Pith Number

pith:7G3WMODE

pith:2011:7G3WMODEHT66XZHR4XWPONKOZA

not attested not anchored not stored refs pending

On some criteria for the balanced projectivity of modules over integral domains

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

arxiv:1112.0605 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{7G3WMODEHT66XZHR4XWPONKOZA}

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	2026-05-18T04:07:06.179334Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

f9b76638643cfdebe4f1e5ecf7354ec80dfe974b611a6a821440b12f47cf15ed

Aliases

arxiv: 1112.0605 · arxiv_version: 1112.0605v1 · doi: 10.48550/arxiv.1112.0605 · pith_short_12: 7G3WMODEHT66 · pith_short_16: 7G3WMODEHT66XZHR · pith_short_8: 7G3WMODE

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/7G3WMODEHT66XZHR4XWPONKOZA \
  | 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: f9b76638643cfdebe4f1e5ecf7354ec80dfe974b611a6a821440b12f47cf15ed

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "677d1c81f663f366781e06b24bae980b9cef8fac21d6345cb64f52a137366c9a",
    "cross_cats_sorted": [
      "math.GR"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2011-12-02T23:11:07Z",
    "title_canon_sha256": "5e672240813662779fa818d9524b6275b9f912ae8adb96c9e96d59e76d075b6b"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.0605",
    "kind": "arxiv",
    "version": 1
  }
}