Pith Number

pith:WL2QYR42

pith:2011:WL2QYR42XPYSUMPWB2NLKRASK7

not attested not anchored not stored refs pending

Stern's type congruences for L(-k,\chi)

Hao Pan, Yong Zhang

arxiv:1101.4806 v2 · 2011-01-25 · 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{WL2QYR42XPYSUMPWB2NLKRASK7}

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	2026-05-18T03:27:01.983292Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b2f50c479abbf12a31f60e9ab5441257d77dc280a0c0099f27c9507285c6c07b

Aliases

arxiv: 1101.4806 · arxiv_version: 1101.4806v2 · doi: 10.48550/arxiv.1101.4806 · pith_short_12: WL2QYR42XPYS · pith_short_16: WL2QYR42XPYSUMPW · pith_short_8: WL2QYR42

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/WL2QYR42XPYSUMPWB2NLKRASK7 \
  | 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: b2f50c479abbf12a31f60e9ab5441257d77dc280a0c0099f27c9507285c6c07b

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "b0e2e95fe20a0750cb0e1febecc80b033ee14542f9ebcb527621ac8e954dc82b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2011-01-25T13:19:13Z",
    "title_canon_sha256": "ccfa2c416a75585edee5a582270fa2894b15642dc84fd03d233720898cdc7bc9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1101.4806",
    "kind": "arxiv",
    "version": 2
  }
}