Pith Number

pith:GVKV4LFR

pith:2007:GVKV4LFRADWGHOXQ2MA3Z4DMZV

not attested not anchored not stored refs pending

Obtaining Measure Concentration from Markov Contraction

Leonid (Aryeh) Kontorovich

arxiv:0711.0987 v2 · 2007-11-07 · math.PR · math.FA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GVKV4LFRADWGHOXQ2MA3Z4DMZV}

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	2026-05-18T03:51:36.378029Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35555e2cb100ec63baf0d301bcf06ccd7cb5d3ff0639df8da22e63be6e311cbf

Aliases

arxiv: 0711.0987 · arxiv_version: 0711.0987v2 · doi: 10.48550/arxiv.0711.0987 · pith_short_12: GVKV4LFRADWG · pith_short_16: GVKV4LFRADWGHOXQ · pith_short_8: GVKV4LFR

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/GVKV4LFRADWGHOXQ2MA3Z4DMZV \
  | 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: 35555e2cb100ec63baf0d301bcf06ccd7cb5d3ff0639df8da22e63be6e311cbf

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f23a7c4dd5d131e81ca0c3b485188d994ed65930681c7dbce6d61d8112f4a402",
    "cross_cats_sorted": [
      "math.FA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.PR",
    "submitted_at": "2007-11-07T00:20:46Z",
    "title_canon_sha256": "0db0f983c09bccc875d315cbec60799227ce4e6264d63193489c621da518979d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0711.0987",
    "kind": "arxiv",
    "version": 2
  }
}