Pith Number

pith:6JWHNN5T

pith:2011:6JWHNN5TBNTV67GJUTO356K26S

not attested not anchored not stored refs pending

Joyce-Song wall-crossing as an asymptotic expansion

Jacopo Stoppa

arxiv:1112.2174 v2 · 2011-12-09 · math.AG · 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{6JWHNN5TBNTV67GJUTO356K26S}

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	2026-05-18T01:28:21.869416Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f26c76b7b30b675f7cc9a4ddbef95af4bfe91a1e3918047e3629dc29068fea3b

Aliases

arxiv: 1112.2174 · arxiv_version: 1112.2174v2 · doi: 10.48550/arxiv.1112.2174 · pith_short_12: 6JWHNN5TBNTV · pith_short_16: 6JWHNN5TBNTV67GJ · pith_short_8: 6JWHNN5T

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/6JWHNN5TBNTV67GJUTO356K26S \
  | 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: f26c76b7b30b675f7cc9a4ddbef95af4bfe91a1e3918047e3629dc29068fea3b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "943ab7a2483f596ea316c2122e3fc885cd2e0214a9b84df43af818948bc648e2",
    "cross_cats_sorted": [
      "math.DG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2011-12-09T18:17:13Z",
    "title_canon_sha256": "bc0c34f3a3fc913f2a376e2f75e84c804a60f27e3d8a4b03ebe6392e1665c555"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.2174",
    "kind": "arxiv",
    "version": 2
  }
}