Pith Number

pith:7JLOB3FY

pith:2011:7JLOB3FYLXHRX7UZEX6LYQPMSP

not attested not anchored not stored refs pending

Aspherical groups and manifolds with extreme properties

Mark Sapir

arxiv:1103.3873 v3 · 2011-03-20 · math.GR · 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{7JLOB3FYLXHRX7UZEX6LYQPMSP}

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	2026-05-18T04:23:33.009012Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa56e0ecb85dcf1bfe9925fcbc41ec93cde5e51657269750705d4c8b11a81580

Aliases

arxiv: 1103.3873 · arxiv_version: 1103.3873v3 · doi: 10.48550/arxiv.1103.3873 · pith_short_12: 7JLOB3FYLXHR · pith_short_16: 7JLOB3FYLXHRX7UZ · pith_short_8: 7JLOB3FY

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/7JLOB3FYLXHRX7UZEX6LYQPMSP \
  | 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: fa56e0ecb85dcf1bfe9925fcbc41ec93cde5e51657269750705d4c8b11a81580

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "20b91ad9d2d1ceb6373158a51ddffdcc31f63e75cd357408e9e615528a873d1d",
    "cross_cats_sorted": [
      "math.GT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-03-20T18:40:12Z",
    "title_canon_sha256": "3fee938c4461b4a7f752d4ccb8f8273dbe9efbed7ba00a3cf9206362369a7fbc"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1103.3873",
    "kind": "arxiv",
    "version": 3
  }
}