Pith Number

pith:BTPPJ3TH

pith:2012:BTPPJ3THMZFOEKXQKSAB6N3HCM

not attested not anchored not stored refs pending

Polynomiality, Wall Crossings and Tropical Geometry of Rational Double Hurwitz Cycles

Aaron Bertram, Hannah Markwig, Renzo Cavalieri

arxiv:1209.5789 v2 · 2012-09-25 · math.AG · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{BTPPJ3THMZFOEKXQKSAB6N3HCM}

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	2026-05-18T03:25:25.600788Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

0cdef4ee67664ae22af054801f37671333e7d409fac0734b48f30066097a5dd5

Aliases

arxiv: 1209.5789 · arxiv_version: 1209.5789v2 · doi: 10.48550/arxiv.1209.5789 · pith_short_12: BTPPJ3THMZFO · pith_short_16: BTPPJ3THMZFOEKXQ · pith_short_8: BTPPJ3TH

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/BTPPJ3THMZFOEKXQKSAB6N3HCM \
  | 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: 0cdef4ee67664ae22af054801f37671333e7d409fac0734b48f30066097a5dd5

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "3a72f15e9d35d77a93e546c5aecab380bd48b7199159023a33479f052a5bc5e1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AG",
    "submitted_at": "2012-09-25T22:52:03Z",
    "title_canon_sha256": "6797fb81ecea08af14329ae9d3a530aaa8837a61875bdcaec349d0eea3184505"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1209.5789",
    "kind": "arxiv",
    "version": 2
  }
}