Pith Number

pith:BVFBOSV4

pith:2004:BVFBOSV45ATX2YCXHNVCAU3OWW

not attested not anchored not stored refs pending

Heegaard gradient and virtual fibers

Joseph Maher

arxiv:math/0411219 v2 · 2004-11-10 · 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{BVFBOSV45ATX2YCXHNVCAU3OWW}

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	2026-05-18T02:37:59.886296Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0d4a174abce8277d60573b6a20536eb580a202402472a97c018ce182bbc7c257

Aliases

arxiv: math/0411219 · arxiv_version: math/0411219v2 · doi: 10.48550/arxiv.math/0411219 · pith_short_12: BVFBOSV45ATX · pith_short_16: BVFBOSV45ATX2YCX · pith_short_8: BVFBOSV4

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/BVFBOSV45ATX2YCXHNVCAU3OWW \
  | 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: 0d4a174abce8277d60573b6a20536eb580a202402472a97c018ce182bbc7c257

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2415bb60427a5171073eedf510885ead619e30f9f293766ccb9e29c414cb1356",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.GT",
    "submitted_at": "2004-11-10T05:40:06Z",
    "title_canon_sha256": "fab3bbeaa45d3075fd1ccf1e872c440547b6417288d155e57bbeb5dfba73fc72"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0411219",
    "kind": "arxiv",
    "version": 2
  }
}