Pith Number

pith:MHZX36FX

pith:2012:MHZX36FXW2BOXRBKGWXJ2ENMPR

not attested not anchored not stored refs pending

Lefschetz fibrations with small slope

Naoyuki Monden

arxiv:1209.1268 v3 · 2012-09-06 · math.GT · math.SG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{MHZX36FXW2BOXRBKGWXJ2ENMPR}

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	2026-05-18T01:22:26.274377Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

61f37df8b7b682ebc42a35ae9d11ac7c6ea67287e754641948d757562977ab25

Aliases

arxiv: 1209.1268 · arxiv_version: 1209.1268v3 · doi: 10.48550/arxiv.1209.1268 · pith_short_12: MHZX36FXW2BO · pith_short_16: MHZX36FXW2BOXRBK · pith_short_8: MHZX36FX

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/MHZX36FXW2BOXRBKGWXJ2ENMPR \
  | 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: 61f37df8b7b682ebc42a35ae9d11ac7c6ea67287e754641948d757562977ab25

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c2861cb1f59dc0705db346cc86f0026be39c520dd71bce1554d20d28c17e089a",
    "cross_cats_sorted": [
      "math.SG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2012-09-06T12:25:40Z",
    "title_canon_sha256": "e0c1334c5470bb0a59df80c639795996646826fc2c1e8064c45ca39fbe5c8049"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.1268",
    "kind": "arxiv",
    "version": 3
  }
}