Pith Number

pith:2VV46YFY

pith:2015:2VV46YFY4GOMIPDITG7BSULVZI

not attested not anchored not stored refs pending

Tests for injectivity of modules over commutative rings

Lars Winther Christensen, Srikanth B. Iyengar

arxiv:1508.04639 v3 · 2015-08-19 · math.AC

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{2VV46YFY4GOMIPDITG7BSULVZI}

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	2026-05-18T01:12:25.229830Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d56bcf60b8e19cc43c6899be195175ca1e668e285afd0ab9aaf474f0334b91a4

Aliases

arxiv: 1508.04639 · arxiv_version: 1508.04639v3 · doi: 10.48550/arxiv.1508.04639 · pith_short_12: 2VV46YFY4GOM · pith_short_16: 2VV46YFY4GOMIPDI · pith_short_8: 2VV46YFY

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/2VV46YFY4GOMIPDITG7BSULVZI \
  | 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: d56bcf60b8e19cc43c6899be195175ca1e668e285afd0ab9aaf474f0334b91a4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "0ca779979fd42b9d6a7123ac222024fba2b6a24e635ad9711ebba7dc08acc791",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-08-19T13:29:23Z",
    "title_canon_sha256": "57c7693497f0e14fc489daf240094364dc9660b916778ca57e56bf57001ded42"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.04639",
    "kind": "arxiv",
    "version": 3
  }
}