Pith Number

pith:NMNKRIZK

pith:2012:NMNKRIZKIFYMUEXBMR5C2UY3JJ

not attested not anchored not stored refs pending

Amenability, locally finite spaces, and bi-lipschitz embeddings

Valerio Capraro

arxiv:1205.0346 v2 · 2012-05-02 · math.MG · math.CO · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NMNKRIZKIFYMUEXBMR5C2UY3JJ}

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	2026-05-18T03:45:55.298413Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6b1aa8a32a4170ca12e1647a2d531b4a5d75d648e73baa1c9dc313b87d770000

Aliases

arxiv: 1205.0346 · arxiv_version: 1205.0346v2 · doi: 10.48550/arxiv.1205.0346 · pith_short_12: NMNKRIZKIFYM · pith_short_16: NMNKRIZKIFYMUEXB · pith_short_8: NMNKRIZK

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/NMNKRIZKIFYMUEXBMR5C2UY3JJ \
  | 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: 6b1aa8a32a4170ca12e1647a2d531b4a5d75d648e73baa1c9dc313b87d770000

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "04d35343d41036883e43b355924e5a6ff7af38b70ececb9ebe28f6ebacb8b857",
    "cross_cats_sorted": [
      "math.CO",
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.MG",
    "submitted_at": "2012-05-02T07:56:13Z",
    "title_canon_sha256": "3be5e7b3ec2b47b1a36e603b077de5421f15cd21b2a2e9b5735811f851770a35"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.0346",
    "kind": "arxiv",
    "version": 2
  }
}