Pith Number

pith:BBWNBNFX

pith:2012:BBWNBNFXSGVTHNA4ZUTAZPLYAP

not attested not anchored not stored refs pending

The asymptotics of ECH capacities

Daniel Cristofaro-Gardiner, Michael Hutchings, Vinicius Gripp Barros Ramos

arxiv:1210.2167 v4 · 2012-10-08 · math.SG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BBWNBNFXSGVTHNA4ZUTAZPLYAP}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:04:59.679666Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

086cd0b4b791ab33b41ccd260cbd7803e5ab62606e46fb7936637f58bc69e31c

Aliases

arxiv: 1210.2167 · arxiv_version: 1210.2167v4 · doi: 10.48550/arxiv.1210.2167 · pith_short_12: BBWNBNFXSGVT · pith_short_16: BBWNBNFXSGVTHNA4 · pith_short_8: BBWNBNFX

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/BBWNBNFXSGVTHNA4ZUTAZPLYAP \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 086cd0b4b791ab33b41ccd260cbd7803e5ab62606e46fb7936637f58bc69e31c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7bf4a2224a5190863b315b58123e48bfe17da7db255c87168b55926ee6787b56",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.SG",
    "submitted_at": "2012-10-08T07:38:03Z",
    "title_canon_sha256": "c2bbb71421dce7a60b018708e751dd5d61d5d45ba14b5594adfc286cf4b82712"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.2167",
    "kind": "arxiv",
    "version": 4
  }
}