Pith Number

pith:MMAV2PCU

pith:2015:MMAV2PCUNFV4NN4GBDUPD4LNMS

not attested not anchored not stored refs pending

Independence of volume and genus $g$ bridge numbers

Alexander Zupan, Jessica S. Purcell

arxiv:1512.03869 v2 · 2015-12-12 · 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{MMAV2PCUNFV4NN4GBDUPD4LNMS}

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	2026-05-18T01:18:08.783506Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

63015d3c54696bc6b78608e8f1f16d64aa3621f40465c444f47472dac96a4ae4

Aliases

arxiv: 1512.03869 · arxiv_version: 1512.03869v2 · doi: 10.48550/arxiv.1512.03869 · pith_short_12: MMAV2PCUNFV4 · pith_short_16: MMAV2PCUNFV4NN4G · pith_short_8: MMAV2PCU

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/MMAV2PCUNFV4NN4GBDUPD4LNMS \
  | 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: 63015d3c54696bc6b78608e8f1f16d64aa3621f40465c444f47472dac96a4ae4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "f6e92be0a6c1fa401d39db4bb047b34020f87e1bae5a18b8d94b5b44a511fdae",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2015-12-12T03:52:41Z",
    "title_canon_sha256": "e5a2b8df4a001c45beecb8c9150db931f42d54b8eff688bbd34228eeb79e78bb"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1512.03869",
    "kind": "arxiv",
    "version": 2
  }
}