Do Caracciolo & Sportiello (2012) and Dickman et al. (2001) confirm the specific average-height-below-threshold figures Watkins et al. (2015) attributes to them?
claim-btw-near-threshold-clustering-is-1d-sandpile-coincidence-not-general-soc-signature carries two specific quantitative figures reported by Watkins et al. (2015, a Tier-1 refereed review) but attributed to two other papers that were not independently fetched or read this session:
- The two-dimensional BTW sandpile's average height is 17/8 = 2.125 against a threshold of 3 — attributed to Grassberger's conjecture, "confirmed analytically by Caracciolo and Sportiello (2012)."
- The Abelian Manna Model's average height is 0.9488(5) against a threshold of 1 — attributed to Dickman et al. (2001).
What to read
- Caracciolo & Sportiello (2012) — the analytic confirmation of Grassberger's 17/8 conjecture for the 2D BTW sandpile's average height.
- Dickman et al. (2001) — the source of the 0.9488(5) Abelian Manna Model average-height figure.
Why it matters
Per sources.md, quantitative claims (specific numbers, decimals, figures)
need a Tier 1–2 source directly — a review's report of someone else's number
is a lead to the primary, not the primary itself, however refereed the review
is. The mechanism point these figures support (local sites in SOC models
typically sit well below threshold on average, contra a "everything is near
threshold" misreading) is independently Tier-1 sourced from BTW's own stated
intent and does not depend on these two figures being exactly right. But the
figures themselves stay [unverified-quant] until read against their own
papers. Confirming them lets the claim-note leave seedling; a discrepancy is
itself worth recording.
Progress log
- 2026-08-31 — answered by claim-caracciolo-sportiello-2012-confirms-17-8-average-height and claim-dickman-2001-critical-density-corroborates-not-exactly-matches-watkins-figure. Both primaries were read directly (extract_pdf at capture). Caracciolo & Sportiello (2012) confirms 17/8 exactly, digit-for-digit, in its own abstract. Dickman et al. (2001) corroborates the ~0.9488 figure's magnitude but prints three distinct estimates (0.94887(7), 0.94883(5), adopted 0.94885(7)), none matching Watkins et al.'s '0.9488(5)' notation verbatim — settled as a partial confirmation with a specific, documented precision gap, not a clean yes or a refutation.