Pith Number

pith:XB22WUAY

pith:2015:XB22WUAY7BCOBQTWNLPUOJ5BLM

not attested not anchored not stored refs pending

Injective modules and torsion functors

Fred Rohrer, Pham Hung Quy

arxiv:1508.07407 v2 · 2015-08-29 · 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{XB22WUAY7BCOBQTWNLPUOJ5BLM}

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	2026-05-18T01:02:31.064052Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b875ab5018f844e0c2766adf4727a15b08a01b8943633572088b4c385cf420ef

Aliases

arxiv: 1508.07407 · arxiv_version: 1508.07407v2 · doi: 10.48550/arxiv.1508.07407 · pith_short_12: XB22WUAY7BCO · pith_short_16: XB22WUAY7BCOBQTW · pith_short_8: XB22WUAY

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/XB22WUAY7BCOBQTWNLPUOJ5BLM \
  | 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: b875ab5018f844e0c2766adf4727a15b08a01b8943633572088b4c385cf420ef

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "8aba1d59abb3514131ca3e65ba770f2a412f448c954acc9f8a94c0bb6da3cb28",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2015-08-29T06:09:58Z",
    "title_canon_sha256": "dea49eb661a8360263ea69057729414df288708b72e9fe6e8cdfbfe8a5a44785"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1508.07407",
    "kind": "arxiv",
    "version": 2
  }
}