Pith Number

pith:HCJK5Z5W

pith:2012:HCJK5Z5WQHS3XEAPYDSNEIIGEA

not attested not anchored not stored refs pending

A linear bound on the tetrahedral number of manifolds of bounded volume (after Jorgensen and Thurston)

Tsuyoshi Kobayashi, Yo'av Rieck

arxiv:1205.2441 v1 · 2012-05-11 · 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{HCJK5Z5WQHS3XEAPYDSNEIIGEA}

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	2026-05-18T03:55:55.507631Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3892aee7b681e5bb900fc0e4d22106201add0d84a712e29b325c72c9a3d9b7f1

Aliases

arxiv: 1205.2441 · arxiv_version: 1205.2441v1 · doi: 10.48550/arxiv.1205.2441 · pith_short_12: HCJK5Z5WQHS3 · pith_short_16: HCJK5Z5WQHS3XEAP · pith_short_8: HCJK5Z5W

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/HCJK5Z5WQHS3XEAPYDSNEIIGEA \
  | 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: 3892aee7b681e5bb900fc0e4d22106201add0d84a712e29b325c72c9a3d9b7f1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8668560e0137cfd0e7b61c554f63b0121234ce311bc3d776709f05c90e7af8ea",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-05-11T06:55:48Z",
    "title_canon_sha256": "fabc539e8c2e6a842e627960a6d8566f15bb5b5371cb68a0a447f75972657a63"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.2441",
    "kind": "arxiv",
    "version": 1
  }
}