Pith Number

pith:M5MSE2QZ

pith:2010:M5MSE2QZOFWOP4SYFSXNELIJXX

not attested not anchored not stored refs pending

The geometry of spheres in free abelian groups

Christopher Mooney, Moon Duchin, Samuel Leli\`evre

arxiv:1004.0053 v3 · 2010-04-01 · math.GR · math.MG

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{M5MSE2QZOFWOP4SYFSXNELIJXX}

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	2026-05-18T04:23:35.251820Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6759226a19716ce7f2582caed22d09bdced49cd0a92b2950ffdf47650ca80c60

Aliases

arxiv: 1004.0053 · arxiv_version: 1004.0053v3 · doi: 10.48550/arxiv.1004.0053 · pith_short_12: M5MSE2QZOFWO · pith_short_16: M5MSE2QZOFWOP4SY · pith_short_8: M5MSE2QZ

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/M5MSE2QZOFWOP4SYFSXNELIJXX \
  | 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: 6759226a19716ce7f2582caed22d09bdced49cd0a92b2950ffdf47650ca80c60

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2439429359090d6710c75570361f35f76b7d60ba544bad23bc4c756bad61e2f7",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2010-04-01T04:40:21Z",
    "title_canon_sha256": "350924978336d6efbcbdce32336cfd268d9c7df9ab9b964b4704a75a08347353"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1004.0053",
    "kind": "arxiv",
    "version": 3
  }
}