Pith Number

pith:MTRAPJOM

pith:2012:MTRAPJOM2X2HUM5RYSYZ4HGLWB

not attested not anchored not stored refs pending

Structures for pairs of mock modular forms with the Zagier duality

Dohoon Choi, Subong Lim

arxiv:1212.0370 v2 · 2012-12-03 · 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{MTRAPJOM2X2HUM5RYSYZ4HGLWB}

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	2026-05-18T03:10:47.972005Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

64e207a5ccd5f47a33b1c4b19e1ccbb07d4796192840e9459bec3c4432f1969f

Aliases

arxiv: 1212.0370 · arxiv_version: 1212.0370v2 · doi: 10.48550/arxiv.1212.0370 · pith_short_12: MTRAPJOM2X2H · pith_short_16: MTRAPJOM2X2HUM5R · pith_short_8: MTRAPJOM

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/MTRAPJOM2X2HUM5RYSYZ4HGLWB \
  | 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: 64e207a5ccd5f47a33b1c4b19e1ccbb07d4796192840e9459bec3c4432f1969f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "66293c1b25c49cef010c356b28670f6ca5c2a3724da5f9d71bee794125a64106",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2012-12-03T12:56:29Z",
    "title_canon_sha256": "b1176a5dd1c8b061c0684f7a9ce97fb92090f526fbe10302f335185d9e71ab7d"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1212.0370",
    "kind": "arxiv",
    "version": 2
  }
}