Pith Number

pith:7ZRLWDOW

pith:2013:7ZRLWDOWIS7NZW33R2DBPWPXRU

not attested not anchored not stored refs pending

Grothendieck Rings of Theories of Modules

Amit Kuber

arxiv:1302.4229 v1 · 2013-02-18 · math.LO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7ZRLWDOWIS7NZW33R2DBPWPXRU}

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	2026-05-18T01:28:35.545962Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fe62bb0dd644bedcdb7b8e8617d9f78d05904dee45086dfbe0fbd9c22197e1db

Aliases

arxiv: 1302.4229 · arxiv_version: 1302.4229v1 · doi: 10.48550/arxiv.1302.4229 · pith_short_12: 7ZRLWDOWIS7N · pith_short_16: 7ZRLWDOWIS7NZW33 · pith_short_8: 7ZRLWDOW

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/7ZRLWDOWIS7NZW33R2DBPWPXRU \
  | 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: fe62bb0dd644bedcdb7b8e8617d9f78d05904dee45086dfbe0fbd9c22197e1db

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e60ea8b7ff486bb2984a6d225c80cfe54d65884203caf66efe132a14640840a5",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.LO",
    "submitted_at": "2013-02-18T11:25:32Z",
    "title_canon_sha256": "adf9f21e2efc4c219f9a98510387001fe7cd955a4e3df454e34af3d1517951be"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1302.4229",
    "kind": "arxiv",
    "version": 1
  }
}