Pith Number

pith:PIEGC3RA

pith:2004:PIEGC3RA7BIOEP5YDM75BQV5LI

not attested not anchored not stored refs pending

Note on the Irreducible Triangulations of the Klein Bottle

Thom Sulanke

arxiv:math/0407008 v2 · 2004-07-01 · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{PIEGC3RA7BIOEP5YDM75BQV5LI}

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	2026-05-18T01:32:58.181272Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

7a08616e20f850e23fb81b3fd0c2bd5a38f8cc3acfe5116e49eb3b28b963fcc2

Aliases

arxiv: math/0407008 · arxiv_version: math/0407008v2 · doi: 10.48550/arxiv.math/0407008 · pith_short_12: PIEGC3RA7BIO · pith_short_16: PIEGC3RA7BIOEP5Y · pith_short_8: PIEGC3RA

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/PIEGC3RA7BIOEP5YDM75BQV5LI \
  | 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: 7a08616e20f850e23fb81b3fd0c2bd5a38f8cc3acfe5116e49eb3b28b963fcc2

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7a207105835792784e390042ea3eb50cf3004c8889e32775630a3e349d399fb5",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.CO",
    "submitted_at": "2004-07-01T19:02:54Z",
    "title_canon_sha256": "c1004a349d77fe1fbfa5f3a360a8fe8e1d03aef3afc703b90dad195bd33112cc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0407008",
    "kind": "arxiv",
    "version": 2
  }
}