Pith Number

pith:HTRHFS3F

pith:2010:HTRHFS3FVWHHOSVOXOOHIEV6G7

not attested not anchored not stored refs pending

Coarse non-amenability and covers with small eigenvalues

Erik Guentner, Goulnara Arzhantseva

arxiv:1009.1966 v1 · 2010-09-10 · math.GR · math.FA · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HTRHFS3FVWHHOSVOXOOHIEV6G7}

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	2026-05-18T04:41:05.651177Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3ce272cb65ad8e774aaebb9c7412be37d638e192cab9d57e262b92913187d72e

Aliases

arxiv: 1009.1966 · arxiv_version: 1009.1966v1 · doi: 10.48550/arxiv.1009.1966 · pith_short_12: HTRHFS3FVWHH · pith_short_16: HTRHFS3FVWHHOSVO · pith_short_8: HTRHFS3F

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/HTRHFS3FVWHHOSVOXOOHIEV6G7 \
  | 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: 3ce272cb65ad8e774aaebb9c7412be37d638e192cab9d57e262b92913187d72e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "df3d439130113f2b477156db5584205d6423e74418845e7c46b54a3bafad4a33",
    "cross_cats_sorted": [
      "math.FA",
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-09-10T09:44:20Z",
    "title_canon_sha256": "8f9fcbb02ef4672b9156b5c300842a9c64fd19460d9140b98c2c64ea5d84f89d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1009.1966",
    "kind": "arxiv",
    "version": 1
  }
}