Pith Number

pith:52TPIXEL

pith:2013:52TPIXELQT5WHSEGQETWAQV7XP

not attested not anchored not stored refs pending

The endomorphism ring of an injective square-free module

Mai Hoang Bien

arxiv:1309.0409 v4 · 2013-09-02 · math.RA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{52TPIXELQT5WHSEGQETWAQV7XP}

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	2026-05-18T03:07:03.600775Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

eea6f45c8b84fb63c88681276042bfbbf495bc59825a2e43c26771080e0ebebc

Aliases

arxiv: 1309.0409 · arxiv_version: 1309.0409v4 · doi: 10.48550/arxiv.1309.0409 · pith_short_12: 52TPIXELQT5W · pith_short_16: 52TPIXELQT5WHSEG · pith_short_8: 52TPIXEL

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/52TPIXELQT5WHSEGQETWAQV7XP \
  | 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: eea6f45c8b84fb63c88681276042bfbbf495bc59825a2e43c26771080e0ebebc

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "abadf4b47c762c6f10c60fdf8f28c0e1a3b5ccfece79c811a8e9a654c7fb40bb",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/publicdomain/",
    "primary_cat": "math.RA",
    "submitted_at": "2013-09-02T14:00:28Z",
    "title_canon_sha256": "411da039263f871c1e85a35e12a856832570b64a84f03c4b1d073ea4fd4bac73"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.0409",
    "kind": "arxiv",
    "version": 4
  }
}