Pith Number

pith:6TMGM5P6

pith:2013:6TMGM5P65V3FPKNSJM3KJQE4SH

not attested not anchored not stored refs pending

Renormalization and quantum modular forms, part II: Mock theta functions

Hieu T. Ngo, Robert C. Rhoades, Yingkun Li

arxiv:1311.3044 v1 · 2013-11-13 · 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{6TMGM5P65V3FPKNSJM3KJQE4SH}

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	2026-05-18T03:07:13.274487Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f4d86675feed7657a9b24b36a4c09c91d26758741b66c19896c9d1b486131f11

Aliases

arxiv: 1311.3044 · arxiv_version: 1311.3044v1 · doi: 10.48550/arxiv.1311.3044 · pith_short_12: 6TMGM5P65V3F · pith_short_16: 6TMGM5P65V3FPKNS · pith_short_8: 6TMGM5P6

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/6TMGM5P65V3FPKNSJM3KJQE4SH \
  | 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: f4d86675feed7657a9b24b36a4c09c91d26758741b66c19896c9d1b486131f11

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "51ced4cbc554a7c339d0b3ef3cc8b36f67a0fee10df59e234e63711e70560e0b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2013-11-13T08:08:30Z",
    "title_canon_sha256": "cf1880bab1036cab8cd2ef289cd0a960a0fb785e75bdb28aa676a2b84f022a13"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1311.3044",
    "kind": "arxiv",
    "version": 1
  }
}