Pith Number

pith:GH4BFP2P

pith:2013:GH4BFP2PJW6LLYYISCO4UJW7N2

not attested not anchored not stored refs pending

Lower bound in the Roth theorem for amenable groups

Pavel Zorin-Kranich, Qing Chu

arxiv:1309.6095 v2 · 2013-09-24 · math.DS · math.CO

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

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{GH4BFP2PJW6LLYYISCO4UJW7N2}

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	2026-05-18T01:35:57.516725Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

31f812bf4f4dbcb5e308909dca26df6ea14e9d8729d8391d3aad580655b76061

Aliases

arxiv: 1309.6095 · arxiv_version: 1309.6095v2 · doi: 10.48550/arxiv.1309.6095 · pith_short_12: GH4BFP2PJW6L · pith_short_16: GH4BFP2PJW6LLYYI · pith_short_8: GH4BFP2P

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/GH4BFP2PJW6LLYYISCO4UJW7N2 \
  | 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: 31f812bf4f4dbcb5e308909dca26df6ea14e9d8729d8391d3aad580655b76061

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "454e3c3e21a9e1ce1c6b19352f0fc58c1ef1284d1060a4ddc9b18b4ce5085cf7",
    "cross_cats_sorted": [
      "math.CO"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2013-09-24T09:31:33Z",
    "title_canon_sha256": "c4239d973e4bd8eb886d532743c5d7b0286b3fb96b225efd977bb7ccee9e3599"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1309.6095",
    "kind": "arxiv",
    "version": 2
  }
}