Pith Number

pith:4HAGFMEW

pith:2011:4HAGFMEW636E23BYSBVPNDYHF4

not attested not anchored not stored refs pending

Universal Lefschetz fibrations over bounded surfaces

Daniele Zuddas

arxiv:1106.3530 v3 · 2011-06-17 · 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{4HAGFMEW636E23BYSBVPNDYHF4}

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	2026-05-18T02:21:43.793845Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e1c062b096f6fc4d6c38906af68f072f2479369d289557ad074eaf1bcd8b9501

Aliases

arxiv: 1106.3530 · arxiv_version: 1106.3530v3 · doi: 10.48550/arxiv.1106.3530 · pith_short_12: 4HAGFMEW636E · pith_short_16: 4HAGFMEW636E23BY · pith_short_8: 4HAGFMEW

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/4HAGFMEW636E23BYSBVPNDYHF4 \
  | 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: e1c062b096f6fc4d6c38906af68f072f2479369d289557ad074eaf1bcd8b9501

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "34784f099d0992f7298cd887f2a258ebe1ce9435a6793e02f38eb0ed98dedce9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2011-06-17T16:54:31Z",
    "title_canon_sha256": "5750e960d265772e36c9d8313b67b5e49b6cd05b7e656a374640cf3388a710ef"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1106.3530",
    "kind": "arxiv",
    "version": 3
  }
}