Pith Number

pith:E557MHAB

pith:2012:E557MHABZN6VQGSO5NXW55ODGT

not attested not anchored not stored refs pending

Sylvester's, Wolstenholme's, Morley's and Lehmer's Congruence Theorems Revisited

Christian Aebi, Grant Cairns

arxiv:1201.6559 v4 · 2012-01-29 · math.HO · 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{E557MHABZN6VQGSO5NXW55ODGT}

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	2026-05-18T03:52:01.176769Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

277bf61c01cb7d581a4eeb6f6ef5c334d64bb8f65c58463af7e5598622527c6f

Aliases

arxiv: 1201.6559 · arxiv_version: 1201.6559v4 · doi: 10.48550/arxiv.1201.6559 · pith_short_12: E557MHABZN6V · pith_short_16: E557MHABZN6VQGSO · pith_short_8: E557MHAB

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/E557MHABZN6VQGSO5NXW55ODGT \
  | 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: 277bf61c01cb7d581a4eeb6f6ef5c334d64bb8f65c58463af7e5598622527c6f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "21be018e49041448abd972096342c01d5f283300bd4481bb8b5d9d6997c4d2a1",
    "cross_cats_sorted": [
      "math.NT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.HO",
    "submitted_at": "2012-01-29T08:33:40Z",
    "title_canon_sha256": "40bf086bf95cf4c40c9cdbea33005e159a49e3215abd6ea1497b05d9ddfb2be0"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1201.6559",
    "kind": "arxiv",
    "version": 4
  }
}