Pith Number

pith:WOUA6HYU

pith:2016:WOUA6HYUSWT7KYZKWKE7GX3KX4

not attested not anchored not stored refs pending

On the arithmetic of the endomorphism ring End($\mathbb{Z}_{p}\times\mathbb{Z}_{p^{m}}$)

Hualu Liu, Xiusheng Liu

arxiv:1605.00805 v1 · 2016-05-03 · 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{WOUA6HYUSWT7KYZKWKE7GX3KX4}

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	2026-05-18T01:15:47.997095Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b3a80f1f1495a7f5632ab289f35f6abf309582e8579584e5db06b6af71a0a76a

Aliases

arxiv: 1605.00805 · arxiv_version: 1605.00805v1 · doi: 10.48550/arxiv.1605.00805 · pith_short_12: WOUA6HYUSWT7 · pith_short_16: WOUA6HYUSWT7KYZK · pith_short_8: WOUA6HYU

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/WOUA6HYUSWT7KYZKWKE7GX3KX4 \
  | 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: b3a80f1f1495a7f5632ab289f35f6abf309582e8579584e5db06b6af71a0a76a

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "bd14e494c3edd0b98efc9afc15d3dab756c10efe3ca328d44ad4d2035b0356c9",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NT",
    "submitted_at": "2016-05-03T09:27:51Z",
    "title_canon_sha256": "4e1cc51dfe3c9591666308bcc6653d9431999e85a7b6adaae4599b391cdcefe3"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1605.00805",
    "kind": "arxiv",
    "version": 1
  }
}