Pith Number

pith:4FKDPOIY

pith:2011:4FKDPOIYJ4XPXLUVC2C3TDQFOH

not attested not anchored not stored refs pending

Bounding the homological finiteness length

Giovanni Gandini

arxiv:1112.3621 v3 · 2011-12-15 · math.GR

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{4FKDPOIYJ4XPXLUVC2C3TDQFOH}

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	2026-05-18T02:57:53.972111Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

e15437b9184f2efbae951685b98e0571e5d1ba82bed26195f2242b2ec22fe1b3

Aliases

arxiv: 1112.3621 · arxiv_version: 1112.3621v3 · doi: 10.48550/arxiv.1112.3621 · pith_short_12: 4FKDPOIYJ4XP · pith_short_16: 4FKDPOIYJ4XPXLUV · pith_short_8: 4FKDPOIY

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/4FKDPOIYJ4XPXLUVC2C3TDQFOH \
  | 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: e15437b9184f2efbae951685b98e0571e5d1ba82bed26195f2242b2ec22fe1b3

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f9c89ff40ed9f4b80590e7b16e0783434ae23ce98f142ae0b2f52a25340e7ee",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2011-12-15T19:38:26Z",
    "title_canon_sha256": "749afeef10fb2d5bf7cbe7bbdaf038aab1aa21aa27ad805bd066ad797ffd9a4a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1112.3621",
    "kind": "arxiv",
    "version": 3
  }
}