Pith Number

pith:7PB5VBDA

pith:2008:7PB5VBDANLK3P3MDWTDTYNBVZQ

not attested not anchored not stored refs pending

The universal Kummer congruences

Jianrong Zhao, Shaofang Hong, Wei Zhao

arxiv:0808.3544 v2 · 2008-08-26 · 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{7PB5VBDANLK3P3MDWTDTYNBVZQ}

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	2026-05-18T03:15:21.310415Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fbc3da84606ad5b7ed83b4c73c3435cc3812134c73643b00ce96a2b36cfb8035

Aliases

arxiv: 0808.3544 · arxiv_version: 0808.3544v2 · doi: 10.48550/arxiv.0808.3544 · pith_short_12: 7PB5VBDANLK3 · pith_short_16: 7PB5VBDANLK3P3MD · pith_short_8: 7PB5VBDA

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/7PB5VBDANLK3P3MDWTDTYNBVZQ \
  | 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: fbc3da84606ad5b7ed83b4c73c3435cc3812134c73643b00ce96a2b36cfb8035

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8ab1c2f94877862280e224f879a7fbc9d9cfa246b24509f5aa503f27e8a4408b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2008-08-26T15:45:34Z",
    "title_canon_sha256": "a9777a571fc91e7687d09174d14c625b4593152f9c84fa86984d89ede49ddb62"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0808.3544",
    "kind": "arxiv",
    "version": 2
  }
}