Pith Number

pith:GHEZNZAB

pith:2011:GHEZNZABE6EAPUFOFQHOPWDLZ2

not attested not anchored not stored refs pending

Computing the crosscap number of a knot using integer programming and normal surfaces

Benjamin A. Burton, Melih Ozlen

arxiv:1107.2382 v2 · 2011-07-12 · math.GT · cs.CG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GHEZNZABE6EAPUFOFQHOPWDLZ2}

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	2026-05-18T03:38:46.428285Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31c996e401278807d0ae2c0ee7d86bcead89b9d5d162eb6983dbd1d6c26617d1

Aliases

arxiv: 1107.2382 · arxiv_version: 1107.2382v2 · doi: 10.48550/arxiv.1107.2382 · pith_short_12: GHEZNZABE6EA · pith_short_16: GHEZNZABE6EAPUFO · pith_short_8: GHEZNZAB

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/GHEZNZABE6EAPUFOFQHOPWDLZ2 \
  | 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: 31c996e401278807d0ae2c0ee7d86bcead89b9d5d162eb6983dbd1d6c26617d1

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6496ca26371233f0b0f831d369b6ff79f57e145ed80fa22dce937c2141d60349",
    "cross_cats_sorted": [
      "cs.CG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-07-12T19:43:52Z",
    "title_canon_sha256": "c83d54788317b80a0ab3d199c3e5517d3a59d1b4416a647c9fec88ab24850341"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1107.2382",
    "kind": "arxiv",
    "version": 2
  }
}