Pith Number

pith:3MQMLOTY

pith:2010:3MQMLOTYLUOLFWAKAQUTK2VNHM

not attested not anchored not stored refs pending

Small optimal Margulis numbers force upper volume bounds

Peter B. Shalen

arxiv:1010.2736 v1 · 2010-10-13 · math.GT · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3MQMLOTYLUOLFWAKAQUTK2VNHM}

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	2026-05-18T04:39:19.741091Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

db20c5ba785d1cb2d80a0429356aad3b1bdd952d70c70599de0d67c1a75352af

Aliases

arxiv: 1010.2736 · arxiv_version: 1010.2736v1 · doi: 10.48550/arxiv.1010.2736 · pith_short_12: 3MQMLOTYLUOL · pith_short_16: 3MQMLOTYLUOLFWAK · pith_short_8: 3MQMLOTY

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/3MQMLOTYLUOLFWAKAQUTK2VNHM \
  | 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: db20c5ba785d1cb2d80a0429356aad3b1bdd952d70c70599de0d67c1a75352af

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5498ef3a296351a42d1202b0ee83a2e5263eaf1d727a4c84ca873d81fb33ba98",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2010-10-13T19:16:58Z",
    "title_canon_sha256": "215c2217f000b685ba6071cde3c4882e02e428f9bf12f40d09b459cf5e205899"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1010.2736",
    "kind": "arxiv",
    "version": 1
  }
}