Pith Number

pith:IS4BUKNN

pith:2009:IS4BUKNN7YG6TWJ25LMJAKK5E6

not attested not anchored not stored refs pending

Surface links which are coverings over the standard torus

Inasa Nakamura

arxiv:0905.0048 v4 · 2009-05-01 · 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{IS4BUKNN7YG6TWJ25LMJAKK5E6}

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	2026-05-18T01:22:31.033397Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

44b81a29adfe0de9d93aead890295d278b0ea6074337192b6929e28fa6aaf66a

Aliases

arxiv: 0905.0048 · arxiv_version: 0905.0048v4 · doi: 10.48550/arxiv.0905.0048 · pith_short_12: IS4BUKNN7YG6 · pith_short_16: IS4BUKNN7YG6TWJ2 · pith_short_8: IS4BUKNN

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/IS4BUKNN7YG6TWJ25LMJAKK5E6 \
  | 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: 44b81a29adfe0de9d93aead890295d278b0ea6074337192b6929e28fa6aaf66a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "af576736e829dba5918496f349f445b991a55fecd03f0128aa969c4d3e09bd13",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2009-05-01T05:24:26Z",
    "title_canon_sha256": "c42df91b71523a17580554ef2b3aa24bac81f6c7e4e7c5e7df1283ea263af644"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0905.0048",
    "kind": "arxiv",
    "version": 4
  }
}