Pith Number

pith:XGS4OX6H

pith:2017:XGS4OX6HRKCEUK5B3PXWJKZJ6R

not attested not anchored not stored refs pending

Vafa-Witten invariants for projective surfaces II: semistable case

Richard P. Thomas, Yuuji Tanaka

arxiv:1702.08488 v4 · 2017-02-27 · math.AG · hep-th · math.DG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XGS4OX6HRKCEUK5B3PXWJKZJ6R}

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	2026-07-05T05:04:43.520179Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b9a5c75fc78a844a2ba1dbef64ab29f466186306b39106a98b994580f98bbc60

Aliases

arxiv: 1702.08488 · arxiv_version: 1702.08488v4 · doi: 10.48550/arxiv.1702.08488 · pith_short_12: XGS4OX6HRKCE · pith_short_16: XGS4OX6HRKCEUK5B · pith_short_8: XGS4OX6H

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/XGS4OX6HRKCEUK5B3PXWJKZJ6R \
  | 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: b9a5c75fc78a844a2ba1dbef64ab29f466186306b39106a98b994580f98bbc60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "fb59cb62071a998541c93bee1c8d52f4989442048a066a2f6e1032da1deedff4",
    "cross_cats_sorted": [
      "hep-th",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2017-02-27T19:44:07Z",
    "title_canon_sha256": "c6840fe05f3986a6783a76851d2d94298fd718b32a444f58386a5f997489c5b5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.08488",
    "kind": "arxiv",
    "version": 4
  }
}