Pith Number

pith:LIW5F54S

pith:2013:LIW5F54S4VIOV46N4MEJ6RSE2Z

not attested not anchored not stored refs pending

k-Marked Dyson Symbols and Congruences for Moments of Cranks

Erin Y.Y. Shen, Kathy Q. Ji, William Y.C. Chen

arxiv:1312.2080 v1 · 2013-12-07 · math.CO · 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{LIW5F54S4VIOV46N4MEJ6RSE2Z}

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	2026-05-18T03:05:17.380026Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5a2dd2f792e550eaf3cde3089f4644d64ebbdeee93e30714a86a520adba48324

Aliases

arxiv: 1312.2080 · arxiv_version: 1312.2080v1 · doi: 10.48550/arxiv.1312.2080 · pith_short_12: LIW5F54S4VIO · pith_short_16: LIW5F54S4VIOV46N · pith_short_8: LIW5F54S

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/LIW5F54S4VIOV46N4MEJ6RSE2Z \
  | 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: 5a2dd2f792e550eaf3cde3089f4644d64ebbdeee93e30714a86a520adba48324

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "421fcd22edc8926cf8993c464e79a754917bbca0f360a6543294eb6ed1ef8b69",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2013-12-07T10:10:49Z",
    "title_canon_sha256": "e0955ee380696cdbf63c26ded5c84e51b095cd243f7360edc75fe4b8f401d21d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1312.2080",
    "kind": "arxiv",
    "version": 1
  }
}