Pith Number

pith:TE2X34FU

pith:2005:TE2X34FUMGRSH4M3353B55AXUM

not attested not anchored not stored refs pending

Combinatorial congruences modulo prime powers

Donald M. Davis, Zhi-Wei Sun

arxiv:math/0508087 v5 · 2005-08-04 · math.NT · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{TE2X34FUMGRSH4M3353B55AXUM}

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	2026-07-04T15:03:15.418278Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

99357df0b461a323f19bdf761ef417a31add71ac4eb76d366f75be5bc14ed383

Aliases

arxiv: math/0508087 · arxiv_version: math/0508087v5 · doi: 10.48550/arxiv.math/0508087 · pith_short_12: TE2X34FUMGRS · pith_short_16: TE2X34FUMGRSH4M3 · pith_short_8: TE2X34FU

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/TE2X34FUMGRSH4M3353B55AXUM \
  | 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: 99357df0b461a323f19bdf761ef417a31add71ac4eb76d366f75be5bc14ed383

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d6d525d6a9cc9de997067dde1cc5d09f7b68e9630458fa9f6574b780b53eb7a1",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "",
    "primary_cat": "math.NT",
    "submitted_at": "2005-08-04T07:28:54Z",
    "title_canon_sha256": "9d03123a8c5ce4cc41a6e95efd7c23dbe5e8059ce2ddebf432235690a1af0988"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0508087",
    "kind": "arxiv",
    "version": 5
  }
}