Pith Number

pith:YL3UCLBR

pith:2009:YL3UCLBRKWXXENVCVVCWV2YGVP

not attested not anchored not stored refs pending

Asymmetry of Outer Space

Mladen Bestvina, Yael Algom-Kfir

arxiv:0910.5408 v3 · 2009-10-28 · math.GR · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YL3UCLBRKWXXENVCVVCWV2YGVP}

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	2026-05-18T04:26:01.524723Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c2f7412c3155af7236a2ad456aeb06abcfb03ba3e61c24fc29d4e33af4904884

Aliases

arxiv: 0910.5408 · arxiv_version: 0910.5408v3 · doi: 10.48550/arxiv.0910.5408 · pith_short_12: YL3UCLBRKWXX · pith_short_16: YL3UCLBRKWXXENVC · pith_short_8: YL3UCLBR

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/YL3UCLBRKWXXENVCVVCWV2YGVP \
  | 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: c2f7412c3155af7236a2ad456aeb06abcfb03ba3e61c24fc29d4e33af4904884

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b635ebf19f5daeb5f4c71f224bac8ff82fcf316de9d4c1a08bcbb9e7362b16fb",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2009-10-28T15:47:35Z",
    "title_canon_sha256": "048e527834e2a82e8cfc059e35d5ecaaa1f190c549a7f43e872f0b417859c2c8"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0910.5408",
    "kind": "arxiv",
    "version": 3
  }
}