Pith Number

pith:XX3DXEAR

pith:2009:XX3DXEART6LKT2RQEU23WUBR5N

not attested not anchored not stored refs pending

Injective Envelopes and (Gorenstein) Flat Covers

Edgar E. Enochs, Zhaoyong Huang

arxiv:0909.2415 v2 · 2009-09-13 · math.RA · math.KT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{XX3DXEART6LKT2RQEU23WUBR5N}

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	2026-05-18T04:26:31.996293Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

bdf63b90119f96a9ea302535bb5031eb5abc24b3443cf92cd8c9acb7ac1d1589

Aliases

arxiv: 0909.2415 · arxiv_version: 0909.2415v2 · doi: 10.48550/arxiv.0909.2415 · pith_short_12: XX3DXEART6LK · pith_short_16: XX3DXEART6LKT2RQ · pith_short_8: XX3DXEAR

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/XX3DXEART6LKT2RQEU23WUBR5N \
  | 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: bdf63b90119f96a9ea302535bb5031eb5abc24b3443cf92cd8c9acb7ac1d1589

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "9f6c2bf4665f7c88a93f7f0f7ee0d6ba7bf792e44b3d5dbd31107d6e2ec529d5",
    "cross_cats_sorted": [
      "math.KT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.RA",
    "submitted_at": "2009-09-13T12:57:48Z",
    "title_canon_sha256": "9ab8fa868105f5f9bd33743650b55ec688886039ecf45f6667a210ddbb7b9092"
  },
  "schema_version": "1.0",
  "source": {
    "id": "0909.2415",
    "kind": "arxiv",
    "version": 2
  }
}