Pith Number

pith:VGZHPG3U

pith:2019:VGZHPG3U5ZLX6ZTHKGEEDEEZUB

not attested not anchored not stored refs pending

Quantum modular forms and singular combinatorial series with repeated roots of unity

Amanda Folsom, Holly Swisher, Min-Joo Jang, Sam Kimport

arxiv:1902.10698 v1 · 2019-02-26 · 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{VGZHPG3U5ZLX6ZTHKGEEDEEZUB}

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	2026-05-17T23:52:29.965464Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

a9b2779b74ee577f66675188419099a046e48a28ffb41164766c8f09edd74570

Aliases

arxiv: 1902.10698 · arxiv_version: 1902.10698v1 · doi: 10.48550/arxiv.1902.10698 · pith_short_12: VGZHPG3U5ZLX · pith_short_16: VGZHPG3U5ZLX6ZTH · pith_short_8: VGZHPG3U

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/VGZHPG3U5ZLX6ZTHKGEEDEEZUB \
  | 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: a9b2779b74ee577f66675188419099a046e48a28ffb41164766c8f09edd74570

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "96e60ecd51b79a9aa6d4df5d2a4ddca1969f197687e15a56d506813da995fbf9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2019-02-26T20:56:30Z",
    "title_canon_sha256": "9c340939d236d1e12f31b6089c4f717c37d741af0f4e8d6927fc93e882de0e42"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1902.10698",
    "kind": "arxiv",
    "version": 1
  }
}