Pith Number

pith:MLAYQFWN

pith:2010:MLAYQFWNLMVJXGHC2YKEU2VS4E

not attested not anchored not stored refs pending

Universal tree-graded spaces and asymptotic cones

Denis Osin, Mark Sapir

arxiv:1010.3673 v3 · 2010-10-18 · 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{MLAYQFWNLMVJXGHC2YKEU2VS4E}

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	2026-05-18T04:26:23.063178Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62c18816cd5b2a9b98e2d6144a6ab2e13df93267c21e86a23880ad845b7badfa

Aliases

arxiv: 1010.3673 · arxiv_version: 1010.3673v3 · doi: 10.48550/arxiv.1010.3673 · pith_short_12: MLAYQFWNLMVJ · pith_short_16: MLAYQFWNLMVJXGHC · pith_short_8: MLAYQFWN

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/MLAYQFWNLMVJXGHC2YKEU2VS4E \
  | 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: 62c18816cd5b2a9b98e2d6144a6ab2e13df93267c21e86a23880ad845b7badfa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "097c15f1efb4d521735d1f7122404d29af9e5e704e4e1fc6c89d1e639c18071b",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-10-18T18:23:56Z",
    "title_canon_sha256": "ffbfb2a5898537e2d12493eea95a129bf577ddeb5490b0fba474750e6f439290"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.3673",
    "kind": "arxiv",
    "version": 3
  }
}