Pith Number

pith:WBG45BFA

pith:2015:WBG45BFAOFWX7YZ2PMYGFP4N52

not attested not anchored not stored refs pending

Ordinary pseudorepresentations and modular forms

Carl Wang-Erickson, Preston Wake

arxiv:1510.01661 v4 · 2015-10-06 · 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{WBG45BFAOFWX7YZ2PMYGFP4N52}

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	2026-05-18T00:25:35.096927Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b04dce84a0716d7fe33a7b3062bf8deebf500a2471aeb8f70161c55feb16acf6

Aliases

arxiv: 1510.01661 · arxiv_version: 1510.01661v4 · doi: 10.48550/arxiv.1510.01661 · pith_short_12: WBG45BFAOFWX · pith_short_16: WBG45BFAOFWX7YZ2 · pith_short_8: WBG45BFA

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/WBG45BFAOFWX7YZ2PMYGFP4N52 \
  | 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: b04dce84a0716d7fe33a7b3062bf8deebf500a2471aeb8f70161c55feb16acf6

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0f88f5196e237332ed0378a60d26453637961cd627684034385282617d896e44",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2015-10-06T16:54:08Z",
    "title_canon_sha256": "7f8e581ee587ec20ecec88219af439a31dd3ec5198a6bc204d9d0c0495ccde33"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1510.01661",
    "kind": "arxiv",
    "version": 4
  }
}