Pith Number

pith:DLFONDYH

pith:2016:DLFONDYHRNPYVHFCGYJ4RO5B2G

not attested not anchored not stored refs pending

On the minimal number of singular fibers in Lefschetz fibrations over the torus

Andr\'as I. Stipsicz, Ki-Heon Yun

arxiv:1604.04877 v3 · 2016-04-17 · 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{DLFONDYHRNPYVHFCGYJ4RO5B2G}

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	2026-05-18T01:12:54.777295Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1acae68f078b5f8a9ca23613c8bba1d18b2714a883219e8c01d821fe11474620

Aliases

arxiv: 1604.04877 · arxiv_version: 1604.04877v3 · doi: 10.48550/arxiv.1604.04877 · pith_short_12: DLFONDYHRNPY · pith_short_16: DLFONDYHRNPYVHFC · pith_short_8: DLFONDYH

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/DLFONDYHRNPYVHFCGYJ4RO5B2G \
  | 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: 1acae68f078b5f8a9ca23613c8bba1d18b2714a883219e8c01d821fe11474620

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2dd0135f0bafb0090ed7b11b9606a036bb8c2da8258a0b4aa1a48f4992433f07",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-04-17T14:57:24Z",
    "title_canon_sha256": "2194b9fa02ce9710d35472e28d8737fe9f834b3b7d648e20451da261b23577fe"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1604.04877",
    "kind": "arxiv",
    "version": 3
  }
}