Pith Number

pith:7QYMCDW3

pith:2004:7QYMCDW3IEI4NSEQHODFP327ZG

not attested not anchored not stored refs pending

A Unique Decomposition Result for HT Factors with Torsion Free Core

Sorin Popa

arxiv:math/0401138 v5 · 2004-01-14 · math.OA

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{7QYMCDW3IEI4NSEQHODFP327ZG}

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	2026-07-04T14:38:09.410592Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fc30c10edb4111c6c8903b8657ef5fc980d35a91969c3df7357671ad4ea9b541

Aliases

arxiv: math/0401138 · arxiv_version: math/0401138v5 · doi: 10.48550/arxiv.math/0401138 · pith_short_12: 7QYMCDW3IEI4 · pith_short_16: 7QYMCDW3IEI4NSEQ · pith_short_8: 7QYMCDW3

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/7QYMCDW3IEI4NSEQHODFP327ZG \
  | 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: fc30c10edb4111c6c8903b8657ef5fc980d35a91969c3df7357671ad4ea9b541

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "4ff6a458d7bd05b94db5ba83ee6bb95b830d741c0f4fa7eea059d6d4d703d7fe",
    "cross_cats_sorted": [],
    "license": "",
    "primary_cat": "math.OA",
    "submitted_at": "2004-01-14T05:28:10Z",
    "title_canon_sha256": "89ec35f11d067e9459405d1686c5d00ef98757c684c960355a60cdd43d8e27d4"
  },
  "schema_version": "1.0",
  "source": {
    "id": "math/0401138",
    "kind": "arxiv",
    "version": 5
  }
}