Pith Number

pith:MVHZHDBF

pith:2016:MVHZHDBFDRQY7IQY7XOOEVRWY3

not attested not anchored not stored refs pending

Bilinear-form invariants of Lefschetz fibrations over the 2-sphere

Takefumi Nosaka

arxiv:1611.04405 v3 · 2016-11-14 · 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{MVHZHDBFDRQY7IQY7XOOEVRWY3}

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	2026-05-18T00:51:37.074509Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

654f938c251c618fa218fddce25636c6c1c42200a9ad8a37668a9109096d5218

Aliases

arxiv: 1611.04405 · arxiv_version: 1611.04405v3 · doi: 10.48550/arxiv.1611.04405 · pith_short_12: MVHZHDBFDRQY · pith_short_16: MVHZHDBFDRQY7IQY · pith_short_8: MVHZHDBF

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/MVHZHDBFDRQY7IQY7XOOEVRWY3 \
  | 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: 654f938c251c618fa218fddce25636c6c1c42200a9ad8a37668a9109096d5218

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ed28ad32339314727cd809f7d82d7f0391016d3c0686d8108ff08a2e63d4ab9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GT",
    "submitted_at": "2016-11-14T15:01:15Z",
    "title_canon_sha256": "3b8e7e48a79668010816b53f4d8a7151cebe7b15171667fb1e8662843e3ad0f6"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1611.04405",
    "kind": "arxiv",
    "version": 3
  }
}