Pith Number

pith:4BHGX6AJ

pith:2008:4BHGX6AJVI4T2ZT3W2PSUSGOYH

not attested not anchored not stored refs pending

Median structures on asymptotic cones and homomorphisms into mapping class groups

C. Drutu, J. Behrstock, M. Sapir

arxiv:0810.5376 v4 · 2008-10-29 · math.GT · 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{4BHGX6AJVI4T2ZT3W2PSUSGOYH}

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	2026-05-18T04:37:34.460222Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e04e6bf809aa393d667bb69f2a48cec1f209801a51d3bfe2fc24dc1618574a6e

Aliases

arxiv: 0810.5376 · arxiv_version: 0810.5376v4 · doi: 10.48550/arxiv.0810.5376 · pith_short_12: 4BHGX6AJVI4T · pith_short_16: 4BHGX6AJVI4T2ZT3 · pith_short_8: 4BHGX6AJ

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/4BHGX6AJVI4T2ZT3W2PSUSGOYH \
  | 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: e04e6bf809aa393d667bb69f2a48cec1f209801a51d3bfe2fc24dc1618574a6e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "95ffe181e1f4a3dcbd587cbe994146521c26ed50e2df2e46a8f0032dc7328e02",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2008-10-29T22:39:38Z",
    "title_canon_sha256": "5526d20b7917fd223f8806557d9efb5c5dbf8b64dc15e0034f033c62f308e422"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0810.5376",
    "kind": "arxiv",
    "version": 4
  }
}