Pith Number

pith:URRDA4DO

pith:2013:URRDA4DOOPYZQEXXEFFSJPS3HV

not attested not anchored not stored refs pending

On Dyson's crank conjecture and the uniform asymptotic behavior of certain inverse theta functions

Jehanne Dousse, Kathrin Bringmann

arxiv:1311.6089 v3 · 2013-11-24 · math.NT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{URRDA4DOOPYZQEXXEFFSJPS3HV}

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	2026-05-18T02:49:12.121169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a46230706e73f19812f7214b24be5b3d6a5bcb8c5b3e2b6bd8a94cda06f48b31

Aliases

arxiv: 1311.6089 · arxiv_version: 1311.6089v3 · doi: 10.48550/arxiv.1311.6089 · pith_short_12: URRDA4DOOPYZ · pith_short_16: URRDA4DOOPYZQEXX · pith_short_8: URRDA4DO

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/URRDA4DOOPYZQEXXEFFSJPS3HV \
  | 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: a46230706e73f19812f7214b24be5b3d6a5bcb8c5b3e2b6bd8a94cda06f48b31

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "065b3606d75846e10dae8269a2cf9558467fd575c61a31bf37f7e7ab74e1ee3d",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-24T07:32:23Z",
    "title_canon_sha256": "45e0ceeeb1c01ca1cbf92ef1af9064acedccf31396baa1e230a538615b23bc6a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.6089",
    "kind": "arxiv",
    "version": 3
  }
}