Pith Number

pith:4ZUDWGFB

pith:2011:4ZUDWGFBUXP243OKUKMVFXUVNR

not attested not anchored not stored refs pending

Every module is an inverse limit of injective modules

George M. Bergman

arxiv:1104.3173 v2 · 2011-04-15 · 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{4ZUDWGFBUXP243OKUKMVFXUVNR}

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	2026-05-18T03:26:10.574169Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e6683b18a1a5dfae6dcaa29952de956c7c224dc8aa117ae4f192424409132616

Aliases

arxiv: 1104.3173 · arxiv_version: 1104.3173v2 · doi: 10.48550/arxiv.1104.3173 · pith_short_12: 4ZUDWGFBUXP2 · pith_short_16: 4ZUDWGFBUXP243OK · pith_short_8: 4ZUDWGFB

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/4ZUDWGFBUXP243OKUKMVFXUVNR \
  | 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: e6683b18a1a5dfae6dcaa29952de956c7c224dc8aa117ae4f192424409132616

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "68847a1a52f9e821b59ab795d942c9e4d8e1fa58c3d5713d898540474e9154a3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2011-04-15T22:56:45Z",
    "title_canon_sha256": "6ec4d5a235c81babcfa9e52a2f023168d4eab84aa9582006eea5e942ae5ca141"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1104.3173",
    "kind": "arxiv",
    "version": 2
  }
}