Pith Number

pith:YIKLH45C

pith:2010:YIKLH45CUAD4LE2RRUTKJ7YIHS

not attested not anchored not stored refs pending

On modules over Laurent polynomial rings

Daniel S. Silver, Susan G. Williams

arxiv:1006.4153 v2 · 2010-06-21 · math.AC · math.GT

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{YIKLH45CUAD4LE2RRUTKJ7YIHS}

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	2026-05-18T04:05:46.022523Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

c214b3f3a2a007c593518d26a4ff083c9c1109d03fa2ff401c628484fb1d04ec

Aliases

arxiv: 1006.4153 · arxiv_version: 1006.4153v2 · doi: 10.48550/arxiv.1006.4153 · pith_short_12: YIKLH45CUAD4 · pith_short_16: YIKLH45CUAD4LE2R · pith_short_8: YIKLH45C

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/YIKLH45CUAD4LE2RRUTKJ7YIHS \
  | 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: c214b3f3a2a007c593518d26a4ff083c9c1109d03fa2ff401c628484fb1d04ec

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "70309158d02e2867e8cb90a364c401d3707d9fd87beeebf77aafb2ab81372b61",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AC",
    "submitted_at": "2010-06-21T19:51:40Z",
    "title_canon_sha256": "5ce946abab9f25bb82039510cb14dbbdced61bb7891efbe5c4ab25b765e37e01"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1006.4153",
    "kind": "arxiv",
    "version": 2
  }
}