Pith Number

pith:2N3O45HX

pith:2009:2N3O45HXGIMYGCXK72IPHWOP74

not attested not anchored not stored refs pending

Quantum Wall Crossing in N=2 Gauge Theories

Sergei Gukov, Tudor Dimofte, Yan Soibelman

arxiv:0912.1346 v1 · 2009-12-08 · hep-th · math.AG · math.QA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2N3O45HXGIMYGCXK72IPHWOP74}

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.

Cited by

1 paper in Pith

Macdonald Index From Refined Kontsevich-Soibelman Operator

Receipt and verification

First computed	2026-05-18T04:32:19.615910Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d376ee74f73219830aeafe90f3d9cfff119006c817a525fe1670f8081f8c619a

Aliases

arxiv: 0912.1346 · arxiv_version: 0912.1346v1 · doi: 10.48550/arxiv.0912.1346 · pith_short_12: 2N3O45HXGIMY · pith_short_16: 2N3O45HXGIMYGCXK · pith_short_8: 2N3O45HX

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/2N3O45HXGIMYGCXK72IPHWOP74 \
  | 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: d376ee74f73219830aeafe90f3d9cfff119006c817a525fe1670f8081f8c619a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1976f4deb87fb47def27c3c553dd500261eaba4ea4fff5557de20f01332029d1",
    "cross_cats_sorted": [
      "math.AG",
      "math.QA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "hep-th",
    "submitted_at": "2009-12-08T19:19:48Z",
    "title_canon_sha256": "eb6cad5f45489f3e4adb34cab60e2f946ca9b3afc17d38d069910228a542abbd"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0912.1346",
    "kind": "arxiv",
    "version": 1
  }
}