Pith Number

pith:HNABC5ZP

pith:2017:HNABC5ZPRQNIRO55QHORJCHQAE

not attested not anchored not stored refs pending

Vafa-Witten invariants for projective surfaces I: stable case

Richard P. Thomas, Yuuji Tanaka

arxiv:1702.08487 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{HNABC5ZPRQNIRO55QHORJCHQAE}

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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.

Cited by

1 paper in Pith

The virtual fundamental class for the moduli space of surfaces of general type

Receipt and verification

First computed	2026-07-05T05:04:43.499721Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3b4011772f8c1a88bbbd81dd1488f001195ad51752c9a52ef243edb9d1f8516e

Aliases

arxiv: 1702.08487 · arxiv_version: 1702.08487v4 · doi: 10.48550/arxiv.1702.08487 · pith_short_12: HNABC5ZPRQNI · pith_short_16: HNABC5ZPRQNIRO55 · pith_short_8: HNABC5ZP

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/HNABC5ZPRQNIRO55QHORJCHQAE \
  | 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: 3b4011772f8c1a88bbbd81dd1488f001195ad51752c9a52ef243edb9d1f8516e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "456166f67b863f54ac70971b1530918f72ff8d6c5b21a448caadc7a0e32a04a7",
    "cross_cats_sorted": [
      "hep-th",
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2017-02-27T19:44:01Z",
    "title_canon_sha256": "c4fec8b077c206b57f7d5c3d36f9897a461d178c3a83cdf823ec487ba0cfd584"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1702.08487",
    "kind": "arxiv",
    "version": 4
  }
}