Pith Number

pith:MLNBUBGS

pith:2012:MLNBUBGS3DDIGWG7ORL5XKTNGP

not attested not anchored not stored refs pending

Factorial growth rates for the number of hyperbolic 3-manifolds of a given volume

Christian Millichap

arxiv:1209.1042 v2 · 2012-09-05 · 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{MLNBUBGS3DDIGWG7ORL5XKTNGP}

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	2026-05-18T01:59:59.260885Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

62da1a04d2d8c68358df7457dbaa6d33df8f7370501161a4f6140b2943d2e89b

Aliases

arxiv: 1209.1042 · arxiv_version: 1209.1042v2 · doi: 10.48550/arxiv.1209.1042 · pith_short_12: MLNBUBGS3DDI · pith_short_16: MLNBUBGS3DDIGWG7 · pith_short_8: MLNBUBGS

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/MLNBUBGS3DDIGWG7ORL5XKTNGP \
  | 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: 62da1a04d2d8c68358df7457dbaa6d33df8f7370501161a4f6140b2943d2e89b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "63d7b634e992ec937a340328e5f5edc62dbbf3d187cf47a0dba806891d97d0a4",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-09-05T16:59:39Z",
    "title_canon_sha256": "55ca54c8e951886f75c8d8d2d44efb3af105f32a09d667023003ef0c6eae0e9b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1042",
    "kind": "arxiv",
    "version": 2
  }
}