Pith Number

pith:PDHRAN2L

pith:2014:PDHRAN2LWK6T7AF2NDMOQNZ7SS

not attested not anchored not stored refs pending

Congruence properties of Borcherds product exponents

Keenan Monks, Lynnelle Ye, Sarah Peluse

arxiv:1407.1294 v1 · 2014-07-04 · 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{PDHRAN2LWK6T7AF2NDMOQNZ7SS}

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	2026-05-18T02:48:18.181299Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

78cf10374bb2bd3f80ba68d8e8373f948a2033095e6ea8d6f950765a7fa14b60

Aliases

arxiv: 1407.1294 · arxiv_version: 1407.1294v1 · doi: 10.48550/arxiv.1407.1294 · pith_short_12: PDHRAN2LWK6T · pith_short_16: PDHRAN2LWK6T7AF2 · pith_short_8: PDHRAN2L

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/PDHRAN2LWK6T7AF2NDMOQNZ7SS \
  | 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: 78cf10374bb2bd3f80ba68d8e8373f948a2033095e6ea8d6f950765a7fa14b60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68c81434d46e10e10d59de1aa4baeabbfe8a87727bd2a0258f083659e8f96c9b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2014-07-04T18:50:49Z",
    "title_canon_sha256": "827d0b7351b4cf406d6b2ecd32c4133f3abfa6d25a437a44f811f8c65f43ad77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1407.1294",
    "kind": "arxiv",
    "version": 1
  }
}