Pith Number

pith:2QBW3L4Z

pith:2007:2QBW3L4Z2CXJWI5L3P7S3IGVHB

not attested not anchored not stored refs pending

Covering spaces and the Kakimizu complex

Jennifer Schultens

arxiv:0707.3926 v4 · 2007-07-26 · 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{2QBW3L4Z2CXJWI5L3P7S3IGVHB}

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	2026-05-18T03:02:18.621059Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d4036daf99d0ae9b23abdbff2da0d53872ec062641c52e078df35e4af8ef25aa

Aliases

arxiv: 0707.3926 · arxiv_version: 0707.3926v4 · doi: 10.48550/arxiv.0707.3926 · pith_short_12: 2QBW3L4Z2CXJ · pith_short_16: 2QBW3L4Z2CXJWI5L · pith_short_8: 2QBW3L4Z

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/2QBW3L4Z2CXJWI5L3P7S3IGVHB \
  | 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: d4036daf99d0ae9b23abdbff2da0d53872ec062641c52e078df35e4af8ef25aa

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "732bfc701f44e11f6fcfe3326ba73bbd12d67e29e8d3f296e21e49aef31fc5a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2007-07-26T14:10:50Z",
    "title_canon_sha256": "49e3e4cceaa209b7848576e7b1b1900fb1e509f225f512af676e21ca0a2cd0c7"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0707.3926",
    "kind": "arxiv",
    "version": 4
  }
}