizes still at their 2026-08-20 prices (G9649 $39.95 / G9651 $69.95 / G9653 $79.95 / G9654 $99.95).

Three corrections to what the note said

• Harbor Freight no longer sells granite surface plates. Their own search returns "Sorry, no items found." The note listed them as the cheap local option; that's dead.
• Grizzly's $69.95 isn't the delivered price. It's a ~79 lb shipment — budget $30–60 more, so realistically $100–130. That gap is most of the argument for phoning locally first. (I couldn't pin parcel-vs-freight per SKU: G9649's record says IsFreight: false, but the bigger three pages carry both flags across the several SKUs on them. Get the real number from the cart.)
• Home Depot and Lowe's don't sell granite slabs — only fabricated tops and samples. What they do have same-day is concrete step stones (the $10 option in the note, still valid). Both sites blocked every request from every IP I tried, so their step-stone stock is unverified and needs a human. KSL is also dry: the only precision plate statewide is a Starrett 36 × 60 grade A in Provo at $4,000 — roughly 600 kg, two orders of magnitude past what this needs.

The four-arm comparison

Your plan is right and I've pre-registered it. Order matters for two reasons:

arm	build
A0	balance on the deck as today	contemporaneous baseline
A	granite flat on the deck	mass loading alone
C	granite on the full sheet	the "gasket" case
B	granite on four 7/8" pads	the compliance case
A′	rebuild of A, unchanged	day-to-day reproducibility

C before B, because cutting the pads destroys the mat. If tensegrity has both the 1/4" and 1/2" 12 × 12 sheets, that's free — mat from the 1/4", pads from the 1/2". With one sheet, run the mat arm first and lop the pads off an edge.

A′ at the end — without it, a real 1.4× and a quiet week look identical. And A0 has to be re-measured, not looked up: reusing the old 600 s baseline assumes the room is stationary, which is the one thing we suspect is false.

C vs A is the sharp test. "A full sheet does essentially nothing" is the shape-factor argument's most falsifiable claim, and it's cheap. If C beats A by more than the CI, the compliance framing is wrong about why — the mechanism would be contact and seating (a conforming layer killing a bistable three-point rock), which is a latching story, not a transmissibility one. That discriminates better than B does, because B confounds compliance with two new modes at once.

The thing that surprised me — the old acceptance test couldn't have worked

At ~6 events/hour, a 600 s survey expects one event. The commissioning step said "run the survey before and after and compare" — one count against one count. That isn't a weak test of the step-event rate, it's no test; a slab that does nothing and a slab that works look the same. python scripts/step_event_rate.py --power:

to detect	events/arm	hours/arm	4 arms
10× reduction	8	1.4	6 h
4× reduction	16	2.6	10 h
2× reduction	46	7.6	31 h
1.5× reduction	117	19.4	78 h

Zero events is worth more than that implies — by the rule of three, 0 events in 2 h already rules out anything worse than 4×. So: ~2 h/arm screens (one working day, kills an arm), 24 h/arm decides (~144 events, resolves 1.4×). 24 and not 8 for a reason beyond counts — the disturbance is building activity, which swings an order of magnitude between 2 pm and 2 am, so anything shorter confounds the configuration with the hour it happened to be tested. It's unattended and read-only, so it's overnight work, not bench time. Hourly chunks, so a USB hiccup costs an hour not a day.

scripts/step_event_rate.py pools the per-arm CSVs, counts events with the same detector the survey uses, and compares with the exact conditional Poisson test — the binomial test on how the pooled count splits. Exactness isn't fussiness here: these arms will produce single-digit counts if anything works, and a normal approximation at n = 3 is wrong, not just imprecise. Verified against hand-computable cases (0-vs-10 → p = 0.001953; Clopper-Pearson for 1 of 10 → [0.0025, 0.4450], both exact) and it recovers injected rates on synthetic data.

Two cheap things worth doing while it runs, because they test the tilt-latching mechanism directly rather than by inference: record the bubble level at the start and end of each arm (if it migrates after 24 h on pads but not on bare granite, that's the creep-tilt story caught in the act), and caliper all four pads at 0 h / 1 h / 24 h in arm B — growth in the corner-to-corner spread is exactly Edison's predicted failure mode.

Two things block the run, one of them seriously

1. scripts/balance_environment_survey.py is not in this repo. It only exists at ~/powder-doser/scripts/ on the Pi — and that directory is not a git checkout. No remote, no history, one SD card in a fume hood. The instrument for this entire experiment is one power failure from gone. I didn't commit it since it's Calibration tests with powders #116's work and may be mid-edit, but say the word and I'll pull it and balance_zero.py in.
2. No calibration weight — each rebuild wants a 100 g class E2/F1 per manual §8-1. Your Kevin Cole note lands exactly here: this isn't a nice-to-have for the protocol, it's five recalibrations.

On method

Run from the Pi as asked; requests came from the campus IP, ~1 req/2.5 s, ~100 requests total, unauthenticated public pages only — no logins, no carts. Local business discovery I did with a search API from the runner instead, because DuckDuckGo returned 202 and Mojeek served a captcha; the Pi was used for fetching pages once I knew which ones. Raw data and the negative results (which vendors block, and how) are committed under outputs/granite-sourcing/ with a reproducible scripts/granite_sourcing_survey.py. One trap documented there for whoever runs it next: the Pi's requests has no brotli decoder, so Accept-Encoding: br gives you HTTP 200 full of binary garbage and every price regex silently finds nothing — it reads exactly like a parser bug.

Docs and analysis only — nothing touched on the Pi except reads, and no hardware changed.
• branch claude/issue-146-20260820-1750