Pith Number

pith:VUBM4X7N

pith:2015:VUBM4X7NTUTKJ5UKBXHDHTZDYF

not attested not anchored not stored refs pending

Explicit congruences for mock modular forms

Ben Kane, Matthias Waldherr

arxiv:1510.02918 v1 · 2015-10-10 · 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{VUBM4X7NTUTKJ5UKBXHDHTZDYF}

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	2026-05-18T01:30:33.369151Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

ad02ce5fed9d26a4f68a0dce33cf23c164eec181d64218cf9ff6ff761489086c

Aliases

arxiv: 1510.02918 · arxiv_version: 1510.02918v1 · doi: 10.48550/arxiv.1510.02918 · pith_short_12: VUBM4X7NTUTK · pith_short_16: VUBM4X7NTUTKJ5UK · pith_short_8: VUBM4X7N

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/VUBM4X7NTUTKJ5UKBXHDHTZDYF \
  | 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: ad02ce5fed9d26a4f68a0dce33cf23c164eec181d64218cf9ff6ff761489086c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e6d8b919d89ffe59a0b67b6710c1db2416778d415a0a1862e29ffaf634db9faf",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-10-10T12:05:56Z",
    "title_canon_sha256": "aa8f7591d7b01cd026cc07fc243c7192026e83296056d8d53df32e778bd85a5b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.02918",
    "kind": "arxiv",
    "version": 1
  }
}