Pith Number

pith:Q4SA4EAD

pith:2011:Q4SA4EADSDT4YMQEBOEMBYUW22

not attested not anchored not stored refs pending

A generalization of the Pontryagin-Hill theorems to projective modules over Pr\"ufer domains

J. E. Mac\'ias-D\'iaz

arxiv:1112.0598 v1 · 2011-12-02 · math.AC · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{Q4SA4EADSDT4YMQEBOEMBYUW22}

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	2026-05-18T04:07:06.219924Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

87240e100390e7cc32040b88c0e296d6931a69a354ade645f9675d0cfaecc77d

Aliases

arxiv: 1112.0598 · arxiv_version: 1112.0598v1 · doi: 10.48550/arxiv.1112.0598 · pith_short_12: Q4SA4EADSDT4 · pith_short_16: Q4SA4EADSDT4YMQE · pith_short_8: Q4SA4EAD

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/Q4SA4EADSDT4YMQEBOEMBYUW22 \
  | 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: 87240e100390e7cc32040b88c0e296d6931a69a354ade645f9675d0cfaecc77d

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "156e29f454a037d217380149363ffbf90139a3c573777f748700f0f61c118419",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-12-02T22:38:44Z",
    "title_canon_sha256": "d32d0ed4cc024af571f927b1b6999fe531fe572846211d0f04bf42528e06bd77"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0598",
    "kind": "arxiv",
    "version": 1
  }
}