Pith Number

pith:UND2WDLY

pith:2011:UND2WDLYL4KLHXJKYNTIQSGQQ4

not attested not anchored not stored refs pending

Complexity and heights of tori

Anders Karlsson, Gautam Chinta, Jay Jorgenson

arxiv:1110.6841 v1 · 2011-10-31 · math-ph · math.CO · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{UND2WDLYL4KLHXJKYNTIQSGQQ4}

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	2026-05-18T04:09:54.079778Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a347ab0d785f14b3dd2ac3668848d0872cbc2389b9d3114513798baae268d2ac

Aliases

arxiv: 1110.6841 · arxiv_version: 1110.6841v1 · doi: 10.48550/arxiv.1110.6841 · pith_short_12: UND2WDLYL4KL · pith_short_16: UND2WDLYL4KLHXJK · pith_short_8: UND2WDLY

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/UND2WDLYL4KLHXJKYNTIQSGQQ4 \
  | 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: a347ab0d785f14b3dd2ac3668848d0872cbc2389b9d3114513798baae268d2ac

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "5b2a72c4caf8130af504f616b31eba19e9f5ac2907cef6805f790b48047b7a1a",
    "cross_cats_sorted": [
      "math.CO",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2011-10-31T15:48:49Z",
    "title_canon_sha256": "12f19dd66b3e9007699a9de00b6c950850e8e1052d38b5e9a826393a89da7f7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1110.6841",
    "kind": "arxiv",
    "version": 1
  }
}