Pith Number

pith:YHYYQXWG

pith:2015:YHYYQXWGMJQ5HUNHTUXJCBMPL6

not attested not anchored not stored refs pending

Lectures on the topological recursion for Higgs bundles and quantum curves

Motohico Mulase, Olivia Dumitrescu

arxiv:1509.09007 v3 · 2015-09-30 · math.AG · math-ph · math.MP

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YHYYQXWGMJQ5HUNHTUXJCBMPL6}

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	2026-05-18T01:07:51.116094Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c1f1885ec66261d3d1a79d2e91058f5fa6bb5bc71d6fa0817f116f7b8589315e

Aliases

arxiv: 1509.09007 · arxiv_version: 1509.09007v3 · doi: 10.48550/arxiv.1509.09007 · pith_short_12: YHYYQXWGMJQ5 · pith_short_16: YHYYQXWGMJQ5HUNH · pith_short_8: YHYYQXWG

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/YHYYQXWGMJQ5HUNHTUXJCBMPL6 \
  | 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: c1f1885ec66261d3d1a79d2e91058f5fa6bb5bc71d6fa0817f116f7b8589315e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "1a483d6da8939c39188b0aee2fede48ea99e0247cc9315d7006fcdba8a5a8614",
    "cross_cats_sorted": [
      "math-ph",
      "math.MP"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2015-09-30T04:14:12Z",
    "title_canon_sha256": "34c7c0cf2786fb466dc94054247934de60e738bdb3f591cb2e001a46077754e1"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1509.09007",
    "kind": "arxiv",
    "version": 3
  }
}