Pith Number

pith:BBJZK4E4

pith:2018:BBJZK4E4K4KVC6HE2OO63SDXZA

not attested not anchored not stored refs pending

Crecimiento y expansion en SL_2

Harald Andres Helfgott

arxiv:1810.00703 v1 · 2018-10-01 · 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{BBJZK4E4K4KVC6HE2OO63SDXZA}

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	2026-05-18T00:04:25.057400Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

085395709c57155178e4d39dedc877c83f9628b42194769c7f07833787123c99

Aliases

arxiv: 1810.00703 · arxiv_version: 1810.00703v1 · doi: 10.48550/arxiv.1810.00703 · pith_short_12: BBJZK4E4K4KV · pith_short_16: BBJZK4E4K4KVC6HE · pith_short_8: BBJZK4E4

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/BBJZK4E4K4KVC6HE2OO63SDXZA \
  | 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: 085395709c57155178e4d39dedc877c83f9628b42194769c7f07833787123c99

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "ff75ea7b0b4adeaf5d7a2531237b7a01c11abca330b11800362252c28b8dd0b0",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.GR",
    "submitted_at": "2018-10-01T13:41:09Z",
    "title_canon_sha256": "07bbcb82a28b422436bb31badce906d4b6fd1c66a131b38c47fd5b6b575e02e5"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1810.00703",
    "kind": "arxiv",
    "version": 1
  }
}